THE LABOUR MARKET ADJUSTMENT OF IMMIGRANT FAMILIES by CHRISTOPHER WORSWICK B.A. (Honours), Queen’s University, 1990 M.A., The University of British Columbia, 1991 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1995 © Christopher Worswick, 1995 for an advanced In presenting this thesis in partial fulfilment of the requirements Library shall make it degree at the University of British Columbia, I agree that the permission for extensive freely available for reference and study. I further agree that d by the head of my copying of this thesis br scholarly purposes may be ‘grante tood that copying or department or by his or her representatives. it is unders d without my written publication of this thesis for financial gain shall not be allowe permission. (Signature) Department of ,é-’ cJ/1 C, r The University of British Columbia Vancouver, Canada Date DE.6 (2/88) /v /4L /‘ ABSTRACT In this thesis, I analyze the labour market adjustment of immigrant families to Canada. The focus of the analysis is on measuring the effects of credit constraints on the labour market behaviour of immigrant family members. Results from the estimation of reduced-form wage, hours and weeks equations indicate that immigrant women face lower wages than similar non-immigrant women, and at the same time work longer hours. Over the 1980s, immigrant women had higher growth in wages and the same growth in hours as non-immigrant women. This could be explained by the immigrant women’s hours being higher in 1980 due to credit constraints, and the immigrant family not needing to borrow in 1990 due to the high wage growth over the decade. While credit constraints can explain the observed differences in labour supply, an alternative explanation is that family preferences towards labour supply differ between immigrant and non-immigrant families. A structural labour supply model is developed in which families choose hours of work for the husband and wife, and family consumption in each time period allowing for credit constraints and uncertainty. The results of the estimation indicate that it is differences in family preferences over labour supply, and not credit constraints, which lead to the observed differences in labour supply between immigrant and non-immigrant families. Immigrant families have a lower disutility to the wife’s labour supply than non-immigrant families. The results do not support the hypothesis that immigrant families are more likely to be credit constrained than non immigrant families. Labour supplies in young families appear to be affected by credit constraints; however, this effect is no larger in immigrant families than in non-immigrant families. 11 TABLE OF CONTENTS Abstract Table of Contents iii List of Tables v List of Figures vii Acknowledgement viii Chapter One Introduction Chapter Two 2.1 2.2 2.3 2.4 2.5 1 Introduction Literature Review Reduced Form Equations and Specification Issues Empirical Analysis Concluding Remarks Chapter Three 3.1 Introduction 3.2 The Model 3.3 Comparisons with Models Used in the Dynamic Labour Supply and Consumption Literatures 3.4 Functional Forms and Estimating Equations 3.5 Empirical Analysis 3.6 Concluding Remarks Chapter Four 4.1 4.2 4.3 4.4 4.5 4.6 Chapter Five Conclusion References Introduction Approaches to Modelling the Participation Decision The Model Functional Forms and Estimating Equations Empirical Analysis Concluding Remarks 6 7 19 24 54 57 58 67 75 82 105 107 108 109 119 127 144 145 206 . Appendix 1 Definitions of Variables Listed in Tables 209 Appendix 2 First Stage Estimates for Two Stage Least Squares Estimation of MRS Function 214 Results from Estimation of Reduced Form Equations Used to Generate the Wife’s Euler Equation Data 223 Appendix 3 111 Appendix 4 Appendix 5 Appendix 6 Appendix 7 Results from Estimation of Reduced Form Equations Used to Generate the Husband’s Euler Equation Data 231 First Stage Estimates Corrected for Participation Selection, for the Two Stage Least Squares Estimation of MRS Function 239 Results from Estimation of Reduced Form Equations Used to Generate the Wife’s Euler Equation Data 247 Results from Estimation of Reduced Form Equations Used to Generate the Husband’s Euler Equation Data 255 iv LIST OF TABLES Table 2.1 Sample Means for Selected Variables 153 Table 2.2 Results from Estimation of Wage, Hours, and Weeks Equations for Wives 155 Table 2.3 Estimates from Wage, Hours and Weeks Regressions for Husbands Table 2.4 1981 Predicted Differences in Wages, Hours and Weeks of Wives by Immigrant Status 164 1991 Predicted Differences in Wages, Hours and Weeks of Wives by Immigrant Status 164 1981 Predicted Differences in Wages, Hours and Weeks of Husbands by Immigrant Status 165 1991 Predicted Differences in Wages, Hours and Weeks of Husbands by Immigrant Status 165 Table 2.8 Results from Probit Estimation on Wife’s Participation 166 Table 2.9 Results from Estimation of Wage, Hours and Weeks Equations for Wives after Controlling for Participation Decision 170 1981 Predicted Differences in Wages, Hours, and Weeks of Wives by Immigrant Status after Correcting for the Participation Selection 175 1991 Predicted Differences in Wages, Hours, and Weeks of Wives by Immigrant Status after Correcting for the Participation Selection 176 Table 3.1 Sample Means for Selected Variables 177 Table 3.2 Results from Estimation of the Family Marginal Rate of Substitution Table 3.3 Results from Estimation of the Euler Equation for the Wife’s Hours Table 3.4 Results from Estimation of the Euler Equation for the Husband’s Hours 186 Table 4.1 Sample Means 190 Table 4.2 Results from Probit Estimation on Wife’s Participation 192 Table 4.3 Results from Estimation of the Family Marginal Rate of Substitution Table 4.4 Results from Estimation of the Euler Equation for the Wife’s Hours Table 2.5 Table 2.6 Table 2.7 Table 2.10 Table 2.11 V . . . . . . . 160 179 183 . . . . . 197 201 Table 4.5 Results from Estimation of the Euler Equation for the Husband’s Hours vi . 202 LIST Of FIGURES Figure 2.1 Immigrant Adjustment Path for Earnings 150 Figure 2.2 Immigrant Adjustment Paths and Cohort Differences 151 Figure 2.3 Immigrant Adjustment Paths and Differences in Rates of Assimilation 152 1981 Non-Labour Time for Immigrant and Non-Immigrant Families Given Non-Immigrant Wages and Artificial Constraint 181 1981 Non-Labour Time for Immigrant and Non-Immigrant Families Given Market Wages and Artificial Constraint 182 Hours of Immigrant and Non-Immigrant Wives Over Time Given Non-Immigrant Wages and Artificial Constraint 185 Hours of Immigrant and Non-Immigrant Wives Over Time Given Non-Immigrant Wages and Artificial Constraint 186 Hours of Immigrant and Non-Immigrant Wives Over Time Given Market Wages and Artificial Constraints 187 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 4.1 The Case of A Non-Worker in the Static Fixed Cost of Work Model Figure 4.2 The Case of a Worker in the Static Fixed Cost of Work Model 189 Figure 4.3 1981 Non-Labour Time for Immigrant and Non-Immigrant Families Given Non-Immigrant Wages and Artificial Constraint 199 1981 Non-Labour Time for Immigrant and Non-Immigrant Families Given Market Wages and Artificial Constraint 200 Hours of Immigrant and Non-Immigrant Wives Over Time Given Non-Immigrant Wages and Artificial Constraint 203 Hours of Immigrant and Non-Immigrant Wives Over Time Given Non-Immigrant Wages and Artificial Constraint 204 Hours of Immigrant and Non-Immigrant Wives Over Time Given Market Wages and Artificial Constraints 205 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 vii . . 188 ACKNOWLEDGEMENT I would like to thank David Green for supervising my research. David has not only made extensive comments and suggestions, but he has also been a great source of support and encouragement for me. I would also like to thank Craig Riddell and Terry Wales for the the many discussions we have shared which have added greatly to this thesis. I have appreciated discussions of my research with Siwan Anderson, Michael Baker, Garry Barrett, Charles Beach, Paul Beaudry, Dwayne Benjamin, Craig Brett, Patrick Coe, Benoit Delage, Denise Doiron, Mukesh Eswaran, Patrick Francois, Mary Gregory, Patrick Kenny, Jon Kesselman, Jim Nason, Makoto Saito, Bill Schworm, and Scott Taylor. Research support was provided through a Social Sciences and Humanities Research Council of Canada doctoral fellowship and a grant from the Centre for Research in Economic and Social Policy at the University of British Columbia. I would like to thank my parents, John and Brenda Worswick, for their support throughout my education. Most importantly, I would like to thank my wife, Karen, and my son, Daniel, for their love and support. viii CHAPTER ONE Introduction In countries like Canada and the United States, one can think of immigration as a contract between the immigrants and the pre-existing population. Under the contract, the immigrants bring their skills, wealth, and ambition to the new country. In exchange, the pre-existing population gives the immigrants full rights associated with being a citizen and the chance to use their skills in the new labour market. Implicit in this agreement is the fact that if immigrants do not succeed economically, or if they do succeed but only after years in the new country, then the immigrants will have access to the country’s social safety net as citizens. Canada’s projected inflow of immigrants for 1995 is 190,000 to 215,000 (Globe and Mail, Oct. 29, 1994). Given the size of this inflow, the costs to the pre-existing population of a widespread failure of immigrants to adjust quickly to the new labour market are large. In order to evaluate the success of immigration policy, we need to know how well immigrants adjust to the new labour market. If it is found that immigrants do succeed in the labour market, but only after many years in the new country, then we need to know the causes of this delay in order to develop sound public policy. In particular, we would like to know what obstacles lie in the path of the immigrant labour market adjustment, and whether or not the effects of these obstacles can be lessened through public policy. Previous research suggests that immigrants have difficulty finding jobs suitable to their ability in the early years after migration. This may be due to imperfect international transferability of skills as suggested by Chiswick (1978), or due to difficulties in having foreign credentials recognised. To get around these problems 1 immigrants may need to invest in search for better jobs or invest in retraining. In order to afford these investments, immigrants must have sufficient savings or access to credit in order to fund consumption in the first years after migration. However, immigrants may have difficulty borrowing from financial institutions immediately after arriving in the new country, before they are able to develop a credit history or physical assets which can serve as collateral. In this thesis, I analyze the role of credit constraints in determining the labour supply of immigrants. In order to evaluate the effects of credit constraints, it is necessary to focus on the labour market adjustment of the immigrant family. Certain family members may be chosen by the family to retrain or search for better jobs, while other family members work long hours in order to fund family consumption in the early years after migration. In order to see the total effects of credit constraints on the immigrant family, we need to analyze the labour market behaviour of both the members who are allowed to search for better jobs or receive the training, and those who fund it. The importance of credit constraints on the labour market behaviour of immigrants was first suggested in Long (1980). Long argued that immigrant families are often credit-constrained after arriving in the new country and are unable to fund human capital investments by bor rowing against future earnings. Long suggested that it may be the immigrant wife who works more hours if the husband is perceived to be the principal earner and must make human capital investments before beginning his career. Subsequent researchers have referred to this expla nation of the labour market behaviour of immigrants as the Family Investment Hypothesis (FIH). 2 If, as the FIR predicts, it is immigrant wives who work more in response to imperfect capital markets, then there may be a role for public policy to reduce the need for the wife to work more hours. In this case, policies such as a government loans program for new immigrants or more funding for retraining of immigrant women may reduce the need for the immigrant wife to distort her labour market behaviour. In Chapter 2, I analyze the labour market adjustment of immigrant married couples using reduced-form estimation. Hourly wage, hours per week, and weeks per year equations are estimated for husbands and wives. The participation decision of the wife is also analyzed. Immigrant husbands and wives are found to have lower wages than non-immigrant husbands and wives. However, immigrants overcome part of the wage differential through higher growth in wages than non-immigrants. Immigrant men and women work fewer weeks than similar nonimmigrants in the first five years of residence. This is likely due to unemployment. Immigrants may need to search for jobs or cycle through jobs not suited to their skilis before settling into more permanent, career oriented jobs. Immigrant husbands and wives work more hours per week than non-immigrant husbands and wives. In light of the lower wages found for immigrants, the hours differences are consistent with the hypothesis that immigrant family members work long hours at low wages upon arrival in the new country when the household lacks access to credit. However, one would expect the effects of credit constraints to diminish with duration of residence leading to a convergence of the immigrant and non-immigrant hours. This is not found in the estimation. It may be that this hours convergence is “masked” in the data by the desire to increase hours by immigrant 3 family members in response to the higher wage growth. The net effect might be a constant hours difference through time between immigrants and non-immigrants. An alternative expla nation for the observed movements in the data is that immigrant family members have a lower disutility to work or lower wealth. These differences, coupled with a small response of the hours of married women to their wage growth, would explain the observed behaviour. These explanations cannot be distinguished using reduced-form estimation. In Chapter 3 and Chapter 4, I develop a structural model of intertemporal labour supply for married couples which allows for uncertainty and the possibility that the household may be credit-constrained in some time periods. The model extends the dynamic labour supply literature by relaxing the assumption of perfect capital markets. A procedure is developed which allows the estimation of the model using synthetic cohort data, or multiple cross sections. The procedure may be of use to other researchers in cases where panel data are not available, but multiple cross section data sets are available. The results of the estimation support the preference-based explanation over the creditconstraint based explanation of differences in labour supply patterns in immigrant versus nonimmigrant families. Immigrant families place a lower value on the wife’s non-labour time relative to the husband’s non-labour than do non-immigrant families. After controlling for all other factors, this would lead immigrant wives to work more hours than non-immigrant wives, and immigrant husbands to work fewer hours than non-immigrant husbands. After controlling for offered wages, immigrant family members are found to supply more labour in all periods due to either a lower disutility of work of its members, or lower wealth. The 4 results indicate that immigrant families are not more likely to be credit-constrained than non immigrant families. The empirical evidence supports the hypothesis that credit constraints are an important determinant of hours of work in young families; however, after controlling for age, immigrant families do not appear to be more likely to be credit-constrained than non immigrant families. 5 CHAPTER TWO 2.1 Introduction In this chapter, the labour market behaviour of immigrant couples is compared to the behaviour of non-immigrant couples through reduced-form estimation. Wage, hours and weeks of work of both immigrant spouses and the participation decision of the wife are studied and compared to those of non-immigrant couples. These labour market outcomes will be used to evaluate the success of immigrants relative to non-immigrants in the labour market measured at time of arrival and with years of residence in Canada. Immigrant husbands and wives are found to earn lower wages and work longer hours than non-immigrant. husbands and wives. Over the 1980s, immigrant husbands and wives experience higher wage growth than their non-immigrant counterparts while their hours and weeks growth are roughly equal. These results are consistent with immigrant families being affected more by credit constraints than non-immigrant families. Immigrant family members may work more hours in order to fund family consumption because they are unable to borrow against future earnings. However, one would expect the effects of credit constraints to diminish with years of residence. The difference between the hours of immigrants and non-immigrants does not fail with years of residence. It is argued that the response of the immigrant family to the higher wage growth of its members may “mask” the credit constraint effect. This would explain the equal growth in hours of husbands and wives across immigrant and non-immigrants given the higher growth in wages of immigrants. However, an alternative explanation is suggested. It may be that immigrant family members work more hours for lower wages than their non 6 immigrant counterparts due to a lower disutility to work or lower wealth. This along with a low response of hours to growth in wages over time would also explain differences by immigrant status found in the reduced-form estimation. 2.2 Literature Review Economic studies of immigrant labour market adjustment typically use labour market char acteristics such as wages and earnings to measure how successful immigrants are relative to non-immigrants. In particular, researchers have focused on how differences in wages and earn ings between immigrants and non-immigrants vary with the immigrant’s years-since-migration (YSM). Chiswick (1978) was the first researcher in economics to analyze earnings differences be tween immigrants and non- immigrants. Using a human capital earnings model, augmented with controls for immigrant status and years-since-migration, Chiswick estimates differences in earnings between immigrant and non-immigrant men using the 1970 U.S. Census. The results indicate that immigrant men with one year of residence in the U.S. have ten to fifteen percent lower annual earnings than otherwise similar non-immigrant men. This earnings difference is smaller for immigrant men with more years of residence. The earnings of immigrant men with fourteen or more years of residence exceed the earnings of similar non-immigrant men. Chiswick refers to fourteen years of residence as the “crossover point”. He interprets the results as describing the path of the difference in earnings of immigrants versus non-immigrants as the years of residence of the immigrants increases, after controffing for other factors. Figure 2.1 demonstrates the Immigrant Adjustment Path (TAP) of earnings found by Chiswick. The TAP 7 is defined as the difference between the expected earnings of immigrants and non-immigrants as years-since-migration rises. The slope of the TAP is interpreted as measuring the labour market adjustment or assimilation of immigrants. Consider the following version of Chiswick’s model: 1 mW = X + XF7F + 5 Y a 0+6 Y a 0+e 7o+ 7 (1) where mW is the natural logarithm of annual earnings, X is a vector of personal characteristics which does not contain a constant term, XF is a subset of these characteristics interacted with an immigrant dummy variable, Y 50 identifies immigrants who arrived before 1960, Y 60 identifies immigrants who arrived in the 1960s; 7° is the intercept, 7 and 7F are parameter vectors, and e is an error term. The expected value of the log of earnings of a non-immigrant with characteristics, xr, is: (2) YrO,N=70+X7 The expected value of the log of earnings of an immigrant from each cohort with the same characteristics is: 2 = 70 Y ,so 7o+ X7 + XF7F + = 70 Y6o (3) 7 + XF7F + QSO +X (4) Chiswick’s results indicate that Y70,N > flo,60 and fl 50 > , 0 or 5 a 0 > a . 6 0 Given that the crossover point is found to be fourteen years, one would need to estimate this specification ‘Chiswick includes a continuous years-since- migration control and its square, rather than the dummy vari ables used here. The specification of equation (1) is chosen to make it comparable to the specifications used in later studies and in the analysis of this thesis. The vector XF is set equal to X over the common set of characteristics in the two vectors. 2 8 to know whether or not 1%,50 infer that 5 , 7 Y 0 > 7o,N If the crossover point were at ten years, then we could > Y70,N. Borjas (1985) presents results from the same model estimated using both the U.S. Census of 1970 and 1980. Borjas finds that Chiswick’s interpretation of his results is incorrect due to the incorrect assumption that the immigrant adjustment paths of earnings are stationary across immigrant entry cohorts. Borjas argues that successive immigrant cohorts have had lower unobserved ability due to a movement away from independent immigrants who are more rigorously selected on personal characteristics, and towards family class immigrants, who are chosen primarily because of being a relative of a U.S. citizen. He also argues that shifting source countries caused this drop in unobserved ability. Borjas’ results indicate that successive immigrant cohorts have had a larger earnings disadvantage at time of arrival in the U.S. After accounting for these differences, Borja.s finds the slope of the lAP of each entry cohort to be smaller than what was found by Chiswick implying a much later earnings crossover point. Borjas’ method of identifying immigrant assimilation from differences across immigrant entry cohorts can be demonstrated using (1), Chiswick’s earnings equation. 3 Let the following equation explain the log of annual earnings of men in the 1980 U.S. Census: mW = 6 + X6 + XFbF + Y 0 5 0+Y 8 6 0+Y 0 7 0+ u where Y 70 identifies immigrants who arrived in the 1970s; 6 is the intercept; 6 and parameter vectors; 7o, 6o, and °50 are parameters; and u (5) F 6 are is an error term. Predictions analogous to (2)-(4) can be derived from equation (5) for non-immigrants and The following discussion is based closely on the discussion in Borjas (1985). 3 9 model: the three immigrant entry cohorts identified in the (6) Ygo,N=60+X6 = 6 +Xb +XFbF 0 Ys 6 , 0 = F + 6 b + X6 + XF 0 , 3 Y 5 = 6o + X6 + XFbF + (7) +070 (8) 060 (9) log earnings in 1980 of individuals with where Y80,N, ‘so,7o, l’so,6o, and o,so are the expected igrants who arrived in the 1970s, immigrants characteristics, X, who are non- immigrants, imm arrived before 1960, respectively. who arrived in the 1960s, and immigrants who measure of the difference between the Using the 1980 data, Chiswick’s cross-section-based and the growth in earnings of nongrowth in earnings of immigrants who arrived in the 1960s 4 immigrants is: (o,6o — Y8o,N) Y80,N) — = 060 — (10) 07o Borjas notes that this can be rewritten: 060 — 07 = [Q9o,o — Y80,N) — (?7o,60 — Y70,N)} + 0c 0 [Q 6 , — Y70,N) — (1>50,70 — Y80,N)] (11) ” growth in earnings of immigrants The first term in square brackets gives the “within cohort s of the native-born. This measures who arrived in the 1960s relative to the growth in earning the 1960s from having one to ten the movement along the TAP of immigrants who arrived in igration. The second term in years-since-migration to having eleven to twenty years-since-m immigrant earnings differential of square brackets gives the difference in the immigrant nonhis is the growth after controlling for age effects in X. 4 T 10 immigrants who arrived in the 1960s relative to those who arrived in the 1970s holding the YSM of each cohort at one to ten years. This term measures average differences in earnings across the two cohorts due to differences in unobserved characteristics shortly after arrival in the U.S., and is often referred to as the difference in earnings due to differences in unobserved 5 ability. If immigrant cohorts differ in terms of unobserved ability then the TAP will be different for each cohort. Borjas finds that successive immigrant cohorts have had lower unobserved ability and this implies that the TAP is lower for these cohorts. This is demonstrated in Figure 2.2. The immigrants who arrived in the 1970s have lower unobserved ability than the immigrants who arrived in the 1960s, and this can be seen in the lower intercept of the TAP for the 1970s cohort. Borjas assumes that rates of assimilation, or the slope of the TAP, for a given level of YSM, is the same for all immigrant cohorts. Given the measured differences in unobserved ability across immigrant entry cohorts, this implies that the TAP of immigrants who arrived in the 1970s lies below the TAP of immigrants who arrived in the 1960s for all values of yearsince-migration. Based on the specification of (6)-(8), O,7O — Yso,N is the average value of the TAP of immigrants who arrived in the 1970s over one to ten years of residence, while 50 Y 6 , — Yso,jv is the average value of the TAP of immigrants who arrived in the 1960s over the range of eleven to twenty years of residence. Chiswick’s measure of the slope of the TAP is presented by the dotted line in Figure 2.2. The upward bias in the slope of the measured TAP 1t would be preferable to have more narrowly defined immigrant arrival year cohorts in the data. The fact 5 that the cohorts are defined in ten year blocks means that, instead of measuring differences in wages across cohorts in the first year after migration, we are measuring differences in average wages over the first ten years of residence. The data sets used in the estimation of this thesis only identifies immigrant arrival year in ten year blocks; therefore, the discussion in the literature review wifi be restricted to this case. 11 is apparent. By assuming that assimilation rates for a given value of YSM are the same across cohorts, Borjas is able to derive the TAP for each cohort from the earnings equation estimates. For example, the immigrants who arrived in the 1970s are only observed in the 1980 data set; however, their entire TAP can be derived. As stated above, the average value of the TAP of immigrants who arrived in the 1970s over one to ten years of residence is — Yso,N. The average value of this group’s TAP from eleven to twenty years of residence is this number plus the earnings assimilation over the decade of the immigrants who arrived in the 1960s, — — — %,N) from having one to ten years of residence to having eleven to twenty years of residence. It is possible to derive these ten year averages of the 1970s cohort’s TAP for increasingly larger values of YSM provided that enough earlier immigrant cohorts are identified in the data. Latonde and Topel (1991) use the 1970 and 1980 U.S. Census data to analyze the sensitivity of Borjas’ results to the choice of comparison group. Instead of comparing immigrants to the total non-immigrant population, they compare immigrants to non-immigrants of the same ethnic group and to immigrants of the same ethnicity but with more years of residence. They find that more recent immigrants have had lower average earnings, ceteris paribus, and that this is due solely to changes in the source countries of the immigrants. However, there appears to be no drop in average “quality” within immigrant ethnic groups. They find that immigrants assimilate quickly in the U.S. labour market with the initial earnings disadvantage overcome after ten years of U.S. experience. Immigrants with the lowest wages upon arrival experience 12 the highest rates of assimilation. They conclude that immigrants have lower initial earnings than non-immigrants of the same ethnicity, but that their earnings quickly converge to those of the non-immigrants of their ethnic group. The different conclusions between Borjas (1985) and Lalonde and Topel (1991) are driven by the choice of comparison group. If members of more recent immigrant cohorts are more likely to be members of ethnic groups which face discrimination in the U.S. labour market than were immigrants from earlier cohorts, then the interpretation that more recent cohorts have lower unobserved ability may be incorrect. In this case, using the total non-immigrant population as the comparison group understates the unobserved ability of recent cohorts since differences in propensity to experience discrimination are interpreted as differences in ability. Therefore, the comparison of immigrants to members of the same ethnic groups is more appropriate. However, if differences in wages of non- immigrants across ethnic groups are due to differences in unobserved ability rather than discrimination then the correct comparison group is the total non-immigrant population. In this case, Latonde and Topel’s estimates of differences in wages between immigrants of recent cohorts at time of arrival and non-immigrants are biased downwards since the comparison group has lower unobserved ability than the rest of the non immigrant population. The data used in this thesis do not contain controls for ethnicity. Therefore, the com parison group used is the non- immigrant population. Differences in labour market outcomes across cohorts will be attributed to either differences in ability or differences in discrimination experienced in the labour market. The issue of testing between these competing explanations 13 of wage differences at year of entry across immigrant cohorts will be left for future research. A second measurement issue raised in LaLonde and Topel (1991) relates to Borjas’ assump tion that rates of assimllation, holding years-since-migration constant, are the same across immigrant entry cohorts. The fact that LaLonde and Topel find that immigrants with lower initial earnings experience the highest rates of assimilation indicates that Borjas’ measured TAP for recent cohorts may be biased. Figure 2.3 gives an example of the case where the TAPs of two immigrant cohorts differ both in terms of unobserved ability at arrival in the new coun try, and in terms of rates of assimilation. The cohort of immigrants who arrived in the 1970s has a larger initial earnings disadvantage relative to the non-immigrants than does the cohort of immigrants who arrived in the 1960s. However, the immigrants who arrived in the 1970s experience a faster rate of assimilation than those of the earlier cohort, so that after ten years in the new labour market, there is only a small difference in the earnings of the two immigrant groups. Tf the TAPs of successive immigrant cohorts have shifted in this manner, then the slope of the TAP of recent cohorts, derived using Borjas’ procedure, is biased downwards. Consider the case of the 1970s cohort. From the 1980 data, we can derive the average value of the TAP for this group between one and ten years of residence. Following Borjas’ interpretation, we can derive the average value of the TAP for this group from eleven to twenty years of residence by adding the movement along the TAP for the 1960s cohort from one to ten years to eleven to twenty years. This understates the expected movement along the TAP for the 1970s cohort because their TAP is steeper than the TAP of the 1960s cohort. Duleep and Regrets (1994) analyze this issue using linked cross section data sets from the 14 Current Population Survey in the U.S. They find that immigrant cohorts with the lowest initial earnings also have the highest growth in earnings, or assimilation. In interpreting the empirical results of this thesis, I allow for the possibility that each immigrant entry cohort has a unique TAP. The TAPs of two immigrant cohorts may differ in terms of the intercept and also the slope at each value of YSM, which measures the rate of assimilation. Two cross section data sets are used; therefore, it is possible to derive two points on the TAP of immigrant cohorts who arrived prior to the first survey, and one point on the TAP of the immigrant cohort which arrived after the first survey and before the second survey. The cost of this interpretation is that we are unable to extrapolate outside the sample periods; however, the benefit is that we do not risk making policy prescriptions based upon incorrect assumptions. The first economic study of immigrant wage adjustment in Canada was Carliner (1981). Using the 1971 Canadian Census, he found that immigrant men who had just arrived in Canada had thirty-three percent lower wages than non-immigrant men. However, this differ ence dropped to around zero for immigrants in earlier cohorts. Abbott and Beach (1993) use the 1973 Canadian Job Mobility Survey to analyze differences between immigrant and non immigrant men’s earnings. The data set contains a measure of years of full-time experience; therefore, they were able to control for both experience and age cohort effects. They find that cross-sectional differences in earnings have widened for immigrant men since the late 1960’s. Bloom and Gunderson (1991) follow Borjas’ approach and use the 1971 and 1981 Canadian Censuses to analyze the issue. They find immigrant men’s earnings grow with time in Canada, 15 but at a low rate, implying a crossover point of thirteen to twenty- five years after arrival. They argue that the unobserved “quality” of immigrant men declined after changes in immigration policies in 1974 leading to more family class immigrants. Baker and Benjamin (1992) extend this analysis using the 1971, 1981, and 1986 Canadian Censuses. They find the same drop in unobserved ability in successive immigrant cohorts observed in Bloom and Gunderson (1991); however, they find lower growth rates of earnings with years of residence. Because they have three cross sections, they are able to test the assumption that the rates of assimilation holding YSM constant are the same across immigrant entry cohorts°, and do not reject this hypothesis. Baker and Benjamin analyze the importance of the choice of comparison group in measuring immigrant earnings differences, as suggested by LaLonde and Topel (1991). They compare new immigrants to non- immigrants and also to immigrants with more years of residence. They also control for changes in the composition of immigrant cohorts in terms of source countries. In each case, rates of assimilation are found to be low. This indicates that the estimates of the assimilation rates in the Canadian data are less sensitive to the choice of comparison group than are the estimates of assimilation of Borjas (1985) and Latonde and Topel (1991) using U.S. data. The economic literature on the labour market adjustment of immigrant women is less de veloped than the one for men. Long (1980) uses the 1970 U.S. Census to estimate Chiswick’s model for immigrant women. The results indicate that immigrant women with one year of res idence have over sixty percent higher earnings than non-immigrant women and this differential is lower for immigrant women with more years of residence. Long interacts marital status 6 T his implies that the lAP of each cohort has the same slope for a given value of YSM. 16 with the years-since-migration controls and finds that the negative earnings/YSM profile is flatter for single immigrant women than for married immigrant women. Annual hours of work for immigrant women are found to decline with years of residence in the U.S. at a rate of approximately one and a half percent a year. Hours of work controls are not included in the earnings regression. It appears that at least part of the negative earnings/YSM relationship is due to a negative hours/YSM relationship. In an attempt to reconcile the large differences in these results compared to what was found for immigrant men, Long hypothesizes that, since immigrant men may be perceived to be the principle earners, they may make human capital investments after arriving in the new country. Given that it is difficult to borrow against fu ture wage income, immigrant wives may need to work more hours or in occupations with high short run earnings, but low growth in earnings, in order to fund family consumption. Once the husband’s earnings begin to reflect the returns to the post-migration investments in human capital, the wife reduces her labour supply or switches to an occupation with better career opportunities. Subsequent researchers have referred to this explanation of the results as the Family Investment Hypothesis (FIR). Beach and Worswick (1993) carry out a similar analysis using the 1973 Canadian Job Mobility Survey. Highly educated immigrant women are found to have lower earnings than similarly educated non-immigrant women; however, foreign-born women with lower levels of education have higher earnings than non-immigrant women with the same level of education. The woman’s duration of residence in Canada is not a significant determinant of her earnings. The data set used does not contain a measure of hours of work for all working women in the sample; therefore, it is impossible to separate changes in labour supply from changes in market 17 7 Beach and Worswick argue that the flat YSM path can be explained by the immigrant wages. family being credit-constrained upon arrival in Canada and the wife responding by working more hours to support family consumption as was suggested by Long (1980). This would imply a negative relationship between the wife’s hours of work and her YSM. The observed flat earnings/YSM profile for women might be due to a combination of a negatively-sloped hours/YSM profile and a positively sloped wage/YSM profile due to assimilation. Both Long (1980) and Beach and Worswick (1993) use a single cross-section data set. Therefore, immigrant earnings adjustment and differences in unobserved ability across immi grant entry cohorts cannot be distinguished in the observed patterns of earnings and hours of work for different values of YSM. In the empirical work of this thesis, the importance of assimilation relative to changes in unobservable characteristics across immigrant entry cohorts will be evaluated in determining the earnings and hours L&Ps of immigrant women. Few papers have studied immigrant adjustment while allowing for family objectives and adjustment strategies. Baker and Benjamin (1994) use data on married couples to test for family investment strategies. They use the 1986 and 1991 Canadian Survey of Consumer Finances. They argue that immigrant women who are married to non-immigrant men are less likely to need to support their husband’s human capital acquisition than are immigrant women with immigrant husbands and; therefore, should have lower labour supplies upon ar rival in Canada and have a steeper wage/YSM profile . Immigrant women with immigrant Estimation of a log hours equation over the sample of womeu with reported hours of work indicates that 7 hours are higher for women with fewer years of residence. they are more likely to make investments in their own human capital accumulation rather than the human capital accumulation of their husband. 18 husbands work more upon arrival and have lower wage assimilation than immigrant women with non-immigrant husbands. The evidence in favour of the FIR relies on the comparability of immigrant women with immigrant husbands versus those with non-immigrant husbands. However, the observed differences could also be explained by differences in preferences toward labour supply and differences in expected lifetime wealth. Immigrant women with immigrant husbands may typically come from different source countries. This might lead to different attitudes towards work. 9 In a reduced-form model, it is not possible to distinguish between a preference- based explanation and a credit-constraint-based explanation for the different labour supply patterns between the two groups of women. Duleep and Sanders (1993) use the 1980 U.S. Census to study the immigrant wife’s partic ipation decision, and conclude that the results are consistent with a family strategy. They find that immigrant women from home countries with high expected growth in immigrant men’s earnings are more likely to participate. They argue that this is due to the husband partici pating in retraining programs and the wife having to work to support the family in the face of constraints on borrowing. They also find that the labour force participation of immigrant wives is inversely associated with their husbands’ years of residence, after controlling for the wife’s years of residence. Since the study uses only one cross- section, it is not possible to separate differences across immigrant entry cohorts from the effects of credit constraints. The observed behaviour which is attributed to an inability on the part of the family to borrow could instead be due to different attitudes towards work across successive immigrant cohorts. 2.3 Reduced Form Equations and Specification Issues The SCF data used by Baker and Benjamin do not contain controls for country of origin. 9 19 In the empirical analysis of this chapter, immigrant married couples are compared to similar non-immigrant couples in terms of wages, hours of work per week, and weeks of work per year for both the husband and the wife. The focus will be on the magnitude of immigrant differences in these labour market outcomes: 1) at time of arrival in Canada, 2) with more years of residence, and 3) across immigrant entry cohorts. The data used come from two cross-sectional surveys, the 1981 and 1991 Census of Canada Family Microdata Files. The specification of the husband’s log wage equation, defined over the pooled sample, has the following form: mW = 91 + X ’ 9 o + X/3 + XFPF + /3rYR91 + 8 3 / 43 5 Y 51 1 /3 6 Y 1 + 71 /3Y + + 61 (YR91 5 , 91 /3 1 * 61 , 91 /3 ) 5 Y 1 + (YR91 * ) 6 Y 1 + (YR91 71 , 91 /3 * ) 7 Y 1 /3 8 Y 7 + 88 +i3 8 Y 81 /3 8 Y 1 + 13s6)f86 + 87 8 + /3 89 + /3 Y 89 90 + e Y 90 (12) where the vector X contains demographic characteristics of the husband, and XF contains a subset of these characteristics interacted with an immigrant dummy variable; YR91 indicates that the individual is from the 1991 survey; the vector X ’ contains age controls interacted 9 with the YR91 variable;’ 0 Y , identifies immigrants who arrived before 1961; Y 5 61 and Y , 7 identify immigrants who arrived between 1961 and 1970, and 1971 and 1980 respectively; Y , 8 identifies immigrants who arrived between 1981 and 1985; Y , 8 6Y 58 Y Y , 8 7 , , 8 9 and 9 Y 0 identify immigrants who arrived in 1986, 1987, 1988, 1989 and 1990 respectively; /3 is the intercept; /3, F 13 and 4391 are parameter vectors; /381, /3,, /37, 4391,51, 591,61, /91,71, 581, 586, /387, ‘°It is assumed that the coefficients on the immigrant interaction terms, 1 F do not vary across time. 20 /88, /389, and flo are parameters; and e is an error term. The controls for the immigrant cohorts are equivalent to the ones used by Borjas (1985). Each cohort has an intercept shift. The dummy variables for the three cohorts which are observed in each survey year are also included as interactions with YR91. The coefficients on these interactions, /391,71, 591,51, 591,61, and measure the wage assimilation over the decade for each cohort. 11 To see this for the case of immigrants who arrived in the 1970s, first define the expected wage in 1981 of a non- immigrant with characteristics 1K to be: (13) Ygl,N=/30+X13 The expected 1981 log wage of an immigrant who arrived in the 1970s with the same charac teristics is: 71 Ysi, o+X/3+XF/ 3 —/ F +/371 (14) The average value of the TAP over one to ten years of residence of an immigrant who arrived in the 1970s with characteristics 7 is: , 8 Y 7 1 Y81,N = F 3 XF/ + (15) 571 In 1991, the expected log wages of a non-immigrant and an immigrant who arrived in the 1970s with these same characteristics are: Y91,N=/30+X/3+/3W , 9 Y 7 1 = /3 +75 + /3g’ + XFI F + 3 +r’’ + Sn + 5i,i (16) (17) For example, #91,71 measures the average increase in the lAP for immigrants who arrived in the 1970s from 1 ‘ having one to ten years of residence to having eleven to twenty years of residence. 21 where X’ is the age control for this person after aging ten years.’ 