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The labour market adjustment of immigrant families Worswick, Christopher 1995

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THE LABOUR MARKET ADJUSTMENT OF IMMIGRANT FAMILIESbyCHRISTOPHER WORSWICKB.A. (Honours), Queen’s University, 1990M.A., The University of British Columbia, 1991A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDepartment of EconomicsWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMay 1995© Christopher Worswick, 1995In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis br scholarly purposes may be ‘granted by the head of mydepartment or by his or her representatives. it is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of ,é-’ cJ/1 C, rThe University of British ColumbiaVancouver, CanadaDate /v /4L /‘DE.6 (2/88)ABSTRACTIn 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 marketbehaviour of immigrant family members.Results from the estimation of reduced-form wage, hours and weeks equations indicatethat immigrant women face lower wages than similar non-immigrant women, and at the sametime work longer hours. Over the 1980s, immigrant women had higher growth in wages and thesame growth in hours as non-immigrant women. This could be explained by the immigrantwomen’s hours being higher in 1980 due to credit constraints, and the immigrant family notneeding to borrow in 1990 due to the high wage growth over the decade. While creditconstraints can explain the observed differences in labour supply, an alternative explanation isthat family preferences towards labour supply differ between immigrant and non-immigrantfamilies.A structural labour supply model is developed in which families choose hours of workfor the husband and wife, and family consumption in each time period allowing for creditconstraints and uncertainty. The results of the estimation indicate that it is differences in familypreferences over labour supply, and not credit constraints, which lead to the observed differencesin labour supply between immigrant and non-immigrant families. Immigrant families have alower disutility to the wife’s labour supply than non-immigrant families. The results do notsupport the hypothesis that immigrant families are more likely to be credit constrained than nonimmigrant 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.11TABLE OF CONTENTSAbstractTable of Contents iiiList of Tables vList of Figures viiAcknowledgement viiiChapter One Introduction 1Chapter Two 2.1 Introduction 62.2 Literature Review 72.3 Reduced Form Equations and Specification Issues 192.4 Empirical Analysis 242.5 Concluding Remarks 54Chapter Three 3.1 Introduction 573.2 The Model 583.3 Comparisons with Models Used in the Dynamic Labour Supply andConsumption Literatures 673.4 Functional Forms and Estimating Equations 753.5 Empirical Analysis 823.6 Concluding Remarks 105Chapter Four 4.1 Introduction 1074.2 Approaches to Modelling the Participation Decision 1084.3 The Model 1094.4 Functional Forms and Estimating Equations 1194.5 Empirical Analysis 1274.6 Concluding Remarks 144Chapter Five Conclusion 145References. 206Appendix 1 Definitions of Variables Listed in Tables 209Appendix 2 First Stage Estimates for Two Stage Least Squares Estimation ofMRS Function 214Appendix 3 Results from Estimation of Reduced Form Equations Used to Generatethe Wife’s Euler Equation Data 223111Appendix 4 Results from Estimation of Reduced Form Equations Used to Generatethe Husband’s Euler Equation Data 231Appendix 5 First Stage Estimates Corrected for Participation Selection, for theTwo Stage Least Squares Estimation of MRS Function 239Appendix 6 Results from Estimation of Reduced Form Equations Used to Generatethe Wife’s Euler Equation Data 247Appendix 7 Results from Estimation of Reduced Form Equations Used to Generatethe Husband’s Euler Equation Data 255ivLIST OF TABLESTable 2.1 Sample Means for Selected Variables 153Table 2.2 Results from Estimation of Wage, Hours, and Weeks Equationsfor Wives 155Table 2.3 Estimates from Wage, Hours and Weeks Regressions for Husbands . . . 160Table 2.4 1981 Predicted Differences in Wages, Hours and Weeks of Wivesby Immigrant Status 164Table 2.5 1991 Predicted Differences in Wages, Hours and Weeks of Wivesby Immigrant Status 164Table 2.6 1981 Predicted Differences in Wages, Hours and Weeks of Husbandsby Immigrant Status 165Table 2.7 1991 Predicted Differences in Wages, Hours and Weeks of Husbandsby Immigrant Status 165Table 2.8 Results from Probit Estimation on Wife’s Participation 166Table 2.9 Results from Estimation of Wage, Hours and Weeks Equations forWives after Controlling for Participation Decision 170Table 2.10 1981 Predicted Differences in Wages, Hours, and Weeks of Wives byImmigrant Status after Correcting for the Participation Selection 175Table 2.11 1991 Predicted Differences in Wages, Hours, and Weeks of Wives byImmigrant Status after Correcting for the Participation Selection 176Table 3.1 Sample Means for Selected Variables 177Table 3.2 Results from Estimation of the Family Marginal Rate of Substitution . . 179Table 3.3 Results from Estimation of the Euler Equation for the Wife’s Hours . . 183Table 3.4 Results from Estimation of the Euler Equation for the Husband’s Hours 186Table 4.1 Sample Means 190Table 4.2 Results from Probit Estimation on Wife’s Participation 192Table 4.3 Results from Estimation of the Family Marginal Rate of Substitution . . 197Table 4.4 Results from Estimation of the Euler Equation for the Wife’s Hours . . . 201VTable 4.5 Results from Estimation of the Euler Equation for the Husband’s Hours . 202viLIST Of FIGURESFigure 2.1 Immigrant Adjustment Path for Earnings 150Figure 2.2 Immigrant Adjustment Paths and Cohort Differences 151Figure 2.3 Immigrant Adjustment Paths and Differences in Rates ofAssimilation 152Figure 3.1 1981 Non-Labour Time for Immigrant and Non-Immigrant FamiliesGiven Non-Immigrant Wages and Artificial Constraint 181Figure 3.2 1981 Non-Labour Time for Immigrant and Non-Immigrant FamiliesGiven Market Wages and Artificial Constraint 182Figure 3.3 Hours of Immigrant and Non-Immigrant Wives Over Time GivenNon-Immigrant Wages and Artificial Constraint 185Figure 3.4 Hours of Immigrant and Non-Immigrant Wives Over Time GivenNon-Immigrant Wages and Artificial Constraint 186Figure 3.5 Hours of Immigrant and Non-Immigrant Wives Over Time GivenMarket Wages and Artificial Constraints 187Figure 4.1 The Case of A Non-Worker in the Static Fixed Cost of Work Model . . 