2 The average value of the TAP of immigrants who arrived in the 1970s over eleven to twenty years of residence is: 91 Y 7 , — Y91,N = F+ 3 XFI 571 + (18) 591,71 The wage assimilation of this cohort over the ten year snrvey period is the movement along the TAP over the period: (1%,,7, — Y91,N) — (1,71 This analysis could be repeated to show that — 591,61 (19) Y81,N) = 591,71 and 5gj, measure the wage assimilation of immigrants who arrived in the 1960s and before 1961, respectively. Controls for age are included to proxy the effect of labour market experience on wages. Measurement issues involved with separating returns to age from differences in wages across birth cohorts, holding age constant, are similar to the issues involved with measuring the TAP of each immigrant entry cohort, discussed above. Six birth cohorts are identified in the specification. In terms of their ages in 1981, the six groups are men aged twenty-five to twenty-nine, thirty to thirty-four, thirty-five to thirty-nine, forty to forty-four, forty-five to forty-nine, and fifty to fifty-four. The age controls in the wage regression have the form: Xf3 + 5g YR91 + 1 5 9 x ’ 9 1 = XNA/ N 3 A For example, if the age of a husband with characteristics 2 ‘ fifty in 1991. 22 * YR81) + 5,, 435 35 * YR81) * YR81) + (A45 45 , 1 3° * YR81) X is forty in 1981, then X ’ indicates that he is 9 * YR81) + 13g’YR91 (A40 4 , 1 +/3 45 , 1 3 0 * YR91) + (A45 * YR91) (A50 5 , 1 +f3 0 * YR91) + (A55 55 * YR91) , 1 i3 (A60 6 , 1 +13 0 * YR91) (20) where XNA are characteristics other than age; A30, .435, .440, .445, .450, .455, and .460 identify individuals age thirty to thirty-four, thirty-five to thirty- nine, forty to forty-four, forty-five to forty-nine, fifty to fifty-four, fifty-five to fifty-nine, and sixty to sixty-four at the time of the survey. The default category contains men age twenty-five to twenty-nine in 1981. One can see the wage/age cross section for 1981 using the parameters and , i3g 130 j3g , i3g 135 , , 140 45 1 i3g Each coefficient measures the percentage difference in average wages between the age cohort represented by the dummy variable and the default age cohort, after controffing for other characteristics. The coefficient 31 measures the growth in wages over the decade of the husbands age twenty-five to twenty-nine in 1981. The specification allows for unique wage/age growth paths for each birth cohort. For example, husbands age forty to forty-four in 1981 have wage growth equal to /33’ + /35 — Age controls are not included in XF; therefore, immigrants and non-immigrants are as sumed to have a common wage/age profile. The assimilation measured by the immigrant cohorts is then interpreted as the difference in returns to post-migration labour market expe rience as originally suggested by Chiswick (1978). The vector XNA contains five education dummy variables with the default group represent ing men with a high school diploma. Controls for region of residence are also included and the 23 default category contains husbands who live in Toronto. Controls for language fluency are also included with the default category containing husbands who speak English but not French. Each of these variables are also included as interactions with an immigrant dummy variable. The log hours equation for the husbands has the same specification as the log wage equa tion. The log weeks equation has the same specification, but also includes a dummy variable identifying immigrants in the 1981 survey who arrived in 1980. The coefficient on this variable picks up the difference in weeks of work for this group from the average weeks of work of immigrants in the 1981 survey who arrived between 1971 and 1979. Since the 1980 cohort arrive part way through the year, their weeks of work are truncated. The wife’s log wage equation has the same specification, but with the husband’s character istics replaced by the wife’s characteristics. Controls for the number of children ever born to the wife are also included to proxy time spent out of the labour market due to child-rearing. The wife’s log hours equation contains the same variables as are in the wife’s wage equation with two exceptions. The controls for number of live births are not included. Instead, controls for presence of children in the household are included to control for demands placed on the wife’s non-labour time. The wife’s log weeks equation contains the same variables as the wife’s hours equation along with a dummy variable identifying wives in the 1981 survey who arrived in 1980. Since their weeks are likely truncated, this specification treats them separately in the analysis. 2.4 Empirical Analysis In order to study an immigrant family’s labour market adjustment, one would ideally use 24 panel data with a large number of immigrant families which follows each household from the time of arrival through several years of residence in the new country. Unfortunately, this type of data does not exist. Panel data sets typically are smaller than cross-sectional data sets; therefore, they do not have enough immigrants in the sample to estimate the dynamic model described above. Instead, two cross-sectional data sets, with a ten year interval, are used. Each cross-section is assumed to be a random sample of the Canadian population at each point in time. Therefore, movements in average labour market behaviour are estimates of the expected labour market movements of households over the period conditioning on family characteristics which are constant across time. The sample used in estimation is from the 1981 and 1991 Canadian Censuses. The Census data come from the Family Files which contain 94,745 census families from 1981 and 345,351 census families from 1991. The data contain extensive information on income, hours and weeks of work, and demographic characteristics of both the husband and wife of the Census family. Weight variables exist in both data sets which adjust sample counts so that the data are representative of the Canadian population at the relevant time period.’ 3 In the estimation, these weights are used. Households where at least one spouse lists his/her main source of income as self-employment income are excluded from the estimation sample. In the 1981 data, households where either spouse is under twenty-five or over fifty-four years of age are excluded from the 1981 sample. In the 1991 data, households where either spouse is under thirty-five or over sixty-four years The 1981 Census Family File does not distinguish between households in Prince Edward Island from those 13 in the Yukon and the NorthWest Territories, subsequently, households from these three regions were excluded from both data sets. 25 of age are excluded from the 1991 sample. Households where one spouse was born outside Canada and the other spouse was Canadianborn are excluded from the analysis. Analysis of the labour market adjustment of immigrants in these “mixed” households will be left for future work. The FIH is more likely to apply to households where both spouses are immigrants than to these mixed households. In the mixed households, the native-born spouse has domestic education credentials; therefore, borrowing is less-likely to be necessary. Also, the native-born spouse has family connections and is more likely to have a credit history with Canadian financial institutions. The sharpest contrast, therefore, is in comparing households where both spouses are foreign-born to those where both are native-born. The labour supply measures used in the analysis of this chapter are the hours worked in the reference week and the weeks worked in the reference year of the husband and the wife.’ 4 Immigrants who arrived part way through the reference year would likely have a truncated weeks of work for the year. To avoid this problem, a dummy variable is used to control for this group in the weeks worked equations. Wage rates are constructed by dividing the product of the reference week hours variable and the weeks worked per year variable into the individual’s annual earnings the previous year. 15 To do this, it was necessary to exclude from the sample households where either spouse had 1n both Census data sets, the hours of work in the reference week variable is top-coded at one hundred. 4 ‘ Households where at least one spouse reported hours of work of one hundred for the reference week were excluded from the analysis. After all other restrictions on the sample were made, this restriction only excluded 0.4 percent of households in the sample. The annual earnings variable from the 1991 data is deflated using the GDP deflator for Canada into 1981 15 dollars. 26 positive earnings and weeks the previous year, and zero hours in the reference week, or vice versa. All households in the 1981 sample where both spouses are immigrants and which meet the above criteria were kept in the sample. Due to the large numbers of non-immigrant households in the two data sets, for both the 1981 and 1991 data, a twenty-five percent random sample of non-immigrant households is taken. As can be seen in Table 2.1, after these restrictions there are 3688 foreign-born households from the 1981 Census, and 10472 households from the 1991 Census. The total number of non-immigrant households from the 1981 Census is 3808, and from the 1991 Census there are 9815 remaining. Appendix 1 contains definitions for the variables listed in the tables. The year of arrival information is more detailed in the 1981 Census than in 1991, therefore, arrival years are grouped. It is possible to identify immigrants arriving between 1971-80, 1961-70, and before 1961 in each data set, as well as immigrants from the arrival cohorts 1981-85, 1986, 1987 ,1988, 1989, and 1990 in the 1991 data set. Other variables used in estimation include variables for whether the person can speak English but not French, French but not English, both English and French, and neither English nor French. Six age indicator variables are defined for each spouse. Region of residence controls as well as separate controls for residence in Vancouver, Toronto, and Montreal are included. Controls for the number and age compositions of children in the census family are also used as was the number of live births of the wife. Table 2.1 contains sample means of the variables used in estimation over the immigrant and non-immigrant samples in each survey year. Immigrant women have a sixty-six percent 27 participation rate in the 1981 sample while the non-immigrant women’s participation rate is only fifty-nine percent. Over the decade, the non-immigrant participation rate rose faster so that, by 1991, seventy-four percent of immigrant women in the sample participate and seventy three percent of the non- immigrant women participate. The average wages of immigrant women are one dollar and thirty- seven cents lower than those of the non-immigrant women in 1981, but this wage gap has dropped to eighty-nine cents by 1991. Immigrant women work 2.2 hours more per week in 1981 and 1.85 more hours per week in 1991. Immigrant women work a third of a week more on average in 1981 and less than one week more in 1991. Immigrant women are over a year older in each year and have a more dispersed education distribution. Immigrant men have eighty-three cents lower wages in 1981, but by 1991 the difference has decreased to twenty-five cents. Their mean hours per week and weeks per year patterns are very similar to the non-immigrant men. Immigrant men are roughly two years older than non-immigrant men in each survey year, and like the immigrant women, have a more dispersed education distribution. The means of the region of residence variables indicate that immigrant families are much more concentrated in Toronto than non-immigrant families. A higher percentage of immigrant families reside in Vancouver than non-immigrant families. Table 2.2 contains results of OLS estimation of log wage, log hours and log weeks equations over the sample of wives who work. The definitions of the variables are presented in Appendix 1. The covariance matrix allows for heteroskedasticity of unknown form and is from White 28 (1980). The coefficients are distributed asymptotically according to the Normal distribution. The asymptotic standard errors are in parentheses. The first column lists estimates from the wage equation for women. In the 1981 crosssection, women age twenty-five to twenty-nine have twelve to fifteen percent lower wages on average than older women. From the coefficient on YR91, we see that the growth in wages over the decade for women of the youngest age cohort is sixteen percent. Older women experience lower wage growth between the two surveys, so that by 1991, the youngest age cohort have no more than six percent lower wages than older women. The wages of non-immigrant women are increasing in their level of education with a re turn of fifty-seven to sixty-eight percent to a university degree. Using the coefficients on the immigrant-education interaction variables, we see that the wages of immigrant wives also rise with education, but the wage/education profile is flatter than that of non-immigrant women. There is a seven to fourteen percent lower return to a university degree for immigrant wives than for non-immigrant wives, and a six to thirteen percent higher return to education below a high school diploma than is the case for non-immigrant wives. This matches the result found by both Long (1980) and Beach and Worswick (1993) that the returns to education are lower for immigrant women than for non-immigrant women. The coefficients on the controls for the number of live births of the wife are negative implying lower wages due to foregone work experience. There is a three percent drop in wages associated with each birth for non-immigrants, and this effect is statistically significant at the 29 five percent level.’ . For immigrants the drop in wages associated with the birth of each child 6 is one percent lower than for non-immigrant wives; however, the difference is not statistically significant The coefficients on Y7180, Y6170 and YBEF61 indicate that the wages of non-immigrants in 1981 are twenty-eight percent higher than the wages of immigrants who arrived in the 1970s, eighteen percent higher than immigrants who arrived in the 1960s, and ten percent higher than immigrants who arrived before 1961, ceteris paribus. Each of these wage differentials 8 The wage differentials describe the TAPs of the three cohorts are statistically significant.’ over the relevant ranges of their years-since-migration. For example, the coefficient on Y7180 implies that the average value of the TAP of the 1970s cohort is — .28 over one to ten years of residence. As was shown in section 2.3, the coefficients on the interactions between the controls for these three immigrant cohorts and Y1191 measure the wage assimilation over the 19 The wages of immigrant women grow by eight to eleven percent more than the wages decade. of similar non-immigrant women, and these differences are statistically significant. ° This wage 2 assimilation is larger for the more recent cohorts. Immigrant wives who arrived in the 1980s had twenty-nine to thirty-nine percent lower wages than similar non-immigrant wives with the larger differences belonging to women who arrived in the second half of the decade. However, this difference is not statistically significant. The hypothesis that more recent cohorts have 15 test statistic equals —4.77 and the prob-value of the test is less than .0001. The The test statistic equals .9, and the prob-value of the test is .37. 7 The test statistics are —6.00, —3.83, and —2.07 for the variables Y7180, Y6170, and YBEF61, respectively. 8 ‘ The prob-values are less than .0001 for the first two coefficients and .04 for the coefficient on YBEF61. For the case of the interaction of YR9I with Y7180, this is the change in the average value of the TAP from 15 having one to ten years-since-migration to having eleven to twenty years-since-migration. The test statistics are 2.15, 2.67, and 3.26 for immigrant who arrived before 1961, between 1961 and 1970, 20 and between 1971 and 1980, respectively; the prob-values of the individual tests are .030, .011, and .001, respectively. 30 lower wages upon entry into Canada than did earlier cohorts, after controffing for observable characteristics, can be tested by comparing the 1981 wages of immigrants who arrived in the 1970s to the 1991 wages of immigrants who arrived in the 1980s. ’ The weighted average 2 22 of the coefficients on the controls for immigrants who arrived in the 1980s equals — .3227. This implies that the average 1991 wage of immigrant wives who arrived in the 1980s is four percent lower than the average 1981 wage of immigrant wives who arrived in the 1970s, ceteris paribus. The hypothesis that the weighted average of the coefficients on the 1980s cohort controls equals the coefficient on Y7180 is not rejected. 23 Therefore, recent cohorts of immigrant women do not appear to have significantly different wages at time of arrival than previous immigrant cohorts, after controlling for observable characteristics. The second column of Table 2.2 lists the parameter estimates from the log hours equation. In the 1981 cross section, women twenty-five to twenty-nine work five to sixteen percent more hours than older women. From the coefficient on YR91 we see that the growth in hours over the decade for the youngest cohort of women is zero. The growth in hours is negative for older women. For example, women age fifty-five to fifty-nine in 1981, reduce their hours by six percent over the decade. Non-immigrant wives with a university education work four to ten percent more hours than This tests the hypothesis that the average value of the lAP of the 1970s cohort over one to ten years-since21 migration equals the average value of the lAP of the 1980s cohort over the same YSM range. It would be preferable to test whether or not the intercept of the 1970s cohort’s lAP differed from the intercept of the 1980s cohort’s lAP; however, that is not possible given the broadly defined immigrant arrival year categories in the data. “The weight placed on each coefficient equalled the percentage share of immigrants who arrived between 1981 and 1990 in the sample who arrived in the period represented by the dummy variable. The shares are .4814, .0629, .1216, .1472, .1100, and .0769 for the variables Y8185, Y86, Y87, Y88, Y89, and Y90, respectively. “The Wald test statistic is distributed asymptotically according to the Chi- square distribution with one degree of freedom and equals .9857. The prob-value of the test is greater than .25 and less than .5. 31 similar wives with a high school education. The increase in hours of work associated with a university education is smaller for immigrants. The increasing hours/education profile can be explained by the increasing wage/education profile found in the wage equation. One would expect women to respond to the higher wage rates by supplying more hours of work. Also, the fact that the hours/education profile is flatter for immigrant women than for non-immigrant women is consistent with the wage/education profile also being flatter for immigrant women. The presence of children in the household has a significant negative effect on the hours of work of the wife. 24 The effect is smaller for immigrant families, with all of the coefficients on the interaction terms significant from zero except the coefficient on the K2PLUS interaction. 25 This result was also found in Long (1980) and Beach and Worswick (1993). It may be that the immigrant family is more likely to have extended family members present, who are able to provide child care for young children . Also, it may be the case that in immigrant families 26 older children are expected to provide greater care for young children than is the case in non-immigrant families. This would free up time for the wife to work more hours. In the 1981 data, immigrant wives who arrived after 1960 work ten percent more hours than similar non-immigrant wives. From the coefficients on the interactions terms of the three earliest cohorts with the YR91 variable, we see that the hours assimilation of immigrant wives was not significantly different from zero for all three cohorts. 27 Immigrant wives who arrived The test statistics for the hypotheses that the coefficients on each control equals zero are —7.60, —7.17, 24 —9.70, and —5.67 for KIDSOS, K1FLUS, KLDS614, and K2PLUS, respectively. The prob-values for the tests are less than .000 1 in each case. The test statistics equal 2.85, 2.86, 3.32, and .73 for the interactions of the immigrant dummy variable with 25 KJDSOS, K1PLUS, K1D5614, and K1PLUS, respectively. The prob-values are .004, .004, .001, and .465. Unfortunately, the Census data does not include information on the presence of other adults in the home. 26 The test- statistics are —.28, —.15, and —.17; and the prob-values are .78, .88, and .87. 27 32 in the 1980s worked three to nine percent more hours in the 1991 reference week than similar non-immigrants. Next, a test is carried out, analogous to the one above for the wage equation, of the hypothesis that the average value of the hours TAP over one to ten years of residence is the same for immigrants who arrived in the 1970s and for immigrants who arrived in the 1980s. A weighted average of the coefficients on the controls for immigrant arrival year in the 1980s is found to equal — .3023. Comparing this to the coefficient on Y7180 indicates that immigrants who arrived in the 1980s worked two percent more hours in 1991 than immigrants who arrived in the 1970s worked in 198128. The hypothesis that this weighted average equals the coefficient on Y7180 is not rejected. 29 Therefore, recent immigrant cohorts do not appear to differ in terms of hours of work at time of arrival, after controlling for observable characteristics. The third column of the table lists estimates from the weeks equation for women. In the 1981 cross section, weeks worked per year are found to be smaller for older women. The group of wives age twenty-five to twenty-nine in 1981 increased their weeks per year over the decade by eleven percent. The growth is much smaller for older women. For example, women age forty-five to forty-nine in 1981 did not change their weeks of work over the decade. Weeks of work are increasing in the wife’s education. From the coefficients on the in teractions of the immigrant dummy variable with the education variables, we see that the weeks/education profile is flatter for immigrant wives. This is consistent with the flatter hours/education profile and wage/education profile found above. The lower returns to educa tion for immigrant women lead them to supply less labour both in terms of hours per week The weights are the same as the ones listed in footnote 22. 28 25 test statistic is distribnted asymptotically according to the Chi-square distribution with one degree of The freedom; the prob-value of the test is between .25 and .5. 33 and weeks per year. The presence of children has a significant negative effect on the weeks worked of wives as was the case in the hours equation. ° The only significant difference by immigrant status in 3 the response of the wife’s weeks to the presence of children is in the case of three or more children age six to fourteen present in the home. ’ Non-immigrant wives reduce their weeks 3 by twenty- four percent while the immigrant wives reduce their weeks by ten percent. Immigrant wives who arrive in the survey year work sixty-one percent fewer weeks in 1990 and seventy-two percent fewer weeks in 1980. This is due to a bias caused by the wives having arrived midway through the year. In the 1981 data, the weeks of work of wives in each of the three immigrant cohorts are not significantly different from the weeks of similar 32 The weeks assimilation of the earliest two cohorts is not significant non- immigrant wives. from zero; 33 however, the immigrant wives who arrived in the 1970s experience five percent higher growth in weeks than similar non-immigrant wives, and this difference is statistically 34 The wives who arrived in the 1980s work fewer weeks per year in general than the significant. non- immigrant wives with large differences for the immigrant women who arrived after 1985. Interestingly, the weeks per year of immigrant wives arriving in 1989 are twenty-five percent lower than the weeks of similar non-immigrant wives. The reference weeks hours for this group do not have the same pattern. It may be that these women have difficulty finding a job that The test statistics are —5.09, —4.59, —7.39, and —6.49 for the variables KIDSO5, K1FLUS, KIDS614, 30 and K2FLUS, respectively. The prob-values are less than .0001 in each test. The test statistic is 3.11; and the prob-valne is .0018. 31 The test statistics are —1.48, .14, and —.62 for the variable Y7180, Y6170, and YBEF61. The prob-values 82 are .14, .89, and .54, respectively. The test statistics equal .12 for the coefficient on YBEF61 and —.52 for the coefficient on Y6170. The 33 prob-values are .90 and .60. The test statistic equals 2.12; and the prob-value is .034. 54 34 suits their skills. If so, then this is not a difference in preferences over labour supply, but instead a difference in the propensity to invest time in job search. The test of the hypothesis that immigrant wives who arrived in the 1970s worked the same number of weeks in 1980 as immigrant wives who arrived in the 1980s worked in 1990 is performed. A weighted average of the coefficients on the coefficient on the controls for immigrant arrival in the 1980s is calculated and equals — .0727. This implies that the immigrant wives who arrived in the 1980s worked three percent fewer weeks in 1990 than the immigrant wives who arrived in the 1970s worked in 1980. However, this difference is not significant. 35 The results of Table 2.2 indicate that immigrant wives generally have lower wages and work more hours and weeks than similar non-immigrant wives. Immigrants wives experience higher wage growth than similar non-immigrant wives; however, their growths of hours and weeks do not differ significantly from the growths of hours and weeks of non-immigrant wives. Differences across recent immigrant entry cohorts of women in terms of wages, hours, and weeks at time of arrival are not significant. These differences in labour market outcomes between immigrant and non-immigrant wives can be explained by credit constraints having a larger impact on labour supply in immigrant families than in non-immigrant families. The fact that immigrant wives work more hours for lower wages could be explained by the immigrant wife being unable to borrow against future income in order to fund current consumption, and responding to this capital market constraint by working more hours. If the non- immigrant wife is able to borrow then she will not need to work as many hours as the non-immigrant wife, ceteris paribus. One would expect The Wald test statistic equals .9025, and the prob-vaine is greater than .25 and less than .5. 35 35 the effects of credit constraints to diminish with years of residence for immigrant families, as suggested by Long (1980). If that were the case, one would expect the hours of immigrant women to approach those of non-immigrant women as years-since-migration rises. Instead, we find that the hours difference between immigrant and non-immigrant wives stays constant over the 1980s. It may be that the wife’s hours are not reduced because the higher growth in wages of immigrants over non-immigrants pushes her towards more hours of work. The desire to increase hours in response to the high growth in wages could “mask” the reduction in the credit constraint effect. Table 2.3 contains the results of the log wage, log hours, and log weeks estimation for the husbands. Definitions of the variables used in estimation are presented in Appendix 1. The coefficient estimates are distributed asymptotically according to the Normal distribution. The covariance matrix of the estimates allows for heteroskedasticity of unknown form and is from White (1980). The first column lists the estimates from the log wage equation. Looking at the age patterns in the 1981 sample, we see that the men age twenty-five to twenty- nine face sixteen to twenty-seven percent lower wages than older men. The growth in wages for the youngest age cohort is twenty-two percent over the decade. Older men experience much lower wage growth. For example, men age forty to forty-four in 1981 have average wage growth of four percent. Wages are increasing in the husband’s education with high returns to university degrees. Using the coefficients on the interactions between education and immigrant status, we see that immigrant and non-immigrant men have similar wage/education profiles. This is inter 36 esting given the large differences in these profiles found in Table 2.2 for women. Given the problems of having education credentials recognized after migration, one would expect lower wage/education profiles for both immigrant men and immigrant women. This difference could be explained by the Family Investment Hypothesis. If the husband is perceived to be the main earner, it may be that the family invests in job search and retraining for the husband so that he can find a job that suits his skills, while the wife settles quickly in a job which may not suit her skills but allows her to fund family consumption. However, this difference might also be due to the family’s migration decision being more closely related to the husband’s career than the wife’s career. Immigrant men who arrived in the 1970s have twenty-eight percent lower wages in 1981 than similar non-immigrant men, while those arriving earlier have twelve to sixteen percent lower wages. The wage assimilation of the earliest and the most recent of the cohorts was seven percent and was significant, while the wage assimilation of immigrant men who arrived in the 37 The immigrant men who arrived in the late 1980s have forty-seven 1960s was not significant. to sixty-four percent lower wages in 1991 than similar non-immigrant men. The hypothesis that the 1981 wages of immigrant men who arrived in the 1970s equal the 1991 wages of immigrant men who arrived in the 1980s is tested. A weighted average of the coefficients on the controls for immigrant arrival year in the 1980s is 38 derived. The weighted average equals — .4379 and implies that the 1991 wages of immigrants who arrived in the 1980s are sixteen The test statistic equals 2.58 for the coefficient on YBEF61 and 2.63 for the coefficient on Y7180; the 36 prob-values are .010 and .009. The test statistic is .92; and the prob-value is .36. 37 Each weight is the ratio of the number of immigrant men in the sample who have a value of one for the 35 cohort dummy variable, divided by the total number of immigrant men in the sample who arrived in the 1980s. The weights are .4446, .0669, .1325, .1410, .1239, and .0911, for the variables Y8185, Y86, Y87, Y88, Y89, and Y90, respectively. 37 percent lower than the 1981 wages of immigrants who arrived in the 1970s, after controlling for observable characteristics. This difference is significant from zero. 39 Therefore, the average wages of immigrant men at time of arrival are significantly lower for more recent cohorts, ceteris paribus. These results are consistent with the findings of Borjas (1985) for the U.S. and Baker and Benjamin (1994) for Canada. Immigrant men have significantly lower wages than nonimmigrant men at time of arrival and experience low rates of wage assimilation. Also, more recent immigrant cohorts have had lower wages in the first years after migration. The second column of Table 2.3 lists estimates from the hours equation for husbands. Men age twenty-five to twenty-nine work three to eight percent fewer hours in 1981 than older men. The youngest age cohort experience six percent growth in hours over the decade. The hours of older men have lower growth in hours. In the 1981 data, immigrant men work uine to ten percent more hours than similar nonimmigrant men, and these differences are statistically significant. ° The hours assimilation of 4 the men who arrived in the 1970s is negative three percent over the decade and is significant. 41 The hours assimilation is not statistically significant for the two earlier cohorts. 42 Immigrant men who arrived after 1980 worked two to seven percent more hours per week than similar non- immigrant men. The test of the hypothesis that immigrant husbands who arrived in the The Wald test statistic is distributed asymptotically according to the Chi-square distribution with one 39 degree of freedom, and equals 22.89, and the prob-value is less than .005. The test statistics are 5.13, 4.62, and 4.77 for the variables YBEF61, Y6170, and Y7180 respectively. The 40 prob-valnes are less than .0001 in each test. tThe test statistic is 1.96; the prob-vaJue is .05. 4 The test statistic is —.16 and —1,08 for the coefficients on YBEF61 * YR91 and Y6170 * YR91 respectively; 42 the prob-values are .87 and .28 respectively. 38 1970s worked the same number of hours in the 1981 survey week as immigrant husbands who arrived in the 1980s worked in the 1991 survey week is performed. A weighted average of the coefficients on the controls for immigrant arrival in the 1980s is calculated and implies that the 1980s cohort worked four percent fewer hours in the 1991 survey week than the 1970s cohort worked in the 1981 survey week. This difference is significant.” 3 The third column of Table 2.3 lists the results from the weeks equation. In the 1981 cross section, men age twenty-five to twenty-nine work eleven to thirteen percent fewer weeks than older men. Over the decade, the weeks of the youngest age cohort grow by eleven percent, while the weeks of older men grow by much less. For example, men age fifty to fifty-four in 1981 reduce their weeks of work by four percent over the 1980s. Immigrant men who arrived in either survey year work fifty- four to fifty-five percent fewer weeks that year. This is due to their having arrived, on average, midway through the year. In the 1981 cross-section, the immigrant men from each of the three earliest immigrant cohorts worked one to three percent more weeks than did similar non-immigrants; however, these differences are not significantly different from zero. 44 The weeks assimilation is not significant for each of the three 45 cohorts. The immigrants who arrived in 1989 have much lower weeks of work (twenty-three percent) than non-immigrants which is similar to the result found for immigrant women. This may be picking up an increased likelihood of being unemployed in The Wald test statistic is distributed asymptotically according to the Chi-square distribution with one 43 degree of freedom, and equals 8.14. The prob-value of the test is less than .005. The test statistics for the individual tests are 1.16, 1.79, and .61 for the immigrants who arrived before 44 1961, the immigrants who arrived in the 1960s, and the immigrants who arrived in the 1970s, respectively. The prob- values for the three groups (in the same order) are .11, .07, and .54. The test statistics are 1.54, .14, and .95 for the before 1961 cohort, the 1961-70 cohort, and the 1971-80 45 cohort, respectively; the prob-values of the tests are .12, .89, and .34, respectively. 39 the first years after arriving. The immigrant men who arrived from 1981 to 1988 have very similar weeks of work to the non-immigrants, ceteris paribus. The hypothesis that the number of weeks in 1990 of immigrant men who arrived in the 1980s equals the number of weeks in 1980 of immigrant men who arrived in the 1970s is rejected. The weighted average t6 of the coefficients on the controls for immigrant arrival year in the 1980s implies that immigrant men who arrived in the 1980s work four percent fewer weeks in 1990 than immigrant men who arrived in the 1970s worked in 1980. However, this difference is not statistically significant. 47 The results of Table 2.3 indicate that immigrant men earn lower wages while working more hours and similar weeks in the year to non-immigrant men. Immigrant men experience higher wage growth, in general, over the 1980s than do non-immigrant men; however, their hours and wage growth are similar to those of non-immigrant men. As was suggested in interpreting the results of Table 2.2 for women, these differences in labour market outcomes between immigrants and non-immigrants can be explained by credit constraints being a more important determinant of labour supply in immigrant families than in non-immigrant families. This would explain the higher hours of immigrant men relative to non-immigrant men given their lower wages. Also, this would explain why immigrant men do not increase their hours of work by more than the non-immigrant men given the higher wage growth over the 1980s. However, an alternative explanation is that immigrant men work more hours for lower wages than non-immigrant men due to a lower disutility to work or a lower expected lifetime wealth. This along with a The coefficient on Y90 was not included in the average to eliminate the truncation of weeks of that cohort. 46 Therefore, the weights are .4892, .0736, .1457, .1551, and .1364 for the variables Y8185, Y86, Y87, Y88, and Y89, respectively. The Wald Test statistic is distributed asymptotically according to the Chi-square distribution with one 47 degree of freedom, and equals 5.22. The prob-va.lue of the test is greater than .25 and less than .5. 40 small hours response by immigrant men to a movement along their intertemporal wage path can also explain the observed differences in labour market outcomes between immigrant and non-immigrant men. Next, differences in wages, hours and weeks for husbands and wives by immigrant status are analyzed holding family characteristics at their mean values over the 1991 non- immigrant sample. The results of Table 2.2 and Table 2.3 indicate that there are important differences across immigrant and non-immigrant families in the way wages, hours and weeks respond to factors such as education, language fluency, and the presence of children. Evaluating the equations at these mean values allow us to look at differences between immigrant and nonimmigrant families with “average” characteristics. Table 2.4 gives predicted differences between immigrant wives and non-immigrant wives over the 1981 cross-section for each of the three reduced form equations; while Table 2.5 gives the analogous predictions over the 1991 crosssection. In each table, the predictions are evaluated at the 1991 non-immigrant wives’ sample means of the regressors. The patterns of wages, hours and weeks differences follow the patterns of coefficient esti mates of the regressions in Table 2.2 very closely. In fact there is a simple relationship between these predicted differences and the marginal effects of being in a particular cohort in a par ticular survey year in the regressions of Table 2.4 and Table 2.5. For example, consider the predicted wage differential of Table 2.4 for immigrants who arrived in the 1970s. This implies twenty-four percent lower wages for immigrants in this group than the non- immigrants in 1981. In equation (14), an expression for this was derived in terms of the specification of the 41 regressions, (12): , 5 Y 7 1 — 81,N = F+ 3 XFI (21) P71 Therefore, this differs from the coefficient estimate only by the value of the interaction terms evaluated at the 1991 non- immigrant sample means. Each predicted difference of the first column of Tables 2.4 and 2.5 differs from the marginal effect of being in that group measured by the coefficients on the immigrant controls of the wage regression by XFJ3F. This term can be measured by taking the difference between the predicted wage difference in Table 2.4 for the 1971-80 group from the coefficient on Y7180 in the wage regression. The difference equals .041, which implies that the 1981 wage difference between immigrants who arrived in the 1970s and non-immigrants is four percentage points smaller when evaluated at the nonimmigrant 1991 sample means than it is when characteristics are set at their default values in the wage regression. However, almost all of the predicted differences imply lower wages for immigrants than non-immigrants in both Table 2.4 and Table 2.5. Therefore, the conclusion that immigrant women generally earn lower wages than non-immigrant women still holds.” 9 Looking at the predicted differences in the second column of Table 2.4 and 2.5, we see that immigrant women generally work more hours than non-immigrant women. The difference between the predicted hours difference for the 1971-80 cohort in Table 2.4 from the coefficient on Y7180 in the hours regression again equals the effect of the immigrant interaction terms in 1n the discussion of the regression specification I focused on the hnsband’s wage equation. However, since 45 the same general specification, is used in all of the regressions, one can easily think of (12) as representing the wage, hours or weeks equation for either spouse. The one case where the predicted difference is positive is the case of women with the most years of residence, 49 those in the 1991 survey who arrived before 1961. Their predicted wage is two percent higher than the predicted wage of the non-immigrants; however, the difference is not significant. The test statistic equals the ratio of the predicted difference to its standard error and is distributed asymptotically according to the Normal distribution. The test statistic equals .69, and the prob-values equals .49. 42 the hours regression evaluated at the 1991 non-immigrant sample means, XFI F. In this case 3 the difference is .0015. This implies that the hours differences by immigrant status are not very sensitive to the values of personal characteristics which are chosen. This comparison can be repeated for the third column of the Tables, the weeks differences. The difference between the predicted differences for the 1971-80 cohort in Table 2.4 and the coefficient on Y7180 in the weeks equation equals .0408. This implies that when characteristics are evaluated at the 1991 non-immigrant mean values rather than the default values of the regression, the difference between the weeks of the immigrants and the weeks of the nonimmigrants rises by four percentage points. Therefore, this reinforces the conclusion that immigrant wives with five or more years of residence do not work fewer weeks than nonimmigrant wives. Table 2.6 and Table 2.7 repeat the comparisons of Table 2.4 and Table 2.5 using the estimates and sample means for the husbands. The difference between the predicted wage difference in Table 2.6 for the 1971-80 group from the coefficient on Y7180 in the wage regression of Table 2.3 equals .068, This implies that the 1981 wage difference between immigrants who arrived in the 1970s and non-immigrants is seven percentage points smaller when evaluated at the non- immigrant 1991 sample means than it is when characteristics are set at their default values in the wage regression. However, aU of the predicted differences imply lower wages for immigrant husbands than non-immigrant husbands in both Table 2.4 and Table 2.5. Therefore, the conclusion that immigrant men earn lower wages than non-immigrant men still holds. From the predicted differences in the second column of Table 2.4 and 2.5, we see that 43 immigrant husbands generally work more hours than non-immigrant women. The difference between the predicted hours difference for the 1971-80 cohort in Table 2.6 from the coefficient on Y7180 in the hours regression equals .062. This implies that the hours differences by immigrant status are sensitive to the chosen values of personal characteristics. When characteristics are held at the non-immigrant 1991 sample means, the difference between the immigrant and nonimmigrant hours for each cohort in each year are six percentage points smaller. This leaves very little difference between hours of work of immigrants and non- immigrants. The only significant differences are for immigrants who arrived before 1981. The predicted differences in the second column of Table 2.6 are all positive and significant implying three to four percent more hours of work for immigrants. ° Also, the predicted hours differences for immigrants 5 arriving before 1971 are positive and significant in Table 2.7.’ This comparison is again repeated for the third column of the Tables, the weeks differences. The difference between the predicted differences for the 1971-80 cohort in Table 2.6 and the coefficient on Y7180 in the husbands’ weeks equation of Table 2.3 equals .040. This implies that when characteristics are evaluated at the 1991 non-immigrant mean values rather than the default values of the regression, the difference between the weeks of the immigrant men and the weeks of the non-immigrant men falls by four percentage points relative to the differences when characteristics are held at the default values in the regression. The only differences in the third column of Table 2.6 and 2.7 which are significantly different from zero are for the The test statistics equal 2.52, 1.96, and 2.02 for the before 1961, 1961-70, and 1971-80 cohorts, respectively. 50 The prob-values are .01, .05, and .04, respectively. The test statistics equal 3.90 for the before 1961 group and 2.13 for the 1961-70 group. The prob-values are 51 less than .0001 and .03, respectively. 44 1988, 1989, and 1990 cohorts. 52 The results of the estimation indicate that immigrant husbands and wives face lower wages immediately alter arrival than non- immigrant husbands and wives. Successive immigrant co horts of men have faced lower wages at entry, after controlling for observable characteristics; however, these differences across immigrant women’s cohorts are insignificant. Immigrant hus bands and wives are found to have higher wage growth than non-immigrant husband and wives. Immigrant men and women work more hours per week than their non-immigrant counterparts. The differences for non-immigrant women are particularly large implying a one to nine percent hours surplus which is striking when you consider that these women are earning one to thirtyfive percent lower wages. For both husbands and wives these differences in hours remain more or less constant with years of residence. The high hours and low wages are consistent with credit constraints being an important determinant of the labour supplies of immigrant families. Also, the fact that immigrant families did not increase their hours of work by more than the non-immigrant families in response to the higher wage growth of immigrants could also be explained by credit constraints. As discussed above, a preference based explanation could also be forwarded that is consistent with the reduced form results. 2.5 Estimation of Wife’s Equations with Endogenous Participation. The estimation so far ignores the endogeneity of the wife’s participation rate. Therefore, the results describe differences in labour market outcomes between the population of immi grants who work and the population of non-immigrants who work. In evaluating the success of The test statistics are —2.43, —5.48, and —8.89, respectively. The prob-values are .02 for the 1988 cohort, 52 and less than .0001 for the other two cohorts. 45 immigration policy and choosing immigrants who adapt well to the new labour market, it may be preferable to compare the total population of immigrants and the total population of nonimmigrants. This distinction is more likely to be an issue for women since their participation rate is lower. An example of how this distinction could be relevant in measuring differences in unobserved ability between immigrant and non-immigrant wives is the foliowing. Consider the extreme case where afl immigrant women choose to work but some non-immigrant women choose not to work. In particular, assume that non-immigrant women with high offered wages are more likely to participate than those with low offered wages. Also, assume that the of fered wage distribution is identical between immigrant and non-immigrant wives. In this case, the expected wage of non- immigrant wives who work is greater than the expected wage of immigrant wives who work, although both groups share the same offered wage distribution. Ig noring the participation decision leads one to the conclusion that immigrant women have lower unobserved ability than non-immigrant women, when the only difference between immigrant and non-immigrant women is in the determinants of their participation decisions. The procedure for handling the endogeneity of the wife’s participation decision is based on the model and estimation procedure in Heckmau (1978), and discussed in detail in Maddala (1983). The log wage, log hours, and log weeks equation for married women are assumed to take the form: lflWtzXw/3w+Ew (22) lnH=Xh/3h+eh (23) InWK Xwk/ w 3 k +Ewk 46 (24) where mW is the log of the wage, lnH is the log of hours, and 1nWK is the log of weeks; X, Xh, and Xk are vectors of personal characteristics and have the same specification as in Table 2.2; 1, and / h 3 wk are parameter vectors; and 9 E, ep,, and 8 wk are error terms. The wage equation explains the wage offered to each married woman on the market. The hours and weeks equations explain the hours and weeks each woman would choose if she were to work. These equations are defined over the entire population of married women. The index defining the wife’s participation decision is: I—_Z/3+e (25) where Z is a vector of family characteristics, j3, is a parameter vector, and e, is an error term. The wife works if I 0, and does not work otherwise. Over the sample of households where the wife works: 1mW = Xj3 + E{e I s —Z/3} + c,, lnH = 3 Xh/ + E{eh j e, : —Z/3} + h 1nWK = Xwk/ wk + E{ewk 3 where E{x I e, eh and ewk; I ep Ch —Z/3} + Cwk (26) (27) (28) —Z/3} is the expectation of x conditional on the wife working, for x = and c, Ch, and Cwk are mean zero error terms over the sample of households where the wife works. It is assumed that the error terms e, e,,,, Eh, 47 and Ek are jointly distributed according to the Normal distribution with covariance matrix: L7 where Cp,w f7, p,h ‘ w 7 ,h Cp,wk w,wk is the variance of q for j,k=p,w,h,wk,wherej $ j = p,h p,wk Uw,h 2 h rJhwk w,wk p, w, h, wk, and h,wk 2 tvk 0 j ,k is the covariance of &j with k 6 for k. Equations (25)-(27) can be rewritten: mW + f2f(Z) + c = (29) Uw lnH = + cj h + 3 Xh/ (30) 1nWK = Xj w + “.(Z) + c 3 (31) wk where (Z) is the inverse Mill’s ratio and is defined as (Z) E f(4.&)/F(), where f and F are the Standard Normal density function and distribution function, respectively. The first stage involves estimation of the determinants of the wife’s participation decision using the Probit estimator. The estimates of /3/a are used to derive a value of the inverse Mill’s ratio, F(Z), over the sample of households where the wife works. The derived Inverse Mill’s ratio variable is then included as a regressor in the estimation of (28)-(30) over the sample of households where the wife works. Table 2.8 contains the results from Probit estimation on the wife’s participation decision. These estimates are of the change in the probability of the wife working due to a unit increase in the explanatory variable. The same set of controls are included as in the regressions of Table 2.2. Controls for the husband’s age, education, and immigrant status were also included. This 48 is to make the results comparable to those of Duleep and Sanders (1993) and Baker and Benjamin (1994). Unlike the specification of the immigrant controls in the previous tables, the default group is no longer the non-immigrants, but instead couples with both spouses having arrived in Canada in the 1980s. 53 A dummy variable for non- immigrant households is included in the model on its own and as an interaction with the 1991 year dummy variable. Interpreting the results of this table is more involved than interpreting the previous results because there are controls for the characteristics of each spouse. Therefore, in order to simplify the discussion, I will focus on the coefficients of the controls for the wife and husband’s arrival cohort variables. The coefficient on the non-immigrant dummy variable, NB, measures the difference in the wife’s participation probability between non-immigrant couples and immigrant couples where both spouses arrived in the 1970s, after holding other characteristics at the default values. The coefficient is significant and implies a seven percent higher participation rate for these immigrant wives. 54 The coefficient on the interaction between the non-immigrant dummy variable and the 1991 survey year dummy variable measures the change in this difference in the wife’s participation rate over the decade. The estimate implies a three percent higher growth in the non-immigrant participation rate than in the immigrant participation rate; however, this difference is not statistically significant. 55 J could not include controls for the both the husband’s immigrant cohort and the wife’s immigrant cohort 53 while having the default group being couples who are both native-born. The sum of the immigrant cohort controls for the wife equals the sum of the immigrant arrival cohorts for the husband over the entire sample. Therefore, the matrix of regressors is not full rank. Therefore, I made the default group immigrant couples who arrived in the 1970s. The test statistic equals —2.39, and the prob-value is .017. 54 The test statistic equals 1.51, and the prob-value equals .13. 55 49 The coefficients on the dummy variables for the wife having arrived before 1961, and the wife having arrived in the 1960s indicate that these women have seven percent higher participation rates than do immigrant women who arrived in the 1970s. 56 The coefficients on the interactions of the 1991 survey dummy variable, YR91, with the wife’s controls for arrival before 1961, YBEF61, and arrival in the 1960s, Y6170, measure how the differences in participation rates across these immigrant cohorts change over the 1980s. In each case, the participation rate of immigrant women who arrived in the 1970s approaches the participation rate of the immigrant wives who arrived before 1970; however, these differences are not significant. 57 Therefore, immigrant women are more likely to work than non- immigrant women. Also, immigrant women who arrive before 1971 are more likely to work than immigrant women who arrived in the 1970s. These differences in the wife’s participation rate do not change significantly over the 1980s. Using the coefficients on the controls for the husband’s immigrant status, we see the marginal effect on the participation rate of the husband having a different arrival cohort. Recall that the default category contains households where both spouses are immigrants who arrived in the 1970s. From the coefficients on the controls for the husband having arrived before 1971, we see that immigrant wives with husbands from earlier cohorts are significantly less likely to work. 58 These differences are significant. The test statistics equal 2.00 for the coefficient on the first variable and 56 2.70 for the coefficient on the second variable. The prob-va.lues are .042 and .007, respectively. The test statistics are —1.28 for the coefficient on the variable for the before 1961 cohort, and —1.64 for the 57 coefficient on the variable for the 1961- 70 cohort. The prob-values are .20 and .10, respectively. The test statistics are —4.93 for the control for the husband having arrived before 1961, and —4.06 for the 55 control for the husband having arrived in the 1960s —4.06. The prob-values are less than .0001 in each case. 50 The coefficients on the interactions between the husband’s arrival cohort with the dummy variable for the 1991 survey year give the change in these relationships over the decade. They imply that these differences in participation rates do not change with time in Canada. 59 This means that the participation rate is higher for immigrant wives whose husbands are from more recent immigrant cohorts, and the magnitude of these differences do not change significantly over the 1980s. This could represent differences in the husband’s attitude towards the wife working across the husband’s immigrant cohort. The husbands from the earliest cohorts may be less supportive of the wife working. Table 2.9 contains estimates from the wage, hours, and weeks regressions for women after controlling for the wife’s participation decision. The results are similar to the ones found in Table 2.2; therefore, I will focus the discussion on the coefficients on the controls for immigrant arrival cohort. The first column contains the result of the wage equation. The variable IMR at the end of the table is the inverse Mill’s ratio variable derived using the Probit estimates of Table 2.8. The coefficient on IMR is positive and significant. ° From equation (28), this is 6 an estimate of the ratio of the covariance of the error term in the wage equation and the error term in the participation index, over the standard error in the wage equation. The positive sign means that the covariance term is positive. Therefore, women with high offered wages are more likely to work, after controlling for observable characteristics. The coefficients on the controls for the wife’s arrival cohort are generally smaller than The test statistics are 1.87 for the before 1961 cohort of men, and 1.22 for the 1961-70 arrival cohort of 59 men. The prob-values are .06 and .22, respectively. The test statistic equals 7.00, and the prob-value is less than .0001. 60 51 those in the wage regression of Table 2.2. For example, the coefficient on Y7180 is .2588 in the wage regression of Table 2.9, and it is — .2821 in Table 2.2. The coefficient on the interactions between the three earlier arrival cohorts with the 1991 survey dummy variable measure the wage assimilation for each cohort ’ The assimilation is smaller in Table 2.9 than in Table 2.2, 6 and it is now only significant for immigrants who arrived after 1960.62 The second column contains the results from the selection corrected reference week hours equation. The coefficient on IMR is negative and significant. 63 This implies that the error term from the hours equation, (29), is negatively correlated with the error term from the participation index, (24). Therefore, women who participate work fewer hours than the women who choose not to participate would work if they were to participate. This relationship was found by Zabel (1993). He compares four models of labour supply behaviour of married women. His generalized Tobit model is equivalent to the reduced form model employed here. He also finds a negative relationship between the error term in the hours of work equation and the error term in the wife’s participation index. In Chapter 4, the wife’s participation decision is analyzed in more detail, within the context of a structural model of the wife’s participation decision and labour supply. The coefficients on the controls for the immigrant wife’s arrival cohort are smaller in Table 2.9 than in Table 2.2. However, the general pattern of the results is unchanged. In the 1981 data, immigrant women who arrived after 1960 have significantly higher hours of work than RecaJl that this is the difference between the growth in wages of each immigrant cohort from the growth in 61 wages of the non-immigrants. The test statistics are 1.75, 2.03 and 2.96 for the before 1961 cohort, the 1961-70 cohort, and the 1971-80 82 cohort, respectively. The prob-valnes are .075, .042, and .003, respectively. The test statistic equals 5.58, and the prob-value is less than .0001. 63 52 non-immigrant women. 64 As was the case in Table 2.2, the coefficients on the interactions between the wife’s arrival cohort and the dummy variable for the 1991 survey year are not statistically significant. 65 This means that the hours differences between immigrants of these cohorts and non-immigrants do not change significantly over the 1980s. The third column gives the estimates from the weeks equation. The coefficient on IMP. is negative and significant. 66 This means that the covariance between the error term in the weeks equation is negatively correlated with the error term in the wife’s participation index. Therefore, wives who choose to work have fewer weeks than the women who do not participate would work if they were to participate. In the 1981 cross section, the coefficients on the controls for immigrant arrival year are very similar to those from the weeks equation of Table 2.2. In each case, the weeks of work are not significantly different between immigrant and non- immigrant women. 67 As was the case in Table 2.2, the weeks assimilation is not significant for immigrant wives who arrived before 1971.68 The weeks of immigrant wives who arrived in the 1970s grow by six percent more than the growth in weeks for non-immigrants over the 19808.69 Finally I derive the predicted differences in wages, hours, and weeks by immigrant arrival The test statistics are 2.40 for the 1961-70 group and 1.99 for the 1971-80 group. The prob-values are .02 64 and .05, respectively. The test statistics are .02, —.75, and .37 for the before 1961 cohort, the 1961-70 cohort, and the 1971-80 65 cohort, respectively. The prob-values are .98, .45, and .71, respectively. eeThe test statistic equals —3.99, and the prob-value is less than .0001. The test statistics are —.06, —.32, and —1.77 for the controls for arrival cohort before 1961, between 1961 67 and 1970, and between 1971 and 1980, respectively. The prob-values are .95, .75, and .08, respectively. esThe test statistics are .33 for the control for arrival year before 1961, and .07 for the control for arrival year in the 1960s. The prob-values are .94 and .74, respectively. The coefficient on the interaction between the control for arrival in the 1960s and the 1991 survey year 69 dummy variable is significant. The test statistic equals 2.22 and the prob- value equals .03. 53 cohort of Table 2.4 and 2.5 using the new estimates. Table 2.10 and 2.22 contain these predicted differences after controlling for the wife’s participation decision. ° In general, there are only 7 small differences in Table 2.4 and 2.5 relative to Tables 2.10 and 2.11. 2.5 Concluding Remarks The results of the reduced form estimation indicate that immigrant men and women face lower average wages than non- immigrant men and women upon arrival in Canada. However, immigrant men and women are found to have higher wage growth than their non-immigrant counterparts. The wage/education profile of immigrant women is not as steep as that of nonimmigrant women. This would reflect difficulties of international transferability of skills and credentials. Interestingly, this difference is not apparent for men. It may be that immigrant wives take jobs that are readily available after migration which do not necessarily suit their training so as to support family consumption while the husbands search for work or invests in retraining. However, an alternative explanation has been suggested. The family’s immigration decision may be tied more closely to the husband’s career prospects if he is perceived to be the principal earner, than to the wife’s career prospects. This would lead to a better expected return on the education of immigrant husband relative to the returns on the education of the immigrant wife. A third possibility is that immigrant wives have difficulty finding training programs which would assist them in having their foreign credentials and skills recognized in the Canadian labour market. Beach and Worswick (1993) comment that most government training programs for recent immigrants are intended for men. It may be that new programs are needed to assist immigrant women in finding jobs suited to their education. The variable 1MR is set to zero so that the predictions do not condition on the wife choosing to participate. 70 54 Recently arrived immigrant men and women work significantly fewer weeks in the year than do non-immigrants. It is likely that immigrants experience unemployment in the first few years after migration as they search for jobs suited to their skills. However, differences between the weeks of immigrants with more than five years of residence and non-immigrants are not significant. Immigrant wives work more hours per week than non-immigrant wives. Immigrant and non-immigrant husbands work very similar hours. Hours growth over the decade is found to be the same for immigrant and non-immigrants. The patterns in the data are consistent with the hypothesis that credit constraints are important determinants of the labour market adjustment of immigrants. Immigrants are found to supply at least as many hours as non-immigrants while earning significantly lower wages than their non-immigrant counterparts. The high labour supply of immigrants given their low wages could be explained by the immigrant family being unable to borrow against future earnings, and responding to this constraint by supplying more labour. If the effects of the credit constraints are only present in the first years after migration, as suggested by Long (1980), then one would expect the hours of immigrants to fall relative to the hours of non-immigrants with years of residence. However, given that immigrant men and women experience higher wage growth than similar non-immigrant men and women, it may be that the immigrant’s response to the higher wage rate in terms of increased hours of work “masks” the decline in his/her hours due to the lessening of the credit constraint effect. An alternative explanation for the hours and wage differences by immigrant status is that immigrant households work 55 more hours in all periods due to either a lower disutility to work or a lower expected lifetime wealth. This coupled with a lower responsiveness of immigrant hours of work to growth in their wage rates over time would explain the movements found in the data. It is uot possible to distinguish between these explanations using reduced form estimation. 56 CHAPTER THREE 3.1 Introduction In this chapter, the hypothesis that credit constraints are important determinants of labour supply decisions in immigrant families is explored within the context of a structural model of intertemporal labour supply. The model extends the literature on dynamic labour supply of women and men by allowing for the possibility that the household may be credit- constrained in some periods. This extension of the existing dynamic labour supply models was needed in order to separate differences by immigrant status in family preferences toward each spouse’s labour supply from differences in terms of access to credit. The results of the estimation of the structural model indicate that it is differences in family preferences towards labour supply (and perhaps differences in lifetime wealth), and not credit constraints, which explain the observed differences in hours of work in immigrant versus nonimmigrant families. The marginal value placed on the wife’s non-labour time relative to the non-labour time of the husband is smaller in immigrant families than in non-immigrant families which would lead to more hours of work by immigrant women, ceteris paribus. After controlling for differences in this marginal rate of substitution between the wife’s non-labour time and the husband’s non-labour time, and differences in market wage rates, immigrant family members were found to work more hours in all periods due to either a lower disutility to work or a lower expected lifetime wealth of the household. 57 3.2 The Model The following is an adaptation of a model of dynamic labour supply and consumption in the presence of uncertainty and taxes developed in MaCurdy (1983). The model is extended to allow for both the husband’s and the wife’s hours of work decisions and for the possibility that households may be credit-constrained in some time periods. The household chooses hours of work for both the husband and the wife and family con sumption so as to maximize the expected value of discounted life-time family utility: UQ) + 1 E {I+ 1 +-- } (1) subject to the asset accumulation constraint: A(r) — A(r — 1)(1 + r(r)) = wi(r)hi(r) + 2 (r)h w ( r) where r indexes future time periods, UQr) = — p(r)c(r) r = 1, .., T (2) U(cQr), hi(r), h (r)) is the within period utility 2 of the family, p is the rate of time preference, p(r) is the price of the composite commodity, cQr) is family consumption; hi(r), 2 h Q r) and 1 w Q r), 2 w Q r) are the husband’s and the wife’s hours and wage rates respectively; AQr) is non- human wealth held at the end of period r; and r(r) is the interest rate. Equation (2) represents the household’s period r budget constraint. For a given value of assets held at the beginning of the period, AQr — 1)(1 + rQr)), and after choosing a level of assets to be held at the end of the period, A(r), then (2) is the constraint the household faces in choosing hours of work for each spouse and family consumption in period t. The household is able to save as much as it wishes at the market interest rate, rQt). However, the household is constrained in their ability to borrow against future income. The credit 58 constraint for period r is represented by a non-negativity constraint on r=t,..,T A(r)O (3) The household can sell off assets which it holds at the beginning of the period, AQr—l)(1+r(r)), but it cannot allow its end of period assets, A(r), to drop below zero. Therefore, it cannot borrow against future income. 1 Given an initial condition, A(O) = , and a terminal condition, A(T) 0 A = AT, this charac terizes the household’s problem. The value function for the household’s problem is: V(AQ),t + 1) E maxEt+i {i+ } (1 (4) where the maximization is over the hours of the husband and wife and family consumption over all periods, and satisfies the asset accumulation constraints and the asset non- negativity constraints in all periods. The value function equals the present discounted value of household utility over the remainder of the household’s T periods under the optimal choices of hours of work and consumption in each period. One can think of the household as maximizing: U(t) + 1 f,jEt{V(A(t),t + l)} + 7 Q)A(t) +AQt)[wi(t)hi(t) + 2 (t)h w ( t) + A(t l)(l + r(t)) A(t) — — — pQt)c(t)] where A(t) is the multiplier for the period t asset accumulation constraint, and 7(t) is the ‘The model can easily be adapted to allow for the family to be able to borrow up to some positive amount which implies that they can aliow their non-human assets to become negative. In this case the constraint would be of the form: A(r)+ll(Z(r))O where ll(Z(r)) represents the amount the household can hold as debt at the end of the period which depends on potentially time-varying exogenous household characteristics, ZQr). In particular, ll(Z(r)) may depend on the immigrant status of the household. 59 ______ multiplier for the period I asset non-negativity constraint. Therefore, the consumer maximizes the above expression subject to (2) and (3). Assuming interior solutions for c(I), h 1 (I), and 2 h ( t), the necessary conditions are: 2 UQ) = )iQ)p(t) (5) 1 (I) Uh = —A(I)wi(t) (6) Uh ( 2 t) = —AQt)w ( 2 t) (7) where U (t.) is the derivative of U(t) with respect to i, for i 1 = c(I), hi(t), 2 h ( I). Given the assumed additive separability of preferences across time, each condition is a function of vari ables observed at time t, utility parameters, and the latent variable, AQ). The effect of income earned outside the period in determining period I choices of hours and consumption enter the necessary conditions through A(I), the marginal utility of wealth held at time I. Since it is unobserved, a procedure must be developed to account for it in estimation. By taking the ratio of (6) and (7), the marginal utility of wealth, A(t), is eliminated: — Uh ( 2 t) — wi(t) w ( 2 I) This condition states that in equilibrium the household sets its marginal rate of substitution (MRS) between the hours of the husband and the hours of the wife equal to the ratio of their wages. The equation describes how the family is prepared to trade fewer hours of work for one spouse at the expense (in terms of utility) of higher hours of work for the other spouse, at different offered wages. It is important to note that whether or not the household is creditconstrained in period I does not affect this condition. Credit constraints affect the family’s The assumption of an interior solution for the wife’s hours of work will be relaxed in Chapter 4. 2 60 ability to trade more hours of work in the future for fewer hours of work in the present. The above MRS condition involves trading more hours of work in period t of one spouse for fewer hours of work in period t of the other spouse. The household does not need to use lending markets in order to make these trades; therefore, the efficiency condition, (8), holds whether or not the household is credit-constrained. The motion equation for the marginal utility of wealth, A(fl, is: 3 1 A(t) 1 = E{A(t + 1)(1 + r(t + 1))} + 7(t) If the household is credit-constrained in period t, ‘y(t) > 0, otherwise 7 (t) (9) = 0. In order to interpret this condition, assume for the moment that the household is not credit-constrained in period t, which implies 7(t) = 0. In this case, the condition equates the expected present value of the increase in utility from another unit of wealth in period t+ 1, thEt{AQ+ 1)(1 +r(t+ 1))}, to the cost in terms of the decrease in utility in period t, A(t). 4 If the household is creditconstrained in period t, this marginal condition does not hold. The household would like to To see this, differentiate the Bellman equation with respect to A(t): 3 1 E ãV(A(t),t-i-1) ÔA(t) At —o (0) Define the Lagrangean: L = 2 +A(r){w1(t(r ( r) )+w2(ñh [(l+SI_1 1 —p(r)c(r) + A(r — 1)(1 + r(r)) — A(r)} + y(r)AQr)] Evaluate L at the optimai values of c(r), hi(r), h (r), A(r), A 2 , A 1 , 7(r), and 6(r); r = t + 1, ..,T. At these 2 values, L = V(A(t), t + 1). Differentiating L with respect to A(t), and applying the envelope theorem, then taking expectations gives: E { OV(A(t),t +1) } = E{(1 + r(t + 1))A(t + 1)} Substituting this into (0) gives (9), the motion equation for A(t) when credit constraints exist. This description is taken from Altonji (1986). 4 61 lower its end of period assets, AQ), below zero by borrowing against future earnings. However, credit is rationed. Therefore, more wealth is aflocated to period t +1 than the honsehold would choose if it could borrow. The increase in utility in period t from lowering A(t) below zero, A(t), is greater than the decrease in expected utility in the future from having one unit less of wealth in period t + 1, -bEt{A(t + 1)(1 + rQt + 1))}. It is assumed that r(r) = r, for all r, and r is known by the household members. Substi tuting (7) into (9) for A(t) and AQ + 1): —Ua ( 2 t) w ( 2 t) — — (1+r) (l+p) f—Uft ( 2 t+1) (t+1) 2 i w When the household is not credit-constrained in period 1, j’(t) +7(t) = (10) 0, and (10) is the intertemporal MRS condition for the wife’s hours in period I and I + 1. The household chooses hours for the wife in each period, so that it is indifferent between marginal trades of hours of work in I for hours or work in I + 1 at the market interest rate, the period I wage rate, and the expected period I + 1 wage rate for the wife. If the household is credit-constrained in period I, then it would strictly prefer to work fewer hours in period I at the expense of more hours in I + 1, at the going interest rate, current wage rate and expected future wage rate. However, it can’t make this trade because credit is rationed. Therefore, it chooses more hours in I so as to increase consumption towards what it would be in the absence of the credit-constraint. To see this in terms of equation (10), first note that the marginal utility of the wife’s hours in period I, Uh (I), is negative. I will refer to —Uh 2 (I) as the marginal disutility of the wife’s hours in I 2 since it is the drop in the household’s within period utility at time I due to a marginal increase in the wife’s hours. Given the concavity of the utility function, U(I), the marginal disutility 62 of the wife’s hours is increasing in her hours. Therefore, since the household chooses a larger value of h (t) when it is credit-constrained in t, this implies a larger value of 2 2 —Uh ( t). This means that the ratio of the marginal disutility of the wife’s hours to her wage rate in t, is greater than the expectation of the present value of the ratio of the marginal disutility of her hours to her wage rate in t + 1, 9$}Et { }. Equation (10) will be referred to as the Euler equation for the wife’s hours. Before proceeding I will give an outline of the estimation procedure. The first equation to be estimated is (8), the within period MRS condition between the husband’s hours and the wife’s hours. These estimates reveal how the household adjusts the hours of work of each spouse to different offered wage rates. In particular, the estimation allows for differences in household preferences over the hours for the husband and wife between immigrant and non-immigrant families. The procedure for identifying the effects of credit constraints in the Euler equation, (10), can be thought of in the following way. The growth of the wife’s wages over the 1980s is observed in the data. Also, the growth of the wife’s hours is observed. Using the estimates from the MRS condition, (8), the growth in the marginal disutility of the wife’s hours, —Uk 2 (t), is derived. 5 Using this information, equation (10) is estimated. From the estimates, we see whether or not the growth in hours and wages is consistent with credit constraints having an important effect on the hours patterns over time. In particular, we are interested in whether or not differences by immigrant status in the parameter estimates of (10) are consistent with the hypothesis that immigrant families are more likely to be credit-constrained than non This is an oversimplification of the estimation procedure. Under the assumed functional form of the utility 5 function, it is not possible to derive all of the parameter estimates of —U,,, (t), from the estimation of (5). The procedure for estimating the remaining parameters is discussed below in Section 3.4. 63 immigrant families. In order to facilitate estimation, equation (10) is rewritten as: —UhJt) (t) 2 w where Q) (l+r)E f_Uh.,(t+l)lr(t) — (l+p) — (11) w ( 2 i+1) j > 0 if the household is credit-constrained, and 1’Q) = 6 The following 0 otherwise. multiplicative structure is assumed for the forecast error in (11): —Uh ( 2 t + 1) (t+ 1) 2 w (—Uh ( t)’\ e_1(t)(1 + p) 2 (1 + c(t+ 1)) w(t) I \. (1+r) = (12) where c(t + 1) is a forecast error uncorrelated with (1 + p)/(l + r) and —Uh (i)/w2(t). 2 Taking the natural logarithm of both sides of (12) and rearranging: in where b+ 1 = (° t t ) — in (7) = — F(t) + iyQ + 1) (13) in(1+p)—in(1+r)+Et{in(1+cQt+1))}, and iì(t+1) is a forecast error uncorrelated with variables known by period t. Therefore, bt+i — Q) is the expected movement between t and t + 1 of the natural logarithm of the ratio of the marginal disutility of the wife’s hours to her wage rate. The results of Chapter 2 can be interpreted in terms of equation (13), the Euler equation for the wife’s hours. Immigrant wives were found to have higher wage growth than non-immigrant wives. The effect of this difference, ceteris paribus, is a smaller value of the left hand side of equation (13) for immigrant wives than for non-immigrant wives. 7 The growth in hours Multiplying by 6 e’(t) scales up fl$}Ee { } until the equality holds. Note that the left hand side of the equation can be rewritten ln(—Uh 7 (t + 1)) ln(—Uh 2 (t)) + ln(w2(t)) 2 ln(w2(t + 1)) is smaller for immigrant wives, then holding the change in the marginal disutility of the wife’s hours the same between immigrant and non-immigrant families, this implies a lower value of the left hand side of (13) for immigrant wives. — In(w2(t + 1)). Since ln(w2(t)) — 64 — between immigrant wives and non-immigrant wives was found to be equal in Chapter 2. It was argued that the fact that the immigrant wives’ hours do not rise by more than the nonimmigrant wives’ hours could be due to credit constraints. In terms of equation (13), this would mean that the differences in the left hand side of the equation by immigrant status are explained by a larger value of the multiplier on the credit constraint, 1’Q), for immigrant families. Since it appears as —I’(t) in (13) this could explain the lower value for immigrant families of the left hand side of the equation due to the higher wage growth of immigrant wives. However, the fact that the growth in the wife’s hours is not significantly different between immigrant and non-immigrant wives does not necessarily imply that the growth in the family’s marginal disutility of her hours, —Uh 2 (1), is the same. It may be that the hours of the wife are not very responsive to increases in her wage. Therefore, a small difference in the hours of work of immigrant and non-immigrant women could imply a large difference in their marginal disutility of work, —Uh Qt). This difference in the marginal disutility of the wife’s 2 hours, could offset the effect of the higher wage growth of immigrant wives in the left hand side of (13).8 The estimation procedure allows us to derive estimates of the marginal disutility of the wife’s hours from the estimation of the within-period MRS condition between the wife’s hours and the husband’s hours, (8). Given these estimates, equation (13) can be estimated to see if the observed movement in the left hand side of (13) implies a lower value of bt+i — FQ) for immigrant families than for non-immigrant families, which would support the hypothesis that immigrant families are more likely to be credit-constrained than non-immigrant families. The larger growth in the marginaJ disutility of the wife’s hours for immigrant bmilies means a larger value 8 of in(—Uh 2 (t + 1)) 2 (t)) for immigrant &miies; therefore, this could offset the effect of the smaller ln(—Uh value of ln(w 2 (t)) ln(w2(t + 1)) leaving no difference in the left hand side of the Euler equation, (13), between immigrant and non-immigrant Thmilies. — — 65 Differences by immigrant status in bt+i — FQ) could result from three sources which cannot be distinguished in the estimation. First, credit constraints as represented by differences in r(t) between immigrant and non-immigrant families could explain these differences. Second, differences between immigrant and non-immigrant families in p, the rate of time preference which appears in bt+i, could explain these differences. This variation would exist if the im migrant household’s preferences over work in the early years after migration relative to work in later years differed from the preferences of non-immigrant households. Finally, differences in the distribution of the forecast error, cQ + 1), between the two groups, could explain the differences in bt+i — rQ). It will be assumed in the analysis that immigrant and non- immigrant households share the same forecast error distribution. This implies that Et{ln(l+c(t+1))} is the same for immigrant and non-immigrant families. The assumption that this error distribution is homogeneous and exogenous is maintained in both the dynamic labour supply literature (MaCurdy (1983)) and in the dynamic consumption literature (Zeldes (1989) and Runkle (1991)). If immigrants have more or less uncertainty about the future than do non- immigrants, then the variance of the forecast error differs by immigrant status and the homogeneity assumption is violated. Also, if the variance of the forecast error term depends on the expectation of future endogenous variables such as wages then the exogeneity assumption is violated. It is impossible to test these assumptions without panel data. Therefore, these assumptions are maintained, and an exploration of their importance is left for future work. Differences by immigrant status in bt+i — F(t) will be attributed to either differences in 66 the rate of time preference, p, or differences in the credit constraint multiplier, T’(t). As the empirical results wili show, the value of bt+i — r(t) for immigrant families is not significantly smafler than for non-immigrant families. This is evidence against the hypothesis that immi grant families are more likely to be credit-constrained than non- immigrant families. It is possible that immigrant families are more likely to be credit-constrained than non-immigrant families, implying a larger value of Q) for immigrant families, but the rate of time preference is also larger in immigrant families, implying a larger value of bt+ . This means that immigrant 1 families place a lower weight on future utility; therefore, they want the wife to work more in the future. However, they are more likely to be credit- constrained; therefore, they are not able to substitute for fewer hours for the wife in the present at the expense of more hours for the wife in the future. While this is possible, it would not explain the differences in the reduced form results of Chapter 2. Since the difference in bt+i offsets the difference in r(t) this cannot explain the fact that immigrant wives do not increase their hours by more than nonimmigrant wives in response to their higher wage growth. Therefore, estimation of bt+i — F(t) is sufficient to address the question of whether or not differences in credit constraints between immigrant and non-immigrant families can explain the observed patterns of hours and wages of immigrant and non-immigrant wives in the reduced-form results of Chapter 2. 3.3 Comparison with Models used in the Dynamic Labour Supply and Consumption Literatures MaCurdy (1981) is the first to analyze the dynamic labour supply of men using panel data. The household problem of section 3.2 is reduced to one where the husband chooses his hours of work and consumption over his lifetime. The husband is assumed to be able to borrow or 67 lend as much as he wishes at the market interest rate. As in section 3.2, the interest rate is assumed to be a constant. Also, he is assumed to have perfect foresight. In terms of (9), the motion equation for the marginal utility of wealth at time t, these assumptions imply: A(t)= A(t+1) (14) Therefore, A(t) can be written as a function of the rate of time preference, p, the interest rate, r, and the marginal utility of wealth at time zero, A(O): A(t)= A(O) (15) Substituting this expression into (6), gives the necessary condition for the husband’s hours as a function of A(O): Uh ( 1 t) A(O)w ( 1 t) = (16) - MaCurdy assumes that the within period utility function, UQ), is additively separable in the husband’s hours and all other goods. Under the assumed functional form for utility, the condition can be solved for the husband’s hours as a function of the marginal utility of wealth at time zero, A(O): h ( 1 i) = 1 h {[ Pj A(O), wiQ)} (17) MaCurdy refers to this as the lambda-constant labour supply function. It describes the move ment in hours in response to movements along the individual’s lifetime wage path. A parametric form for the utility function is assumed so that, after taking the natural logarithm of both sides of the equation, the log of A(O) appears additively. MaCurdy takes the first difference across time of the log hours equation and estimates this difference equation. 68 The marginal utility of wealth term, A(O), fails out of the difference equation since it is constant through time. Under the assumed functional forms, the coefficient on the change in log wages in the log hours difference equation is an estimate of the intertemporal elasticity of substitution for hours. Using data from the PSID, MaCurdy estimates the hours difference equation and finds this elasticity to be between .1 and .5. Therefore, the hours of the husband rise by .1 to .5 percent in response to a one percent increase in his wage over time. MaCurdy (1983) extends the intertemporal choice model for men to allow for uncertainty. It is assumed that the household is able to borrow as much as it wants at the market interest rate. MaCurdy takes the ratio of the marginal condition for the husband’s hours, (6), and the marginal condition for consumption, (5), to give: 9 Uh ( 1 t) = Uc(t) wiQ) p(t) “18 This is the condition that the household’s MRS between the hours of work of the husband and family consumption equals the real wage rate, in period 1. This MRS condition is estimated using instrumental variables methods to give consistent estimates of the parameters of the within period utility function, UQ). As in section 3.2, MaCurdy assumes that the interest rate is constant and known by the household. Therefore, equation (9) can be written: AQ)= gEt{A(t+1)} (19) Next, MaCurdy substitutes into condition (19) for )t(t) using the marginal condition for con MaCurdy includes the after tax wage in place of the observed wage in this equation. In this thesis, tax 9 issues are not addressed. 69 sumption, (5), and derives the Euler equation for consumption: UQt) pQ) — (l+r)E fU(t+1) (l+p) t lp(t+l) (20) Using the estimates from the first stage, the marginal utility of consumption is derived in each period and then the Euler equation, (20), is estimated by instrumental variables methods treating consumption in each period as endogenous. Using these estimates he is able to char acterize the dynamic labour supply choices of married men. MaCurdy finds a greater degree of substitutability in the hours of the husband than was found in MaCurdy (1981). The main advantage of this procedure over the one used in MaCurdy (1981) is that it allows for the fact that the husband may be uncertain of his future wage path. Another advantage of this procedure is that the estimation of (18) takes advantage of the detailed information in each cross-section of how the family trades more hours for the husband in order to have higher consumption. This information is incorporated into the estimation of the Euler equation for consumption, (20). Browning, Deaton, and Irish (1985) take the standard household intertemporal choice model and redefine it in terms of dual functions. They define profit functions for the house hold from which they are able to derive Frisch labour supply functions. The Frisch labour supply function describes the individuals’ hours of work as a function of the period t prices of all goods, and the marginal utility of wealth at time zero, A(0). The main advantage to this procedure over the one used in MaCurdy (1981) is that it does not require that utility be additively separable in the husband’s hours and other goods. However, since the marginal utility of wealth, A(0), is not observed, a procedure must be developed to eliminate it from 70 the equation to be estimated. It is assumed that after taking the natural logarithm of the Frisch hours equation, the log of the marginal utility of wealth appears additively. Next the first difference of the equation is taken, eliminating the marginal utility of wealth. It is this difference equation which is then estimated. The difficulty with this is that strong assumptions about preferences are necessary in order for the log of the marginal utility of wealth to appear additively in the log hours equation. In the empirical work, they focus on the hours of married men and assume that preferences are additively separable between the husbands hours and other goods. In this case the Frisch labour supply function is the lambda-constant labour supply function, (17), used by MaCurdy (1981). In the estimation, Browning, Deaton, and Irish (1985) use synthetic cohort data generated from the U.K. Family Expenditure surveys. The annual cross sectional data sets from 1970 through 1976 are used. Each cross section is treated as a random sample of the same population at each point in time. They define sub-populations in terms of five year birth cohorts and whether or not the person is a manual or a non- manual worker. They next define cohort sample means for these sub-populations in each of the seven cross sections. For example, manual workers age eighteen to twenty-two in 1970 are considered to be the same underlying population as manual workers who are nineteen to twenty-three in the 1971 survey. The data used in estimating the hours difference equation are the means of the log hours and log wages of these groups in each year, which they refer to as a “panel of cohort means”. The results of the estimation are not supportive of the life cycle model of labour supply for men. They find very small responses of hours to changes in wages for men and suggest that the standard life cycle model must be extended in order for it to be consistent with the results of the estimation. 71 The dynamic labour supply literature for married women is not as well developed as the literature for men. Heckman and MaCurdy (1980) are the first to study the intertemporal hours choices of married women using panel data. They derive a lambda-constant leisure demand function for married women and address the possibility that the wife may not work in some periods using a simple Tobit 10 specification The estimation involves treating the . marginal utility of wealth term, A(0), as an individual specific fixed effect. They find evidence in support of the life-cycle model for married women. They test for the effects of transitory income shocks on the wife’s labour supply, and find that spells of unemployment experienced by the husband do not have a significant effect on the wife’s labour supply. Heckman and MaCurdy find children to be important determinants of the wife’s hours decision. Blundell and Walker (1986) are the first to study the labour supply of married couples within the context of a life-cycle model. They use a single cross section from the U.K Family Expenditure Survey from 1980. Therefore, they are not measuring the intertemporal labour supply behaviour of the couples. Instead, they are analyzing the hours of the husband and wife at a point in time using a model which is consistent with the household choosing these hours in every period subject to a lifetime budget constraint. The model is equivalent to the one developed in Section 2.3 with the added assumption that the household is never creditconstrained. Their approach to modelling the household’s decisions is as a two-stage budgeting problem. Instead of thinking of the household choosing hours of each spouse in each period subject to a lifetime budget constraint, the problem is reformulated as the choice of hours in each period subject to an allocation of income to that period. Therefore, consumption and ‘°Their approach to modelling the wife’s participation will be discussed in detail in Chapter 4. 72 leisure are chosen so that the household’s budget constraint for that period is satisfied. The income allocated to that period is endogenous to the problem. The household chooses hours conditional on the income, and then the income is chosen optimally. The estimated hours of work equations condition on this income variable. The advantage to this approach is that you do not have to make strong assumptions on within period preferences over the hours of the two spouses (the previous literature assumes additive separability of the wife’s hours and the husband’s hours). However, the drawback is that the income allocated to that period is a function of exogenous income which is difficult to measure in practice. Bernhardt and Backus (1990) use a theoretical model to study the effects of credit con straints on the labour supply and occupational choice in married couples. In an optimal control framework, they derive predictions for a family which chooses consumption, labour supply, and occupations for the husband and wife over the lifetime of the household. They find that credit constraints will lead household members to supply more labour in periods when they are young so as to increase consumption towards the level it would be if the family were able to borrow against future wage income. Bernhardt and Backus (1990) argue that specialization in terms of occupational choice allows the married couple to separate the borrowing and investing aspects of occupational choice. One spouse enters an occupation with low human capital accumulation and a high current wage, and supports the other spouse’s entry into the occupation with a low starting wage, but high human capital accumulation. Empirical work on the existence of credit constraints on family behaviour has been restricted primarily to the consumption literature. Zeldes (1989) uses PSID data to estimate a dynamic 73 model of household consumption and tests for credit constraints. The test is based on the Euler equation for consumption. The equation used in estimation can be derived from the equations of section 2.3 by substituting the marginal condition for consumption, (5), into the motion equation for the marginal utility of wealth, (9): U(t) p(t) — - (1+r) fUc(i+1)j p(t+1) j +7(0 )Et 1 ( (1) 2 The test for credit constraints involves splitting the sample in terms of households with a high assets to income ratio and households with a low assets to income ratio. The first group are unlikely to be credit-constrained while the second group may be affected by credit constraints. Zeldes’ results indicate that 7 (t) is positive for the group with the low asset to income ratio. He concludes that credit constraints have an effect on the consumption patterns of these families. Runkle (1991) repeats the analysis of Zeldes (1991) after accounting for the effects of aggre gate shocks and measurement error in consumption. Runkle finds that both aggregate shocks and measurement error are important issues in estimation. 11 The results of his estimation do not support the hypothesis that credit constraints affect consumption decisions. Therefore, the importance of credit constraints on family behaviour remains an unresolved issue. The model developed in section 3.3 can be thought of as an extension of the one in MaCurdy (1983) to the case where both the husband’s and the wife’s hours are the focus of the analysis and credit constraints affect household behaviour in the same way as they appear in Zeldes (1989). Given that only two cross section data sets are available, MaCurdy’s method of esti mating a within period MRS condition takes advantage of the extensive information on hours ‘TIn this thesis, aggregate shocks are assumed to affect immigrant and non-immigrant families in the same way. The issue of measurement error wifi be addressed below in the discussion of the data. 74 and wage combinations of husbands and wives in each cross section. Also, MaCurdy’s method of estimating an intertemporal MRS condition is conducive to incorporating credit constraints into the model in the same way as in the intertemporal consumption choice literature. 3.4 Functional Forms and Estimating Equations The functional forms are chosen to suit the modelling of both spouse’s labour supplies and the absence of consumption data.’ 2 The following functional form for the within period utility function is used:’ 3 (1 ( 1 t) = QQ) { [T — h g 1 (t)] + KQ) [7’ — h.(t)]a2 } (22) where 7’ is the maximum number of hours a person can work in a year,’ 4 iq(t) and 1 12 ( t) are age specific modifiers of taste and a and a 2 are parameters.’ 5 Using (22), equation (8), the within period MRS condition between the husband’s hours and the wife’s hours, becomes: [7’ — h ( 1 t)]@i’) — (t)](a2-l) 2 h 1 — — w,(t) 21 w (t) 23) ‘ 1 2 n what follows, consumption will be excluded from the notation. The restriction that within period utility is additively separable in consumption is required since the data 3 ‘ sets employed do not contain measures of consumption. It is common in both the labour supply and the consumption demand literature to assume that utility is additively separable in hours and consumption. To the author’s knowledge there has been no research using dynamic household models which uses both labour supply and consumption analysis; therefore, it is impossible to say whether or not this assumption imposes important restrictions on the model. MaCurdy (1983) uses data on the husband’s hours of work and fhmily consumption; however, the assumption that utility is additively separable in hours and consumption is maintained, and he does not report the results of tests of the separability assumption. 1n the estimation, 2’ is set at 5252 hours. Other values were used with only small changes in the results. 14 While the utillty function assumed is restrictive, it does nest commonly used utility functions such as the 5 ‘ CES and Cobb-Douglas. This type of utility function has been used in Heckman and MaCurdy (1980), MaCurdy (1981), and Altonji (1988). 75 The following functional forms for the taste-shifters, 1 Q ( t) and it ( 1 t), are assumed: = exp{X(t)4 + a(t)} (24) = exp{X(t)3 + e(t)} (25) where X(t) is a vector of exogenous characteristics which includes age controls; ci and /3 are parameter vectors; and a(t) and 1 e ( t) are error terms. The effect of the demographic characteristics, XQ), in 1 tc Q ) is to shift the weight placed on the wife’s non-labour time in period t relative to the weight placed on the husband’s period t non-labour time in the household utility function. This difference appears in the MRS function between the husband’s hours and the wife’s hours in period t, (23). Changes in 1 n ( t) shift the slope of the family’s indifference curve between the wife’s hours and the husband’s hours in a given period. The effect of 1 X ( t) in 1 Q ( t) is to shift the weight placed on the utility the family receives from the non- labour time of the two spouses in period t, in the lifetime utility function, (1). This effect does not appear in (23), the within period MRS condition between the hours of the wife and husband, but it does appear in the Euler equation, (13). For example, if the household places a higher weight on periods where young children are present then the household will increase the non-labour hours of both spouses in those periods. 76 Taking the natural logarithm of both sides of (23) and rearranging:’ 6 in[T where 3* — h ( 2 t)] = X(t)/3* + cx,in[T —/3/(c — 2 4), a = h,(t)] + 4{ln(wi(t)) — (ai—1)/(a — 2 1), a = — in(w ( 2 t))] + e’(t) and E(t) —1/(a — 2 1), = (26) —e(t)/(c — 2 l). This gives the MRS condition in terms of the log of the wife’s non-labour time, in[T — as a function of household characteristics, X(t), the log of the husband’s non- labour time, in[T — h,Qt)], and the difference in the log of the husband’s wage and the log of the wife’s wage, in(wi:(t)) — in(w ( 2 t)). Using the assumed functional forms, the Euler equation, (13), can be rewritten: in (iq(t i + 1)[T — h ( 2 t+ 1)](a2_1) \i ) — in (ic(t)[T I — h ( 2 t)](a2—l) w ( 2 t) — i ) — — —(X ( 1 t + 1) — +c(t + 1) where c(t+1) a(t)—a(t+1)+ii(t+1) is an error term. Since period MRS condition, (26), the parameter vector 4 (t) (27) falls out of the within must be estimated in the Euler equation. Recall that (t) is the weight placed on period t utility within the lifetime utility function, (1). The left hand side of the equation can be thought of as the change in the log of the ratio of the marginal disutility of the wife’s hours to her wage rate when the weight placed on period t utility, Q(t), does not change between t and t + i.’ The expression (X (t + 1) 1 — X(t))q 161n the model, the variables tn[T h (t)] and ln[T h 2 (t)] are endogenous. In the econometric framework, 1 {ln(w ( 1 t)) ln(w (t))] is also treated as an endogenous variable due to the concern that the method of deriving 2 the wage rates creates a statistical endogeneity. Therefore, one could solve the equation placing any of these three variables as the left hand side variable. This specification was chosen based upon a comparison of the results of regressing each of the endogenous variable on all of the exogenous variables. The value of the R 2 was lowest in the regressions with ln[T h (t)] as the dependent variable. Therefore, this was chosen as the left 2 hand side variable, since the instruments appear to be better at explaining the other two endogenous variables. The weight on period t utility, p T ‘ (t), changes only when the household characteristics, X(t), change. If 1 — — — — 77 appears on the right hand side of the equation. This represents the part of the change in the log of the marginal disutility of the wife’s hours, in(—Uh (t)), between t and t + 1, which 2 is due to changes in household characteristics over the period. Changes in these household characteristics shift the weight, 2(t), placed on utility from period t compared with the utility from period t + 1 in the family’s lifetime utility function, (1). Therefore, b+ 1 — T’(t) equals the net change in the log of the ratio of the marginal disutility of the wife’s hours to her wage rate between t and t + 1. In order to simplify the notation, define: Yj(r) where r = t, t + 1. Therefore, = Y Q 1 r) in (tt ( 1 r)[T — (r)](a2_l) 2 h 1 (28) is the log of the ratio of the marginal disutility of the wife’s hours to her wage rate, for the case where the weight placed on period t utility, 1 (1 ( t), equals one. Therefore, equation (27) can be rewritten: Yj(t + 1) — YQ) = — — Q + 1) 1 (X — X Q 1 )) + c(t + 1) (29) Equation (26) can be estimated by two-stage least squares (2SLS) treating both spouses hours and wages as endogenous. If panel data were available, one could estimate (29) by 2SLS treating hours and wages as endogenous. However, the data used in estimation will be from two cross-sections. In estimating (29) using this data, one cannot compare the same household at two points in time. Next, I will outline the procedure used to estimate (29). Each cross section is treated as a household characteristics do not change between t and t + 1 then the left hand side of (27) equals b+, which is the change in the log of the ratio of the marginal disutility of the wife’s honrs to her wage rate. — 78 random sample of the same population at two points in time, 1981 and 1991. The results from the estimation of (26) are used to derive estimates of a 2 and ic(t).’ 5 Given these estimates we can derive values of Y(t) for the household’s in the 1981 cross section and l’(t + 1) for households in the 1991 cross section. Equation (29) is estimated over the 1981 cross-section. The derived values of Y Q) are used in (29) in place of the true values. Predictions of Yj(t + 1) 1 and X Q + 1), derived using households in the 1991 cross section, are used in (29) in place of 1 the actual values of Yj(t + 1) and X (t + 1). 1 Let Z 1 be a vector of time-constant family characteristics (e.g. birth year, immigrant status, immigrant arrival year, and education.). Assume the following relationships exist: Y(t + 1) XQ + 1) = = 2 + Zf3h (30) l2 1 V 1 + Z13x÷ (31) The assumption that (30) and (31) are of this form means that if we see a household in 1981, or period t, with characteristics Z , and we have consistent estimates of / 1 2 and / h 3 , then 1 x 3 we can derive consistent predictions of this household’s 1991, or t + 1, values of Y Qt + 1) and 1 X(t + 1). These predictions can then be used in estimation of (29), the Euler equation. Substituting (30) and (31) into (29) gives the following expression for the Euler equation: — where u Q +1) 1 = Yj(t) q (t + 1)— = — — vf’ T’(t) ‘. — 1 (Zj/3x÷ — XQ)))-.- u(t + 1) (32) The true value of Y (t +1) is replaced by the expected 1 value, Z/ , in the left hand side of (32). Also, the true values of X(t + 1) are replaced on 2 h 3 The derived value of n(t) is k(t) 5 ‘ and a2 from the estimation of (26). = 249 where 79 &t and Lt2 are the derived values of at the right hand side of (32) by their expected values, Zd3x. . The error terms 1 h2 1 X and 1 v are absorbed into 1 u + 1). Q Using the observed values of X(t) and Z , the derived values of Yj(t) and consistent esti 1 mates of 4 2 and , h 3 1 x 8 ÷ one could estimate (32) over the 1981 sample. However, due to the concern that the household characteristics, X(t), may contain stochastic components which are correlated with c7Q + 1), it was decided to treat X (t) as a set of endogenous variables. 1 The following equations are assumed to determine the household characteristics, 1 X ( t): = x + vft 3 Z/ (33) The assumed form of (33) enables us to replace the set of endogenous variables X(t) in equation (32), with consistent predictions of these variables using the estimates of and the exogenous family characteristics, Z. Substituting (33) into (32) gives the following expression for the Euler equation: — where u7Qt + 1) = YQ) = — I’Q) — (Zj(/3x+, — i x 3 )) + u(t + 1) (34) u(t + 1) + vftqs The estimation involves three steps. First, the MRS condition between the husband’s hours and the wife’s hours, (26), is estimated by 25115 over both the 1981 and 1991 cross sections treating the hours and wages of the spouses as endogenous. This gives consistent estimates of ,3*, o, and #4. These estimates are used to derive predictions of Y Q + 1) using (28), over 1 the 1991 sample. Second, equations (30) and (31) are estimated by OLS over the 1991 cross section using the predictions described above and the observed values of 1 X ( t + 1). This gives 80 consistent estimates of /3j, and . 1 x 3 / + Also, equation (33) is estimated over the 1981 sample giving us consistent estimates of [ x. In the final stage of estimation, 12(t) is derived over the 3 1981 sample using the estimates from the first stage and equation (28). The Euler equation for the wife’s hours, (34), is then estimated over the 1981 sample, by OLS, using the estimates of , 2 h 3 1 x from the second stage. Under the assumptions, this estimation yields 3 1 x 3 I ÷ and j consistent estimates of bt+i — I’j(t), and . In summary, for each household in the 1981 data, a predicted value is derived of Y(t + 1) — Y ( 1 t), the change from t to t + 1 in the log of the ratio of the marginal disutility of the wife’ hours to her wage rate, when family characteristics do not change between t and I + 1. Also, for each household a predicted value is derived of 1 X ( t + 1) — X(t), the change in household characteristics between I and I + 1. Next, the predictions of Yj(t + 1) the predictions of XQt + 1) — — Yj(t) are regressed on X ( 1 t) and controls for age and immigrant arrival year, 19 over the 1981 sample. The procedure creates a synthetic panel by creating predictions of the 1991 behaviour of each household in the 1981 survey using the 1991 cross section data. The key assumptions which are required in order for this method to yield consistent esti mates of the Euler equation, and which are not required in an analysis using panel data are: 1) the two cross-sections represent random samples from the same population at different points in time; 2) the characteristics Z do not vary over time; and 3) equations (30), (31) and (33) are correctly specified. In the estimation, Z is a vector of thirty-five dummy variables and an intercept representing ‘ 1 9 n the estimation, b+ 1 — F ( 1 t) is assumed to be a function of age and immigrant arrival year. 81 thirty-six distinct groups in the data defined in terms of time-constant characteristics. No restrictions are placed on variation in the conditional mean of the dependent variable across these thirty-six groups, in each equation of (30), (31) and (33); however, the conditional mean of the dependent variable is assumed to be the same within each of these groups. The advantage of this procedure over the one in Browning et a!. (1985) which uses a panel of cohort sample means is that the final estimation is over households rather than sub-sample means. Using this procedure, the error term in the Euler equation contains the error term in the Euler equation if one were to estimate using panel data. The error term also includes the prediction error terms resulting from using predicted values. Therefore, the cost of using this procedure as opposed to using panel data is only a loss of efficiency. 3.5 Empirical Analysis The sample used in estimation is from the 1981 and 1991 Canadian Censuses. The sample selection criteria are the same as those used in Chapter 2 with the following modifications. It is necessary to exclude households where at least one spouse arrived in Canada after 1980. This ensures that every household in the survey arrived in Canada before the 1981 survey date. Unlike the sample used in Chapter 2, households where the wife did not work are excluded from the analysis. The labour supply measure used in this analysis is the annual hours of work of the husband and the wife. Annual hours is constructed by multiplying the annual weeks of work in the previous year by the hours of work in the reference week. This measure of annual hours will contain measurement error. This is addressed in the estimation by treating the hours of each spouse as endogenous. However, the hours of the husband and the wife appear 82 in the equations as the log of the non- labour hours of each spouse, which is a non-linear transformation of the hours variables. Therefore, the effect of measurement error in hours on the results will depend on the choice of T, potential hours of work. In the estimation, different values of T were employed with only small changes in the results. Immigrants who arrived part way through the reference year likely have a truncated annual hours of work. To avoid this problem, immigrant families where at least one spouse arrived in 1980 are excluded from the 1981 data. In the 1991 data, immigrants who had arrived in 1980 cannot be distinguished from those who arrived between 1971 and 1979. Therefore, in the analysis that follows, immigrants in 1981 who arrived between 1971 and 1979 are compared to immigrants in 1991 who arrived between 1971 and 1980.20 Wage rates are constructed by dividing the hours measure into the individual’s annual earnings the previous year. The resulting measure of the wage rate contains noise and may contain division bias. However, instrumental variables techniques are used to address this issue. As in Chapter 2, all households in the 1981 sample where both spouses are immigrants and which meet the above criteria are kept in the sample. Due to the large numbers of nonimmigrant households in the two data sets, a twenty-five percent random sample is taken of non-immigrant households. As can be seen in Table 3.1, after the restrictions there are 2372 foreign- born households from the 1981 Census, and 6400 households from the 1991 Census. The total number of non-immigrant households from the 1981 Census is 2244 and from the A comparison of the 1981 sample means for demographic characteristics and wage rates for the 1971 to 1979 20 cohort versus the 1979 cohort implied relatively small differences in these two groups. 83 1991 Census there are 7194 remaining. ’ 2 Sample selection issues are not addressed in this chapter. Handling the endogeneity of the wife’s participation might lead to different predictions from this model. However, it is common in the immigration literature to restrict the sample to individuals who work in the reference period. The studies on immigrant men typically restrict the sample to individuals who work full-time and for more than forty weeks in the reference year. Baker and Benjamin (1994) and Duleep and Sanders (1993) are the first studies to look at the effect of the wife’s participation decision on her earnings and labour supply. In Chapter 4, a method is developed to incorporate the wife’s labour force participation decision into the analysis. Table 3.1 lists sample means of selected variables used in estimation. 22 Average hours of work for wives in immigrant families are 103 hours higher in 1981 and 110 hours higher in 1991 than for non-immigrant wives. The mean hours for immigrant and non-immigrant men are almost identical in both years. The wages of the non-immigrant women are one dollar and thirty cents higher in 1981 but by 1991 the difference has dropped to sixty-three cents. For the immigrant men, their wages are thirty-two cents lower in 1981; however, by 1991 their wages have caught up to the wages of the non-immigrant men. Immigrant men and women in the sample are one to three years older in each cross-section, and have a more dispersed education distribution. Immigrant families are more likely to have children present in 1981; however, by 1n Table 2.1, immigrant wives have a higher participation rate in 1981 than non-immigrant wives; however, 21 the non-immigrant wives participation grows at a faster rate over the decade. The effects of this on the sample selected are evident in the sample counts in this Chapter. The random sampling should lead to roughly fifty percent of both the 1981 sample and the 1991 sample being foreign-born. However, the fraction is 51.8 percent in 1981 and 47.3 percent in 1991. This is due to the differences in participation rates between the two groups in each year. The importance of ignoring these differences will be analyzed in Chapter 4. The definitions of the variables are presented in Appendix 1. 22 84 1991 the composition of children in the household is almost the same. Results from the 2515 estimation of (26), the MRS condition between the husband’s and wife’s hours at time t, are presented in Table 3.2.23 The log of the husband’s non-labour time and the difference in the log of the husband’s wage from the log of the wife’s wage are treated as endogenous left hand side variables. The variables used as instruments are the occupation, industry, age, education, and language fluency of each spouse. Controls for number of live births of the wife are also used. These instruments are fully interacted with a dummy variable for immigrant status. The covariance matrix used allows for heteroskedasticity of unknown form and is from White (1980). The parameter estimates are distributed asymptotically according to the Normal distribution. The asymptotic standard errors are listed in parentheses. The coefficient estimates on the controls for household characteristics measure the effect of the household characteristics on the log of the non-labour time of the wife ln[T — Qt)j, 2 h holding the non-labour time of the husband, ln[T—h (t)], and the difference in the spouses’ log 11 wages, ln(wi Q)) 1 — ln(w2Qt)), constant. The household characteristics vector, X (t), includes 1 controls for immigrant status, immigrant arrival year, the age of each spouse, and the presence of children in the household. The specification is very similar to the one used in the wife’s participation index from Chapter 2.24 Controls for presence of children are included on their own and as interactions with the immigrant dummy variable. This allows for separate effects of the presence of children on household preferences over the labour supply of the wife relative to the husband. The estimates of the reduced form equations for the difference in the log wages of the husband and the wife 23 and the log leisure of the husband are included in Appendix 2. To compare the specifications, see Table 2.8. 24 85 The specification of the immigrant cohort controls is the same as the one used in the wife’s participation index of Chapter 2 after accounting for the fact that immigrants who arrived after 1980 have been excluded from the sample used in this chapter. The default group contains immigrant couples who arrived in the 1970s. A dummy variable indicating that the household is from the 1991 survey is included. Its coefficient measures the percent change in the nonlabour hours of wives in the default group over the 1980s holding the husband’s non-labour time and both spouses’ wages constant. A dummy variable for non-immigrant couples is included. Its coefficient measures the difference in the non-labour hours of the wife in non-immigrant families compared to those in the default group for given values of the husband’s hours and the market wages of both spouses. An interaction of the non- immigrant dummy variable with the dummy variable for households in the 1991 survey year, Y1191, is included. The coefficient on, NB, plus the coefficient on NB*YR91 measures the percent growth in the non-labour hours of non- immigrant wives over the 1980s, ceteris paribus. Controls for the immigrant wife having arrived in the 1960s and before 1961 are also included on their own and as interactions with the 1991 survey year variable, YR91. From these coefficients we see differences in the non-labour hours of wives who arrived before 1971 relative to those who arrived after 1971. Controls for the immigrant husband having arrived in the 1960s and before 1961 are also included on their own and as interactions with the YR91 variable. From these coefficients, we see the marginal change in the immigrant family’s preferences over the non-labour hours of the wife when the husband is from an earlier arrival cohort. The age controls are identical to the ones used in the wife’s participation index of Chapter 2. Age controls are included for both the husband and the wife. Therefore, it is possible 86 to see the non-labour hours of the wife for each combination of the wife’s birth cohort, and the husband’s birth cohort, holding the husband’s non-labour time and both spouses wages constant. Also, for each of the possible combinations of the husband’s and the wife’s birth cohorts, we can derive the change in the non-labour time of the wife over the 1980s, ceteris paribus. The estimate of the coefficient on the difference between the log of the husband’s wage and the log of the wife’s wage implies that a , the curvature parameter on the wife’s non-labour 2 hours in the utility function, is —10.49. Using this estimate and the coefficient on the log of the husband’s non-labour hours, one can impute a value of 0.8783 for a , the curvature parameter 1 on the husband’s non-labour hours. The estimates imply that the husband’s hours are more responsive to movements along his wage profile than are the wife’s hours to movements along her wage profile. To see how the MRS between the husband’s hours and the wife’s hours varies with the hours of the husband and wife consider the case where both the husband and wife supply 2000 hours of work in period t. Using (23) and the parameter estimates we can see that the MRS in this case is .7023. Therefore, the household places a higher marginal value on the wife’s non- labour time than the husband’s non-labour time. However, as we decrease the hours of work of the wife and husband while holding them equal, h (t) 1 1 = h ( 2 t), we see that the relative value placed on the wife’s non-labour time decreases relative to the husband’s since a 2 < a . Evaluating both the husband’s hours and the wife’s hours at the immigrant 1 wives’ 1981 sample mean of 1538 hours, the MRS has risen to 3.041, meaning that the relative marginal value that the household places on the wife’s non-labour time is now lower than that of the husband. 87 The presence of children in the household leads the non- immigrant wife to increase her non-labour hours by three to thirteen percent for given values of the husband’s non-labour time and the offered wages. These effects are significant at the five percent level. 25 The effect of children is smaller in immigrant families, and these differences are in general significant at the five percent level. 26 Therefore, family preferences are such that the immigrant wife lowers her hours of work by less than the non-immigrant wife when children are present in the household. This matches the result found in the reduced form estimation of the hours and weeks equations of Chapter 2. The coefficient on NB indicates that non-immigrant wives have three percent more nonlabour hours, ceteris paribus, than wives in immigrant couples where both spouses arrived in the 1970s, and this difference is significant. 27 From the coefficient on the 1991 survey year dummy variable, YR91, we see that the non-labour hours of immigrant wives who arrived in the 1970s fall by five percent over the 1980s, ceteris paribus, and this change is significant. From the coefficient on the variable NB * YR91 we see the difference in the change of the non-labour hours of the wife over the 1980s between non- immigrant wives and the default group, immigrant wives who arrived in the 1970s. This coefficient is not significant. 29 These results are consistent with the general trend in the Canadian economy over the 1980s towards full-time work for married women. All of the coefficients on the controls for the wife’s and The test statistic in each case is the ratio of the coefficient estimate to the estimate of its standard error. 25 The test statistics are distributed asymptotically according to the Standard Normal distribution, and equal 9.76, 8.88, 10.70, and 7.55, for the variables KIDSO5, KO5FLUS, KIDS614, and K614FLUS, respectively. The prob-values are less than .0001 in each case. The test statistics are —2.44, —2.46, —2.23, and —1.18, for the variables ED * KIDSO5 ED * KO5PLUS, 26 ED * KIDS614, and ED * K614PLUS, respectively. The prob-values are .01, .01, .03, and .24, respectively. The test statistic equals 2.87, and the prob-value equals .004. The test statistic equals —3.38, and the prob-value equals .001. 26 The test statistic equals 1.27, and the prob-value equals .20. 29 88 husband’s immigrant arrival cohort, and the interactions of these variables with the 1991 survey year variable are not individually significant at the five percent level. 30 Therefore, the results indicate that immigrant families prefer the wife to work more hours than do non-immigrant families for a given value of the husband’s hours and the offered wages, and this difference does not change significantly over the decade. The coefficients on the age controls for the husband and the wife are not significant at the five percent level except for the coefficients on the following variables for the wife: .44044 YR91, .44549 * YR91, .45054 * YR91, .45559 * YR91, and .46064 * * 31 The fact that all YR91. of the age interactions with the 1981 survey year dummy variable, YR81, are not significant from zero means that the non-labour hours of the wife, ceteris paribus, are the same across the six age cohorts in the 1981 survey. However, the growth in the non-labour hours of the wife, holding the husband’s hours and the offered wages constant, is not equal across these age cohorts. Women under forty see their non- labour hours drop by five percent over the decade. Older women reduce their non-labour hours by less. For example, wives who are fifty to fifty-four in 1981 see their non-labour hours fall by one percent over the 1980s. The difficulty with interpreting these results is that we are holding the husband’s nonlabour hours constant throughout. A more interesting comparison would be between the choice of hours of work of the wife and husband in immigrant versus non- immigrant families when facing the same constraints. In Figure 3.1 an experiment is carried out which demonstrates the The test statistics equal —.31, .77, .24, .26, —.87, .63, 1.19, and .37 for the variables Y6170, YBEF61, 30 Y6170 * YR91, YBEF61 * YR9I for the wife and Y6170, YBEF61, Y6170 * YR91, YBEF61 * YR91 for the husband. The prob-values are .76, .44, .81, .79, .38, .53, .23, and .71, respectively. The test statistics for these variables are 2.45, 3.29, 3.53, 5.78, and 3.24,respectively. The prob-values are 31 .01 for the variable A4044 * YR91 and less than .0001 for the other variables. 89 importance of the observed differences by immigrant status in the family preferences towards labour supply found in the MRS function. For expositional purposes, assumptions are made which translate the dynamic household problem into a static problem of choosing the husband’s hours and the wife’s hours, in period t, subject to an artificial constraint. One can think of this artificial constraint as a requirement that each household consume Cb dollars worth of the consumption good given that their savings are zero at the beginning of the period and they cannot borrow against future income. The households choose the wife’s and the husband’s hours in period t so as to fund Cno consumption. Each household is assumed to face the same wage rate for the husband’s hours and the same wage rate for the wife’s hours. The experiment holds everything constant across the immigrant and non-immigrant families, except the estimated differences in the MRS function. This is meant to highlight the importance of these differences in preferences in terms of hours of work. 32 The artificial constraint is: 7’ where — hi(t) uii(t), i (t), 2 1 iv ( t), — (t)JT 2 {v Q 1 ) + iu — and ) ( 2 t) — CNB — — h ( 2 t)] (35) are the sample means of the hours and wages of the husbands and wives in the 1981 sub-sample of non-immigrant households where both spouses work; and CNB 2 {w ( 1 ( 2 ( t)+zi t)]. t)7 t)i This constraint is meant to approximate the “typ Alternatively, one can think of the hours choices of each household in the experiment as the solution to the 32 hours choices for period t in the household’s dynamic problem under the following assumptions. Assume that the immigrant family is constrained to have the same hours and consumption choices, and the same access to credit, in all future periods as the native-born families have along their optimal program. Also, the savings which immigrant and non- immigrant families have at the beginning of period t are assumed to be the same. The wages offered to the members of the immigrant family in period t equal those offered to the non-immigrant family. Finally, the level of family consumption in period t in immigrant families is constrained to equal the consumption in non-immigrant families. Under these assumptions, the dynamic problem reduces to the static problem of choosing hours of work of the husband and the wife in period t subject to the artificial budget constraint. 90 ical” constraint faced by non-immigrant families at time t, as they choose hours combinations for period t which are consistent with the family’s lifetime optimal program. The exercise forces an immigrant and non- immigrant family with identical characteristics (eg. ages and composition of children present) to choose their optimal hours combinations subject to this constraint. In Figure 3.1, the optimal hours of the husband and the wife in immigrant and nonimmigrant families are shown as the tangency of the relevant indifference curve to the artificial constraint, (35).33 The indifference curves are derived using the parameter estimates from the MRS estimation and are for the case where no children are present in the household, and both the wife and husband are age forty to forty-four. The immigrant family’s preferences are for the case where both spouses arrived in Canada in the 1970s. The optimal non-labour hours combinations are derived by a grid search over the wife’s hours using the MRS condition to derive the associated husband’s hours and choosing the optimal combination of hours which satisfies the budget constraint. 34 For the immigrant family this was found to be T family T — hi(t) = 3392 and T — — h ( 1 t) = 3468 and T h ( 2 t) = 3568. — h ( 2 t) = 3471. For the non-immigrant As can be seen in the figure, the immigrant family’s indifference curve is flatter than the indifference curve of the non-immigrant family. This leads the foreign-born household to choose Non-labour time of spouse j is defined as?’— h 33 Qt) for j = 1,2 and 7’ = 5252. 1 34 functional form for U(t) as defined in (22) permits a closed form solution for leisure demand functions The in the static case only when ai(t) = 2 (t) which is the case of a CES utility function. Given the parameter estimates, it was necessary to use this grid search method. Given that the utility function is strictly concave and increasing in the non-labour time of the husband and the wife, there exists a unique hours combination which satisfies the MRS condition and which satisfies the budget constraint. 91 to have the wife work ninety-seven more hours and the husband work seventy-six fewer hours than is the case in the native-born family. This serves to explain in part the reduced form results of Chapter 2. Immigrant families have a lower disutility to the wife working than non- immigrant families. The figure demonstrates that this difference has large impacts, implying just under one hundred more hours of work per year for the wife in immigrant versus nonimmigrant families under the experiment of Figure 3.1. In Figure 3.2, immigrant families face an artificial constraint based on their own mean behaviour. The new constraint incorporates into the analysis: 1) differences by immigrant status in the ratio of the husband’s wage and the wife’s wage (captured by the slope of the constraint), and 2) differences by immigrant status in either the household’s disutility to work or their wealth at time I (captured by the height of the intercept of the constraint). Figure 3.2 shows the hours choices of immigrant and non- immigrant families in 1981. The non-immigrant constraint is the same as in Figure 3.1. The immigrant constraint is defined in the same way, but using the 1981 sample means of the hours and wages of husbands and wives in immigrant families. As in Figure 3.1, the optimal hours combinations for nonimmigrant families were derived using the MRS condition and the budget constraint. The exercise was repeated for the immigrant family using the immigrant family’s MRS condition and an analogous artificial constraint based on the sample means of hours and wages of the husband and wife in immigrant families from the 1981 sub-sample. Indifference curves are plotted going through these derived hours combinations for each type of family. The “flatter” indifference curve for immigrant families is apparent. The lower ratio of the wife’s wage to the 92 husband’s wage in immigrant families versus non-immigrant families can be seen in the flatter constraint for the immigrant family. This tends to push the immigrant family towards more hours of work for the husband rather than the wife due to the higher relative returns to his labour. However, the magnitude of this effect appears to be small relative to the differences in the MRS function. The fact that the FB artificial constraint lies below the NB constraint is due to either the immigrant household having a lower disutility to the labour supplies of its members, 35 or the immigrant family’s wealth at time t being lower than in non-immigrant 36 These two explanations cannot be distinguished using the data at hand. families. So far, the results from the structural model indicate that the value of the wife’s non-labour time relative to the husband’s non-labour time is smaller in immigrant families than in nonimmigrant families. Also, the presence of children does not increase the relative value of the wife’s non-labour time in immigrant families to the same extent as it does in non-immigrant families. These results are consistent with what was found in Chapter 2. It should be noted that the observed lower value placed on the wife’s non-labour time relative to the husband’s non-labour time in immigrant families does not necessarily imply that the immigrant wife places a lower value on her non-labour time than the non-immigrant wife does. The family utility function should be interpreted as a summary of the family decision making process. The observed differences in family preferences toward the wife’s labour supply between immigrants and non-immigrants could be explained by the immigrant wife having a This would appear iu (6) and (7) as a time-iuvariaut component of £ 35 (t), the weight placed on period t 1 utility in the lifetime utility function. This difference would appear in A(t) in (6) and (7). Since A(t) is the marginal utility of wealth held at time 36 t, an increase in wealth at time t leads to a lower value of A(t). 93 lower bargaining power in the family than the non- immigrant wife. An alternative explanation, which is related to the FIR, is that the immigrant husband may be making investments in schooling which make his non-labour market time relatively more valuable than the non-labour market time of the wife, ceteris paribus. An evaluation of these alternative explanations will be left for future work. Table 3.3 contains estimates from the Euler equation for the wife’s hours, (34). Thirtysix sub-groups within the sample are defined based on the wife’s characteristic 37 s: immigrant status, the three entry cohort categories, three age categories (age twenty-five to thirty-four in 1981, age thirty-five to forty-four in 1981, and age forty-five to fifty-four in 1981), and three education categories (below a high school diploma, a high school diploma, and above a high school diploma). 38 Indicator variables are defined for thirty-five of the subgroups and are included along with an intercept in the estimation of equations (30), (31), and (33).39 Predictions are generated from this estimation over the 1981 sample and equation (34) is estimated using these predictions. In the estimation of (34), b+i — I’(t) is assumed to be a function of the wife’s age and arrival cohort. The household characteristics, 1 X ( t), are controls for the presence of children in the household. These controls are interacted with an immigrant dummy variable. 40 This allows for the estimation of separate effects by immigrant status of 1t would be preferable to sample on both the husband’s and the wife’s characteristics. However, birth year 37 and immigrant arrival year are highly correlated between husbands and wives; therefore, one would have to choose very broad categories of these variables in order to ensure that there are households in each category. This is equivalent to the dimensionality problem which arises in non-parametric estimation. Education may be time-varying, but for most people, the education levels are determined before starting 35 worh. Since the sample has been restricted to individuals who were older than twenty-five in 1981, it is unlikely that the education of many of the women in the sample would change between 1981 and 1991. The results of the estimation are presented in Appendix 3 39 °ln the specification of the utility function, (22), the demographic characteristics X 4 (t) enter into both 12 1 (t) 1 and n(t). The demographic characteristics enter into the MRS equation through ,c(t), while they enter into the estimation of the Euler equation through 9 (t). I include only a subset of the household characteristics 1 used in the estimation of the MRS equation in the estimation of the Euler equation. Since panel data is not 94 the presence of children on the weight placed on period t utility in the family’s lifetime utility function. The default category contains households where the wife is native-born and age thirty-five to forty-four in 1981. The intercept gives the value of b+i — T’(t) for this group. Recall that this is the change over the 1980s of the log of the ratio of the marginal disutility of the wife’s hours to her wage rate. The estimate is negative and significant from zero, 41 implying an annual value of b+i — F(t) of — .56. This means that their marginal disutility of hours of the wife is not growing as quickly as the wage rate. The wage rate causes the ratio of the marginal disutility of the wife’s hours to fall. Since the marginal disutility of the wife’ hours rises with her hours, the wife’s hours are not growing sufficiently to keep this ratio constant. MaCurdy (1983) estimates — I’(t) to be .15 over the entire population. 42 It may be that households where the wife is age thirty-five to forty-four in 1981 are credit- constrained, implying a negative value of — FQ). The coefficient on the dummy variable for wives age twenty- five to thirty-four in 1981 is negative and significant.” 3 This means that the value of 2 b + i — I’(t) is smaller for this group. Given that young households typically face steeper wage profiles and own little in the way of assets relative to older households, it is reasonable to think that they are more likely to be credit- constralned than households where the wife is older. Therefore, it is likely that this difference in b,+ 1 — I’(t) between these households and the default group of households, where the wife is ten years older, is due to the effects of credit constraints. Also consistent with this available, and I am conditioning on the wife’s characteristics in the estimation of the Euler equation, it is not feasible to control for many other household characteristics (such as the husband’s age and immigrant arrival cohort information) in the estimation of the Euler equation. The test statistic equals —6.95, and the prob-value is less than .0001. 41 MaGurdy interprets this number as b+ 42 , since, in his model, it is assumed that the household is never 1 credit-constrained; therefore, 1(t) = 0, for all t. The test statistic equals —3.08, and the prob-value equals .002. 43 95 argument is that fact that households where the wife is forty- five to fifty-four in 1981 have a significantly larger value of bt+i — r(t) than do the households in the default group, where the wife is ten years younger. 44 In both cases these age effects are strongly significant. Therefore, the empirical evidence supports the hypothesis that credit constraint effects decrease with age. The effect of changes in the presence of children in the household between 1981 and 1991 in the Euler equation represents the change in 1 12 ( t), the weight on period t utility in the family’s lifetime utility function, over the 1980s. The estimates listed are of the parameters of the vector from equation (24). One would expect households to place a higher weight on periods when young children are present, which would imply a positive value of qS. This was found in MaCurdy (1983). The results of Table 3.3 indicate that this is generally the case for non-immigrant households. The estimates of the parameter of the vector for the difference in the dummy variable, KIDSO5, between 1981 and 1991 is the wrong sign but is not 45 The coefficient on the change in the dummy variables KO5PLUS and KIDS614 significant. are positive and significant implying that non-immigrant families place a higher weight in the lifetime utility function on periods when two or more children under the age of six are present in the household and when one or two children age six to fourteen are present in the household. ° 4 The estimate of the parameter from 4’ on the change in the variable K614PLUS over the 1980s is negative and significant, implying that non-immigrant households place a lower weight on periods where three or more children age six to fourteen are present in the household. 47 This may be picking up a credit constraint effect. Having at least three children in the household The 44 45 The The 46 The 47 test test test test statistic equals 5.93, and the prob-value is less than .0001. statistic equals —.32; the prob-value equals .75. statistics are 6.79 and 5.23, respectively. The prob-values are less than .0001. statistic equals —2.93, and the prob-value equals .003. 96 is unlikely to force the wife to stay at home since the children would be attending full-time school. However, the household must make large expenditures on food and clothing for these children. The household may wish to borrow against labour income in the future when the children are adults and no longer living at home. If households typically cannot borrow against future earnings, then this variable may be proxying a credit constraint effect. The coefficients on all of the interactions of the immigrant dummy variable, FB, with these controls for the change in the presence of children variables over the decade are significant. 48 Adding the coefficient on each interaction with the coefficient on the analogous variable gives the change in X(t)q5 for immigrant families. The effect of additional children present in the household is to increase the weight placed on that period in the immigrant family’s lifetime utility function. 49 In particular, unlike what was found for non- immigrants, a higher weight is placed on periods when three or more children age six to fourteen are present in the home. It was suggested above that this may be proxying a credit constraint effect. It is interesting that this effect does not show up for immigrant families. It may not be present for immigrant families because children in this age group are expected to care for younger children after school in immigrant families compared with non-immigrant families. This supervision might free up more time for the wife to supply to the market. The controls for immigrant status and entry cohort do not support the hypothesis that immigrant families are more likely to be credit-constrained than non-immigrant families, ceteris The test statistics equal 5.18, —6.27, —4.99, aud 2.86, for the KIDSO5, KO5PLUS, K1D5614, and 45 K614PLUS interactions, respectively. The prob-values are less thau .0001 for the first three variables, and is .004 for the K614FLUS variable. The only exception to this rule is the effect of one to two children present age six to fourteen. This has a 49 small negative effect on the weight placed on that period. 97 paribus. The coefficients on all of the immigrant cohort controls are positive and significant. ° 5 Therefore, the estimate of bt+i — rQ), the change in the log of the ratio of the marginal disutility of the wife’s hours to her wage rate, is larger in immigrant families than in non- immigrant families. This means that after accounting for differences in wage growth over the 1980s, 51 and after accounting for differences in the marginal disutility function of the wife’s hours, 52 the movements of the wife’s hours in immigrant and non-immigrant families indicate that immigrant families are not more likely to be credit-constrained than non-immigrant families. In order to analyze the robustness of the results, I derive and estimate the Euler equation for the husband’s hours. The MRS coudition between the husband’s hours and the wife’s hours, as represented by equation (23), can be rearranged to give: (h 2 fl](a2_i) 21 w (t) — — [7’ — — (t)] 1 h 1 (aj—i) (t) 1 w (36) The left hand side of this equation is the log of the ratio of the marginal disutility of the wife’s hours to her wage rate, when the weight, Q(t), placed on period I utility in the lifetime utility function equals one. This expression appears in equation (27), the Euler equation for the wife’s hours. Substituting (36) into (27) gives: ([7’— In, (t 1 h 1 + 1)](al—1)”\ ([T i—in, wi(t+l) J — (t)](a1—1)\ 1 h 1 wj(t) i J — — Q + 1) 1 —(X +c(t + 1) — (37) The test statistics equal 2.82, 3.18, and 5.35, for the variables Y7180, Y6170, YBEF61, respectively. The 50 prob-valnes are .005, .001, and .0001, respectively. Which appear in the denominator of the ratio. 5t Using the estimates from the MRS equation, and by controffing for changes in the presence of children in 52 the household in the estimation. 98 the Euler equation for the husband’s hours. Next redefine: (FT Yj(r)=ln( 1 where r = — h “str1(0i1Y\ I wij(r) j (38) t, t + 1. Given this definition of Y (r) one could then proceed with the derivation 4 involved in equations (29) through (34). The only difference is that the dependent variable is now the change in the log of the ratio of the marginal disutility of the husband’s hours to his wage rate, holding household characteristics constant, rather than the change in the log of the ratio of the marginal disutility of the wife’s hours to her wage rate. In estimating equations (30), (31), and (33) I use the values of the husband’s age, education, and immigrant arrival cohort in defining the thirty-six dummy variables. 53 Therefore, the vector Z now contains the husband’s characteristics rather than the wife’s. Also, in estimating (34), which is now the Euler equation for the husband’s hours, I define b+i — I’(t) to be a function of the husband’s age and immigrant arrival cohort. This is to make it consistent with the use of the husband’s characteristics in Z. The estimates of equations (30), (31) and (33) are reported in Appendix 4. The results of the estimation of the Euler equation for the husband’s hours are reported in Table 3.4. The coefficient estimates are very different from those of Table 3.3. In principle, this could be due to the fact that I am conditioning on the husband’s characteristics rather than the wife’s characteristics in the estimation. It may be that bt+i — Q) is a function of both spouses’ characteristics. Investigating this possibility would require including both spouses As discussed above, since age and immigrant arrival year information are highly correlated between hus 53 band’s and wives, it is impossible to define sub-samples in the data based on both spouses characteristics without ending up with no households in some sub-samples. This is the “curse of dimensionality” which arises in the non-parametric econometrics literature. 99 characteristics in the vector Z. As discussed above, this is not feasible. It is also possible that the wife’s characteristics are better explanatory variables for the presence of children in the household than are the husband’s variables. This is supported by the higher values of the fl2 in the results from the estimation of equations (31) and (33) for women (found in Appendix 3) than for men (found in Appendix 4). If the husband’s characteristics are not as effective at explaining the presence of children, then the predictions of changes in the presence of children in the household over the 1980s will not be as good in the Euler equation for the husband as they are in the Euler equation for the wife. This could lead to different estimates of bt+i — 12(1) in the Euler equation for the husband’s hours than in the Euler equation for the wife’s hours. However, I would expect the wife’s age, education, and immigrant arrival year to be correlated with the husband’s values of these variables. Therefore, it is a concern that the results are different. Panel data would be needed in order to investigate the causes of the differences in the two Euler equations. Given the data limitations, an investigation of the possible explanations is left for future research. In the discussion of the results of Table 3.4, I will focus on the controls for the husband’s arrival cohort. Unlike in Table 3.3, the coefficients on the arrival cohorts are all negative implying a smaller value of b+ 1 — I’(t) for immigrant families; however, in each case, these differences are small in magnitude and not statistically significant at the five percent level. 54 Therefore, we still reject the hypothesis that immigrant families are more likely to be creditconstrained than non-immigrant families. The test statistics are —1.61, —1.10, and —1.12, for the variables Y7180, Y6170, and YBEF61, respectively. 54 The prob-values are .11, .27, and .26. 100 In the remainder of the discussion of this chapter, I will focus on interpreting the results of Table 3.3. Since Long (1980) first suggested that credit constraints may be important in determining the wife’s hours of work, it seems reasonable to focus on the results of the Euler equation for the wife. Next, three experiments are carried out which are similar to the ones generating Figure 3.1 and Figure 3.2. An artificial constraint is defined which reduces the family’s dynamic problem into a choice of the wife’s hours in 1981 and 1991 subject to this constraint. In Figure 3.3 and 3.4, the wife in the immigrant and non-immigrant households faces wages equal to the sub-sample means for non-immigrant women in 1981 and 1991. The wife’s hours choices in 1981 and 1991 must generate income equal the income the wife earns at those wages when working the mean hours of wives in the 1981 and 1991 non- immigrant sub-samples. In Figure 3.3, the immigrant families preferences over intertemporal labour supply when children are present will be constrained to be the same as those in the non-immigrant family. In Figure 3.4, the immigrant family’s preferences over children will be allowed to differ from those of the non-immigrant family. In Figure 3.5, the non-immigrant family will solve the same problem as in Figure 3.4; however, the immigrant family will face a different constraint. As in Figure 3.2, the constraint will be defined by the wages of the immigrant women in the 1981 and 1991 data, and the income required will equal the income earned at those wages when the wife works the 1981 and 1991 sample mean hours for immigrant women. In all of these experiments, the variation in bt+i — I’Q), the change in the log of the ratio of the marginal disutility of the wife’s hours to her wage rate, will be attributed to variation 101 in p, the rate of time preference. Therefore, in the diagrams, the indifference curves will be tangent to the artificial constraints, rather than crossing the constraints, as would be the case if the household were credit-constrained. This avoids the problem of choosing a value of p relative to the value of r, the interest rate, while still highlighting the differences in hours of the immigrant and non-immigrant families implied by the results of the Euler equation. In Figure 3.3, the focus is on the differences in — F ( 1 i) by immigrant status. Immigrant households are forced to have the non-immigrant responses to the presence of children 55 and the intertemporal MRS is defined as the non-immigrant sample means for the changes in the presence of children variables. Each spouse is age forty to forty-four. Equal probability is placed on the immigrant husband and wife being from each of the entry cohorts. As in Figure 3.1, an artificial constraint based on the non-immigrant family’s dynamic problem is defined. The constraint can be written: T — ht + 1) Q 2 = Q + 1)JT 2 [iu Q 2 ) + ui — CNBQ, t + 1) — w Q 2 + 1) — h ( 2 t)] (39) where uJ (t), iu 2 (t), 1i 2 (t + 1), and i 2 (t + 1) are the mean wages and hours of non-immigrant 2 wives in 1981 and 1991; and CNB(1, t + 1) E (t)E 2 ui ( t) + 1z7 (t + 1)E 2 (t + 1). The immigrant 2 and non-immigrant families choose the hours of the wife in 1981 and 1991 subject to this constraint. The steeper immigrant indifference curve leads the immigrant wife to work three hundred and sixteen fewer hours in 1981 and two hundred and seventy-two more hours in 1991 than non- immigrant wives. This is opposite to what would be expected under the hypothesis that This was done by ignoring the coefficients on the interaction terms in Table 3.3. 55 102 immigrant families are more likely to be credit-constrained. In that case, the wife would work more in 1981 so as to increase consumption since the family is unable to borrow against the labour income in 1991. In Figure 3.4, the combined effect of differences in b+ 1 — r) due to immigrant status and Q 1 differences due to immigrant status in 1 Q ( t), the weight placed on utility in periods when young children are present, are analyzed. Using the same constraint as in Figure 3.3, the household’s problem is solved for immigrant and non-immigrant households. The non-immigrant house hold’s intertemporal MRS is the same as in Figure 3.3. For the immigrant household, the coefficients on the interaction of immigrant status with the presence of children variables from Table 3.3 are used. This allows for different responses between immigrant and non- immigrant families to the changes in the composition of children present over the decade. In determining the immigrant MRS, the sample means for changes in presence of children in the immigrant sample are used. As can be seen in Figure 3.4, the immigrant indifference curve is now flatter than the non-immigrant curve. Immigrant women work one hundred hours more in 1981 and eighty-five fewer hours in 1991. In the within period MRS estimation of Table 3.2, differences in the intercept by immigrant status and differences in family responses to the presence of children in the household work in the same direction. With no children present, immigrant households place a lower weight on the wife’s hours relative to the husband’s hours than do non-immigrant households. If children are present, this difference grows. The effect of children means the household places an even higher weight on the wife’s hours relative to the husband’s hours, and this effect is 103 more pronounced for non-immigrant families than for immigrant families. In contrast, differences in the intercept of the Euler equation, or — (t), by immigrant 1 status and differences by immigrant status in the weight placed on the period if children are present work in the opposite direction. The intercept differences imply that immigrant women are more likely to work in later years than the non-immigrant women (either due to a higher rate of time preference or a smaller effect of credit constraints). The higher weight placed on periods where children are present by non-immigrant families than immigrant families, and the fact that average number of children present in the home under each age category is higher in 1981 than in 1991, means that immigrant wives work more hours in earlier years since they restrict their hours less when children are present. In Figure 3.5, an artificial constraint is defined for immigrant families, in an analogous fashion to the non- immigrant constraint, (39), but using sample means over immigrant fam ilies. Next the optimal choices of the wife’s hours in each period were derived and plotted as tangencies between the immigrant intertemporal indifference curve and the immigrant ar tificial constraint. The same MRS functions were used as those in Figure 3.4. As in Figure 3.2, the immigrant constraint lies below and to the left of the non-immigrant constraint. This implies that, either due to a lower disutility to work, or due to lower life-time wealth, im migrant women supply more labour in each period than non- immigrant women. The flatter immigrant indifference curve is apparent. As in Figure 3.4, the fact that the immigrant wife’s hours are less sensitive to the presence of children is dominating the differences in — The higher growth rate in immigrant women’s wages over the decade is evident in the slightly 104 flatter artificial constraint. This would encourage the immigrant women to supply relatively more hours in 1991 than in 1981 compared to non-immigrant women. However, this effect appears to be small. Five key differences between immigrant and non-immigrant families are apparent in Figures 3.1-3.5. First, immigrant families have a larger MRS between the husband’s hours and the wife’s hours, in a given period. Second, the ratio of the husband’s wage to the wife’s wage is larger in immigrant families; however, the effect of this on differences in hours by immigrant status is small. Third, immigrant husbands and wives will work more hours in all periods, ceteris paribus, due to either a lower disutility to work or a lower expected lifetime wealth. Fourth, the difference in the growth rate in the wife’s wages between immigrants and nonimmigrants in the 1980s does not appear to be an important determinant in the differences in their hours of work. Fifth, when immigrant and non-immigrant households are forced to place the same weight on periods when young children are present and when the composition of children in the household over the decade is forced to be the same, immigrant wives work fewer hours in the current period and more hours in the future relative to non- immigrant wives. It is this measured tendency for immigrant wives to work fewer hours in the current period and more hours in future periods, ceteris paribus, that is the reason why we cannot reject the hypothesis that immigrant families are equally likely to be credit-constrained as non-immigrant families. 3.6 Concluding Remarks The results from the estimation of the structural model indicate that the marginal rate 105 of substitution between the husband’s hours and the wife’s hours, in a given period, is larger in immigrant households than in non-immigrant households implying a higher labour supply for immigrant women than for non-immigrant women, ceteris paribus. This difference is more pronounced when young children are present. Also, the results indicate that immigrant hus bands and wives supply more labour than non-immigrant husbands and wives, after controffing for the difference in the marginal rate of substitution, and the market wage rates. This is at tributed to either a lower disutility to the labour supply of family members or to a lower value of lifetime wealth in immigrant families. Finally, the empirical evidence indicates that young families are more likely to be credit-constrained; however, after controlling for age, immigrant families are not more likely to be credit-constrained. 106 CHAPTER FOUR 4.1 Introduction In this chapter, the model of Chapter 3 is extended to allow for the possibility that the wife supplies zero hours of work in a given time period. In creating the synthetic panel of Chapter 3, it was assumed that each cross section data set was a random sample of the same population at the two points in time. If the wife’s participation decision is endogenous then the sample of married couples where the wife works is not a random sample of the population of married couples. In the sample means of Table 2.1, we see that the participation rate of non-immigrant women rose more quickly over the 1980s than the participation rate of immigrant women. Therefore, there is reason to believe that this non-random selection might bias the dynamic labour market behaviour of non-immigrant and immigrant families to different extents. This could lead to biased results in Chapter 3. The results of the estimation of this Chapter support the conclusions from Chapter 3. The MRS estimates indicate that the wife’s hours are less responsive to changes in the ratio of the husband’s wage to the wife’s wage than was the case in Chapter 3. Immigrant families are found to place a lower value on the wife’s time relative to the husband’s time compared with non-immigrant families; however, this difference is smaller than what was found in Chapter 3. Differences in the Euler equation estimates support the conclusions of Chapter 3, that immigrant families do not appear more likely to be credit-constrained than non-immigrant families. 107 4.2 Approaches to Modelling the Participation Decision In their analysis of the intertemporal labour supply decisions of married women, Heckman and MaCurdy (1980) model the wife’s participation decision using the simple Tobit specifica tion. Blundell and Walker (1986) also use this specification of the wife’s participation decision in their analysis of the labour supply decision of married couples. In the simple Tobit spec ification, the woman does not work if the marginal disutility she receives from the first hour of work exceeds the value of the wage rate in terms of utility. This implies that equation (7) from Chapter 3, the marginal condition for the wife’s hours, does not hold when the wife does not work in period t: —Uh (t). 2 (t) > A(t)w 2 In the static labour supply literature, researchers have found that the simple Tobit spec ification does not fit the data as well as other models. Zabel (1993) compares four different static models of married women’s labour force participation and labour supply and finds the simple Tobit specification was the least consistent with the data. In particular, Zabel (1993) finds the fixed cost of work model of Cogan (1981) to dominate the simple Tobit model. Cogan (1981) develops a model of female labour supply and participation in which the woman must pay a fixed cost in order to work. The fixed cost is independent of the number of hours of work she chooses that period. The version of the model considered here is one in which there is a monetary cost to working, but no costs in terms of time associated with the job other than hours paid for at the market wage rate. The fixed cost could be thought of as a cost of organizing childcare which is independent of the number of hours of work. The woman’s problem is to maximize the utility function: U(c, h) where c is consumption and h is 108 hours of work subject to the following budget constraint: c=y+wh—Fd (1) where y is exogenous income, F is the fixed cost, and d is an indicator variable which equals one if h> 0 and zero otherwise. The budget constraint is represented by the line ABC in Figure 4.1 and Figure 4.2. The wife has exogenous income of 1000 dollars. Total hours in the period, T, is set at 1000. The wife faces the offered wage of one dollar, and must pay a 500 dollar fixed cost of work. Figure 4.1 shows the case of a non-worker. The woman works zero hours and consumes 500 dollars worth of the consumption good. In Figure 4.2, the woman chooses to work 800 hours and consume 1300 dollars worth of the consumption good. In this chapter, the fixed cost of work model is incorporated into the dynamic labour supply model of Chapter 3. This is a significant extension of the intertemporal labour supply literature for women. Analogous conditions to the within period MRS condition between the husband’s hours and the wife’s hours, and the Euler equation for the wife’s hours are derived. A procedure for estimating these conditions is developed which accounts for the endogeneity of the wife’s participation decision. 4.3 The Model The household chooses hours of work for both the husband and the wife and family con sumption so as to maximize the expected value of discounted life-time family utility: U(t) } + 1 109 (2) where r indexes future time periods, pis the rate of time preference, and U(T) = U(c(T), h,(r), 2 h ( r)) is the within period utility of the family which is assumed to be strictly concave and twice continuously differentiable, c(T) is family consumption; and h, (T), 2 h ( r) are the hours of work of the husband and the wife, respectively. The household is assumed to face a fixed cost, F(t), which it must pay each period before the wife can work. This can be thought of as a cost of arranging chuldcare or some other cost associated with a job, which is independent of how many hours the wife works that period.’ The household’s asset accumulation constraint for period t is: A(r) — A(r where d(t) — = 1)(1 + r(r)) = — F(t)d() —p(r)c(r) r = t, ..4 (3) 1 if the wife works in period t, and zero otherwise; p(r) is the price of the com posite commodity; w,(r) and A(T) w,(r)h,(r) + 2 (T)h w ( T) w2(T) are the husband’s and the wife’s wage rates, respectively; is non-human wealth held at the end of period r; and r(r) is the interest rate. Equation (3) is equivalent to the asset accumulation constraint of Chapter 3, after accounting for the fact that the household must pay the fixed cost, FQ), before the wife can work in period t. This equation can be thought of as the household’s period r budget constraint. For a given value of assets held at the beginning of the period, A(r — 1)(1 +r(r)), and after choosing a level of assets to be held at the end of the period, A(T), then (3) is the constraint the household faces in choosing hours of work for each spouse and family consumption in period t. ‘Since the husband is assumed to work a positive number of hours of work each period, fixed costs associated with his work are not modelled. 110 As in Chapter 3, the credit constraints are a set of non- negativity constraints on A(r)>O r=t,..,T (4) Therefore, the household is able to save as much as it wants at the market interest rate, r(t). However, the household is unable to borrow against future income. The wife’s hours are restricted to be non-negative in all periods: h ( 2 r)O r=t,..,T (5) The household will choose zero hours of work for the wife in period t if the returns to working a positive number of hours do not cover both the fixed cost of work that period, FQt), and the disutility the family receives from having the wife work. Given an initial condition for assets, A(O) A(T) = , and a terminal condition for assets, 0 A , this characterizes the household’s problem. The value function for the household’s 7 A problem is: V(A(t), t + 1) maxEt+i (1 +t_i } (6) where the maximization is over hours of the husband and wife and family consumption over all periods, and satisfies the asset accumulation constraints, and both the asset non- negativity constraints and the wife’s hours non-negativity constraints, in all periods. The value function equals the present discounted value of household utility over the remainder of the household’s periods under the optimal choices of hours of work and consumption in each period. 111 One can think of the household as maximizing: U(t) + + 1)} + -y(t)A(t) + 5(t)h (t) 2 1 +Ap(t) ( t) [wj(t)h + ( (t)h 2 w t) — F(t) + A(t +AN(t)[Wl(t)hl(t) + AQ — — 1)(1 + r(t)) 1)(1 + r(t)) — A(t) — — A(t) — p(t)c(t)j p(t)c(t)] where Ap(t) is the multiplier for the period t asset accumulation constraint when the wife participates in the labour market in period t and AAT(t) is the multiplier for the period t asset accumulation constraint when the wife does not work in period t; ( 7 t) is the multiplier for the period t asset non-negativity constraint; and (t) is the multiplier on the non-negativity constraint for the wife’s hours. The constraints associated with the multipliers Ap(t) and AN(t) define the budget constraint the household faces in period t for given values of A(t — 1) and A(t). The first constraint defines the downward sloping part of the budget constraint, 2 while the second constraint defines the budget constraint at zero hours of work for the wife. 3 Under the strict concavity of the utility function, either )pQ) or AN(t) equals zero. The only instance when both versions of the asset accumulation savings constraint could bind would be when the household chooses 2 h ( t) = F(t)/w ( 2 t). This would only occur if the household had Leontief preferences which is ruled out by the strict concavity of the utility function. The necessary conditions are: = [Apt) Uh ( 1 t) + .XN(t)]p(t) (7) + )N(t)]w1(t) (8) = —[.kp(t) Uh(t) —Ap(t)w ( 2 t) — 6(t) 2 T he analogue in the static case is the line AB of Figure 4.1 and Figure 4.2. This is equivalent to point C of Figure 4.1 and 4.2 in the static case. 3 112 (9) ____ where U(t) is the derivative of U(t) with respect to i, i Ap(t) = c(t), h (t), h 1 (t). The expression 2 + )N(t) is the marginal utility of wealth held at time t for the household. 4 If the wife works in period t then the marginal utility of wealth equals ,\p(t + 1); otherwise, the marginal utility of wealth at time t is ).N(t + 1). Next, the wife’s participation index is defined. Let Vjy(A(t 1),t) be the value of utility — to the household from period t onward when the wife works zero hours in period t and the household chooses all other levels of hours and consumption given this restriction and initial assets, A(t — 1). Let Vp(A(t — 1),t) be the value of utility from t onward when the wife pays F(t) and 5 works and the family then chooses the hours of both spouses and consumption from t onward subject to this constraint and the initial assets A(t — 1). The wife’s participation To see this, first define assets held at the beginning of period t to be A*(t) 4 the Lagrangean: U = E + (i —p(r)c(r) + A*(T) — +AN(T){’wI(T)hl (i-) +7(T)A(T) p(T){wi(T)hi(r) A(t (r)h w ( r) +2 — — 1)(1 + r(t)). Next define F(r) A(r)} — p(r)c(r) + A*(T) — A(r)} +2 6(r)h ( r)] Evaluate U at the optimal values of c(T), hl(T), h (r), A(r), .Xp(T), .)iN(T), y(r), and 5 2 (T); r = t,..,. At these values, U equals the present value of utility that the household receives from period t forward under its optimal program. Differentiating U with respect to A*() and applying the envelope theorem gives: = p(t) + XN(t) Therefore, .p(t) + AN(t) is the marginal utility of wealth at time t. This is not quite correct. The budget set is not closed. Consider the case where the wife would prefer to 5 work zero hours to working any positive number of hours even if she had to pay the fixed cost at zero hours. In the static model of Figure 4.1 and 4.2 this means that point B yields higher utility to the household then any point on the budget line to the left of B. This is the case of nonparticipation in the simple Tobit model. To ensure that, in period 1, Vp(A( 1), t) is defined, assume that the wife has to pay the fixed cost whether or not she works. The household then chooses the hours for both spouses and consumption in all periods subject to this constraint, and initial assets. — 113 index is defined to be: 1(t) The wife works if 1(t) Vp(A(t — 1),t) — VN(A(t — 0 and does not work otherwise. 1),t) (10) It is easy to see the effect of the fixed cost on the participation decision. Increasing F(t) lowers Vp(A(t — 1), t) since the household must now pay more in order for the wife to work in period t, but this has no effect on Vj(A(t — 1), t) since the wife does not work in period t. Therefore, as the fixed cost of working rises, the value of the index 1(t) falls, ceteris paribus. If both the husband and the wife work, then the last two necessary conditions can be rewritten: 1 (t) Uh = —Ap(t)w ( 1 t) (11) Uh ( 2 t) = —Ap(t)w (t) 2 (12) Taking the ratio of (11) and (12), over the sample where both spouses work, gives the MRS condition from Chapter 3: Uh ( 1 t) (t) 2 Uh — — wi(t) (t) 2 w (13) This is the within period MRS condition between the husband’s hours and the wife’s hours in period t, which was used in the estimation of Chapter 3. It states that in equilibrium the household sets its MRS between the hours of the husband and the hours of the wife equal to the ratio of their wages. The equation describes how the family is prepared to trade fewer hours of work for one spouse at the expense (in terms of utility) of higher hours of work for the other spouse, at different offered wages. As in Chapter 3, the MRS condition between the husband’s hours and the wife’s hours is the first equation estimated. A procedure is developed 114 ___ to address the fact that this condition is only defined over the subsample of households where the wife works in period t. The motion equation for the marginal utility of wealth, )‘p(t) + \p(t) + AN(t) = Et{[(t 1 Aiv(t), 6 is: + 1) + AN(t + 1)](1 + r(t + 1))} + 7(t) (14) This condition replaces the motion condition for .X(t) from Chapter 3. If the household is credit-constrained in period t, ( 7 t) > 0; otherwise 7 (t) = 0. When the household is not credit- constrained in t, the condition equates the expected present value of the increase in utility from another unit of wealth in period t + 1, 1 E{[)p(t + 1) + )N(t + 1)j(1 + r(t + 1))}, to the cost in terms of the decrease in utility in period t, ).p(t) + AN(t). If the household is creditconstrained in period t, this marginal condition does not hold. The household would like to lower its end of period assets, A(t), below zero by borrowing against future earnings. However, credit is rationed. Therefore, more wealth is allocated to period t+ 1 than the household would 6 T o see this, differentiate the Bellman equation with respect to A(t): + l) - p(t) - AN(t) +( 7 t) =0 (0) Define the Lagrangean: L [( + 1 L- = +p(r){wi(r)h ( 2 ( r)-F( r)h i(r)+w r) T=t+1 —p(r)c(r) + A(i- — 1)(1 + +AN(T){wl(T)hl(T) — r(r)) p(r)c(r) — A(T)} + A(T — 1)(1 + r(T)) — A(r)} + ( 7 (r)] 2 r)A(r) + 5(r)h Evaluate L at the optimal values of c(T), hj(r), 2 h ( r), A(r), )p(r), )N(r), 7(r), and 5(r); r = t + 1, ..,T. At these values, L = V(A(), t + 1). Differentiating L with respect to A(t), and applying the envelope theorem, then taking expectations gives: = Et{(1+r(t+1))[p(t+1)+N(t+1)} Substituting this into (0) gives (14), the motion equation for 115 kp(t) + AN(t) when credit constraints exist. choose if it could borrow. The increase in utility in period t from lowering A(t) below zero, ;\pQ) + AN(t), is greater than the decrease in expected utility in the future from having one unit less of wealth in period t + 1, 1 E{[)p(t + 1) + AN(t + 1)](1 + r(t + 1))}. In Chapter 3, the marginal condition for the wife’s hours was substituted into the motion equation for AQ). When the wife does not work, this condition does not hold. The procedure used in this chapter is to substitute for )p(r) in (14) from (12) for households where the wife works, for i- = t, t + 1. For households where the wife does not work in substitute into (14) for T = ).N(r) T, i\p(r) = 0, and we using (8), the marginal condition for the husband’s hours, for t, t + 1. Under this procedure, the following expression can be derived: Ap(t) + N(t) = { —U (t) d(t) w ( 2 t)] { —U (t) (1—d(t)) w ( 1 t)] MU(t) (15) This allows us to express the marginal utility of wealth at time t as a function of the marginal disutility of the husband’s hours, the marginal disutility of the wife’s hours, both spouses wages, and the wife’s participation decision. If the wife works in period t, then MU(t) = the ratio of the marginal disutility of the wife’s hours to her wage rate. If the wife does not work in t then MU(t) = the ratio of the marginal disutility of the husband’s hours to his wage rate. It is assumed that r(t + 1) and \p(t + 1) + AN(t = r and r is known. Substituting (15) into (14) for Ap(t) + )N(t) + 1) gives: MU(t) = (t) E{MU(t + 1)} + 7 (16) Before proceeding I will give an outline of the estimation procedure. The first equation 116 to be estimated is (13), the within period MRS condition between the husband’s hours and the wife’s hours. This condition is estimated over the sample of households where the wife works. A procedure similar to the one in Section 2.5, is employed to address the fact that this is not a random sample of the population of married women. The estimation yields consistent estimates of the parameters of the within period utility function, U(t). 7 These estimates reveal how the household adjusts the hours of work of each spouse to different offered wage rates. In particular, the estimation allows for differences in household preferences over the hours for the husband and wife between immigrant and non-immigrant families. The procedure for estimating the effects of credit constraints on household labour suppiy can be thought of in the following way. The wages and hours of husbands and wives are observed in the 1981 and the 1991 cross sections. Using this information and the estimates from the MRS estimation, an estimate of the ratio of the marginal disutility of the wife s hours to her wage rate, —U (t) w ( 2 t) is derived for households where the wife works in the survey period. If the wife does not work in the survey period, an estimate of the ratio of the marginal disutility of the husband’s hours to his wage rate, is derived. Using this information and equation (15), we derive a value of the marginal utility of wealth at t, MU(t), for each household in the sample. By comparing households with similar time-constant characteristics in the two data sets we can derive an estimate of the change in MU(t) over the 1980s. From this comparison, we see whether or not the growth in hours and wages of husbands and wives is consistent with credit constraints having an important effect on the hours patterns over time. In particular, we are interested in whether or not differences by immigrant status in the parameter estimates are As in Chapter 3, this description is an oversimplification of the procedure. Not all of the parameters of the 7 utility function can be derived from this estimation. In particular, the parameters of the weight, j(t), placed on period t, utility in the lifetime utility function, (2), must be estimated in the second stage of estimation. 117 consistent with the hypothesis that immigrant families are more likely to be credit-constrained than non-immigrant families. In order to facilitate estimation, equation (16) is rewritten: MU(t) = + E{MU(t+ 1)}eF(t) where I’(t) > 0 if the household is credit-constrained, and f(t) = (17) 0 otherwise. The following multiplicative structure is assumed for the forecast error in (17): MU(t + 1) = e_F(t) + MU(t)(1 + c(t + 1)) (18) where c(t + 1) is a forecast error uncorrelated with (1 + p)/(l + r) and variables known at time t. Taking the natural logarithm of (18): ln(.lvIU(t + 1)) where b+ 1 = ln(1 + p) — — ln(MU(t)) = 1 b+ — P(t) + (t + 1) (19) ln(1 + r) + Et{lri(1 + c(t + 1))}, and ? (t + 1) is a forecast error 7 uncorrelated with variables known by period t. In Chapter 3, bt 1 — P(t) was the change in the log of the ratio of the marginal disutility of the wife’s hours to her wage rate from t to t + 1. Since we have relaxed the assumption that the wife works in every period, this is no longer correct. In the subsequent discussion, I will refer to bt+ 1 — F(t) as the change in the log of the marginal utility of wealth from t to t + 1. Also, I will refer to equation (19) as the Euler equation for the wife’s hours. 8 Referring to (19) as the motion equation for the log of the marginal utility of wealth would be more accurate. 8 However, I will refer to (19) as the Euler equation for the wife’s hours so as to make it easier to compare to the estimation procedure of Chapter 3. 118 4.4 Functional Forms and Estimating Equations The same functional forms are used as in Chapter 3: U(t) = c2(t) { [T hQ)]a1 + k(t) [T - 2 Q)]a where T is the maximum number of hours a person can work in a year, specific modifiers of taste and and c2 are (20) ii(t) and (t) i(t), E(t) age are assumed: = exp-fX(t) + a(t)} (21) = exp{X(t)/3 + (t)} (22) where X(t) is a vector of exogenous characteristics which includes age controls; parameter vectors; and a(t) and are parameters. The following functional forms for the taste-shifters, Q(t) and ic(t) } and are are error terms. The effect of the demographic characteristics, X(t), in itj(t) is to shift the weight placed on the wife’s non-labour time in period t relative to the weight placed on the husband’s non-labour time in the household utility function. This difference appears in the MRS function between the husband’s hours and the wife’s hours in period t, (13). Changes in ic(t) shift the slope of the family’s indifference curve between the wife’s hours and the husband’s hours in a given period. The effect of X(t) in Q(t) is to shift the weight placed on the utility the family receives from non- labour time of the two spouses in period t relative to that received in period t + 1. This effect does not appear in the MRS function but does appear in the Euler equation, (19). 119 For example, if the household places a higher weight on periods where young children are present then they will increase their non-labour hours in those periods. Equation (13), the MRS condition between the husband’s hours and the wife’s hours, can be rewritten using the functional forms as: [T — — — — (t) 1 w 1 (t) 2 w (23) Taking the natural logarithm of both sides of (19) and rearranging: ln[T where/* — = h ( 2 t)] = X(t),8* + aln[T —i3/(a — 2 1), c = — k ( 1 t)] + a[ln(w (t)) 1 (ai—1)/(a — 2 1), a = — ln(w ( 2 t))] + e (t) 2 —1/(a — 2 1), and r (t) 2 (24) = It should be noted that (24) is only defined for households where both spouses work. The error term, E(t), is defined to be mean zero over all households in the sample. The mean of E2j(t) over the sample where the wife works may not be zero. This is where the selection issue enters into this part of the model. If this conditional mean is non-zero then, conditional on the other explanatory variables in (24), the MRS results of Chapter 3 will be biased. Next, a procedure is developed which allows for consistent estimation of the parameters: , 2 1 a a’ and , ij(t). The procedure is similar to the one used in section 2.5. Let W(t) be a vector of all exogenous characteristics of the household at time t. The following equations are assumed to explain the husband’s non-labour hours and the difference between the log of the husband’s wage and the log of the wife’s wage, for all households in the sample: 9 ln[T — h ( 1 t)] = 1+ W(t)i3 Ei(t) l9 dentification of the model requires that the vector W(t) contains variables not included in X(t). 120 (25) ln[wi(t)) where ,6 and — ln(w ( 2 t)] are parameter vectors; and = T’V(t)i3 + e(t) Ei(t) (26) and E(t) are error terms. These are equivalent to the first stage equations estimated in the 2SLS estimation of the MRS condition for the wife’s hours and the husband’s hours of Chapter 3. For households where the wife works, substituting (25) and (26) into (24) gives: ln[T — h ( 2 t)] = X(t),3* + 4[T’Vi(t)/3 1 + Ei(t)] + a[T’Vj(t),8 + E(t)] + E2(t) (27) The participation index (10), is expressed as a first order approximation in all of the exogenous variables in period t: I(t) where f3J3 is a parameter vector and Ej(t) W(t)/3 + E(t) (28) is an error term. 10 Over the sample of households where the wife works, equations (25)-(27) can be rewritten: ln[T ln[w ( 1 t)) ln[T — — — h ( 1 t)J = 1 + Et{ei(t) I ei(t) T’Vj(t)/3 ln(w ( 2 t)1 h ( 2 t)] = = —T’V(t)3} + c (t) 1 Wj(t)i3 + .Et{E(t) I piQ) —T’Vj(t)i3} + c (t) 0 (29) (30) X(t)/3* + a[T’V(t)/3 1 + Et{Ei(t) 1 ,(t) > —T’V(t)3}] +4[W(t)i3 + E{(t) I E,j(t) > —WQ)/3}] +Et{e ( 2 t) I e(t) —WQ)/3 , 1 } + c(t) (31) J Cogan (1981), the participation index relates the hours chosen by the wife to a reservation hours function 10 which is the hours the wife would work when facing her reservation wage, the lowest wage rate which induces her to work. There does not exist a simple analogue to Cogan’s index in the dynamic context, since it relies on a static uncompensated labour supply function. 121 where Et{x x = Ei(t), I —w(t)j3} e(t) is the expectation of x conditional on the wife working, for (t); and ci(t), c(t), and c 2 (t) are mean zero error terms over the 2 &(t) and E sample of households where the wife works; and c(t) £ ( t), E(t), e Assume that 1 (t) and 2 ,(t) 7 E = c4ci(t) + cci(t) + c (t). 2 are distributed according to the joint Normal distribution with covariance matrix: 12 a ai where a is the variance of E(t) for for j = 1,2, w,p, where j ln[w ( 1 t)) - a2 alp apw j 2w 2w 1,2, w,p, and Ujk is the covariance of e(t) with EkQ) (t)] 2 h — — = (t)] 1 h 2 = I’Vj(t),di + ln(w ( 2 t)j = = (t) 1 +c (32) W(t)/3 + (t) + c(t) (33) X(t)/* + a[W(t)/3 1 + 0+ +c4[T’Vi(t)i3 where (t) ptv k. The three equations to be estimated can be rewritten as: ln[T ln[T 2w l2 + is the inverse Mill’s ratio, and + c(t) f (34) and F are the Standard Normal density function and distribution function. The estimation involves a multiple step procedure similar to the two step procedure first suggested by Heckman (1979), and similar procedures discussed in detail in Maddala (1983). First, the wife’s participation decision, represented by the index function, (28), is estimated using the Probit estimator over the entire sample. The estimates of are used to derive estimates of (t) which are used in the estimation of (32) and (33). This yields consistent 122 estimates of j3, /3w, -r and . These estimates along with the derived estimates of ‘1,(t) are then used in the estimation of the MRS function, (34). This procedure accounts for both the endogeneity of the wife’s participation decision and the endogeneity of the husband’s hours and the wages of both spouses in the estimation of (34). Next, an estimation procedure is developed for the Euler equation for the wife’s hours, (19), which is based on the method used in Chapter 3. First, consistent estimates of MU(t) are derived. Taking the natural logarithm of both sides of equation (15): ln(MU(t)) = d(t){ln(—Uh ( 2 t)) — ln(w ( 2 t))} + (1 — dQ)){lm(—Uh ( 1 t)) — ln(wi(t))} (35) Under the assumed functional forms, this can be rewritten: ln(JVIU(t)) = d(t){X(t)j3 + E(t) + (a 2 +(1 — 1 d(t)){(a — 1)ln(T — — 1)ln(T h ( 1 t)) — — !i ( 2 t)) — ln(w Q 2 ))} (t))} + X(t)q + a(t) (36) 11 ln(w The error term E(t) appears only in the expression for the marginal utility of the wife’s hours, and only when the wife works in period t, d(t) = 1. In general, the expected value of ej(t) conditional on the wife working does not equal zero. However, using the assumed distribution of the error terms it is possible to derive an expression for its conditional mean. Using the definition of 1 (t), j(t) can be expressed as: 2 E ’ = 2 —(a — 1)E[s ( 2 t) I d(t) = 1] — 2 (a — 1)c ( 2 t) over the sample of households where the wife works. Recall that from equation (31), 2 c ( t) is mean zero over the sample of households where the wife works. Under the assumed distribution “The definition is found below equation (24). 123 of the error terms, this can be rewritten: 2 —(a = 1)(t) — 2 (a — 2 U (37) — Substituting this expression into (36) for e(t) gives: ln(MU(t)) d(t){X(t) = 2 (a — 1)(t) — — 2 (a — 2 U 2 +(a +(1 1)ln(T — — d(t)){(ai — (t)) 2 h — — 1)lrt(T (t) 2 1)c (t))} 2 ln(w — hi(t)) — (t))} + X(t) + a(t) (38) 1 ln(w Next, define: Yj(r) d(r){X ( 1 r) — for r = — 2 (a 1 d(r)){(a — t, t + 1. Therefore, MU(r) — 1)(r) + (a 2 1)ln[T = Yj(r) (r)1 1 h — — 2 (a — — — 1)ln[T — (r)] 2 h — ln(wi(r))} (r))} 2 ln(w (39) 1)d(r)c ( 2 r) + X(r)ql + a(r). We can now derive consistent predictions of Y(r) for each household in the sample using the parameter estimates from the MRS estimation, the hours and wage information of each spouse, the participation decision of the wife, and the household characteristics. Therefore, equation (19) can be rewritten: 1’(t + 1) where c(t + 1) = 2 (a — — 1’(t) = — r(t) 1)[d(t + 2 1)c ( t + 1) — — (XQ + 1) — x(t)) + c(t + 1) (t)c 1 d Q 2 )1 + [a(t) — (40) a(t + 1)] + (t + 1). Recall 21 is mean zero over the sample of households where the wife works; therefore, c(t+ 1) c that (t) is mean zero over all households in the sample. 124 The procedure used to estimate (40) is the same as the procedure used to estimate equation (29), the Euler equation for the wife’s hours, in Chapter 3. Let Z be a vector of time- constant family characteristics (e.g. birth year, immigrant status, immigrant arrival year, and education). Assume the following relationships exist: Yj(t+1) X(t + 1) = = 2 Zj3h (41) +V2 (42) 1 + Z[3x The assumption that (41) and (42) are of this form means that if we see a household in 1981, or period t, with characteristics Z, and we have consistent estimates of 2 h 3 / and , 11 then x 3 i we can derive consistent predictions of this household’s 1991, or t + 1, values of Yj(t + 1) and X(t + 1). These predictions can then be used in estimation of (40), the Euler equation. Substituting (41) and (42) into (40) gives the following expression for the Euler equation: — where u(t + 1) = Y(t) c’(t + 1) — = V2 1 b+ — — v’’ I(t) . — 1 (Z/3y+ — (t)))q5 + u 1 X (t + 1) 2 (43) The true value of Y(t + 1) is replaced by the expected value, Z,I3h , in the left hand side of (43). Also, the true values of X(t + 1) are replaced on 2 the right hand side of (43) by their expected values, Zx . The error terms 1 V2 and v’ are absorbed into u(t + 1). Using the observed values of X(t) and Z, the derived values of Y(t) and consistent esti mates of 2 h 3 / and 1 5x one could estimate (43) over the 1981 sample. However, due to the concern that the household characteristics, X(t), may contain stochastic components which are correlated with u(t + 1), it was decided to treat X(t) as a set of endogenous variables. 125 The following equations are assumed to determine the household characteristics, X (t): 2 (t) 1 X = ZjJ3x + (44) The assumed form of (44) enables us to replace the set of endogenous variables X(t) in equation (43), with consistent predictions of these variables using the estimates of / x and the 3 exogenous family characteristics, Z . Substituting (44) into (43) gives the following expression 2 for the Euler equation: /3h Z 2 where u(t + 1) = — (t) 2 Y = 1 b+ — I’(t) — 1 (Zj(/3xt+ — i x 3 )) + u’(t + 1) (45) u(t + 1) + Vftb The estimation involves three steps. First, the MRS condition between the husband’s hours and the wife’s hours, (34), is estimated by the procedure discussed above over both the 1981 and 1991 cross sections. This gives consistent estimates of , a, a, , and (t). These estimates are used to derive predictions of (t + 1) using (39), over the 1991 sample. Second, equations (41) and (42) are estimated by OLS over the 1991 cross section using the predictions of Yj(t + 1) and the observed values of X(t + 1). This gives consistent estimates of 2 h 3 / and . 1 x 3 I 1 Also, equation (44) is estimated over the 1981 sample giving us consistent estimates of x. In the final stage of estimation, Y(t) is derived over the 1981 sample using the estimates 3 I from the first stage and equation (39). The Euler equation for the wife’s hours, (45), is then estimated over the 1981 sample, by OLS, using the estimates of / h,, 3 x+ 3 / 1 and ! x from the 3 second stage. Tinder the assumptions, this estimation yields consistent estimates of b+ 1 — and q. In summary, for each household in the 1981 data, a predicted value is derived of Y(t + 1) 126 — Yj(t). Also, for each household a predicted value is derived of XQ + 1) — X(t), the change in household characteristics between t and t + 1. Next, the predictions of Y(t + 1) regressed on the predictions of 2 X ( t + 1) — — Yj(t) are X(t) and controls for age and immigrant arrival 2 over the 1981 sample. The procedure creates a synthetic panel by creating predictions year,’ of the 1991 behaviour of each household in the 1981 survey using the 1991 cross section data. The key assumptions which are required in order for this method to yield consistent esti mates of the Euler equation, and which are not required in an analysis using panel data are: 1) the two cross-sections represent random samples from the same population at different points in time; 2) the characteristics Z do not vary over time; and 3) equations (41), (42) and (44) are correctly specified. In the estimation, Z is a vector of thirty-five dummy variables and an intercept representing thirty-six distinct groups in the data defined in terms of time-constant characteristics. No restrictions are placed on variation in the conditional mean of the dependent variable across these thirty-six groups, in each equation of (41), (42) and (44); however, the conditional mean of the dependent variable is assumed to be the same within each of these groups. 4.5 Empirical Analysis The sample used in estimation contains the data used in Chapter 3 and also includes households where the wife does not work in the reference year and the survey week. Table 4.1 lists sample means of variables used in estimation.’ 3 Average hours and wages for the wives are calculated over the sample of workers. Therefore, they are equal to the sample means in 12 the estimation, b+ J 1 F(t) is assumed to be a function of age and immigrant arrival year. The variables are defined in Appendix 1. 13 — 127 Table 3.1. Sixty-six percent of immigrant women work in 1981 while fifty-nine percent of nonimmigrant women work. Both participation rates rise over the 1980s with the non- immigrant rate growing by more. In 1991, both non-immigrant and immigrant women have average participation rates of seventy-three percent. Comparing the education distribution for women to the one in Table 3.1 we see that more women are in the lowest education groups in Table 4.1 indicating that these women are more likely to be out of the labour market. The distribution of children present in the home is very similar between immigrant and non-immigrant families in each cross-section, and is also similar to the distributions found in Chapter 3.1. The results from the Probit estimation based on the participation index, (28), are listed in Table 4.2. The estimates are of the change in the probability of the wife working for a unit increase in the regressor. The specification of the participation index, (28), is the same as the one used in Chapter 2 with two differences. Since immigrant households where at least one spouse arrived in Canada after 1980 are excluded from the sample, controls for immigrant arrival year are for arrival before 1981. Also, controls for the husband’s occupation and industry are included. Due to the large number of variables included in the estimation, I will focus on the coefficient estimates on the controls for the wife’s and husband’s immigrant arrival cohort. The coefficient on NB, the dummy variable indicating non-immigrant families, is negative implying a lower probability of working for non-immigrant wives than for wives in the default category, wives in immigrant households where both the wife and the husband arrived in the 1970s. However, the coefficient estimate is not significant.’ 4 The coefficient on YR91 is positive indicating an increase in the participation rate of the wives in the default category The test statistic equals —.61, and the prob-value equals .54. 4 ‘ 128 over the decade, but again this coefficient estimate is not significant.’ 5 The coefficient on the variable NB * YR91 is close to zero indicating that the growth in the participation rate of non- immigrant wives is the same as the growth for immigrant wives who arrived in the 1970s. The coefficients on the variables Y6170 and YBEF61 for the wife indicate that immigrant wives who arrived before 1971 are five percent more likely to work than those who arrived after 1970.16 The coefficients on the interactions of these controls with the 1991 survey year dummy variable, YR91, are not significant from 17 zero. The coefficients on the controls for the husband’s arrival cohort indicate that an immigrant wife whose husband is a member of an earlier arrival cohort is significantly less likely to work than one whose husband is from a recent arrival cohort.’ 8 From the coefficients on the interactions of these variables with the 1991 survey year variable, we see that immigrant wives with husbands from earlier arrival cohorts experience a higher growth in the participation rate over the 1980s than do wives whose husbands are from recent cohorts.’ 9 Results from the Two Stage Least Squares (2SLS) estimation of the MRS function, (34), are presented in Table 4.3. The hours and wages of the husband and wife are treated as endogenous variables. The variables used as instruments are the age, education, and language fluency of each spouse. Controls for number of live births of the wife are also used. Controls for the occupation and industry for the husband are included. The analogous variables for the wife are not included since they are only defined for women who work. The instruments ‘ T 5 he test statistic equals 1.02. The prob-value equals .31. The test statistics are 1.86 and 1.39, respectively. The prob- values are .07 and .16, respectively. 6 ‘ The test statistics are .95 and .64, respectively. The prob-values are .34 and .52, respectively. 7 ‘ The test statistics equal —4.35 and —5.41 for the variables Y6170 and YBEF61 for the husband. The 8 ‘ prob-value is less than .0001 in each case. The test statistics equals 1.51 and 2.15 for Y6170 and YBEF61, respectively. The prob-values are .13 and 9 ‘ .03, respectively. — — 129 are fully interacted with a dummy variable for immigrant status. The age controls and the controls for immigrant arrival cohort are also interacted with a dummy variable for being in the 1991 sample. The parameter estimates are distributed asymptotically according to the Normal distribution. The asymptotic standard errors are in parentheses. The MRS specification includes the same demographic controls as were used in the MRS estimation of Chapter 3. Controls for presence of children are included and interacted with the immigrant dummy variable. The default category contains immigrant households in 1981 where both spouses arrived in the 1970’s, both are age twenty-five to twenty-nine, and no children are present. A control for native-born households is included and interacted with the year 1991 dummy variable. Controls for membership in the two earlier immigrant cohorts for both the husband and the wife are also included, and are interacted with the year 1991 20 variable. The estimate of the coefficient on the difference between the log of the husband’s wage and the log of the wife’s wage implies that a2, the curvature parameter on the wife’s hours in the utility function is —21.44, which is almost twice as large in absolute value as the value found in the analysis of Chapter 3. This is similar to the result found by Cogan (1981). Once the participation index is allowed to differ from the hours of work equation, the effect of a change in the wife’s wage on her hours of work is smaller. Cogan argues that this implies that most of the variation in hours for married women involves movement in and out of the labour market and not changes in hours of work of women in the labour market. Using this estimate of a , 2 one can impute a value of 0.7931 for ai, the curvature parameter on the husband’s hours in Appendix 5 contains the results of the first stage estimation of equations (32) and (33). 20 130 the utility function. This value is smaller than the value found in Chapter 3. To see how the MRS function varies with the hours of the husband and the wife, consider the case where both the husband and wife supply 2000 hours of work in period t. Using (23) we can see that the MRS in this case is .35. Therefore, the household places a higher marginal value on the wife’s non-labour time than the husband’s non- labour time. However, as we decrease the hours of work of the wife and husband while maintaining hi(t) = h ( 2 t), we see that the relative value of the wife’s non-labour time decreases relative to the husband’s since a 2 < a . When 1 we evaluate both the husband’s hours and the wife’s hours at the sample mean of hours of immigrant wives who worked in 1981, which is 1538, the MRS has risen above one to 6.939, meaning that the household now values the husband’s non-labour time more than the wife’s non- labour time. When children are present, the non-immigrant household chooses five to eight percent more non-labour hours for the wife for given values of the husband’s non-labour time and the offered wages. These effects are significant at the five percent level. ’ In immigrant families, the effect 2 of children is smaller, and these differences are in general significant at the five percent level. 22 Therefore, family preferences are such that the immigrant wife lowers her hours of work by less than the non-immigrant wife when children are present in the household. This matches the results found in the estimation of the structural model of Chapter 3 and the reduced-form estimation of Chapter 2. The test statistic in each case is the ratio of the coefficient estimate to the estimate of its standard error. 21 The test statistics are distributed asymptotically according to the Standard Normal distribution, and equal 5.97, 4.59, 870, and 5.98, for the variables KIDSO5, KO5PLUS, KIDS614, and K614FLUS, respectively. The prob-values are less than .0001 in each case. The test statistics are —2.25, —1.92, —1.98, and —1.30, for the variables FB * KIDSO5 FB * KOSFLUS, 22 FB * KIDS614, and FB * K614PLUS, respectively. The prob-values are .02, .05, .05, and .19, respectively. 131 From the coefficient on NB, we see that non-immigrant wives have three percent more non-labour hours, ceteris paribus, than wives in immigrant couples where both spouses arrived in the 1970s; however, this difference is not significant. 23 From the coefficient on the 1991 survey year dummy variable, YR91, the non-labour hours of immigrant wives who arrived in the 1970s fall by five percent over the 1980s, ceteris paribus, and this change is significant. 24 From the coefficient on the variable NB * YR91 we see that the decrease in the non-labour hours of the wife over the 1980s in non-immigrant families is two percent smaller than the decrease in immigrant families. 25 All of the coefficients on the controls for the wife’s and husband’s immigrant arrival cohort, and the interactions of these variables with the 1991 survey year variable are not individually significant at the five percent level. 26 Therefore, the results indicate that the 1981 non-labour hours of wives are the same in immigrant and nonimmigrant families for given values of the husband’s hours and the offered wages. However, the non-labour hours of the wives in immigrant families decrease by more than the non-labour hours in non-immigrant families, ceteris paribus. The effect of the wife’s age and the husband’s age in the MRS condition are very similar to the relationships found in the estimation of Chapter 3. The coefficients on the age controls for the husband and the wife are not significant at the five percent level except for the coefficients on the following variables for the wife: A4549 * YR91, A5054 * YR91, and A5559 * YR91 27 The The test statistic equals 1.23, and the prob-value equals .22. 23 24 test statistic equals —3.47, and the prob-value equals .001. The The test statistic equals 2.00, and the prob-value equals .05. 25 The test statistics equal —.09, .83, —.02, —.10, —1.47, —.35, 1.60, and .94 for the variables Y6170, YBEF61, 26 Y6170 * YR91, YBEF61 * YR91 for the wife and 16l70, YBEF61, 16l70 * YR91, YBEF61 * YR91 for the husband. The prob-values are .93, .41, .98, .92, .14, .73, .11, and .35, respectively. The test statistics for these variables are 2.04, 1.97, and 3.00,respectively. The prob-values are .04, .05 and 27 .003, respectively. 132 fact that all of the age interactions with the 1981 survey year dummy variable, YR81, are not significant from zero means that the non-labour hours of the wife, ceteris paribus, is the same across the six age cohorts in the 1981 survey. However, the growth in the non-labour hours of the wife, holding the husband’s hours and the offered wages constant, is not equal across these age cohorts. Women under forty-five see their non-labour hours drop by five percent over the decade. Older women reduce their non-labour hours by less. The IMR variable is the Inverse Mill’s ratio, j(t), from equation (34). Its coefficient is positive and significant implying 2 u > 0, from (34). Therefore, households where there is a , preference for the wife to work longer hours (due to a small value of 2 (t)), tend to be the households where the wife is less likely to work (due to a small value of ,j(t)). This can be explained by the households with the preference for the wife to work long hours also being the households which face a large value of the fixed cost of work, F(t). This would be the case if women who work very few hours have an easier time arranging childcare than do women who work longer hours. The fact that this result was found supports using a fixed cost model over the simple Tobit model. In the Tobit model, the decision to work and the number of hours worked are identical. Therefore, this negative correlation between the decision to work and the hours worked given that the wife works is not possible. The importance of the observed differences in family preferences found in the MRS esti mates will be demonstrated in an experiment analogous to the one which created Figure 3.1. In figure 4.3, the dynamic household problem is reduced to a static problem of choosing the husband’s hours and the wife’s hours, in period t, subject to an artificial constraint. The ar 133 tificial constraint requires the household to consume C , dollars worth of consumption when: 1 1) savings are zero, 2) the household is unable to borrow, and 3) both immigrant and nonimmigrant households face the mean non- immigrant wages of husbands and wives in the 1981 sample of Table 3.1.28 The experiment holds everything constant across the immigrant and non-immigrant families, except the estimated differences in the MRS function. The artificial constraint is defined as in Chapter 3: T — (t) 1 h = [n ( 1 t) + 2 (t)]T — GNB — (t)[T 2 i — (t)] 2 h (t) 1 (46) where 1 (t), and i 2 (t), i (t), Y 1 (t) are the sample means of the hours and wages of the 2 husbands and wives in the 1981 sub-sample of non-immigrant households where both spouses work; and CNB E 1 ( t) + 2 i ( t)] t). In Figure 4.3, the optimal hours of the husband and the wife in immigrant and nonimmigrant families are shown as the tangency of the relevant indifference curve to the artificial constraint, (46). The indifference curves are derived using the parameter estimates from the MRS estimation and are for the case where no children are present in the household, and both the wife and husband are age forty to forty-four. The immigrant curves are for immigrant families where both spouses arrived in Canada in the 1970s. The immigrant family’s indifference curve is flatter than the indifference curve of the non immigrant family. Therefore, the foreign-born household will choose to have the wife work forty-two more hours and the husband work thirty-nine fewer hours than is the case in the native-born family. These differences are smaller than those found in Figure 3.1 reflecting the These are used in order to make the budget constraint the same as the one used in Figure 3.1. 28 134 smaller differences in the MRS function due to immigrant status. Figure 4.4 repeats the exercise of Figure 3.2 using the new MRS estimates. An artificial constraint is defined for immigrants and their optimal hours are chosen subject to this con straint. The new constraint incorporates into the analysis: 1) differences by immigrant status in the ratio of the husband’s wage and the wife’s wage (captured by the slope of the constraint), and 2) differences by immigrant status in either the household’s disutility to work or wealth at time t (captured by the height of the intercept of the constraint). Figure 4.4 shows the hours choices of immigrant and non- immigrant families in 1981. The immigrant constraint is defined using the 1981 means of the hours and wages of husbands and wives over the sample of immigrant families where both spouses work. The results are similar to those found in Chapter 3. The indifference curve for immigrant families is”flatter” than that of non-immigrant families. The lower ratio of the wife’s wage to the husband’s wage in immigrant families versus non-immigrant families can be seen in the flatter artificial constraint for the immigrant family. The fact that the FB artificial constraint lies below the NB constraint is due to either the immigrant household having a lower disutility to the labour supplies of its members, or the immigrant family’s wealth being lower than the wealth of non- immigrant families. The results of the MRS estimation when the endogeneity of the wife’s participation decision is modelled are similar to those found in the previous chapter. The value of the wife’s non labour time relative to the husband’s non-labour time is smaller in immigrant families than in non-immigrant families. Also, the presence of children does not increase the relative value of 135 the wife’s non-labour time in immigrant families to the same extent as it does in non-immigrant families. The main difference is that the wife’s hours are less responsive to the ratio of their wages after controlling for the husband’s hours. Next the Euler equation for the wife’s hours, (45), is estimated to see if modelling the wife’s participation decision changes the results of Chapter 3. Table 4.4 contains estimates from the Euler equation estimation. 29 The default category contains households where the wife is native-born and age thirty-five to forty-four in 1981. The intercept gives the value of — r(t) for this group. Recall that this is the change over the 1980s of the log of the marginal utility of wealth, ?p(t) + AN(t). The estimate is negative and significant from zero, 30 implying an annual value of bt+i — F(t) of —1.25, which is larger in magnitude than the value found in Chapter 3. Differences in the Euler equation by age have the same pattern as in Chapter 3. The coefficient on the dummy variable for wives age twenty-five to thirty-four in 1981 is negative and significant. 31 This means that the value of b+i — I’(t) is smaller for this group. Given that young households typically face steeper wage profiles and own little in the way of assets relative to older households, it is reasonable to think that they are more likely to be credit-constrained than households where the wife is older. As was found in Chapter 3, the value of bt+ 1 — I’(t) is significantly larger for where the wife is forty-five to fifty-four in 1981.32 In both cases these age effects are strongly significant. Therefore, the empirical evidence supports the hypothesis that credit constraint effects decrease with age. The 29 30 The The The 32 results of the estimation of equations (41), (42), and (44) are presented in Appendix 6. test statistic equals —8.25, and the prob-value is less than .0001. test statistic equals —3.37, and the prob-value equals .001. test statistic equals 6.62, and the prob-value is less than .0001. 136 The effect of changes in the presence of children in the household between 1981 and 1991 in the Euler equation represents the change in c(t), the weight on period t utility in the family’s lifetime utility function, over the 1980s. The estimates listed are of the parameters of the vector from equation (45). The estimates of the parameter of the vector q for the difference in the dummy variable, KIDSO5, between 1981 and 1991 is the wrong sign and is 33 The coefficient on the change in the dummy variables KO5PLUS and KID S614 significant. are positive and significant implying that non-immigrant families place a higher weight in the lifetime utility function on periods when two or more childreu under the age of six are present in the household and when one or two children age six to fourteen are present in the household. 34 The estimate of the parameter from q.’ on the change in the variable K614PLUS over the 1980s is negative and significant, implying that non- immigrant households place a lower weight on periods where three or more children age six to fourteen are present in the household. 35 As was discussed in Chapter 3, this may be picking up a credit constraint effect. Having at least three children in the household is unlikely to force the wife to stay at home since the children would be attending full-time school. However, the household must make large expenditures on food and clothing for these children. The household may wish to borrow against labour income in the future when the children are adults and no longer living at home. If households typically cannot borrow against future earnings, then this variable may be proxying a credit constraint effect. As was found in Chapter 3, the coefficients on all of the interactions of the immigrant 33 test statistic equals —8.37; the prob-value is less than .0001. The The test statistics are 8.30 and 8.21, respectively. The prob-values are less than .0001. 34 The test statistic equals —3.48, and the prob-value equals .001. 35 137 dummy variable, FB, with these controls for the change in the presence of children variables over the decade are significant. ° Adding the coefficient on each interaction with the coefficient 3 on the analogous variable gives the change in X(t)4 for immigrant families. The effect of additional children present in the household is to increase the weight placed on that period in the immigrant family’s lifetime utility 37 function. As in Chapter 3, a higher weight is placed on periods when three or more children age six to fourteen are present in the home. The effect of the presence of these children in non-immigrant families is a significantly lower weight being placed on those periods. It was suggested above that this may be proxying a credit constraint effect. It is interesting that this effect does not show up for immigrant families. It may not be present for immigrant families because children in this age group are more likely to be expected to care for younger children after school in immigrant families compared with non-immigrant families. This supervision might free up more time for the wife to supply to the market. The controls for immigrant status and entry cohort do not support the hypothesis that immigrant families are more likely to be credit-constrained than non-immigrant families, ceteris paribus. The coefficients on all of the immigrant cohort controls are positive and significant. 38 Therefore, the estimate of bt+i — T’(t), the change in the log of the marginal utility of wealth is larger in immigrant families than in non-immigrant families. Therefore, the movement of hours and wages in immigrant versus non-immigrant families over the l980s is not consistent with the immigrant families being more likely to be credit-constrained than the non-immigrant The test statistics equal 7.67, —7.90, —8.21, and 3.56, for the KIDSOS, KO5PLUS, KIDS614, and 35 K614PLUS interactions, respectively. The prob-values are less than .0001 in each case. “The only exception to this rule is the effect of one to two children present age six to fourteen. This has a small negative effect on the weight placed on that period. The test statistics equal 5.86, 5.43, and 7.62, for the variables Y7180, Y6170, YBEF61, respectively. The 35 prob-values are less than .0001. 138 families. As in Chapter 3, I next derive and estimate the Euler equation for the husband’s hours. The husband is assumed to work in all periods. Therefore, using the marginal condition for the husband’s hours, (8), we see that the marginal utility of wealth, ratio of the marginal utility of the husband s hours to his wage rate, ApQ) + —Uh(t) , ;\N(t) equals the as was the case in Chapter 3. In fact the Euler equation for the husband’s hours derived in Chapter 3 holds over the sample being analyzed in this chapter. The only difference is that in Chapter 3 the Euler equation for the husband’s hours was estimated over the sample of households where the wife works, and in this chapter the estimation is over all households. Redefine equation (39) as: Y(r) where r = = lrt[T — h ( 1 r)] — ln(w ( 1 r)) (47) t, t + 1. Given this definition of Y(r) one can proceed with the derivation involved in equations (40) through (45). The only difference is that the dependent variable is now the change in the log of the ratio of the marginal disutility of the husband’s hours to his wage rate, holding household characteristics constant. In estimating equations (41), (42), and (44) I use the values of the husband’s age, education, and immigrant arrival cohort in defining the thirty-six dummy variables. Therefore, the vector now contains the husband’s characteristics rather than the wife’s. Also, in estimating (45), which is now the Euler equation for the husband’s hours, I define b+ 1 — F(t) to be a function of the husband’s age and immigrant arrival cohort. This is to make it consistent with the use of the husband’s characteristics in Z?. The estimates of equations (41), (42) and (44) are 139 reported in Appendix 7. The results of the estimation of the Euler equation for the husband’s hours are reported in Table 4.5. The coefficient estimates are very different from those of Table 4.4. As discussed in Chapter 3, there are a number of explanations for these differences. An exploration of these explanations would require the use of panel data. Therefore, it is left for future research. In the discussion of the results of Table 4.5, I will focus on the controls for the husband’s arrival cohort. Unlike in Table 4.4, the coefficients on the arrival cohorts all imply a smaller value of b+ 1 — F(t) for immigrant familles; however, in each case, these differences are small in magnitude and not statistically significant at the five percent level. 39 Therefore, the hypothesis that immigrant faniilles are more likely to be credit-constrained than non-immigrant familles is rejected. Next, the three experiments from Chapter 3 are repeated using the MRS and Euler es timates. An artificial constraint is defined which reduces the family’s dynamic problem into a choice of the wife’s hours in 1981 and 1991 subject to this constraint. In Figures 4.5 and 4.6, the wife in the immigrant and non-immigrant households faces wages equal to the sub sample means for non-immigrant women in 1981 and 1991. The wife must work enough hours in 1981 and 1991 to support consumption equal to the income the wife earns at those wages when working the mean hours of wives in the 1981 and 1991 non- immigrant sub-samples. In Figure 4.5, the immigrant families preferences over intertemporal labour supply when children are present will be constrained to be the same as those in the non-immigrant family. In Figure The test statistics are —.92, —.96, and —1.90, for the variables 1’7180, Y6170, and YBEF61, respectively. 39 The prob-values are .36, .34, and .06. 140 4.6, the immigrant family’s preferences over children will be allowed to differ from those of the non-immigrant family. In Figure 4.7, the non-immigrant family will solve the same problem as in Figure 4.6; however, the immigrant family will face a different constraint. The constraint will be defined by the wages of the immigrant women in the 1981 and 1991 data, and the income required will equal the income earned at those wages when the wife works the 1981 and 1991 sample mean hours for immigrant women. In Figure 4.5, the focus is on the differences in bt+ 1 — I’(t) by immigrant status. Immigrant households are forced to have the non-immigrant responses to the presence of children ° and 4 the intertemporal MRS is defined at the non-immigrant sample means for the changes in the presence of children variables. Each spouse is age forty to forty-four. Equal probability is placed on the immigrant husband and wife being from each of the entry cohorts. The constraint can be written: T — h ( 2 t + 1) = [u ( 2 t) + ii (t + 1)]T 2 — CNB(t,t + 1) — — h ( 2 t)] w ( 2 t + 1) (48) where ( 2 t), 2 i ( t), w (t + 1), and h 2 (t + 1) are the mean wages and hours of non-immigrant 2 wivesin 1981 and 1991’; and CNB(t,t+ 1) 2 ( ( ( t)+tzY t)] t+ 2 1) ( t+ 1). As can be seen in Figure 4.5, the differences in hours are even larger than those of Chapter 3. In Figure 3.3, the immigrant wife works 363 fewer hours in 1981 and 272 more hours in 1991. In Figure 4.5, the immigrant wife works 519 fewer hours in 1981 and 456 more hours in 1991.42 These large differences are due to the wife’s hours being less responsive to changes This was done by ignoring the coefficients on the interaction terms in Table 4.4. 40 41 the diagram, these are the sample means of the hours and wages of non-immigrant women in 1981 and 1n 1991 from Table 3.1 so as to make the figure comparable to Figure 3.3. The non-immigrant family’s tangency is to the left of the range of the graph. 42 141 in her wages 43 than in Chapter 3, and the fact that immigrant families in general respond less to the presence of children than do non-immigrant families. In this experiment, we are forcing the immigrant family to respond to the presence of children in the same way that the non-immigrant family responds. As was the case in Chapter 3, there is evidence against the hypothesis that immigrant families are more likely to be credit-constrained than non-immigrant families. The estimates indicate that wives in immigrant families work more in later years and less in earlier years than do non-immigrant wives, after controlling for their wage paths, and difference in the within period MRS function. In Figure 4.6, the combined effect of differences due to immigrant status in b+i — I’(t) of the Euler equation for the wife’s hours and differences due to immigrant status in the weight placed on periods where young children are present are analyzed. Using the same constraint as in Figure 4.5, the household’s problem is solved for immigrant and non-immigrant households. The non-immigrant household’s intertemporal MRS is the same as in Figure 4.4 and Figure 4.5. For the immigrant household, the coefficients on the interaction of immigrant status with the presence of children variables from Table 4.4 are used. This allows for different responses between immigrant and non-immigrant families to the changes in the composition of children present over the decade. In determining the immigrant MRS, the sample means for changes in presence of children in the immigrant sample were used. As can be seen in Figure 4.6, the immigrant indifference curve is much flatter than in Figure 4.5 and is now only slightly steeper than the non-immigrant curve. Immigrant women work one hundred hours more in 1981 and eighty-five hours fewer in 1991. Due to the larger value for the curvature parameter 43 a’2. 142 As discussed in Chapter 3, intercept differences in the within period MRS estimation of Table 4.3 by immigrant status, and differences in family responses to the presence of children in the household worked in the same direction. With no children present, immigrant house holds placed a lower weight on the wife’s hours relative to the husband’s hours than did nonimmigrant households. If children were present, this difference grew. The effect of children was that the household placed an even higher weight on the wife’s hours relative to the husband’s hours, and this effect was more pronounced for non-immigrant families than for immigrant families. In contrast, differences in the intercept, bt+ 1 — P(t) of the Euler equation by immigrant status and differences by immigrant status in the weight placed on the period if children are present work in the opposite direction. The intercept differences imply that immigrant women are more likely to work in later years than the non-immigrant women (either due to a higher rate of time preference or a smaller effect of credit constraints). The higher weight placed on periods where children are present by non-immigrant families than immigrant families, and the fact that average number of children present in the home under each age category is higher in 1981 than in 1991, means that immigrant wives work more hours in earlier years since they restrict their hours less when children are present. In Figure 4.7, an artificial constraint is defined for immigrant families, in an analogous fashion to the non- immigrant constraint, (48), but using sample means over immigrant fam ilies. Next the optimal choices of the wife’s hours in each period were derived and plotted as tangencies between the immigrant intertemporal indifference curve and the immigrant artificial 143 constraint. The same MRS functions were used as those in Figure 4.6. As in Figure 4.4, the immigrant constraint lies below and to the left of the non-immigrant constraint. This implies that, either due to a lower disutility to work, or due to lower life-time wealth, immigrant women supply more labour in each period than non- immigrant women. The higher growth rate in immigrant women’s wages over the decade is evident in the slightly flatter artificial constraint. This would encourage the immigrant women to supply relatively more hours in 1991 than in 1981 compared to non-immigrant women. However, this effect appears to be small. 4.6 Concluding Remarks The empirical results from the estimation of the model accounting for the wife’s endogenous participation decision reinforce the conclusion of Chapter 3. Immigrant families place a lower value on the wife’s non-labour time relative to the husband’s non-labour time compared with non-immigrant families. Immigrant families are less responsive to the presence of children in terms of the hours of work for the wife for given hours of work of the husband and market wage rates of both spouses. The results do not support the hypothesis that immigrant families are more likely to be credit constrained than non-immigrant families. There is evidence in support of credit constraints being important determinants of the hours of work of young women; however, after controliing for this effect, immigrant families do not appear to be more likely to be credit-constrained than non- immigrant families. 144 CHAPTER FIVE Conclusions This thesis has analyzed the labour market adjustment of immigrant families. The empirical evidence indicates that the labour market adjustment of immigrants is difficult in the first years after migration. However, with time in Canada, the labour market performance of immigrant men and women compares favourably to the performance of non-immigrants. Immigrant men and women face much lower wages than non-immigrant men and women in the first years after migration. Also, this initial difference in wages has been larger for more recent cohorts. However, immigrants have higher wage growth than non-immigrants; therefore, much of this initial differential is overcome with years of residence. Immigrant men and women with less than five years of residence work significantly fewer weeks in the year than non-immigrants. This appears to be due to higher unemployment over this period. After the first five years, the weeks of work of the immigrant husbands and wives are similar to those of the non-immigrant husbands and wives. A similar pattern emerges in the probability of the wife working. Immigrant women with fewer than five years of experience are less likely to participate than non-immigrant women. However, immigrant women with more years of residence are significantly more likely to work than non-immigrant women. Immigrant husbands and wives work more hours per week than non- immigrants for almost every immigrant cohort. 145 The economic literature on labour market adjustment has focused almost exclusively on wage rates and whether or not immigrants are of poorer “quality” than the pre-existing pop ulation. This analysis has broadened the focus to include other labour market characteristics. A larger initial wage gap for recent immigrant men does exist. It is conceivable that recent immigrants may never have wages that are on average equal to similar non-immigrants. How ever, the evidence on other labour market traits of these individuals indicates that they are prepared to supply more labour to the market than are non-immigrants. Taken as a whole, the evidence indicates that immigrants are succeeding in the long run in the Canadian labour market. The hypothesis that credit constraints are important determinants of hours of work in immigrant families has been explored. In the reduced-form estimation of Chapter 2, immigrant family members were found to work more hours than non-immigrants. These differences do not vary through time in spite of larger wage growth experienced by the immigrants. Since the credit constraint eases with years of residence, it was argued that this may be due to the immigrant household not increasing their hours of work by more than the non-immigrant family in response to the higher wage growth. A preference-based argument was also put forward. It may be that immigrant families have a lower disutility to its members labour or a lower expected lifetime wealth. Combined with a lower responsiveness of immigrants to movements along their lifetime wage proffle, this would also explain the movements in the data. 146 In Chapter 3, a structural model of household labour supply allowing for uncertainty and credit constraints was developed. The estimation procedure allowed for the estimation of structural labour supply equations using multiple cross sections of data rather than panel data, and may be of use in other applications where panel data is not available, but multiple cross section data sets are available. The results of the estimation indicate that immigrant families place a lower value on the wife’s non-labour time relative to the non-labour time of the husband than is the case in non-immigrant families. This difference would explain in part the higher hours of immigrant wives than non-immigrant wives despite their lower wages. After controlling for offered wages, immigrants were found to work more hours than non- immigrants due to a lower disutility to work or lower wealth. The results do not support the hypothesis that immigrant families are more likely to be credit-constrained than non- immigrant families. In Chapter 4, the model was extended to allow for the participation decision of the wife to be endogenous. The model is a significant extension of the dynamic labour supply literature for women which in the past used the simple Tobit model of married women’s participation. A fixed cost of work is modelled which the family must pay at beginning of a time period in order for the wife to work that period, as suggested by Cogan (1981) in the static labour supply model. After accounting for the participation decision, the wife’s hours are found to be less responsive to movements along her lifetime wage path. The results of the estimation of the Euler equation for the wife’s hours support the conclusions of Chapter 3. After controlling for age, immigrant families do not appear to be more likely to be credit- constrained than non-immigrant families. 147 The assumption that immigrant families are more likely to be credit-constrained than non- immigrant families is critical to the Family Investment Hypothesis, which predicts that immigrant married women will work long hours in the first years after migration when the family is unable to borrow and then reduce their hours after years of residence in the new country when the need to borrow has diminished. The results of this thesis are strong evidence against the FIR. Immigrant family members do not appear to distort their hours of work in the first years after migration in order to fund family consumption. In particular, the immigrant wives do work more hours at lower wages than their non-immigrant counterparts. However, their hours patterns over time are not consistent with the FIR. The results of Chapter 3 and Chapter 4 indicate that the hours of immgirant wives are consistent with immigrant families being less likely to be credit-constrained than non-immigrant families. Under the FIR, immigrant wives are predicted to bear the brunt of the distortion on family labour supply decisions. The results of the estimation are opposite to what one would expect under the FIR. The results of this thesis indicate that immigrants to Canada have been successful at gen erating incomes for their families which are comparable to those of non-immigrant families within ten years of residence in Canada. This is strong support for recent Canadian immigra tion policy. There does not appear to be an economic rational for adjusting either the size of the immigrant inflow or the current policies aimed at assisting immigrants adjust to the Canadian labour market. Future research should analyze the determinants of the higher hours of work of immigrants after controlling for offered wages. It may be possible to distinguish the preference-based 148 explanation from the explanation based on lower wealth of immigrants. A study of the weeks of work of immigrants in the first five years after migration would also be interesting given the lower weeks worked for these immigrants for both men and women. Finally, further research should focus on the causes of the differential rates of return on the education of immigrant versus non-immigrant women. 149 C En z En CD 0 CD 0 0 0 0 d b b CD I 4 I 8 0 0 I 28 24 20 16 12 YEARS—SINCE—MICRATION I lAP Equal Earnings Line I — I — I 0 I I 0 I FICUE 2.1 mmgrant Adjustment Path for Eornngs 32 01 C U m C m z 0 . (0 0 R co 0 0 0 0 c (0 b b (0 0 — — — 4 — — 8 I 12 I II 16 — — — — — ,,I — — 11111 -. I — — — — — — — — — — I 20 24 28 lAP for 1 960s cohort lAP for 1 970s cohort lAP under stationarity assumption Equal Earnings Line ,IIIIII — — — IIIII I YEARS—SINCE—MIGRATION — — — — — 0’ ‘‘I II III IIII•II_ —— FIGURE 2.2 Immigrant Adjustment Paths and Cohort Differences 32 c_fl m — - - z LJ.J 0 b 0 I 0 . L N 0 (0 0 0 -i’’’ — - 4 I I 8 I 16 I 12 111,1111111 — ‘III I — I — 20 — — IIIIll — I — — IIrIII — YEARS—SINCE—MIGRATION I — I — 0• 0 24 28 lAP for 1 960s cohort AP for 1 970s cohort Equal Earnings Line jirilill — Immigrant Adjustment Paths Differences in Assimilation Rates FIGURE 2.3 32 Table 2.1 Sample Means for Selected Variables FB 1981, N=3688 FB 1991, N=10472 NB 1981, N=3808 NB 1991, N=9815 PART .6551 .7357 .5885 .7330 WAGE* 8.00 10.03 9.37 10.92 HOURS* 34.67 35.47 32.47 33.64 WEEKS* 43.37 46.71 43.04 46.11 AGE 38.01 46.32 36.77 44.74 EDO8 .2400 .2042 .1253 .1110 BD913NG .1883 .1621 .2661 .1960 EDHSGRAD .1280 .1598 .1895 .1372 EDPS .3364 .3346 .3364 .3933 EDBACH .0848 .1038 .0734 .1185 EDGRAD .0225 .0355 .0093 .0440 KIDSO5 .2208 .0835 .1911 .0731 K1PLUS .1008 .0171 .1016 .0184 KIDS614 .7028 .5025 .6265 .4988 K2PLUS .0589 .0324 .0466 .0338 BIRTHS 2.200 2.391 2.218 2.293 BIRTH9 .0018 .1234 .0050 .1237 ENGOFF .7981 .8151 .6102 .6208 FREOFF .0354 .0358 .2009 .1967 BILOFF .0996 .0940 .1884 .1820 OTHOFF .0669 .0551 .0005 .0005 Wife’s Variables * . The mean is calculated over the sample of women who worked. For Immigrant families the sample size is 2372 in 1981 and 6400 in 1991. For non-immigrant families the sample size is 2244 in 1981 and 7194 in 1991. 153 Table 2.1 cont. FB 1981, N=3688 FB 1991, N=10472 NB 1981, N=3808 NB 1991, N9815 WAGE 11.36 13.29 12.09 13.54 HOURS 42.87 42.07 42.69 42.31 WEEKS 47.56 48.25 48.26 48.38 AGE 41.04 49.35 38.90 46.90 EDO8 .1956 .1748 .1322 .1110 ED913NG .1261 .1309 .1988 .1960 EDHSGRAD .0576 .0885 .1238 .1372 EDPS .4431 .3965 .3994 .3933 EDBACH .1099 .1277 .1099 .1185 EDGRAD .0677 .0816 .0359 .0440 ENGOFF .8525 .8627 .6065 .5213 FREOFF .0284 .0289 .1475 .1967 BILOFF .1191 .1084 .2460 .2820 OTHOFF .035 1 .0360 .0003 .0005 ATL .0078 .0099 .1077 .1037 QUENM .0075 .0086 .1896 .1889 MONT .1247 .1134 .1278 .1148 TOR .3808 .3961 .0773 .0830 ONTNT .2170 .2001 .2408 .2410 PRAIR .1228 .1210 .1613 .1636 BCNV .0482 .0413 .0592 .0616 VANC .0915 .1096 .0363 .0434 Husband’s Variables 154 Table 2.2 Results from Estimation of Wage, Hours, and Weeks Equations for Wives 1nWAGE 1nHOURS 1nWEEKS Intercept 1.914 (.037) 3.560 (.027) 3.787 (.027) YR91 .1598 (.029) .0001 (.020) .1139 (.022) ATL -.2559 (.033) .0203 (.023) -.1183 (.023) QUENM -.1123 (.040) -.0386 (.029) .0028 (.027) MONT -.0581 (.039) -.0475 (.028) .0323 (.025) ONTNT -.1411 (.028) -.0384 (.020) .0077 (.017) PRAIR -.1493 (.031) -.0297 (.022) BCNV -.1274 (.044) -.0879 (.029) -.0592 (.025) VANC .0332 (.044) -.0570 (.033) -.0024 (.028) A3034*YR81 .1216 (.032) -.0476 (.023) .0360 (.026) A3539*YR81 .1524 (.033) -.0777 (.025) .0413 (.029) A4044*YR81 .1275 (.035) -.1082 (.025) .0638 (.027) A4549*YR81 .1523 (.040) -.1403 (.031) .0641 (.030) A5054*YR8I .1388 (.049) -.1589 (.036) .0865 (.034) A4044*YR9I .0035 (.018) -.0389 (.011) -.0134 (.010) 155 .0025 (.018) - Table 2.2 cont. [ 1nWEEKS InWAGE 1nHOURS A4549*YR91 .0614 (.018) -.0763 (.012) -.0123 (.011) A5054*YR91 .0240 (.023) -.1259 (.015) -.0240 (.013) p.5559*yR91 .0577 (.028) -.1890 (.020) -.0540 (.016) A6064*Y981 -.0074 (.055) -.1532 (.033) -.0499 (.026) EDO8 -.2679 (.041) -.022 1 (.026) -.1329 (.026) ED913NG -.0998 (.024) .0083 (.016) -.0555 (.015) EDPS .1901 (.021) -.0084 (.014) .0097 (.012) EDBACH .5699 (.027) .0421 (.020) .0153 (.018) EDGRAD .6774 (.043) .1012 (.036) .0552 (.022) FREOFF -.0480 (.037) .0047 (.026) -.0729 (.025) BILOFF .0366 (.027) .0449 (.019) -.0399 (.019) OTHOFF .5790 (.332) -.3554 (.434) .3228 (.032) BIRTHS -.0334 (.007) BLRTH9 -.0113 (.026) KIDSO5 -.1520 (.020) -.1017 (.020) KIPLUS -.3153 (.044) -.2020 (.044) 156 Table 2.2 cont. InHOURS 1nWEEKS KIDS614 -.0776 (.008) -M517 (.007) K2PLUS -.1815 (.032) -.2401 (.037) InWAGE YBEF61 -.1036 (.050) .0202 (.036) -.0206 (.033) Y6170 -.1802 (.047) .0987 (.033) .0046 (.032) Y7180 -.2821 (.047) .0914 (.032) -.0472 (.032) -.7219 (.123) Y80 YBEF61*YR91 .0838 (.039) -.0085 (.030) .0032 (.027) Y6170*YR91 .0908 (.034) -.0037 (.024) -.0125 (.024) Y7180*YR91 .1142 (.035) -.0038 (.023) .0508 (.024) Y8185 -.2930 (.054) .0901 (.03 1) -.0097 (.027) Y86 -.2869 (.103) .0824 (.058) -.1027 (.051) Y87 -.3380 (.087) .0611 (.046) -.0728 (.044) Y88 -.3845 (.082) .0672 (.037) -.1330 (.047) Y89 -.3238 (.085) .0263 (.048) -.2506 (.061) Y90 -.3935 (.105) .0316 (.058) -.6097 (.081) FB*ATL .0576 (.094) -.0552 (.055) .0573 (.049) 157 Table 2.2 cont. InWAGE IriHOURS 1nWEEKS FB*QUENM -.0929 (.139) .0952 (.063) -.0674 (.069) FB*MONT -.0121 (.052) .0158 (.034) -.0848 (.03 1) FB*ONTNT .0223 (.036) -.0672 (.024) -.0444 (.020) FB*PRAIR .0430 (.040) -.0768 (.027) -.0559 (.023) FB*BCNV .0704 (.059) FB*VANC .0750 (.041) .0744 (.035) - - -.0412 (.051) -.0489 (.036) -.077 1 (.032) FB*EDO8 .1266 (.051) .0398 (.031) .0952 (.031) FB*ED913NG .0556 (.038) -.0252 (.023) .0261 (.022) FB*EDPS -.0190 (.032) -.0199 (.020) -.0182 (.019) FB*EDBACH -.1356 (.042) -.0399 (.028) .0127 (.025) FB*EDGRAD -.0688 (.058) -.0764 (.044) -.0345 (.03 1) FB*FREOFF -.0485 (.066) -.0257 (.038) -.0026 (.043) FB*BILOFF -.0500 (.043) -.0818 (.027) .0326 (.025) FB*OTHOFF -.7180 (.335) .3764 (.434) -.3934 (.041) FB*BIRTHS .0090 (.010) FB*BIRTH9 -.059 1 (.038) . 158 Table 2.2 cont. * [ InHOURS InWEEKS FB*KIDSO5 .0742 (.026) .0152 (.027) FB*K1PLUS .1604 (.056) .0374 (.054) FB*KIDS614 .0332 (.010) .0157 (.009) FB*K2PLUS .0312 (.043) .1400 (.045) InWAGE 2 R .0983 .0369 .0558 F 32.29 12.26 18.59 N 19 558 19 558 19 558 Standard errors are in parentheses. 159 Table 2.3 Estimates from Wage, Hours and Weeks Regressions for Husbands Variable ln(WAGE) ln(HOURS) ln(WEEKS) Intercept 2.139 (.034) 3.616 (.018) 3.735 (.020) A3034*YR81 .1625 (.027) .0605 (.014) .1193 (.019) A3539*YR81 .2263 (.028) .0750 (.015) .1337 (.019) A4044*YR81 .2448 (.030) .0567 (.016) .1251 (.020) A4549*YR81 .2724 (.030) .0319 (.015) .1063 (.020) A5054*YR81 .2645 (.031) .0384 (.017) .1266 (.021) YR91 .2183 (.027) .0558 (.014) .1114 (.018) A4044*YR91 .0436 (.018) .0037 (.007) .0105 (.007) A4549*YR91 .0772 (.018) .0010 (.007) .0138 (.007) A5054*YR91 .0665 (.020) -.0200 (.008) .0084 (.008) A5559*YR9I .0160 (.021) -.0379 (.009) .0023 (.008) A6064*YR91 .0210 (.026) -.0945 (.012) -.0216 (.011) ATL -.2198 (.026) .0330 (.013) -.0480 (.012) QUENM -.1481 (.031) .0067 (.015) .0204 (.013) MONT -.0612 (.030) -.0005 (.015) .0458 (.013) 160 Table 2.3 cont. Variable ln(WAGE) ln(HOURS) ln(WEEKS) ONTNT -.1135 (.024) .0408 (.012) .0279 (.008) PRAIR -.1700 (.027) .0650 (.013) .0094 (.010) BCNV -.0592 (.034) .0197 (.016) -.0190 (.012) VANC -.0003 (.037) .0502 (.017) .0155 (.017) FB*ATL .3076 (.066) -.0394 (.043) .0685 (.020) FB*QUENM -.0674 (.097) .0030 (.044) -.1147 (.043) FB*MONT -.1237 (.042) -.0358 (.019) -.0735 (.018) FB*ONTNT .0964 (.029) -.0134 (.013) -.0334 (.011) FB*PRAIR .0634 (.034) -.0365 (.015) -.0304 (.013) FB*BCNV .0203 (.048) -.0540 (.022) -.0363 (.019) FB*VANC -.0790 (.043) -.0565 (.020) -.0456 (.019) EDO8 -.1508 (.026) .0161 (.011) -.0818 (.011) ED913NG -.0354 (.022) .0238 (.009) -0166 (.009) EDPS .1140 (.019) .0181 (.008) .0137 (.008) EDBACH .4328 (.023) .0067 (.011) .0455 (.009) EDGRAD .4848 (.030) .0365 (.015) .0138 (.013) 161 Table 2.3 cont. - ln(WAGE) ln(HOURS) ln(WEEKS) FB*EDO8 .0677 (.039) -.0558 (.015) .0168 (.017) FB*ED913NG -.0305 (.037) -.0485 (.014) -.0033 (.015) FB*EDPS .0409 (.031) -.0392 (.012) -.0168 (.013) FB*EDBACH -.0793 (037) -.0470 (.016) -.0215 (.015) FB*EDGRAD .0555 (.042) -.0481 (.019) .0322 (.018) FREOFF -.0423 (.027) .0098 (.013) -.0593 (.014) BILOFF .0204 (.020) .0101 (.0 10) -.0222 (.009) OTHOFF -.2593 (.107) -.0282 (.030) .1410 (.021) FB*FREOFF .0634 (.053) -.0060 (.022) .0 133 (.027) FB*BILOFF .0412 (.032) .0029 (.015) .0199 (.014) FB*OTHOFF .1419 (.114) .0117 (.034) -.2059 (.030) YBEF61 -.1594 (.042) .0975 (.019) .0305 (.019) Y6170 -.1231 (.040) .0877 (.019) .0305 (.017) Y7180 -.2803 (.042) .0906 (.019) .0116 (.019) Variable -.5531 (.094) Y80 YBEF61*YR91 -.0051 (.013) .0723 (.028) 162 .0215 (.014) Table 2.3 cont. ln(WAGE) ln(HOURS) ln(WEEKS) Y6170*YR91 .0230 (.025) -.0130 (.012) .0017 (.012) Y7180*YR91 .0735 (.028) -.0254 (.013) .0133 (.014) Y8185 -.3707 (.047) .0629 (.019) .0176 (.019) Y86 -.3876 (.080) .0724 (.033) -.0259 (.046) Y87 -.3985 (.070) .0544 (.027) .0084 (.026) Y88 -.6353 (.081) .0319 (.029) -.0234 (.027) Y89 -.4679 (.069) .0201 (.028) -.2284 (.050) Y90 -.5134 (.084) .0335 (.037) -.5432 (.066) 27 783 27 783 27 783 Variable 2 R F N * Standard errors are in parentheses. 163 Table 2.4 1981 Predicted Differences in Wages, Hours, and Weeks of Wives by Immigrant Status 1nWAGE 1nHOURS InWEEKS Before 1961 -.0625 (.039) .0187 (.022) .0202 (.024) 1961-70 -.1392 (.035) .0973 (.021) .0455 (.022) 1971-80 -.2411 (.039) .0899 (.022) -.0064 (.024) Table 2.5 1991 Predicted Differences in Wages, Hours, and Weeks of Wives by Inuuigrant Status * ( 1nWEEKS 1nWAGE 1nHOURS Before 1961 .0213 (.031) .0102 (.018) .0234 (.016) 1961-70 -.0484 (.028) .0607 (.015) .0329 (.015) 1971-80 -.1269 (.027) .0861 (.015) .0444 (.013) 1981-85 -.2520 (.042) .0886 (.020) .0311 (.018) 1986 -.2459 (.095) .0810 (.052) -.0619 (.047) 1987 -.2970 (.079) .0596 (.040) -.0319 (.038) 1988 -.3435 (.074) .0658 (.030) -.0922 (.042) 1989 -.2828 (.076) .0249 (.041) -.2097 (.057) 1990 -.3525 (.099) .0301 (.054) -.5689 (078) Standard errors are in parentheses. 164 Table 2.6 1981 Predicted Differences in Wages, Hours, and Weeks of Husbands by Immigrant Status [ InWEEKS 1nWAGE 1nHOURS Before 1961 -.0912 (.029) .0353 (.014) -.0095 (.014) 1961-70 -.0549 (.026) .0254 (.013) -.0095 (.013) 1971-80 -.2121 (.030) .0283 (.014) -.0283 (.015) Table 2.7 1991 Predicted Differences in Wages, Hours, and Weeks of Husbands by Immigrant Status * 1nWAGE 1nHOURS Before 1961 -.0298 (.024) .0390 (.010) .0172 (.009) 1961-70 -.0428 (.022) .0213 (.010) -.0027 (.009) 1971-80 -.1495 (.023) .0119 (.0 10) -.0100 (.009) 1981-85 -.3134 (.036) .0095 (.014) -.0173 (.015) 1986 -.3303 (.074) .0191 (.031) -.0608 (.044) 1987 -.3413 (.061) .0011 (.024) -.0264 (.024) 1988 -.5780 (.076) -.0215 (.026) -.0582 (.024) 1989 -4107 (.063) -.0332 (.025) -.2632 (.048) 1990 -.4562 (.078) -.0199 (.035) -.5781 (.065) Standard errors are in parentheses. 165 Table 28 Results from Probit Estimation on Wife’s Participation VARIABLE VARIABLE YR9I .0428 (.266) FB*QUENM .0271 (.05 1) NB -.0740 (.03 1) FB*MONT .0165 (.030) NB*YR9I .0302 (.020) FB*ONTNT -.03 52 (.020) YBEF6I (WIFE) .0651 (.032) FB*PRAIR .0129 (.022) Y6170 (WIFE) .0728 (.027) FB*VANC .0293 (.028) YBEF6I*YR9I (WIFE) -.0485 (.03 8) FB*BCNV .0118 (.029) Y6170*YR9I (WIFE) -.0526 (.032) EDO8 (WIFE) -.1864 (.0 16) Y8185 (WIFE) .0031 (.032) ED913NG (WIFE) -.0749 (.012) Y86 (WIFE) -.0495 (.071) EDPS (WIFE) .1246 (.0 11) Y87 (WIFE) -.03 06 (.063) EDBACH (WIFE) .2215 (.019) Y88 (WIFE) -.1148 (.069) EDGRAD (WIFE) .3201 (.044) Y89 (WIFE) -.1844 (.079) FB*EDO8 (WIFE) .0833 (.022) Y90 (WIFE) -.2868 (.083) FB*ED9I3NG (WIFE) .0259 (.019) YBEF61 (HUSBAND) -.1578 (.032) FB*EDPS (WIFE) -.0504 (.0 17) Y6170 (HUSBAND) -.1097 (.027) FB*EDBACH (WIFE) -.0541 (.027) 166 Table 2.8 cont. VARIABLE VARIABLE YBEF61*YR91 (HUSBAND) .0711 (.03 8) FB*EDGRAD (WIFE) -.0556 (.054) Y6170*YR91 (HUSBAND) .0402 (.033) EDO8 (HUSBAND) -.0242 (.0 17) Y8185 (HUSBAND) -.0114 (.033) ED9I3NG (HUSBAND) .0082 (.015) Y86 (HUSBAND) .0109 (.071) EDPS (HUSBAND) -.0401 (.0 13) Y87 (HUSBAND) -.0230 (.063) EDBACH (HUSBAND) -.0757 (.017) Y88 (HUSBAND) .0571 (.072) EDGRAD (HUSBAND) -.1234 (.024) Y89 (HUSBAND) .0048 (.082) FB*EDO8 (HUSBAND) .0252 (.025) Y90 (HUSBAND) .0458 (.033) FB*ED9I3NG (HUSBAND) .0246 (.024) A3034*YR8I (WIFE) -.0089 (.019) FB*EDPS (HUSBAND) .0349 (.02 1) A3539*YR81 (WiFE) -.0261 (.023) FB*EDBACH (HUSBAND) .0348 (.026) A4044*YRSI (WIFE) -.0508 (.027) FB*EDGRAD (HUSBAND) -.0245 (.033) A4549*YR8I (WIFE) -.1462 (.031) BIRTHS -.0091 (.003) A5054*YR8 1 (WIFE) -.2399 (.03 5) BIRTH9 -.0256 (.0 15) A3034*YR81 (HUSBAND) -.0586 (.023) FB*BIRTHS -.0039 (.005) A3539*YR8I (HUSBAND) -.0720 (.026) FB*BIRTH9 -.0089 (.022) A4044*YR8I (HUSBAND) -.0582 (.029) KIDSO5 -.1957 (.013) 167 Table 2.8 cont. VARIABLE _VARIABLE I__________ A4549*YR81 (HUSBAND) -.0489 (.032) KIPLUS -.4219 (.02 1) A5054*YR81 (HUSBAND) -.0434 (.03 5) KIDS6I4 -.0629 (.006) A4044*YR91 (WIFE) -.0490 (.011) K2PLUS -.1916 (.022) A4549*YR9I (WIFE) -.0779 (.014) FB*KIDSO5 .0027 (.0 18) A5054*YR91 (WIFE) -.1361 (.017) FB*KIPLUS .0718 (.028) A5559*YR9 (WIFE) -.2560 (.019) FB*K6I4PLUS .0174 (.008) A6064*YR9I (WIFE) -.3891 (.024) FB*K2PLUS .0464 (.029) A4044*YR9I (HUSBAND) -.00002 (.013) FREOFF (WIFE) -.03 06 (.024) A4549*YR9I (HUSBAND) -.0457 (.0 15) BILOFF (WIFE) .0485 (.0 18) A5054*YR9I (HTJSBAND) -.0592 (.0 17) OTHOFF (WIFE) .0529 (.228) A5559*YR91 (HUSBAND) -.0805 (.019) FB*FREOFF (WIFE) .0304 (.039) A6064*YR91 (HUSBAND) -.0934 (.022) FB*BILOFF (WIFE) .0029 (.026) ATL -.0979 (.019) FB*OTHOFF (WIFE) -.1269 (.229) QUENM -.1015 (.025) FREOFF (HUSBAND) -.0085 (.024) MONT -.0943 (.024) BILOFF (HUSBAND) -.0141 (.018) ONTNT -.0289 (.0 17) OTHOFF (1{USBAND) -.1551 (.301) 168 Table 2.8 cont. VARIABLE PRAIR .0103 (.018) FB*FREOFF (HUSBAND) .0184 (.04 1) VANC -.0527 (.025) FB*BILOFF (HUSBAND) -.0157 (.025) BCNV -.0781 (.022) FB*OTHOFF (HUSBAND) .2144 (.3 02) FB*ATL -.0056 (.044) 2 R .2083 LR 4401 N * VARIABLE 27783 Standard errors are in parentheses. 169 Table 2.9 Results from Estimation of Wage, Hours and Weeks Equations for Wives after Controlling for Participation Decision InWAGE InHOURS 1nWEEKS Intercept 1.7834 (.047) 3.638 (.031) 3.847 (.035) A3034*YR81 .1058 (.036) -.0329 (.023) .0228 (.026) A3539*YR81 .1513 (.038) -.0538 (.024) .0347 (.028) A4044*YR81 .1504 (.039) -.0791 (.025) .0605 (.029) A4549*YR8I .1460 (.043) -.0742 (.030) .0857 (.033) A5054*YR81 .0925 (.056) -.0527 (.040) .1464 (.043) YR91 .2195 (.033) -.0326 (.021) .0879 (.025) A4044*YR91 .0062 (.017) -.0153 (.012) .0006 (.015) A4549*YR91 .0602 (.019) -.0343 (.0125 .0 134 (.018) A5054*YR91 .0009 (.022) -.0571 (.020) .0211 (.022) A5559*YR91 -.0279 (.03 1) -.0615 (.030) .0356 (.033) A6064*YR91 -.1750 (.052) .0463 (.046) .0941 (.049) ATL -.2916 (.038) .0542 (.024) -.0920 (.028) QUENM -.1526 (.047) -.0042 (.030) .0295 (.035) MONT -.0953 (.045) -.0149 (.029) .0575 (.034) 170 Table 2.9 cont. [ 1nWEEKS 1nWAGE 1nHOURS ONTNT -.1491 (.031) -.0297 (.020) -.0194 (.024) PRAIR -.1454 (.033) -.0290 (.021) -.0411 (.025) BCNV -.1536 (.042) -.0616 (.027) -.0682 (.032) VANC .0113 (.047) -.0407 (.030) -.0360 (.035) FB*ATL .0458 (.092) -.0203 (.058) .0913 (.067) FB*QUENM -.0922 (.104) .0972 (.066) -.0652 (.076) FB*MONT .0 129 (.057) .0440 (.036) -.054 1 (.041) FB*ONTNT .0023 (.038) -.0250 (.024) -.0044 (.029) FB*PRAIR .0437 (.041) -.0425 (.026) -.0184 (.031) FB*BCNV .0646 (.059) -.0321 (.037) -.0292 (.043) .0290 (.054) -.0060 (.034) -.0293 (.040) EDO8 -.3664 (.041) .0714 (.029) -.0604 (.031) ED9I3NG -.1302 (.026) .0372 (.017) -.033 1 (.019) EDPS .2282 (.023) -.0471 (.016) -.0397 (.018) EDBACH .6216 (.032) -.1730 (.022) -.0308 (.026) EDGRAD .7482 (.061) .0251 (.041) -.0038 (.050) FB*VANC - 171 Table 2.9 cont. InWAGE 1nHOURS FB*EDO8 .1796 (.049) .0082 (.03 1) .0760 (.034) FB*ED913NG .07 12 (.038) -.0 120 (.024) .0442 (.027) FB*EDPS -.0352 (.032) .0197 (.021) .0194 (.024) FB*EDBACH -.1540 (.044) -.00001 (.028) .0494 (.033) FB*EDGRAD -.0943 (.075) -.0305 (.048) .0066 (.059) FREOFF -.0670 (.041) .0207 (.026) -.0605 (.030) BILOFF .0509 (.029) .0324 (.018) -.0590 (.021) OTHOFF .5256 (.541) -.3127 (.335) .3512 (.306) *FPOFF -.0246 (.068) -.0272 (.043) .0009 (.049) p,3*BILOFF -.0530 (.042) -.0683 (.027) .0464 (.03 1) FB*OTHOFF -.6891 (.542) .3534 (.336) -.4028 (.307) BIRTHS -.0474 (.007) BIRTH9 -.0257 (.029) FB*BIRTHS .0080 (.009) FB*BLRTH9 -.0645 (.040) -.0792 (.022) -.0452 (.025) KIDSO5 172 Table 2.9 cont. 1nHOURS 1nWEEKS K1PLUS -.1373 (.046) -.0639 (.049) KIDS614 -.0554 (.008) -.0344 (.010) K2PLUS -.1064 (M32) -.1818 (.036) FB*KIDSO5 .0704 (.024) .0123 (.027) FB*KIPLUS .1208 (.046) .0066 (.047) FB*KIDS614 .0270 (.010) .0109 (.012) FB*K2PLUS .0143 (.039) .1267 (.044) 1nWAGE YBEF61 -.0940 (.056) .0143 (.034) -.0251 (.039) Y6170 -.1578 (.052) .0769 (.032) -.0 123 (.038) Y7180 -.2588 (.052) .0652 (.033) -.0672 (.038) -.7281 (.074) Y80 YBEF61*YR91 .0751 (.043) .0004 (.027) .0101 (.031) Y6170*YR91 .0750 (.037) -.0181 (.024) .0018 (.027) Y7180*YR91 .1097 (.037) .0084 (.023) .0600 (.027) Y8185 -.2812 (.055) .0761 (.033) -.0205 (.039) Y86 -.2774 (.100) .0788 (.062) -.1055 (.073) , 173 Table 2.9 cont. InWAGE InHOURS InWEEKS Y87 -.3364 (.078) .0629 (.048) -.0713 (.057) Y88 -.3828 (.073) .0711 (.045) -.1300 (.053) Y89 -.3684 (.081) .0708 (.050) -.2161 (.057) Y90 -.4491 (.092) .0868 (.058) -.5669 (.065) IM.R .3078 (.044) -.2676 (.048) -.2076 (.052) 2 R .1006 .0386 .0570 F 37.60 12.61 18.69 N 19 558 19 558 19 558 ___ _____ _____ * Standard errors are in parentheses. 174 Table 2.10 1981 Predicted Differences in Wages, Hours, and Weeks of Wives by Immigrant Status after Correcting for the Participation Selection * InWAGE InHOURS InWEEKS Before 1961 -.0602 (.040) .0141 (.025) .0167 (.028) 1961-70 -.1241 (.035) .0767 (.023) .0295 (.026) 1971-80 -.2250 (.036) .0650 (.023) -.0254 (.027) Standard errors are in parentheses. 175 Table 2.11 1991 Predicted Differences in Wages, Hours, and Weeks of Wives by Immigrant Status after Correcting for the Participation Selection * JnWAGE 1nFIOURS Before 1961 .0149 (.028) .0145 (.018) .0268 (.020) 1961-70 -.0490 (.024) .0586 (.015) .0313 (.018) 1971-80 -.1153 (.015) .0734 (.023) .0346 (.017) 1981-85 -.2475 (.035) .0760 (.022) .02 13 (;026) 1986 -.2436 (.090) .0786 (.057) -.0637 (.067) 1987 -.3026 (.066) .0628 (.042) -.0295 (.049) 1988 -.3491 (.060) .0709 (.038) -.0882 (.045) 1989 -.3346 (.069) .0706 (.044) -.1742 (.050) 1990 -.4153 (.082) .0866 (.053) -.525 1 (.059) Standard errors are in parentheses. 176 Table 3.1 Sample Means for Selected Variables Wife’s Variables PB 1981, N=2372 FB 1991, N=6400 NB 1981, N=2244 NB 1991, N =7194 AHOURS 1537 1692 1434 1582 WAGE 8.07 10.29 9.37 10.92 AGE 37.91 46.02 36.30 43.81 EDO8 2105 .1602 .0777 .0496 ED913NG .1770 .1527 .2392 .1896 EDHSGRAD .1248 .1170 .1699 .2127 EDPS .3610 .3684 .3982 .4166 EDBACH .0992 .1170 .1015 .1093 EDGRAD .0275 .0361 .0135 .0222 KJDSO5 .2065 .0623 .1643 .0708 KO5PLUS .0691 .0075 .0574 .0132 KIDS614 .6760 .5192 .5700 .5257 K614PLUS .0542 .0280 .0391 .03 14 Y7180 .3568 .4169 Y6170 .3799 .3597 YBEF61 .2633 .2234 177 Table 3.1 cont. Husband’s Variables FB 1981, N=2372 FB 1991, N=6400 NB 1981, N=2244 NB 1991, N7194 AHOURS 2057 2088 2060 2071 WAGE 11.04 13.31 11.88 13.28 AGE 40.87 49.15 38.43 46.08 EDO8 .1804 .1491 .1039 .0865 ED9I3NG .1244 .1283 .2139 .1909 EDHSGRAD .0604 .0816 .1182 .1442 EDPS .4555 .4245 .4083 .4042 EDBACH .1145 A359 .1171 .1275 EDGRAD .0647 .0775 .0383 .0467 Y7180 .3423 .3983 Y6170 .3628 .3534 YBEF61 .2950 .2483 178 - Table 3.2 Results from Estimation of the Family Marginal Rate of Substitution Function VARIABLE VARIABLE Intercept 8.036 (.062) YBEF61*YR91 (HUSBAND) .0077 (.021) LNTHRS .0106 (.008) A3034*YR81 (WIFE) -.0066 (.011) WDIFF .0871 (.006) A3539*YR81 (WIFE) .0020 (.014) KIDSO5 .0781 (.008) A4044*YR81 (WIFE) .0019 (.016) KO5PLUS .1332 (.015) A4549*YR81 (WIFE) .0 100 (.018) KIDS614 .0321 (.003) A5054*YR81 (WIFE) .0161 (.021) K614PLUS .0906 (.012) A4044*YR91 (WIFE) .0147 (.006) FB*KIDSO5 -.0268 (.011) A4549*YR91 (WIFE) .0230 (.007) FB*KO5PLUS -.0516 (.021) A5054*YR91 (WIFE) .03 18 (.009) FB*KIDS614 -.0089 (.004) A5559*YR91 (WIFE) .0636 (.011) FB*K614PLUS -.0200 (.017) A6064*YR9I (WIFE) .0518 (.016) NB .0287 (.010) A3034*YR81 (HUSBAND) .0061 (.0 13) YR91 -.0473 (.0 14) A3539*YR81 (HUSBAND) .0077 (.015) NB*YR91 .0127 (.010) A4044*YR81 (HUSBAND) .0064 (.016) Y6170 (WIFE) -.0046 (.015) A4549*YR81 (HUSBAND) .0 140 (.018) 179 Table 3.2 cont. VARIABLE VARIABLE * YBEF61 (WIFE) .0139 (.018) A5054*YR81 (HUSBAND) .0050 (.020) Y6170*YR91 (WIFE) .0044 (.017) A4044*YR91 (HUSBAND) -.00534 (.008) YBEF61*YR91 (WIFE) .0054 (.021) A4549*YR91 (HUSBAND) -.0053 (.008) Y6170 (HUSBAND) -.0131 (.015) A5054*YR91 (HUSBAND) .0075 (.009) YBEF6I (HUSBAND) .0114 (.018) A5559*YR91 (HUSBAND) .0090 (.010) Y6170*YR91 (HUSBAND) .0214 (.0 18) A6064*YR91 (HUSBAND) .0036 (.012) 2 R .069 F 20.21 N 18210 Standard errors are in parentheses. 180 :3 I (I) -D C 0 (I) z C 0 oD :3 0 E cv 0 0 0 0 0 0 0 0 0 0 LI) r) 0 0 (0 0 0 N 0 0 OD V) 3300 1981 3400 3600 3700 Wife’s Non—Labour Time 3500 3800 3900 FIGURE 3.1 Non—Labour Time for Immigrant and Non—Immigrant Families Given Non—Immigrant Wages and Artificial Constraint I (I) - o 0 0 0 IO 3300 - - 0. 0 (0 0 E OD 0 0 1981 3400 %% I ‘ I 3600 I ‘ — 3700 I — — FB NB FB NB 111111,11 I Wife’s Non—Labour Time 3500 I II I I — 3800 I Constraint Constraint Indifference Curve Indifference Curve I 3900 FIGURE 3.2 Non—Labour Time for Immigrant and Non—Immigrant Families Given Market Wages and Artificial Constraint Table 3.3 Results from Estimation of the Euler Equation for the Wife’s VARIABLE -5.559 (.800) Intercept A2534 -3.020 (WIFE) (.979) 2.478 A4554 (WIFE) (.418) 1.804 Y7180 (WIFE) (.639) 2.193 Y6170 (WIFE) (.690) YBEF61 3.560 (.665) (WIFE) KIDSO5 (1991) - KO5PLUS (1991) KIDS614 (1991) - - K614PLUS (1991) FB*[KTDSO5 118.8 (17.5) KO5PLUS (1981) KIDS614 - (1991) 7.536 (1.44) (1981) K614PLUS (1981) -23.32 (7.96) KIDSO5 (1981)] 18.54 (3.58) - FB*[KO5PLUS (1991) -KO5PLUS (1981)] -105.4 (16.8) FB*[KIDS614 (1991) (1981)] -7.786 (1.56) KTDS614 - FB*[K614PLUS (1991) (1981)1 * -.58 15 (1.812) KIDSO5 (1981) - 24.00 (8.38) K614PLUS 2 R .0344 F 20.26 N 4616 Standard errors are in parentheses. 183 Hours Table 3.4 Results from Estimation of the Euler Equation for the Husband’s Hours VARIABLE -.1280 Intercept (.082) .0273 (.118) A2534 (HUSBAND) - A4554 (HUSBAND) 1693 (.043) Y7180 (HUSBAND) -.1177 (.073) Y6170 (HUSBAND) -.0691 (.063) YBEF61 (HUSBAND) -.0671 (.060) KIDSO5 (1991) - . .6905 KIDO5 (1981) (.3 73) KO5PLUS (1991) - 1.268 KO5PLUS (1981) (1.04) KIDS614 (1991) - K614PLUS (1991) .1095 (.202) KIDS6I4 (1981) - FB*[KIDSO5 (1991) -1.312 (1.03) K6I4PLUS (1981) - .9457 KIDSO5 (1981)1 (.42 1) FB*[KO5PLUS (1991) -KO5PLUS (1981)] -2.387 (1.18) FB*[KIDS6I4 (1991) (1981)1 -.1760 (.159) - (1981)] .7478 (1.12) 2 R .0236 F 13.76 N 4616 FB*[K614PLUS (1991) * KIDS614 - K614PLUS Standard errors are in parentheses. 184 ci) U) 0) 0) z 0 C ui_J 0 :3 0 (I) 0 0 N) 0 0 Co 0 0 0 0 0 0 0 3700 ‘4 3800 ‘I I I Wife’s 1981 3900 4100 — Non—Labour Hours 4000 — I 4200 NB Constraint NB Indifference Curve FB Indifference Curve 11111111111111111 FIGURE 3.3 Hours of Immigrant and Non—Immigrant Wives Over Time Given Non—Immigrant Wages and Artificial Constraint I 4300 0 0 0 0 N 0 0 aD r) 0) 0 0 0 0 0 0 0 LI) 0 0 (° - ) “-‘ 0) — z 0 coO 0 :3 0 :3 L. (I) 0 0 3550 I I 3600 I 3700 I 3750 I I I — I 3800 — I I I 3850 I 3900 NB Constraint NB Indifference Curve FB Indifference Curve - Wife’s 1981 Non—Labour Hours 3650 I I FIGURE 3.4 Hours of Immigrant and Non—Immigrant Wives Over Time Given Non—Immigrant Wages and Artificial Constraint 3950 — 0 (I) 0) 0) z 0 C 0 :3 0 I :5 (I) 0 0 LI) 0 0 0 0 V) 0) 0 0 0 0 3600 3650 I I 3750 I 3800 I — 3850 — • — I NB FB NB FB Wife’s 1981 Non—Labour Hours 3700 I z I 1111 I 3900 I 3950 I Constraint Constraint Indifference Curve Indifference Curve 11111111111 I FIGURE 3.5 Hours of Immigrant and Non—Immigrant Wives Over Time Given Market Wages and Artificial Constraints 4000 0 C) C C/) 15 E co-I--’ C 0 0 0 CN 0 0 (0 0 0 0 0 0 0 0 co 0 0 200 400 800 1000 Wife’s Non—Labour Time 600 1200 FIGURE 4.1 The Case of a Non—worker in the Static Fixed Cost of Work Model 1400 1600 D ,- 0 0 0 :5 (I) C E -i-’ 0 0 0 (N (D 0 0 0 0 0 0 0 0 0 0 200 400 800 1000 Wife’s Non—Labour Time 600 1200 FIGURE 4.2 The Case of a Worker in the Static Fixed Cost of Work Model 1400 1 600 Table 4.1 Sample Meaiis FB 1981, N=3593 FB 1991, N=8730 NB 1981, N=3808 NB 1991, N=9815 PART .6601 .7331 .5885 .7330 WAGE* 8.07 10.29 9.37 10.92 AHOURS* 1537 1692 1434 1582 AGE 38.15 47.04 36.77 44.74 EDO8 .2423 .2137 .1253 .1110 ED913NG .1866 .1658 .2661 .1960 EDHSGRAD .1267 .1631 .1895 .1372 EDPS .3406 .3301 .3364 .3933 EDBACH .0823 .0979 .0734 .1185 EDGRAD .0215 .0293 .0093 .0440 .2206 .0645 .1911 .0731 K1PLUS .0998 .0100 .1016 .0184 KIDS614 .7074 .4723 .6265 .4988 K2PLUS .0598 .0290 .0466 .0338 BIRTHS 2.217 2.404 2.218 2.293 BIRTH9 .0016 .1144 .0050 .123-7 ENGOFF .7983 .8298 .6102 .6208 FREOFF .0358 .0334 .2009 .1967 BILOFF .1014 .0961 .1884 .1820 OTHOFF .0646 .0405 .0005 .0005 Wife’s Variables KIDSO5 * - The mean is calculated over the sample of women who worked. For Immigrant families the sample size is 2372 in 1981 and 6400 in 1991. For non-immigrant families the sample size is 2244 in 1981 and 7194 in 1991. 190 Table 4.1 cont. FB 1981, N=3593 PB 1991, N=8730 NB 1981, N=3808 NB 1991, N=9815 WAGE 11.45 13.61 12.09 13.54 AHOURS 2057 2061 2065 2055 AGE 41.18 50.10 38.90 46.90 EDO8 .1978 .1864 .1322 .1110 ED913NG .1247 .1322 .1988 .1960 EDHSGRAD .0573 .0885 .1238 .1372 EDPS .4445 .4026 .3994 .3933 EDBACH .1090 .1200 .1099 .1185 EDGRAD .0667 .0739 .0359 .0440 ENGOFF .8188 .8367 .6065 .5213 FREOFF .0289 .0271 .1475 .1967 BILOFF .1195 .1123 .2460 .2820 OTHOFF .0328 .0239 .0003 .0005 ATh .0080 .0101 .1077 .1037 QUENM .0077 .0082 .1896 .1889 MONT .1258 .1126 .1278 .1148 TOR .3796 .3908 .0773 .0830 ONTNT .2189 .2143 .2408 .2410 PRA.IR .1199 .1165 .1613 .1636 BCNV .0920 .0436 .0592 .06 16 VANC .0481 .1037 .0363 .0434 Husband’s Variables 191 Table 4.2 Results from Probit Estimation on Wife’s Participation VARIABLE VARIABLE YR91 .0450 FREOFF (WIFE) -.0284 (.024) NB -.0354 (.057) BILOFF (WIFE) -.0501 (.018) NB*YR91 .0017 (.052) OTHOFF (WIFE) .1061 (.235) Y6170 (WIFE) .0521 (.028) FB*FREOFF (WIFE) .0072 (.041) YBEF61 (WIFE) .0458 (.033) FB*BILOFF (WIFE) -.0041 (.027) Y6170*YR91 (WIFE) -.0313 (.033) FB*OTHOFF (WIFE) -.2119 (.236) YBEF6 1 *YR9 1 (WIFE) -.0248 (.039) FREOFF (HUSBAND) -.0066 (.024) Y6170 (HUSBAND) -.1217 (.028) BILOFF (HUSBAND) -.0131 (.018) YBEF61 (HUSBAND) -.1784 (.033) OTHOFF (HUSBAND) .1833 (.3 18) Y6170*YR91 (HUSBAND) .0512 (.034) FB*FREOFF (HUSBAND) .0210 (.044) YBEF61*YR91 (HUSBAND) .0858 (.040) FB*BILOFF (HUSBAND) -.0061 (.026) A3034*YR81 (WIFE) -.0258 (.027) FB*OTHOFF (HUSBAND) .2184 (.3 19) j\3539* -.0697 (.033) KIDSO5 (WIFE) -.2154 (.015) A4044*YR81 (WIFE) -.0741 (.040) K1PLUS -.4523 (.022) A4549*YR81 (WIFE) -.1849 (.045) KIDS614 -.0686 (.007) 192 Table 4.2 cont. VARIABLE VARIABLE A5054*YR81 (WIFE) -.3012 (.052) K2PLUS A4044*YR9 1 (WIFE) -.0708 (.016) FB*KIDSO5 .0276 (.021) A4549*YR91 (WIFE) -.1060 (.021) FB*K1PLUS .0767 (.034) A5054*YR9I (WIFE) -.1583 (.025) FB*KIDS614 .0245 (.0 10) A5559*YR91 (WIFE) -.2840 (.029) FB*K2PLUS .0708 (.034) A6064*YR9 1 (WIFE) -.4674 (.037) BIRTHS -.005 1 (.003) FB*A3034*YR8 1 (WIFE) .0097 (.040) BIRTH9 -.0219 (.0 16) FB*A3539*YR81 (WIFE) .0536 (.048) FB*BIRTHS -.0119 (.005) FB*A4044*YR81 (WIFE) .0190 (.056) *BIRTH9 -.0210 (.023) FB*A4549*YR8 1 (WIFE) .0499 (.063) ATL -.0934 (.019) FB*A5054*YR81 (WIFE) .0833 (.072) QUENM -.1054 (.025) FB*A4044*YR91 (WIFE) .0382 (.025) MONT -.0983 (.024) FB*A4549*YR9 1 (WIFE) .0495 (.03 1) ONTNT -.0259 (.017) FB*A5054*YR91 (WIFE) .0427 (.036) PRAIR .0063 (.018) FB*A5559*YR91 (WIFE) .0508 (.041) VANC -.0541 (.023) FB*A6064*YR91 (WIFE) .1202 (.051) BCNV -.0653 (.023) 193 .2087 (.023) - Table 4.2 cont. VARIABLE VARIABLE A3034*YR81 (HUSBAND) -.0758 (.030) FB*ATL -.0554 (.047) ft..3539*YR81 (HUSBAND) -.0754 (.035) FB*QUENM .0260 (.055) A4044*YR81 (HUSBAND) -.0721 (.041) FB*MONT .0 124 (.031) A4549*YR81 (HUSBAND) -.0662 (.045) FB*ONTNT -.0419 (.021) A5054*YR81 (HUSBAND) -.06 14 (.050) FB*PRAIR M204 (.024) A4044*YR91 (HUSBAND) .0043 (.0 17) FB*VANC .0188 (.028) A4549*YR91 (HUSBAND) -.0427 (.020) FB*BCNV .0215 (.029) A5054*YR91 (HUSBAND) -.0638 (.024) PRIM -.1695 (.024) M559*Y1 (HUSBAND) -.0939 (.027) MANUF -.076 1 (.0 17) A6064*YR91 (HUSBAND) -.0871 (.033) CONSTR -.0244 (.022) FB*A3034*YR8 1 (HUSBAND) .05 15 (.05 1) TRANSP -.0910 (.019) FB*A3539*YR81 (HUSBAND) .0348 (.057) TRADE -.0322 (.018) FB*A4044*YR8 1 (HUSBAND) .0486 (.063) FINANCE -.04 15 (.023) F*A4549*YR81 (HUSBAND) .0532 (.068) PUBLIC -.0468 (.018) FB*A5054*YR81 (HUSBAND) .0530 (.074) OTHIND -.0307 (.020) *A4J44*YR91 (HUSBAND) -.0216 (.03 1) FB*AGRIC .1154 (.06 1) 194 Table 4.2 cont. VARIABLE VARIABLE FB*A4549*YR91 (HUSBAND) -.0341 (.035) FB*PRIM -.0699 (.042) FB*A5054*YR91 (HUSBAND) -.0146 (.039) FB*MANUF .0 145 (.024) FB*A5559*YR91 (HUSBAND) -.0077 (.043) FB*CONSTR -.07 17 (.03 1) FB*A6064*YR91 (HUSBAND) -X472 (.049) FB*TRANSP .0282 (.027) EDO8 (WIFE) -.1801 (.016) FB*TRADE -.0103 (.025) ED913NG (WIFE) -.0734 (.012) FB*FINANCE -.0007 (.034) EDPS (WIFE) .1233 (.011) FB*PUBLIC .0015 (.029) EDBACH (WIFE) .2 177 (.0 19) FB*OTHIND .0029 (.028) EDGRAD (WIFE) .3090 (.044) AGRIC .0211 (.038) FB*EDO8 (WIFE) .0721 (.023) OSCI .0367 (.166) FB*ED913NG (WIFE) .0259 (.020) OTEACH .0539 (.025) FB*EDPS (WIFE) -.0487 (.018) OCLER .0630 (.020) 3*EDBACH (WIFE) -.0269 (.029) OSSERV .0082 (.0 14) FB*EDGRAD (WIFE) -.0236 (.057) OPRPROC -.0071 (.0 14) EDO8 (HUSBAND) -.0053 (.017) OCONSTR ED913NG (HUSBAND) .0145 (.0 15) OTROTH 195 .0507 (.0 18) - -.0222 (.015) Table 4.2 cont. VARIABLE VARIABLE * EDPS (HUSBAND) -.0394 (.013) FB*OSCI -.0229 (.024) EDBACH (HUSBAND) -.1127 (.019) FB*OTEACH -.0277 (.037) EDGRAD (HUSBAND) -.1628 (.026) FB*OCLER .0190 (.030) FB*EDO8 (HUSBAND) .0291 (.027) FB*OSSERV .0262 (.022) FB*ED913NG (HUSBAND) .0172 (.026) FB*OPRPROC M053 (.020) FB*EDPS (HUSBAND) .0368 (.022) FB*OCONSTR .0 175 (.027) 3*EDBACH (HUSBAND) .0633 (.029) FB*OTROTH .0161 (.024) FB*EDGRAD (HUSBAND) -.0004 (.037) 2 R .2309 LR 4605 N 25946 Standard errors are in parentheses. 196 Table 4.3 Results from Estimation of the Family Marginal Rate of Substitution VARIABLE VARIABLE Intercept 8.058 (.072) Y6170 (WIFE) -.0013 (.015) LNTHRS .0092 (.009) YBEF61 (WIFE) .0157 (.019) WDIFF .0446 (.009) Y6170*YR9I (WIFE) -.0004 (.018) KIDSO5 .0537 (.009) YBEF61*YR91 (WIFE) -.0022 (.022) KO5PLUS .078 1 (.017) Y6170 (HUSBAND) -.0221 (.015) KIDS614 .026 1 (.003) YBEF61 (HUSBAND) -.0067 (.019) K614PLUS .0778 (.013) Y6I70*YR9I (HUSBAND) .0288 (.018) FB*KJDSO5 -.0248 (.011) YBEF61*YR91 (HUSBAND) .0207 (.022) FB*KO5PLUS -.0404 (.021) A3034*YR81 (WIFE) -.0077 (.011) FB*KIDS614 -.0079 (.004) A3539*YR81 (WIFE) -.0026 (.014) .0234 (.018) A4044*YR81 (WIFE) -.0022 (.016) NB .0123 (.0 10) A4549*YR81 (WIFE) -.0060 (.018) YR91 -.0486 (.014) A5054*YR81 (WIFE) -.0106 (.022) NB*YR91 .0220 (.0 11) A4044*YR91 (WIFE) .0096 (.006) A4549*YR91 (WIFE) .0143 (.007) A4549*YR8I (HUSBAND) .0082 (.018) FB*K614PLUS - 197 Table 4.3 cont. VARIABLE VARIABLE * A5054*YR91 (WIFE) .0 177 (.009) A5054*YR8 1 (HUSBAND) .0006 (.020) A5559*YR91 (WIFE) .0360 (.012) A4044*YR91 (HUSBAND) -.0058 (.007) A6064*YR91 (WIFE) .0056 (.017) A4549*YR9I (HUSBAND) -.0086 (.008) A3034*YR81 (HUSBAND) .0006 (.013) A5054*YR91 (HUSBAND) .0012 (.009) A3539*YR81 (HUSBAND) .0009 (.015) A5559*YR91 (HUSBAND) -.0029 (.0 10) A4044*YR81 (HUSBAND) .0013 (.0 17) A6064*YR91 (HUSBAND) -.0114 (.013) IMR .0772 (.011) 2 R .042 F 18.9 N 18210 Standard errors are in parentheses. 198 0 N) 0 0 C’) 0 0 V) CN o 0 0 0 0 0 LI) 0 0 Co r-o 0 0 0 0 N -D (I) z C 0 ø—J D :5 0 E ci) 0 0 OD 3300 1981 3400 3600 3700 Wife’s Non—Labour Time 3500 3800 3900 FIGURE 4.3 Non—Labour Time for Immigrant and Non—Immigrant Families Given Non—Immigrant Wages and Artificial Constraint C) Cl) 0 0 0) 0 0 0 I’O CN ri-) (D aD 0 0 3.300 - I .3400 I 3600 I I I 3700 I I I • — — — Wife’s Non—Labour Time 3500 I I — — — I — I I 3800 I FB Indifference Curve NB Indifference Curve 3900 — 11111111111111,,,, I FB Constraint NB Constraint lii — I FIGURE 4.4 1961 Non—Labour Time for Immigrant and Non—Immigrant Families Given Market Wages and Artificial Constraint Table 4.4 Results from Estimation of the Euler Equation for the Wife’s Hours VARIABLE Intercept -12.46 (1.51) A2534 (WIFE) -3.849 (1.14) A4554 (WIFE) 5.402 (.8 16) Y7180 (WIFE) 5.769 (.984) Y6170 (WIFE) 5.540 (1.02) YBEF61 (WIFE) 7777 (1.02) KIDSO5 (1991) - KIDO5 (1981) -88.71 (10.6) KO5PLUS 237.4 (28.6) KO5PLUS (1991) (1981) KIDS614 (1991) (1981) - - K614PLUS (1991) K6I4PLUS (1981) -26.86 (7.72) - FB*[KIDSO5 (1991) (1981)] - FB*[KIDS614 (1991) KIDS614 (1981)] 121.1 (15.9) KIDSO5 FB*[KO5PLUS (1991) KO5PLUS (1981)] -226.0 (28.6) - -22.42 (2.73) - FB*[K614PLUS (1991) K614PLUS (1981)] * 21.60 (2.63) KIDS614 36.34 (10.2) - 2 R .0344 F 20.26 N 7401 Standard errors are in parentheses. 201 Table 4.5 Results from Estimation of the Euler Equation for the Husband’s Hours VARIABLE -.1823 (.094) Intercept A2534 .0486 (HUSBAND) (.125) A4554 .1726 (HUSBAND) (.048) Y7180 (HUSBAND) -.0708 (.077) Y6170 (HUSBAND) -.0642 (.067) YBEF61 (HUSBAND) -.1220 (.064) KIDSO5 (1991) - KO5PLUS (1991) KIDS614 (1991) - - K614PLUS (1991) .8520 (.897) KO5PLUS (1981) .0924 (.251) KIDS614 (1981) - FB*[KIDSO5 (1991) K614PLUS (1981) -1.245 (1.11) KIDSO5 (1981)] 1.089 (.480) - FB*[KO5PLUS (1991) -KO5PLUS (198 1)1 -1.531 (.933) f*[}(JDS614 (1991) (1981)] -.2824 (.198) - FB*[K6I4PLUS (1991) (1981)] * -.9198 (.438) KIDO5 (1981) KIDS614 - 1.045 (1.20) K614PLUS 2 R .0176 F 10.17 N 7401 Standard errors are in parentheses. 202 I_*.) N) 0 N) (0 0 - G) ‘— 0) 0 0 0 N) 0 0 0)0 — z 0 C C o—J liii DOl 00 CN 0 0 4080 11111111 I III 4120 I 111111 4160 I 111111 I II I I II I 4240 I Illillill I I I I III 4280 ii I III III III I III 4320 I 4360 4400 liii Indifference Curve Indifference Curve 111111 Non—Labour Hours 4200 1111111 Wife’s 1981 Iii I FIGURE 4.5 Hours of Immigrant and Non—Immigrant Wives Over Time Given Non—Immigrant Wages and Artificial Constraint 0 C’) 0) z 0 C MO -o 0 0 :5 C,) (0 0 0 N V) 0 0 OD 0 0 0) 0 0 0 0 0 3600 3640 3720 Wife’s 1981 3680 3800 3840 Non—Labour Hours 3760 3880 FIGURE 4.6 Hours of Immigrant and Non—Immigrant Wives Over Time Given Non—Immigrant Wages and Artificial Constraint 3920 (I) 0) cY) 0 C uiJ C L’J 0 :5 0 D (I) a rr N) a 0 LI) a a N 0 O) a a a a 3500 3600 I 3800 II 111111111,1 I — 3900 — — a — a I NB FB NB FB Wife’s 1981 Non—Labour Hours 3700 I — 4000 constraint constraint Indifference Curve Indifference Curve — I FIGURE 4.7 Hours of Immigrant and Non—Immigrant Wives Over Time Given Market Wages and Artificial Constraints 4100 REFERENCES Abbott, M. and C. 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Zero to eight years of education and no further education. 6) ED913NG Nine to thirteen years of education but without graduating from high school - and no further education. 7) EDHSGR.AD 8) EDPS - - Graduated from high school and no further education. Some post-secondary education, but not a university degree. 9) EDBACH - 10) EDGRAD University Bachelor’s degree. - University degree above Bachelor’s Degree. Includes professional degrees. 11) ED Graduated from High School and may have a university degree or other post-secondary - education. 12) NB - Non-immigrant family. 209 13) Y90 14) Y89 15) Y88 16) Y87 17) Y86 - - - - - 18) Y8185 19) Y80 - 20) Y7180 21) Y6170 Immigrant who arrived in 1990. Immigrant who arrived in 1989. Immigrant who arrived in 1988. Immigrant who arrived in 1987. Immigrant who arrived in 1986. Immigrant who arrived 1981-85. - Immigrant who arrived in 1980. Immigrant who arrived 1971-80. - Immigrant who arrived 1961-70. - 22) YBEF61 23) KIDSO5 Immigrant who arrived before 1961. - - 24) KO5PLUS 25) K10S614 One child present under six years of age. - - More than one child present under six years of age. Number of children present between six and fourteen years of age, up to a maximum of two. 26) K614PLUS 27) A3034 28) A3539 - - - More than two children present between the ages of six and fourteen. Age thirty to thirty-four. Age thirty-five to thirty-nine. 210 29) A4044 30) A4549 Age sixty to sixty-four in 1981. - 34) A2534 Age twenty-five to thirty-four in 1981. - 35) A4554 - Age fifty-five to fifty-nine. - 33) A6064 38) ATTJ Age fifty to fifty-four. - 32) A5559 37) Y1t81 Age forty-five to forty-nine. - 31) A5054 36) YR91 Age forty to forty-four. - Age forty-five to fifty-four in 1981. - Household from the 1991 sample. - Household from the 1981 sample. - Household resides in Newfoundland, New Brunswick, Nova Scotia, or PEI. 39) QUENM 40) MONT - Household resides in Montreal. - 41) ONTNT 42) PItAIR 43) VANC 44) BCNV - Household resides in Ontario outside Toronto. - Household resides in Manitoba, Saskatchewan, or Alberta. - - Household resides in Quebec outside of Montreal. Household resides in Vancouver. Household resides in British Columbia outside Vancouver. 45) FREOFF - Individual’s official language is French. 211 46) BILOFF Individual speaks both official languages. - 47) OTHOFF 48) OSCI - Individual speaks neither official language. - managerial, science, medical, and related occupations. 49) OTEACH 50) OCIJER clerical and related occupations. - 51) OSSERV teaching and related occupations. - sales and services occupations. - 52) OPRPROC 53) OCONSTR 54) OTROTH 55) AGRIC 56) PRIM - construction trades and occupations transport equipment operating, related occupations, and other occupations. other primary industry. manufacturing. - 58) CONSTR 59) TRANSP construction. - transportation and storage. - - 61) FINANCE 62) PUBLIC - primary, processing, machining, and related occupations. Agricultural industry. - 57) MANUF 60) TRADE - - - wholesale trade and related industries. - finance, insurance, and real estate. public administration and defense. 212 63) OTHIND - other industries. 213 Appendix 2 First Stage Estimates for Two Stage Least Squares Estimation of MRS Function DIFF Variable* Coefficient Standard Error LNTHRS Coefficient Standard Error ati -0.0193 0.0403 0.0297 0.0112 quenm -0.1116 0.0527 0.0066 0.0146 mont -0.0841 0.0504 0.0103 0.0139 ontnt -0.0186 0.0340 -0.0038 0.0094 prair -0.0755 0.0358 -0.0218 0.0099 vane -0.0866 0,0488 -0.0047 0.0135 bcnv -0.0090 0.0466 0.0048 0.0129 wa3034*yr8l -0.0110 0.0616 -0.0064 0.0170 wa3539*yr8l -0.1469 0.0794 -0.0325 0.0220 wa4044*yr8l -0.0146 0.0936 -0.0381 0.0259 wa4549*yr8l -0.0844 0.1077 -0.0195 0.0298 wa5054*yr8l -0.0372 0.1284 -0.0447 0.0356 a3034*yr8l 0.0506 0.0648 -0.0168 0.0179 a3539*yr8l 0.1274 0.0784 -0.0255 0.0217 a4044*yr8l 0,1501 0.0924 0.0107 0.0256 a4549*yr8l 0.0870 0.1034 0.0128 0.0286 a5054*yr8l 0.0832 0.1164 0.0076 0.0322 wa4044*yr9l -0.0013 0.0301 -0.0106 0.0083 wa4549*yr9l 0,0109 0.0391 -0.0045 0.0108 214 Appendix 2 cont. DIFF LNTHRS Coefficient Variable* Coefficient Standard Error wa5054*yr9l -0.0186 0.0503 -0.0179 0.0139 wa5559*yr9l -0.0214 0.0655 -0.0006 0.0181 wa6064*yr9l 0.0134 0.1011 -0.0117 0.0280 a4044*yr9l 0.0084 0.0319 -0.0038 0.0088 a4549*yr9l 0.0175 0.0386 -0.0057 0.0107 a5054*yr9l -0.0405 0.0463 0.0170 0.0128 a5559*91 -0.0530 0.0569 0.0140 0.0157 a6064*yr9l -0.0795 0.0757 0.0560 0.0210 births 0.0213 0.0080 -0.0033 0.0022 birth9 -0.0345 0.0308 -0.0091 0.0085 edO8 -0.1139 0.0399 0.0099 0.0110 ed9l3ng -0.0516 0.0317 0.0061 0.0088 edps 0.0103 0.0276 -0.0023 0.0076 edbach 0.1394 0.0390 -0.0194 0.0108 edgrad 0.2655 0.0528 -0.0342 0.0146 wed08 0.1076 0.0447 0.0110 0.0124 wed9l3ng 0.0812 0.0288 -0.0014 0.0080 wedps -0.0934 0.0249 -0.0153 0.0069 wedbach -0.2778 0.0399 -0.0127 0.0111 wedgrad -0.4360 0,0687 -0.0064 0.0190 kids05 -0.1328 0.0325 -0.0042 0.0090 215 Standard Error Appendix 2 cont. DIFF LNTHRS Coefficient Variable* Coefficient Standard Error kiplus -0.2130 0.0603 -0.0170 0.0167 k2plus 0.0852 0.0533 -0.0132 0.0148 kids6l4 -0.0123 0.0143 -0.0043 0.0040 freoff 0.0341 0.0525 0.0148 0.0145 biloff 0.0127 0.0360 0.0021 0.0100 othoff 0.6363 1.1801 -0.0579 0.3267 wfreoff 0.0235 0.0518 0.0263 0.0144 wbiloff 0.0265 0.0359 0.0135 0.0099 wothoff -1.0124 0.8351 0.0536 0.2312 osci -0.0432 0.0334 0.0513 0.0092 oteach 0.1776 0.0485 0.0933 0.0134 ocler -0.2319 0.0399 0.0673 0.0110 osserv -0.1815 0.0293 0.0289 0.0081 oprproc -0.1281 0.0308 0.0620 0.0085 oconstr -0.0902 0.0403 0.0709 0.0112 otroth -0.1730 0.0343 0.0436 0.0095 agric -0.6176 0,0814 -0.2817 0.0225 prim 0.3528 0.0545 0.0112 0.0151 manuf 0.2171 0.0367 -0.0049 0.0102 constr 0.1196 0.0479 0.0332 0.0133 transp 0,2829 0.0398 -0.0218 0.0110 216 Standard Error Appendix 2 cont. DIFF LNTHRS Coefficient Variable* Coefficient Standard Error trade -0.0221 0.0373 -0.0374 0.0103 finance 0.1594 0.0480 -0.0057 0.0133 public 0.2484 0.0373 0.0250 0.0103 othind -0.0244 0.0420 0.0140 0.01 16 wosci -0.0524 0.0371 0.0035 0.0103 woteach -0.0376 0.0441 0.0115 0.0122 wocler 0.1667 0.0305 0.0026 0.0085 wosserv 0.3261 0.0346 0.0076 0.0096 woprproc 0.2067 0.0532 0.0032 0.0147 wotroth 0.1934 0.0614 -0.0287 0.0170 wagric 0.1634 0.0926 -0.1514 0.0257 wprman -0.0624 0.0387 0.0046 0.0107 wconstr -0.3124 0.0683 -0.1169 0.0189 wtransp -0.1184 0.0444 -0.0171 0.0123 wtrade 0.1263 0.0315 -0.0240 0.0087 wfinance 0.0189 0.0382 -0.0070 0.0106 wpublic -0.0709 0.0378 0.0146 0.0105 wothind 0.0692 0.0300 0.0068 0.0083 yr9l 0.0012 0.085 1 -0.0052 0.0236 nb 0.0247 0.1193 0.0893 0.0330 nyr9l 0.0351 0.1000 -0.0168 0.0277 217 Standard Error Appendix 2 cont. DIFF Variable* Coefficient Standard Error LNTHRS Coefficient Standard Error l7O 6 y 0.0661 0.0609 -0.0320 0.0169 ybef6l -0.0443 0.0740 -0.0227 0.0205 wy6170 -0.0778 0.0604 0.0097 0.0167 wybef6l -0.0911 0.0748 -0.0052 0.0207 y6170*yr9l 0.0176 0.0709 0.0263 0.0196 ybef6l*yr9l 0.1094 0.0856 0.0126 0.0237 wy6170*yr9l 0.0070 0.0703 -0.0126 0.0195 wybef6l*yr9l -0.0758 0.0860 -0.0147 0.0238 flJ*atl 0.9138 0.1065 -0.0804 0.0295 fb*quenm -0.0872 0. 1207 0.0139 0.0334 fl,*mont -0.0546 0.0658 0.0064 0.0182 flJ*ontnt 0.0908 0.0422 -0.0062 0.01 17 fij*prajr 0.0442 0.0465 -0.0068 0.0129 0,0148 0.0592 0.0165 0.0164 fl,*bcnv -0.0046 0.0620 -0.0092 0.0172 flJ*wa3034*yr81 0.0824 0.0900 -0.0099 0,0249 flJ*wa3539*yrgl 0.2203 0.1108 0.0241 0.0307 fl*wa4O44*yr81 0.1309 0.1281 0.0390 0.0355 flJ*wa4549*yr8l 0,1902 0.1462 0.0030 0.0405 fIJ*wa5O54*yi.81 0.0752 0.1730 0.0146 0.0479 fb*a3034*yr8l -0.0584 0.1061 0.0245 0.0294 218 Appendix 2 cont. DIFF LNTHRS Coefficient Variable* Coefficient Standard Error fb*a3539*yr8l -0.1455 0.1210 0.0241 0.0335 fIJ*a4044*yrgl -0.1478 0.1362 -0.0123 0.0377 fb*a4549*yr8l -0.0432 0.1488 0.0012 0.0412 fb*a5054*yr8l 0.0328 0.1655 0.0151 0.0458 fb*wa4044*yr9l -0.0077 0.0465 -0.0026 0.0129 fb*wa4549*yr9l -0.0780 0.0581 -0.0132 0.0161 flj*wa5054*yij.91 0.0094 0.0710 0.0026 0.0197 fb*wa5559*yr9l 0.0312 0.0894 0.0032 0.0247 flJ*wa6064*yr91 -0.0057 0.1318 0.0168 0.0365 fb*a4044*yr9l 0.0770 0.0563 0.0049 0.0156 fl,*a4549*yj91 0.0436 0.0640 0.0054 0.0177 fb*a5054*yij.91 0.1196 0.0724 -0.0063 0.0201 fb*a5559*yr9l 0.0522 0.0840 0.0056 0.0233 fb*a6064*yr9l 0.0914 0.1045 -0.0088 0.0289 fl,*bjfths 0.0099 0.0120 -0.0026 0.0033 fl*bih9 0.0595 0.0463 0.0169 0.0128 fjJ*edO8 0.1100 0.0611 0.0308 0.0169 fb*ed913 0.0490 0.0540 0.0118 0.0150 fIJ*edps 0.0826 0.0454 0.0125 0.0126 fl,*edbach -0.0018 0.0596 0.0249 0.0165 fb*edgrad 0.0458 0.0761 0.0091 0.0211 219 Standard Error Appendix 2 cont, DIFF Variable* Coefficient Standard Error LNTHRS Coefficient Standard Error fb*wed08 -0.0999 0.0599 -0.0236 0.0166 3*wed913 1 f -0.1089 0.0453 -0.0175 0.0126 ffi*wedps -0.0230 0.0380 -0.0017 0.0105 fIJ*wedbach 0.0029 0.0572 0.0028 0.0158 fb*wedgrad 0.0561 0.0929 -0.0233 0.0257 fl*kidsO5 0.0481 0,0468 0.0125 0.0130 flJ*klplus 0.1957 0.0877 0.0127 0.0243 fb*k2plus -0.0558 0.0763 0.0184 0.0211 fl,*kjds614 0.0083 0.0209 -0.0009 0.0058 fIJ*freoff -0.0513 0.0986 -0.0317 0.0273 f13*bioff 0.0068 0.0534 -0,0223 0.0148 fb*othoff -0.6492 1.1826 0.0941 0.3274 flj*wfreoff 0.1067 0.0941 0.0218 0.0260 fb*wbjloff 0.1074 0.0535 0.0026 0.0148 fb*wothoff 0.9452 0.8376 -0.0566 0.2319 fb*oscj 0.0841 0.0476 0.0284 0.0132 fb*oteach -0.0238 0.073 1 0.0264 0.0202 fb*ocler -0.0013 0.0591 0.0308 0.0164 fb*osserv -0.0302 0.0444 0.0024 0.0123 fla*oprproc 0.0521 0.0441 0.0096 0.0122 fb*oconstr 0.1692 0.0605 0.0356 0.0168 220 Appendix 2 cont, DIFF LNTHRS Coefficient Variable* Coefficient Standard Error fb*otroth 0.0454 0.0518 0.0284 0.0143 0.4559 0.1367 0.1967 0.0378 flJ*pñm 0.1659 0.1012 0.0449 0.0280 flJ*manuf -0.0793 0.0494 0.0273 0.0137 flJ*constr -0,0044 0.0685 0.0202 0.0190 fIJ*transp -0.0966 0.0572 0.0514 0.0158 flo*trarje -0.0257 0.0522 0.0187 0,0145 fl*finance -0.1424 0.0680 0.0177 0.0188 fb*public -0.0690 0.0591 0.0320 0.0164 fb*othind 0.0041 0.0572 0.0056 0.0158 f1*j 0.0621 0.0549 0.0358 0.0152 flJ*woteach 0.0289 0.0687 0.0435 0.0190 fIJ*wocler -0.0061 0.0458 0.0306 0.0127 flJ*wossep,r -0.0432 0.0506 0.0223 0.0140 flj*woprp -0.0300 0.0695 0.0440 0.0192 fIJ*wotroth 0.0005 0.0826 0.0685 0.0229 -0.2344 0.1432 -0.0074 0.0396 flJ*wpan 0.0779 0.0531 0.0007 0.0147 fjj*wconstr -0.0435 0.1006 0.0563 0.0278 -0.0426 0.0709 0.0131 0.0196 -0.0539 0.0457 0.0185 0.0126 221 Standard Error Appendix 2 cont. DIFF LNTHRS Coefficient Variable* Coefficient Standard Error flj*wfinance -0.0224 0.0547 0.0410 0.0152 fl,*wpublic -0.0630 0.0618 0.0361 0.0171 fl,*wothjfld -0.0849 0.043 1 0.0175 0.0119 intercept 0.1641 0.0928 7.9542 0.0257 .0921 .0817 F 9.494 10.83 N 18 210 18 210 * Variable names preceded by the letter w are the wife’s variables. 222 Standard Error 0.069 (.009) -.0581 (.011) -3.262 (.097) -.0142 (.123) -.1151 (.110) .0254 (.145) -.1075 (.141) -.0844 (.132) Intercept A2534*HS*NB A2534*AHS*NB A3544*BHS*NB A3544*HS*NB A3544*AHS*NB -.0691 (.018) -.3298 (.223) (.026) (.306) A4554*AHS*NB -.0691 -.1272 A4554*HS*NB -.0691 (.018) -.0367 (.222) A4554*BHS*NB -.0648 (.014) -.0606 (.012) .0737 (.010) .0044 (.012) (1991) 1991 MU Expression KIDSO5 (.008) -.0101 (.011) -.0101 -.0101 (.008) (.005) -.0084 -.0101 (.006) -.0101 (.005) .0187 (.004) .0024 (.005) .0101 (.004) K1PLUS (1991) Results from Estimation of Equations Used to Generate Wife’s Euler Equation Data Appendix 3 (.050) -.6849 (.070) -.6985 -.6940 (.050) -.4953 (.030) -.5826 (.038) -.6205 (.033) (.027) .1351 .0861 (.031) (.013) -.0289 (.018) -.0289 -.0289 (.013) -.0238 (.008) -.0289 (.010) -.0289 (.009) .0326 (.007) .0136 (.008) .0289 (.006) .6985 (.023) K2PLUS (1991) KIDS614 (1991) “3 .0532 (.150) .0350 (.191) .0670 (.102) .0422 (.202) .0475 (.261) .0341 (.167) -.0774 (.432) -.3143 (.580) .1154 (.393) -.1285 (.206) -.2260 (.187) A2534*BHS*Y7180 A2534*HS*Y7180 A2534*AHS*Y7180 A3544*BHS*Y7180 A3544*HS*Y7180 A3544*AHS*Y7180 A4554*BHS*Y7180 A4554*HS*Y7180 A4554*AHS*Y7180 A2534*BHS*Y6170 A2534*HS*Y6170 1991 MU Expression .0390 (.021) -.0288 (.017) .0000 (.036) .0000 (.057) .0000 (.041) .0043 (.013) -.0043 (.024) -.0086 (.018) .0306 (.009) .0376 (.017) .0515 (.015) KIDSO5 (1991) .0063 (.009) -.0064 (.007) .0000 (.015) -.0000 (.024) -.0000 (.017) -.0017 (.006) .0000 (.010) .0000 (.008) -.0080 (.004) .0029 (.007) -.0025 (.006) K1PLUS (1991) Appendix 3 cont. .0340 (.056) -.0648 (.046) .0410 (.099) -.0000 (.154) .0431 (.110) .2020 (.036) .1029 (.065) .2499 (.048) .1588 (.024) .2153 (.046) .2186 (.040) KJDS614 (1991) -.0300 (.015) .0041 (.012) .0000 (.025) -.0000 (.028) -.0000 (.028) .0058 (.009) .0000 (.017) .0122 (.012) .0029 (.006) .0380 (.012) .0339 (.010) K2PLUS (1991) t\J I’) Ui -.0543 (.141) .0604 (.187) .0900 (.213) -.1873 (.144) .4853 (.296) .1220 (.540) .1010 (.318) .5603 (.495) -.1708 (.244) -.2906 (.182) .1463 (.216) A2534*AHS*Y6170 A3544*BHS*Y6170 A3544*HS*Y6170 A3544*AHS*Y6170 A4554*BHS*Y6170 A4554*HS*Y6170 A4554*AHS*Y6170 A2534*BHS*YBEF61 A2534*HS*YBEF61 534*AHS*YBEf61 A3544*BHS*YBEF61 1991 MU Expression -.0085 (.017) .0051 (.017) .0124 (.023) -.0464 (.027) .0000 (.028) .0000 (.047) .0000 (.029) -.0026 (.011) .0073 (.022) -.0009 (.015) -.0088 (.014) KIDSO5 (1991) .0000 (.007) -.0157 (.007) .0032 (.010) -.0101 (.011) .0000 (.012) -.0000 (.020) -.0000 (.012) -.0003 (.005) .0000 (.009) -.0000 (.006) -.0020 (.006) K1PLUS (1991) Appendix 3 cont. -.0011 (.047) .0403 (.045) -.0347 (.062) -.0508 (.073) .0123 (.075) -.0000 (.126) .0057 (.079) .1166 (.031) .1225 (.058) .0794 (.041) .0116 (.038) KIDS614 (1991) .0000 (.012) -.0180 (.016) -.0591 (.016) -.0175 (.019) .0000 (.019) -.0000 (.032) -.0000 (.020) .0033 (.008) .0058 (.015) -.0000 (.010) -.0169 (.010) K2PLUS (1991) M t\J * 45.02 13 954 1.362 13 954 F N Standard errors are in parentheses. .0785 .0026 .0000 (.040) 2 R -.0158 (.407) A4554*HS*YBEF61 .0000 (.024) .0000 (.026) .4670 (.315) A4554*BHS*YBEF61 -.0110 (.017) -.4083 (.291) -.1991 (.204) A3544*AHS*YBEF61 -.0043 (.028) KIDSO5 (1991) A4554*AHS*YBEF61 .0580 (.368) A3544*HS*YBEF61 1991 MU Expression 13 954 11.89 .0220 .0000 (.011) -.0000 (.017) -.0000 (.010) -.0017 (.007) .0000 (.012) K1PLUS (1991) Appendix 3 cont. 13 954 177.7 .2515 .0006 (.071) -.0000 (.107) -.0046 (.065) -.0416 (.047) .0037 (.075) KIDS614 (1991) 13 954 17.46 .0320 .0000 (.018) -.0000 (.027) -.0000 (.017) -.0051 (.012) .0000 (.019) K2PLUS (1991) I\) .0742 A2534*HS*NB -.0387 (.028) -.2640 (.032) -.2211 (.040) -.1916 (.031) -.2896 (.036) -.2989 (.057) -.2989 (.036) .0458 (.039) .0133 (.050) A2534*AHS*NB A3544*BHS*NB A3544*HS*NB A3544*AHS*NB A4554*BHS*NB A4554*HS*NB A4554*AHS*NB A2534*BHS*Y7180 A2534*HS*Y7180 .1009 (.033) .1489 (.025) -.093 1 (.024) -.093 1 (.037) -.093 1 (.023) -.0698 (.020) -.0774 (.026) -.0867 (.021) .0286 (.018) -.0023 (.023) .0931 (.015) .2989 (.024) Intercept (.035) K1PLUS (1981) KIDSO5 (1981) Appendix 3 cont. -.0734 (.101) -.1303 (.078) -.3909 (.073) -.5078 (.114) -.5009 (.072) .0226 (.061) .0896 (.080) (.064) -.0665 (.056) -.3939 -.2363 (.070) .7828 (.047) KIDS614 (1981) .0119 (.029) .0030 (.022) -.0723 (.021) -.0779 (.032) -.0725 (.021) -.0058 (.017) -.0474 (.023) -.0209 (.018) -.0535 (.016) -.0481 (.020) .0779 (.014) K2PLUS (1981) N) N) .1285 (.026) .1863 (.042) .2036 (.072) .0771 (.035) .0479 (.070) .0000 (.156) .0000 (.083) .1374 (.043) .0231 (.066) .1705 (.039) .0889 (.033) A2534*AHS*Y7180 A3544*BHS*Y7180 A3544*HS*Y7180 A3544*AHS*Y7180 A4554*BHS*Y7180 A4554*HS*Y7180 A4554*AHS*Y7180 A2534*BHS*Y6170 A2534*HS*Y6170 A2534*AHS*Y6170 A3544*BHS*Y6170 KIDSO5 (1981) .0078 (.021) -.0535 (.025) .0485 (.042) -.0353 (.028) .0000 (.054) .0000 (.101) .0000 (.045) .0551 (.023) -.0157 (.047) .0536 (.027) .0284 (.017) K1PLUS (1981) Appendix 3 cont. .1247 (.066) .3471 (.078) .2037 (.131)1 .4022 (.086) .0333 (.167) .2304 (.313) .3 124 (.140) .231 (.070) .1328 (.145) .1578 (.085) -.0068 (.052) KIDS614 (1981) .0657 (.019) -.0051 (.022) -.0298 (.038) -.0105 (.025) -.0056 (.048) .0000 (.089) .0280 (.040) .0107 (.020) .0656 (.041) .1151 (.024) .0068 (.015) K2PLUS (1981) .0515 A4554*AHS*Y6170 .0118 (.072) -.0113 (.082) -.0326 (.048) .0122 (.040) -.0447 (.073) -.0072 (.043) A2534*BHS*YBEF61 A2534*HS*YBEF61 A2534*AHS*YBEF61 A3544*BHS*YBEF61 A3544*HS*YBEF61 A3544*AHS*YBEF61 (.049) .1177 (.091) (.037) (.057) A4554*HS*Y6170 -.0000 -.0093 A4554*BHS*Y6170 -.0002 (.028) -.0157 (.047) -.0064 (.026) (.031) .0479 (.053) .1411 -.0578 (.047) .0000 (.032) .0000 (.059) .0296 (.020) .0922 (.030) A3544*AHS*Y6170 .0234 (.039) .0337 (.060) K1PLUS (1981) A3544*HS*Y6170 KIDSO5 (1981) Appendix 3 cont. .0011 (.087) .0388 (.146) .1126 (.079) .0083 (.096) -.0552 (.164) (.144) .0762 -.0256 (.098) -.0376 (.025) (.042) .0351 (.023) -.0405 .0390 (.027) .1117 (.047) .1599 (.041) -.0056 (.028) .0399 (.052) .0305 (.032) .0124 -.0282 (.017) .0276 (.034) K2PLUS (1981) (.182) (.113) .0140 .1334 (.060) .0046 (.121) KIDS614 (1981) w C * .0000 (.029) .0090 (.045) A4554*AHS*YBEF61 39.81 4616 52.73 4616 F Standard errors are in parentheses. N .1042 .1335 2 R .0000 (.058) .0000 (.089) A4554*HS*YBEF61 -.0000 (.026) .0075 (.041) K1PLUS (1981) A4554*BHS*YBEF61 KIDSO5 (1981) Appendix 3 cont. 4616 40.16 .1050 (.090) -.0910 -.1076 (.179) -.0086 (.081) KIDS614 (1981) 4616 12.25 .0346 -.0056 (.026) .0000 (.051) .0018 (.023) K2PLUS (1981) w -.0642 A4554*HS*NB -.2774 (.049) (.075) .0154 (.047) A4554*BHS*NB (.035) -.3828 A3544*AHS*NB (.015) -.0863 -.0863 (.023) -.0797 (.015) -.0644 (.011) (.015) -.0690 (.012) -.2128 (.046) -.0745 (.040) A3544*HS*NB A4554*AHS*NB .0695 (.010) -.0540 -.2941 (.034) A2534*AHS*NB A3544*BHS*NB -.0532 (.048) .0204 (.014) .0863 (.009) (.031) -3.125 A2534*HS*NB Intercept KIDSO5 (1991) 1991 MU Expression -.0086 (.006) -.0086 (.010) -.0086 (.006) (.005) -.0073 -.0062 (.006) (.005) -.0075 .0243 (.004) .0171 (.006) .0086 (.004) K1PLUS (1991) Results from Estimation of Reduced Form Equations Used to Generate Men’s Euler Equation Data Appendix 4 (.040) -.7554 -.7988 (.063) -.7747 (.040) -.4991 (.030) -.5174 (.041) (.034) -.6052 .0728 (.029) .0631 (.038) (.025) .8144 KIDS614 (1991) (.010) -.024 1 -.0288 (.016) -.0266 (.010) -.0152 (.008) -.0189 (.010) -.0241 (.009) (.007) .0407 .0147 (.010) .0289 (.006) K2PLUS (1991) (\J .3593 (.104) .1649 (.129) .1353 A4554*BHS*Y7180 A4554*HS*Y7180 A4554*AHS*Y7180 A2534*HS*Y6170 A2534*BHS*Y6170 .1523 (.034) A3544*AHS*Y7180 .0758 (.132) (.067) -.0456 (.065) .0945 (.078) .0035 .0711 (.037) .0240 (.023) .0000 (.023) .0000 (.050) -.0035 (.016) (.009) -.0086 .0000 (.010) .0000 (.021) .0000 (.012) (.028) .0000 (.004) -.0025 (.011) (.008) -.0066 .0108 (.011) .0223 (.027) .0252 (.018) (.004) (.010) (.030) .1023 (.060) -.0066 (.011) -.0059 .0376 .0418 (.026) (.008) .0179 K1PLUS (1991) .0182 (.092) -.0355 .0508 (.018) .2133 KIDSO5 (1991) (.075) A3544*HS*Y7180 A3544*BHS*Y7180 A2534*AHS*Y7180 A2534*HS*Y7180 A2534*BHS*Y7180 1991 MU Expression Appendix 4 cont. -.0108 (.102) .1562 (.062) .0744 (.062) .0558 (.137) .1492 (.076) .2365 (.029) .1386 (.073) .3140 (.050) (.026) .1929 .0928 (.072) (.050) .2210 KIDS614 (1991) .0676 (.026) .0153 (.016) (.016) -.0047 .0000 (.035) (.019) -.0022 (.007) .0140 .0099 (.019) .0138 (.013) (.007) .0049 (.018) .0555 (.013) .0243 K2PLUS (1991) r’J LJ (JJ -.0633 (.040) .0582 (.061) .1043 (.070) -.0023 (.028) .0687 (.082) -.0628 (.110) -.0513 (.063) -.2266 (.181) .0077 (.166) -.1078 (.038) -.0814 (.054) A2534*AHS*Y6170 A3544*BHS*Y6170 A3544*HS*Y6170 A3544*AHS*Y6170 A4554*BHS*Y6170 A4554*HS*Y6170 A4554*AHS*Y6170 A2534*BHS*YBEF61 A2534*HS*YBEF61 &534*ft.J{S*YBEF61 A3544*BHS*YBEF61 1991 MU Expression -.0028 (.018) .0119 (.020) .0223 (.044) .0618 (.047) .0103 (.018) -.0000 (.041) -.0009 (.021) .0077 (.010) -.0063 (.028) .0006 (.016) .0073 (.015) KIDSO5 (1991) -.0012 (.008) -.0143 (.008) -.0257 (.019) -.0086 (.020) .0000 (.008) -.0000 (.017) .0000 (.009) .0010 (.004) -.0025 (.012) -.0012 (.007) -.0075 (.006) K1PLUS (1991) Appendix 4 cont. .0520 (.050) .0507 (.054) .2193 (.122) .1486 (.129) .0541 (.050) .1120 (.112) .0400 (.058) .1244 (.028) .0546 (.076) .1490 (.043) .0005 (.042) KIDS614 (1991) -.0002 (.013) .0175 (.014) -.0112 (.031) .0823 (.033) -.0047 (.013) -.0000 (.029) .0092 (.015) .0001 (.007) .0121 (.019) .0046 (.011) -.0223 (.011) K2PLUS (1991) N) * (.017) .0730 30.53 13 954 (.054) .0026 1.362 13 954 2 R F N Standard errors are in parentheses. .0027 .0000 (.038) (.111) -.0066 (.017) -.0244 (.056) -.0113 -.0063 (.015) .0090 (.041) KIDSO5 (1991) .0775 A4554*AHS*YBEF61 A4554*HS*YBEF61 A4554*BHS*YBEF61 .1913 A3544*AHS*YBEF61 (.054) -.0235 (.077) A3544*HS*YBEF61 1991 MU Expression 13 954 6.51 .0165 -.0000 (.007) .0000 (.016) (.007) .0000 (.006) .0050 (.017) -.0025 K1PLUS (1991) Appendix 4 cont. 13 954 107.8 .2177 -.0075 (.047) .0177 (.103) (.046) .0047 (.040) .0223 .0714 (.111) KJDS614 (1991) 13 954 11.0 .0276 -.0047 (.012) .0000 (.026) (.012) -.0022 -.0042 (.010) -.0099 (.028) K2PLUS (1991) (\j C.) Ui .1065 (.018) .2747 (.028) .0730 (.046) -.0049 (.032) -.1699 (.036) -.1376 (.046) -.1044 (.033) -.2400 (.036) -.2423 (.056) -.2579 (.036) .0816 (.053) .2239 (.078) Intercept &534*HS*NB A2534*AHS*NB A3544*BHS*NB A3544*HS*NB A3544*AHS*NB A4554*BHS*NB A4554*HS*NB A4554*AHS*NB A2534*BHS*Y7180 A2534*HS*Y7180 .0479 (.050) .1515 (.034) -.1065 (.023) -.1065 (.036) -.0992 (.023) -.0570 (.021) -.0870 (.029) -.0923 (.023) .0192 (.020) -.0132 (.029) K1PLUS (1981) KIDSO5 (1981) Appendix 4 cont. -.1394 (.155) -.1751 (.105) -.2430 (.071) -.3390 (.110) -.2259 (.071) .2088 (.065) .1935 (.090) .1478 (.071) -.2808 (.063) -.2245 (.090) .6493 (.055) KIDS614 (1981) .0375 (.044) .0248 (.030) -.0273 (.020) -.0563 (.031) -.038 1 (.020) .0166 (.019) -.0281 (.026) .0261 (.020) -.0407 (.018) -.0563 (.026) .0563 (.016) K2PLUS (1981) (%j (j .2788 (.119) .1097 (.043) .1036 (.040) 4534*pJS*Y6170 A3544*BHS*Y6170 .0321 (.026) -.0085 (.028) -.0933 (.076) .0247 (.042) .2534 .2463 (.079) .1412 (.085) .4752 (.235) (.130) .2012 (.109) (.035) (.055) (.065) .2792 .0194 .3595 (.263) (.116) .1317 .0643 (.022) -.0036 (.024) .0000 (.067) (.037) .0229 (.031) -.0290 (.075) .0000 (.033) .1402 .0455 (.017) .0900 (.049) .1600 (.059) (.172) .1041 .0154 (.027) (.015) (.054) .1615 (.093) -.0015 K2PLUS (1981) -.0463 KIDS614 (1981) .0196 (.133) P534*HS*Y6170 &534*BHS*Y617O A4554*AHS*Y7180 .1104 (.085) -.0324 (.038) (.058) A4554*HS*Y7180 .0127 .1089 A4554*BHS*Y7180 (.056) (.087) .0519 (.019) -.0195 .1804 .0941 (.030) .1088 (.030) .1732 (.047) .0371 (.017) .1228 (.027) K1PLUS (1981) A3544*AHS*Y7180 A3544*HS*Y7180 A3544*BHS*Y7180 A2534*AHS*Y7180 KIDSO5 (1981) Appendix 4 cont. M w .0615 A3544*AHS*Y6170 .0144 (.051) .1417 (.117) -.0109 (.038) A3544*BHS*YBEF61 A3544*HS*YBEF61 A3544*AHS*YBEF61 .0384 (.035) .0285 (.055) A2534*AHS*YBEF61 -.0238 (.025) .0707 (.075) .0028 (.033) .0312 (.093) .0963 (.145) A2534*HS*YBEF61 .1403 (.120) .0065 (.024) -.0302 (.187) .0532 (.037) .0000 (.068) (.027) .0113 .0166 (.018) -.0195 (.056) K1PLUS (1981) A2534*BHS*YBEF61 A4554*AHS*Y6170 .0866 A4554*HS*Y6170 (.105) .0263 (.043) A4554*BHS*Y6170 (.027) .0692 (.087) A3544*HS*Y6170 KIDSO5 (1981) Appendix 4 cont. .0439 .1670 (.076) -.2030 (.232) .2746 (.102) (.109) .1567 -.0007 (.287) -.1389 (.370) .1892 (.074) (.209) -.0294 (.022) -.0283 (.066) .0915 (.029) (.031) -.0157 .0000 (.081) (.105) .1882 (.021) .0028 .0000 (.059) .0183 (.024) (.015) .0451 (.085) -.0179 .0248 -.0283 (.049) K2PLUS (1981) (.054) .5317 (.173) KIDS614 (1981) * .0573 8.0 4616 .1086 15.9 4616 2 R F N Standard errors are in parentheses. .0045 (.021) .0000 (.062) .0104 (.033) (.097) -.0324 .0029 (.022) .0144 (.034) (1981) (1981) A4554*AHS*YBEF61 A4554*HS*YBEF61 A4554*BHS*YBEF61 K1PLUS KIDSO5 Appendix 4 cont. 4616 15.6 .1068 (.065) .0349 (.192) -.0369 (.068) .0468 KIDS614 (1981) 4616 5.5 .0401 -.0162 (.019) .0517 (.055) (.019) -.0077 (1981) K2PLUS Appendix 5 First Stage Estimates Corrected for Participation Selection, for the Two Stage Least Squares Estimation of MRS Function DIFF LNTHRS Variable* Coefficient Standard Error Coefficient Standard Error ati -0.01 17 0.0438 0.0266 0.0120 quenm -0.1163 0.0561 0.0015 0.0154 mont -0.0861 0.0535 0.0037 0.0147 ontnt -0.0160 0.0345 -0.0042 0.0095 prair -0.0559 0,0361 -0.0206 0.0099 vanc -0.0748 0.0502 -0.0078 0.0138 bcnv 0.0100 0.0483 0.0015 0.0133 wa3034*yr8l -0.0230 0.0624 -0.0082 0.0172 wa3539*yr8l -0.1722 0.0811 -0.0360 0.0223 wa4044*yr8l -0.0466 0.0952 -0.0400 0.0262 wa4549*yr8l -0.1321 0.1136 -0.0286 0.0312 wa.5054*yr8l -0.1048 0.1419 -0.0628 0.0390 a3034*yr8l 0.0475 0.0670 -0.0225 0.0184 a3539*yr8l 0.1259 0.0805 -0.0328 0.0221 a4044*yr8l 0.1517 0,0944 0.0039 0.0259 a4549*yr8l 0.1020 0.1052 0.0067 0.0289 a5054*yr8l 0.1047 0.1182 0.0046 0.0325 wa4044*yr9l -0.0142 0.0325 -0.0137 0.0089 wa4549*yr9l -0.0095 0,0428 -0.0081 0,0118 239 Appendix 5 cont, DIFF Variable* Coefficient LNTHRS Standard Error Coefficient Standard Error wa5054*yr9l -0.0394 0.0570 -0.0255 0.0157 wa5559*yr9l -0.0552 0.0854 -0.0174 0.0235 wa6064*yr9l -0.0260 0.1427 -0.0405 0.0392 a4044*yr9l 0.0098 0.0323 -0.0033 0.0089 a4549*yr9l 0.0175 0.0398 -0.0077 0.0109 a5054*yr9l -0.0422 0.0480 0.0134 0.0132 a5559*yr9l -0.0504 0.0599 0.0089 0.0165 a6064*yr9l -0.0990 0.0781 0.0545 0.0215 births 0.0296 0.0081 -0.0043 0.0022 birth9 -0.0383 0.03 14 -0.0112 0.0086 edO8 -0.1277 0.0403 0.0092 0.0111 ed9l3ng -0.0559 0.0322 0.0075 0.0089 edps 0.0001 0.0289 -0.0059 0.0079 edbach 0.1180 0.0438 -0,0256 0.0120 edgrad 0.2352 0.0597 -0.0429 0,0164 wed08 0.1291 0.0635 -0.0023 0.0175 wed9l3ng 0.0980 0.0325 -0.0084 0.0089 wedps -0.1469 0.0324 -0.0033 0.0089 wedbach -0.4118 0,0498 0.0075 0,0137 wedgrad -0.5741 0.0810 0.0170 0.0223 240 Appendix 5 cont. DIFF Variable* Coefficient LNTHRS Standard Error Coefficient Standard Error kids05 -0.1618 0.0504 -0.0156 0.0139 kiplus -0.2871 0.1104 -0.0436 0.0303 k2plus 0.0670 0.0652 -0.0223 0.0179 kids6l4 -0.0238 0.0185 -0.0072 0.0051 freoff 0.0582 0.053 1 0.0155 0.0146 biloff 0.0268 0.0365 0.0023 0.0100 othoff 0.5669 1.1939 -0.1111 0.3283 wfreoff 0.0092 0.0529 0.0260 0.0145 wbiloff 0.0107 0,0371 0.0182 0.0102 wothoff -0.8900 0.8450 0.0813 0.2323 osci -0.0451 0.0341 0.0544 0.0094 oteach 0. 1715 0.0497 0.0977 0.0137 ocler -0.2196 0.0416 0.0710 0.0114 osserv -0.1473 0.0295 0.0309 0.0081 oprproc -0.1126 0.0311 0.0643 0.0085 oconstr -0.0763 0.0418 0.0698 0.0115 otroth -0.1458 0.0346 0.0423 0,0095 agric -0.5580 0.0766 -0.3336 0.0211 prim 0.3474 0.0633 -0.0008 0.0174 manuf 0.2170 0.0388 -0.0109 0.0107 241 Appendix 5 cont. DIFF Variable* Coefficient LNTHRS Standard Error Coefficient Standard Error constr 0.0837 0.0474 0.0150 0.0130 transp 0.2703 0.0428 -0.0309 0.0118 trade 0.0113 0.0375 -0.0446 0.0103 finance 0.1699 0.0484 -0.0090 0.0133 public 0.2367 0.0380 0.0231 0.0105 othind -0.0104 0.0421 0.0147 0.0116 yr9l -0.0325 0.0864 -0.0036 0.0238 nb 0.0026 0.1122 0.0523 0.0308 nyr9l 0.0696 0.1009 -0.0175 0.0277 y6l7O 0.0574 0.0658 -0.0375 0.0181 ybef6l -0.0420 0.0821 -0.0318 0.0226 wy6170 -0.0888 0.0620 0.0125 0.0170 wybef6l -0.1208 0.0760 -0.0054 0.0209 y6l7O*yr9l 0.0322 0.0727 0.0255 0.0200 ybef6l*yr9l 0.1111 0.0885 0.0130 0.0243 wy6170*yr9l 0.0045 0.0714 -0.0111 0.0196 wybef6l*yr9l -0.0730 0.0871 -0.0143 0.0239 fb*atl 0.3037 0.1081 -0.0859 0.0297 fl,*quepm -0.0749 0.1220 0.0077 0.0335 fb*mont -0.0576 0.0663 0.0087 0.0182 242 Appendix 5 cont. DIFF Variable* Coefficient LNTHRS Standard Error Coefficient Standard Error fb*ontnt 0.0920 0.0432 -0.0132 0.0119 fb*prair 0.0399 0.0469 -0.0064 0.0129 0.0155 0.0597 0.0158 0.0164 fb*bcnv -0.0029 0.0625 -0.0120 0.0172 flJ*wa3O34*yi.81 0.0752 0.0910 -0.0097 0.0250 fb*wa3539*yr8l 0.2221 0.1126 0.0275 0.0310 fb*wa4044*yr8l 0.1355 0.1295 0.0401 0.0356 flj*wa4549*yr8l 0.1971 0.1480 0.0078 0.0407 fb*wa5054*yr8l 0.0853 0.1757 0.0260 0.0483 fb*a3034*yrgl -0.0603 0.1080 0.0315 0.0297 fb*a3539*yr8l -0.1473 0.1227 0.0285 0.0337 fb*a4044*yr8l -0.1540 0.1382 -0.0081 0.0380 fb*a4549*yr8l -0.0541 0.1510 0.0063 0.0415 fl3*a5054*yr81 0.0249 0.1679 0.0147 0.0462 flJ*wa4044*yr91 -0.0155 0.0473 0.0026 0,0130 fb*wa4549*yr9l -0.0953 0.0590 -0.0088 0.0162 fIJ*wa5O54*yj91 -0.0091 0.0719 0.0088 0.0198 fb*wa5559*yr91 0.0202 0.0907 0.0109 0.0249 flj*wa6O64*yj91 -0.0321 0.1353 0.0269 0.0372 fl,*a4044*yr91 0.0798 0.0570 0.0008 0.0157 243 Appendix 5 cont. DIFF LNTHRS Variable* Coefficient Standard Error Coefficient Standard Error fb*a4549*yr9l 0.0557 0.0648 0.0018 0.0178 fIJ*a5054*yj.91 0.1413 0.0732 -0.0087 0.0201 fb*a5559*yr91 0.0743 0.0849 0.0031 0.0234 fl,*a6o64*yj91 0.1191 0.1060 -0.0183 0.0291 fb*births -0.0162 0.0123 -0.0030 0.0034 fb*birth9 0.0606 0.0470 0.0159 0.0129 fl,*edO8 0.1401 0.0621 0.0339 0.0171 fIJ*ed913 0.0634 0.0547 0.0145 0.0150 fb*edps 0.0989 0.0464 0.0169 0.0128 fIJ*edbach 0.0185 0.0611 0.0296 0.0168 lb*edgrad 0.0643 0.0769 0.0103 0.0212 flJ*wed08 -0.1012 0.0633 -0.0159 0.0174 fIJ*wed9l3 -0.1163 0.0458 -0.0152 0.0126 fIJ*wedps -0.0066 0.0386 -0.0056 0.0106 fb*wedbach 0.0612 0.0540 -0.0031 0.0148 fb*wedgrad 0.1064 0.0914 -0,0268 0.0251 fb*kidsO5 0.0506 0.0476 0.0163 0.0131 fb*klplus 0.2092 0.0906 0.0160 0.0249 fb*k2plus -0.0587 0.0781 0.0242 0.0215 fb*kids6l4 0.0118 0.0215 0.0010 0.0059 244 Appendix 5 cont. DIFF Variable* Coefficient LNTHRS Standard Error Coefficient Standard Error fb*freoff -0.0642 0.0998 -0.03 10 0.0274 fb*biloff -0.0049 0.0540 -0.0242 0.0148 fb*othoff -0.5604 1.1966 0.1536 0.3290 fb*wfreoff 0.1142 0.0950 0.0251 0.0261 fb*wbiloff 0.1123 0.0540 -0.0004 0.0149 fl*wothoff 0.8 158 0.8480 -0.0897 0.2332 fl*cj 0.0827 0.0480 0.0323 0.0132 fIJ*oteach -0.022 1 0.0734 0.0337 0.0202 fb*ocler 0.0021 0.0595 0.0410 0.0164 fl,*ossep,r -0.0141 0.0447 0.0084 0.0123 flJ*oprproc 0.0619 0.0441 0.0168 0.0121 flJ*oconstr 0.1849 0.0610 0.0455 0.0168 fl,*otroth 0.0461 0.0520 0.0374 0.0143 0.3286 0.1214 0.1620 0.0334 fb*prim 0.1615 0.1031 0,0429 0.0284 flJ*manuf -0.0799 0.0493 0,0309 0.0136 flJ*constr -0.0290 0.0689 0.0247 0,0189 fb*transp -0.1029 0.0574 0.0567 0.0158 flJ*trje -0.0379 0.0518 0.0203 0.0142 flj*finance -0.1676 0.0677 0.0262 0.0186 245 Appendix 5 cont. DIFF LNTHRS Variable* Coefficient Standard Error Coefficient Standard Error fb*publjc -0.0863 0.0591 0.0401 0.0163 fb*othjnd -0.0239 0.0567 0.0121 0.0156 imr 0.0702 0.1364 0.0414 0.0375 intercept 0.3308 0.0881 7.9859 0.0242 2 R .0686 .0710 F 9.377 9.718 18 210 18 210 N * Variable names preceded by the letter w are the wife’s variables. 246 tJ —1 -.2113 (.182) -.2221 (.183) -.0011 (.183) -.3186 (.298) -.5607 (.241) A3544*HS*NB A3544*AHS*NB A4554*BHS*NB A4554*HS*NB A4554*AHS*NB -.2306 (.144) A2534*AHS*NB .0498 (.167) -.05 10 (.169) A2534*HS*NB A3544*BHS*NB 0.0804 (.005) -3.895 (.119) Intercept -.0778 (.011) -.0804 (.014) -.0787 (.009) -.0699 (.007) -.0772 (.009) -.0746 (.008) .0782 (.006) .0193 (.007) KIDSO5 (1991) 1991 MU Expression -.0133 (.005) -.0133 (.007) -.0133 (.005) -.0119 (.004) -.0133 (.004) -.0133 (.004) .0344 (.003) .0043 (.004) .0133 (.003) K1PLUS (1991) Results from Estimation of Equations Used to Generate Wife’s Euler Equation Data Appendix 6 -.7157 (.028) -.7289 (.037) -.7186 (.024) -.5194 (.019) -.6035 (.024) -.6305 (.020) .1139 (.016) .0860 (.019) 0.7289 (.014) KIDS614 (1991) -.0850 (.013) -.0923 (.019) -.0834 (.011) -.0023 (.011) -.0439 (.014) -.0274 (.011) -.0656 (.010) -.0644 (.012) .0923 (.008) K2PLUS (1991) (‘J .0014 (.190) -.0081 (.272) .1179 (.161) .0137 (.244) -.0176 (.372) .0530 (.267) -.0270 (.335) -.4474 (.604) -.0852 (.526) .1467 (.252) -.4251 (.276) A2534*BHS*Y7180 A2534*HS*Y7180 A2534*AHS*Y7180 A3544*BHS*Y7180 A3544*HS*Y7180 A3544*AHS*Y7180 A4554*BHS*Y7180 A4554*HS*Y7180 A4554*AHS*Y7180 534*BHS*Y617O &,2534*HS*y617O 1991 MU Expression .0378 (.014) -.0111 (.012) -.0026 (.024) -.0000 (.034) .0017 (.020) .0047 (.009) -.0032 (.016) .0001 (.011) .0302 (.006) .0366 (.011) .0908 (.010) KIDSO5 (1991) Appendix 6 cont. .0036 (.007) -.0083 (.005) .0000 (.012) -.0000 (.016) -.0000 (.010) .0005 (.005) -.0000 (.008) .0029 (.006) -.0205 (.003) .0158 (.006) .0013 (.005) K1PLUS (1991) .0053 (.037) -.0977 (.027) .0285 (.061) -.0000 (.088) .0388 (.051) .2055 (.025) .0783 (.042) .2262 (.029) .1556 (.016) .1549 (.030) .2402 (.025) KIDS614 (1991) .0107 (.026) -.0153 (.015) .0303 (.035) .0000 (.053) .0323 (.026) .0018 (.014) .0764 (.029) .0922 (.017) .0014 (.011) .0219 (.019) -.0370 (.014) K2PLUS (1991) I’J .3136 (.217) .2944 (.532) .1062 (.375) A4554*BHS*Y6170 A4554*HS*Y6170 A4554*AHS*Y6170 .0054 -.0058 (.010) .0625 (.237) A3544*BHS*YBEF61 .0125 (.012) -.4403 (.291) p.,534*,}IS*yBEF61 .0058 (.016) -.3167 (.372) -.0201 (.018) -.0000 (.026) -.0017 (.014) -.0011 (.008) (.014) &.534*HS*yBEF61 (.700) .7167 (.017) -.2632 (.227) A3544*AHS*Y6170 A2534*BHS*YBEF61 -.0026 .0588 (.278) A3544*HS*Y6170 -.0010 (.009) .1131 (.212) A3544*BHS*Y6170 -.0128 (.010) -.0798 (.221) KIDSO5 (1991) A2534*AHS*Y6170 1991 MU Expression Appendix 6 cont. .0000 (.005) -.023 1 (.026) .0187 (.031) (.041) -.0215 (.006) -.0095 .0041 -.0651 (.047) .0045 (.044) -.0000 (.068) .0022 (.037) .1014 (.021) (.008) -.0047 (.009) .0000 (.008) -.0000 (.013) -.0000 (.007) -.0002 (.004) .1117 (.037) (.024) (.004) -.0000 (.007) .0654 -.0039 (.026) KIDS614 (1991) .0000 (.005) -.0068 K1PLUS (1991) -.0287 (.015) .0217 (.020) .0626 (.027) (.025) .1412 .0023 (.020) .0260 (.033) .0000 (.019) -.0292 (.012) .0047 (.023) (.012) .0755 .0034 (.015) K2PLUS (1991) N) ()1 C * .1487 .4086 (.310) A4554*AHS*YBEF61 Standard errors are in parentheses. N F 13 954 -.0467 (.380) A4554*HS*YBEF61 2 R .3121 (.223) (.310) -.3705 (.454) A4554*BHS*YBEF61 A3544*AHS*YBEF61 A3544*HS*YBEF61 1991 MU Expression 13 954 -.0026 (.015) -.0000 (.022) .0004 (.011) -.0106 (.012) -.0032 (.017) KIDSO5 (1991) Appendix 6 cont. 13 954 .0000 (.007) -.0000 (.010) (.006) -.0000 (.006) -.0014 -.0000 (.008) K1PLUS (1991) 13 954 -.0046 (.040) -.0000 (.056) -.0040 (.029) -.0614 (.031) .0185 (.045) KJDS614 (1991) 13 954 (.018) -.0014 -.0000 (.030) -.0020 (.013) (.017) -.0256 (.027) .0943 K2PLUS (1991) r\.) Lii -.3368 (.033) -.3444 (.023) .05384 (.023) A4554*HS*NB A4554*AHS*NB A2534*BHS*Y7180 (.033) -.0109 -.3374 (.019) A4554*BHS*NB A2534*HS*Y7180 .1464 (.018) -.2106 (.019) A3544*AHS*NB .0500 (.025) (.045) -.1719 (.065) (.045) -.1307 -.4244 (.017) -.4836 (.064) (.038) -.5095 .0622 (.037) .0670 (.046) -.0104 (.036) (.033) -.3913 -.1880 (.039) .8204 (.026) KIDS614 (1981) -.1780 (.025) -.1780 -.1780 (.015) -.1237 (.014) -.1350 (.018) -.2260 (.024) A3544*HS*NB -.1616 (.014) -.2592 (.018) A3544*BHS*NB .0217 (.013) (.015) (.020) (.017) .0346 .0527 &534*HS*NB -.0533 .1780 (.010) .3468 (.013) Intercept A2534*AHS*NB K1PLUS (1981) KIDSO5 (1981) Appendix 6 cont. .1009 (.033) (.025) .1489 (.024) -.093 1 -.093 1 (.037) -.0931 (.023) -.0698 (.020) -.0774 (.026) -.0867 (.021) (.018) .0286 -.0023 (.023) (.015) .0931 K2PLUS (1981) L”J -.0000 (.045) -.0024 (.060) .0698 (.026) .0487 (.044) .1657 (.026) .0870 (.021) A4554*AHS*Y7180 A534*BHS*y617O A2534*HS*Y6170 A2534*AHS*Y6170 A3544*BHS*Y6170 .0034 (.016) -.0770 (.020) -.0321 (.033) -.0358 (.020) .0000 (.068) -.0100 (.091) A4554*HS*Y7180 .0000 (.033) .0561 .0367 (.018) .1018 (.038) (.024) -.0179 .1232 .1113 (.041) .3441 (.052) .1314 (.087) .0078 (.021) -.0535 (.025) .0485 (.042) -.0353 (.028) (.054) (.117) .3455 (.051) .0000 -.0354 .0000 (.101) (.178) (.045) .0000 (.023) .0551 (.047) -.0157 (.027) .0536 (.017) .0284 (1981) K2PLUS -.0807 (.087) .2835 (.047) .1490 (.099) .0189 .0685 (.056) .0645 (.022) .1184 (.029) (.050) (.035) .0346 (.014) .0988 -.0423 (1981) KIDS614 (.018) (1981) (1981) (.044) A4554*BHS*Y7180 A3544*AHS*Y7180 A3544*HS*Y7180 A3544*BHS*Y7180 A&534*AHS*Y718O K1PLUS KIDSO5 Appendix 6 cont. I’J 1-fl A3544*AHS*YBEF61 -.1266 (.091) -.0231 (.035) -.0304 (.030) (.046) -.0420 A3544*HS*YBEF61 -.0065 (.023) (.019) .0569 (.049) -.0056 .0048 (.025) A3544*BHS*YBEF61 -.0058 (.059) (.067) (.026) .0578 (.091) .1004 (.082) -.0018 .0248 (.067) (.112) -.0069 -.0210 (.046) .0736 (.063) .0005 .1267 (.035) -.0667 .0083 (.032) (.042) (.026) -.0205 -.0000 .0469 (.034) .0000 (.043) .0669 (.057) .0000 (.024) .1017 (.041) (.077) .0841 (1981) KIDS614 (.034) &.534*jJ{S*yBEF61 A2534*HS*YBEF61 A2534*BHS*YBEF61 A4554*AHS*Y6170 A4554*HS*Y6170 .0102 (.032) A4554*BHS*Y6170 .0031 (.016) (.030) .0898 (.021) -.0032 (.039) K1PLUS (1981) -.0033 A3544*AHS*Y6170 A3544*HS*Y6170 (1981) KIDSO5 Appendix 6 cont. -.0002 (.028) -.0157 (.047) -.0064 (.026) (.031) .0479 (.053) .1411 (.047) -.0578 (.032) .0000 .0000 (.059) (.037) -.0000 .0296 (.020) (.039) .0234 (1981) K2PLUS I’J * Standard errors are in parentheses. N F 2 R A4554*AHS*YBEF61 -.0100 A4554*HS*YBEF61 4616 .0036 (.030) (.052) .0049 (.023) A4554*BHS*YBEF61 KIDSO5 (1981) 4616 -.0000 (.023) .0000 (.039) .0000 (.017) K1PLUS (1981) Appendix 6 cont. 4616 4616 .0000 (.029) .0271 .0000 (.058) -.0000 (.026) K2PLUS (1981) (.059) (.102) -.1454 .0630 (.045) KIDS614 (1981) U’ .0996 (.006) -3.819 (.027) -.0561 (.043) -.2988 (.034) -.0633 (.034) -.2171 (.040) -.3977 (.03 1) -.0259 (.038) -.1503 (.058) -.3633 (.041) .1267 (.066) Intercept 534*HS*NB A2534*AHS*NB A3544*BHS*NB A3544*HS*NB A3544*AHS*NB A4554*BHS*NB A4554*HS*NB A4554*AHS*NB A2534*BHS*Y7180 .0921 (.013) -.0968 (.009) -.0945 (.015) -.0938 (.009) -.0754 (.007) -.0960 (.010) -.0843 (.008) .0736 (.007) .0158 (.010) KIDSO5 (1991) 1991 MU Expression .0214 (.006) -.0134 (.004) -.0134 (.007) -.0134 (.004) -.0104 (.004) -.0115 (.005) -.0110 (.004) .0371 (.003) .0198 (.005) .0134 (.003) K1PLUS (1991) .2541 (.033) -.7561 (.024) -.7866 (.038) -.7721 (.023) -.4911 (.019) -.5225 (.027) -.6039 (.021) .0961 (.019) .0726 (.025) .8121 (.016) KIDS614 (1991) Results from Estimation of Equations Used to Generate Husband’s Euler Equation Data Appendix 7 .0156 (.009) -.0409 (.007) -.0436 (.010) -.0413 (.006) -.0300 (.005) -.0320 (.007) -.0057 (.006) .0343 (.005) .0101 (.007) .0436 (.004) K2PLUS (1991) Ui .0039 (.027) .1309 A2534*AHS*Y7180 A3544*BHS*Y7180 .1416 (.104) .1517 (.060) -.0426 (.064) .0469 (.109) -.0847 (.040) A4554*AHS*Y7180 &,534*BHS*Y617O p.534*Hs*y617o A2534*AHS*Y6170 .0005 (.011) .0542 (.025) (.015) (.005) -.0176 -.0162 (.012) -.0023 (.007) (.015) .0116 .0000 (.007) -.0027 .0000 (.015) (.032) .0000 (.008) (.004) .0037 -.0019 (.009) -.0051 .0011 (.016) .3406 (.090) A4554*HS*Y7180 A4554*BHS*Y7180 .0172 (.007) .1498 (.030) A3544*AHS*Y7180 .0615 (.019) .1069 (.068) (.006) .0042 (.003) .0246 (.012) -.0152 .0416 .0002 (.009) K1PLUS (1991) (.007) .0847 (.018) KIDSO5 (1991) A3544*HS*Y7180 (.050) -.0584 (.082) A2534*HS*Y7180 1991 MU Expression Appendix 7 cont. -.0129 (.028) -.0372 (.066) .1546 (.039) (.038) .0622 (.083) .0233 .1312 (.043) (.019) .2444 (.049) .1438 .3267 (.031) .1713 (.018) (.048) .1570 KJDS614 (1991) -.0211 (.008) .0819 (.018) .0175 (.011) (.010) -.0027 (.022) .0000 -.0023 (.012) (.005) .0177 .0384 (.013) .0160 (.008) (.005) .0034 .0380 (.013) K2PLUS (1991) I’.j UI (.012) .0678 (.114) A3544*HS*YBEF61 (.007) (.014) .0326 (.024) -.0019 (.012) -.0024 (.006) -.0137 .0006 -.1554 (.039) -.0058 (.012) -.0029 (.016) .0059 (.033) -.0268 (.161) -.0781 (.048) (.015) A3544*BHS*YBEF61 -.0134 .0393 (.031) .0489 (.063) .0172 (.030) .0129 (.036) .2365 (.086) (.082) -.0116 (.017) (.008) -.0041 .0168 (.010) -.0234 (.023) (.022) .0675 (.008) .1046 -.0004 .0380 .0000 (.018) (.009) .0073 (.005) .0030 (.013) .0119 (.007) .0093 K2PLUS (1991) (.029) (.067) (.012) .0000 (.005) .0872 .0367 (.032) .1220 (.018) (.048) .0776 .1417 (.026) KIDS614 (1991) .0000 (.147) (.050) .0000 (.006) -.2123 -.0043 A4554*AHS*Y6170 A2534*BHS*YBEF61 .0064 (.011) .0973 (.098) -.0051 (.026) -.0025 .0945 (.003) (.057) -.0012 .0118 (.009) -.0019 (.005) -.0003 K1PLUS (1991) (.007) (.018) -.0106 (.024) -.0057 .0613 (.059) .0116 (.010) .0518 (.052) KIDSO5 (1991) A4554*HS*Y6170 A4554*BHS*Y6170 A3544*AHS*Y6170 A3544*HS*Y6170 A3544*BHS*Y6170 1991 MU Expression Appendix 7 cont. N) (ii * Standard errors are in parentheses. N 54.5 252.9 F (.043) .0560 .0000 .0096 (.010) .2161 .0862 A4554*AHS*YBEF61 -.0051 (.022) .0000 (.005) 2 R .0047 (.079) A4554*HS*YBEF61 (.009) -.0043 (.005) -.0113 (.041) A4554*BHS*YBEF61 .0041 (.005) (.010) K1PLUS (1991) -.0005 KIDSO5 (1991) -.0012 (.010) .1682 (.044) A3544*AHS*YBEF61 1991 MU Expression Appendix 7 cont. 1519 .6235 (.026) 99.9 .0982 (.007) -.0027 (.016) (.058) -.0174 .0000 (.007) -.0009 -.0017 (.007) K2PLUS (1991) .0130 (.024) -.0011 -.0042 (.026) KJDS614 (1991) t\.) Ui ‘.0 -.3694 A3544*AHS*NB .0509 (.070) .2664 A2534*BHS*Y7180 &534*HS*Y718O (.127) -.3517 (.047) A4554*AHS*NB -.1965 -.0025 (.039) (.102) -.1830 (.067) -.2726 (.043) -.3590 (.068) -.2847 (.042) .2378 (.040) .1926 (.026) -.1663 (.017) -.1726 (.026) (.016) -.2364 (.074) -.1655 (.045) -.0944 (.015) .2094 (.055) (.021) .0419 (.030) -.0166 (.020) -.0471 (.013) (.020) -.0704 -.0464 (.013) .008 1 (.013) (.016) -.0095 .0209 (.013) (.044) -.0458 (.012) (.016) -.0591 .0704 (.010) K2PLUS (1981) .1544 -.2770 (.039) -.2062 (.054) .7072 (.034) KIDS614 (1981) -.1333 -.1308 (.017) -.0737 A4554*HS*NB A4554*BHS*NB -.2004 (.056) A3544*HS*NB (.044) -.0784 (.048) A3544*BHS*NB (.021) (.052) .0580 (.015) .0557 -.0299 A2534*HS*NB -.1606 (.042) .1726 (.013) -3.783 (.037) Intercept A2534*AHS*NB K1PLUS (1981) KIDSO5 (1981) Appendix 7 cont. (“j C .1092 (.024) .1548 A3544*BHS*Y7180 .1851 (.049) .0255 (.019) .0261 (.052) A3544*BHS*Y6170 .1263 (.056) -.0101 (.022) (.056) -.0109 .3358 (.140) &534*AHS*y617O (.054) -.0155 .2213 (.080) .2340 (.235) .0690 (.03 1) (.074) (.027) (.100) -.1591 .1463 (.070) .0063 .1287 .0533 (.015) .0011 (.017) -.0113 (.042) (.024) -.0230 .0132 (.021) .0000 (.058) .2554 (.195) .0994 (.075) .4072 (.024) .1236 (.012) .0502 .0919 (.036) .0036 (.019) -.0140 (.011) (1981) K2PLUS (.081) (.152) (.031) (.130) .1996 A2534*HS*Y6170 A2534*BHS*Y6170 A4554*AHS*Y7180 A4554*HS*Y7180 .0093 .3324 (.039) A4554*BHS*Y7180 -.0462 .0500 (.015) .2350 (.048) A3544*AHS*Y7180 (.120) .0092 -.0393 (.046) .5150 (.148) .1340 (.064) -.0968 (.036) (1981) KIDS614 A3544*HS*Y7180 (.070) .0177 (.014) .0671 (.036) (1981) (1981) A2534*AHS*Y7180 K1PLUS KIDSO5 Appendix 7 cont. .2290 -.0026 (.126) -.0144 (.107) .0621 (.114) .2007 (.090) .0132 (.098) .1191 (.051) b534*HS*yBEF61 ft534*AHS*yBEF61 A3544*BHS*YBEF61 A3544*HS*YBEF61 A3544*AHS*YBEF61 -.0292 (.019) .0762 (.057) .0073 (.024) -.0484 (.026) -.1038 (.087) .2637 (.057) (.051) L&.2534*BHS*YBEF61 .0028 (.018) -.0475 .0906 (.048) .0152 (.148) .1682 (.063) .1555 (.068) -.0769 (.225) .1109 (.148) (.048) .1937 .2755 (.139) .0000 (.054) .1567 (.114) A4554*HS*Y6170 A4554*AHS*Y6170 .0902 (.054) .0118 (.021) (.034) .0023 (.107) .0593 (.056) .0188 (.013) .0806 (.036) .0393 (.041) .1810 (1981) (1981) (.138) KIDS614 K1PLUS A4554*BHS*Y6170 A3544*AHS*Y6170 A3544*HS*Y6170 KIDSO5 (1981) Appendix 7 cont. -.0004 (.014) -.0609 (.044) .0978 (.019) -.0246 (.020) -.0113 (.067) .0534 (.044) (.014) .0076 (.041) .0466 (.016) .0229 -.0062 (.010) (.032) -.0071 (1981) K2PLUS I’J * 38.4 43.5 F Standard errors are in parentheses. N .1009 .1127 2 R -.0007 (.016) .0000 (.046) -.0596 (.105) .0837 (.042) .0040 (.015) .0179 (.044) K1PLUS (1981) A4554*AHS*YBEF61 A4554*HS*YBEF61 A4554*BHS*YBEF61 KIDSO5 (1981) Appendix 7 cont. 37.7 12.0 .0340 (.012) (.040) .0993 -.0078 .0767 .0634 (.036) .0512 -.0071 (.012) K2PLUS (1981) (.119) .1109 (.040) KIDS614 (1981)
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The labour market adjustment of immigrant families Worswick, Christopher 1995
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Title | The labour market adjustment of immigrant families |
Creator |
Worswick, Christopher |
Date Issued | 1995 |
Description | In this thesis, I analyze the labour market adjustment of immigrant families to Canada. The focus of the analysis is on measuring the effects of credit constraints on the labour market behaviour of immigrant family members. Results from the estimation of reduced-form wage, hours and weeks equations indicate that immigrant women face lower wages than similar non-immigrant women, and at the same time work longer hours. Over the 1980s, immigrant women had higher growth in wages and the same growth in hours as non-immigrant women. This could be explained by the immigrant women’s hours being higher in 1980 due to credit constraints, and the immigrant family not needing to borrow in 1990 due to the high wage growth over the decade. While credit constraints can explain the observed differences in labour supply, an alternative explanation is that family preferences towards labour supply differ between immigrant and non-immigrant families. A structural labour supply model is developed in which families choose hours of work for the husband and wife, and family consumption in each time period allowing for credit constraints and uncertainty. The results of the estimation indicate that it is differences in family preferences over labour supply, and not credit constraints, which lead to the observed differences in labour supply between immigrant and non-immigrant families. Immigrant families have a lower disutility to the wife’s labour supply than non-immigrant families. The results do not support the hypothesis that immigrant families are more likely to be credit constrained than non-immigrant families. Labour supplies in young families appear to be affected by credit constraints; however, this effect is no larger in immigrant families than in non-immigrant families. |
Extent | 4765402 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-04-22 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0088317 |
URI | http://hdl.handle.net/2429/7464 |
Degree |
Doctor of Philosophy - PhD |
Program |
Economics |
Affiliation |
Arts, Faculty of Vancouver School of Economics |
Degree Grantor | University of British Columbia |
Graduation Date | 1995-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
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