188Figure 4.2 The Case of a Worker in the Static Fixed Cost of Work Model 189Figure 4.3 1981 Non-Labour Time for Immigrant and Non-Immigrant FamiliesGiven Non-Immigrant Wages and Artificial Constraint 199Figure 4.4 1981 Non-Labour Time for Immigrant and Non-Immigrant FamiliesGiven Market Wages and Artificial Constraint 200Figure 4.5 Hours of Immigrant and Non-Immigrant Wives Over Time GivenNon-Immigrant Wages and Artificial Constraint 203Figure 4.6 Hours of Immigrant and Non-Immigrant Wives Over Time GivenNon-Immigrant Wages and Artificial Constraint 204Figure 4.7 Hours of Immigrant and Non-Immigrant Wives Over Time GivenMarket Wages and Artificial Constraints 205viiACKNOWLEDGEMENTI would like to thank David Green for supervising my research. David has not only madeextensive comments and suggestions, but he has also been a great source of support andencouragement for me. I would also like to thank Craig Riddell and Terry Wales for thethe many discussions we have shared which have added greatly to this thesis. I have appreciateddiscussions 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 SocialSciences and Humanities Research Council of Canada doctoral fellowship and a grant from theCentre 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 supportthroughout my education. Most importantly, I would like to thank my wife, Karen, and my son,Daniel, for their love and support.viiiCHAPTER ONEIntroductionIn countries like Canada and the United States, one can think of immigration as a contractbetween the immigrants and the pre-existing population. Under the contract, the immigrantsbring their skills, wealth, and ambition to the new country. In exchange, the pre-existingpopulation gives the immigrants full rights associated with being a citizen and the chanceto use their skills in the new labour market. Implicit in this agreement is the fact that ifimmigrants do not succeed economically, or if they do succeed but only after years in the newcountry, 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 widespreadfailure 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 immigrantsadjust 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 inorder to develop sound public policy. In particular, we would like to know what obstacles lie inthe path of the immigrant labour market adjustment, and whether or not the effects of theseobstacles can be lessened through public policy. Previous research suggests that immigrantshave difficulty finding jobs suitable to their ability in the early years after migration. Thismay 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 problems1immigrants may need to invest in search for better jobs or invest in retraining. In order toafford these investments, immigrants must have sufficient savings or access to credit in order tofund consumption in the first years after migration. However, immigrants may have difficultyborrowing from financial institutions immediately after arriving in the new country, beforethey 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 supplyof immigrants. In order to evaluate the effects of credit constraints, it is necessary to focuson the labour market adjustment of the immigrant family. Certain family members may bechosen by the family to retrain or search for better jobs, while other family members work longhours in order to fund family consumption in the early years after migration. In order to seethe total effects of credit constraints on the immigrant family, we need to analyze the labourmarket behaviour of both the members who are allowed to search for better jobs or receive thetraining, and those who fund it.The importance of credit constraints on the labour market behaviour of immigrants was firstsuggested in Long (1980). Long argued that immigrant families are often credit-constrainedafter arriving in the new country and are unable to fund human capital investments by borrowing against future earnings. Long suggested that it may be the immigrant wife who worksmore hours if the husband is perceived to be the principal earner and must make human capitalinvestments before beginning his career. Subsequent researchers have referred to this explanation of the labour market behaviour of immigrants as the Family Investment Hypothesis(FIH).2If, as the FIR predicts, it is immigrant wives who work more in response to imperfectcapital markets, then there may be a role for public policy to reduce the need for the wife towork more hours. In this case, policies such as a government loans program for new immigrantsor more funding for retraining of immigrant women may reduce the need for the immigrantwife to distort her labour market behaviour.In Chapter 2, I analyze the labour market adjustment of immigrant married couples usingreduced-form estimation. Hourly wage, hours per week, and weeks per year equations areestimated 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 husbandsand wives. However, immigrants overcome part of the wage differential through higher growthin wages than non-immigrants. Immigrant men and women work fewer weeks than similar non-immigrants in the first five years of residence. This is likely due to unemployment. Immigrantsmay need to search for jobs or cycle through jobs not suited to their skilis before settling intomore permanent, career oriented jobs. Immigrant husbands and wives work more hours perweek than non-immigrant husbands and wives.In light of the lower wages found for immigrants, the hours differences are consistent withthe hypothesis that immigrant family members work long hours at low wages upon arrival inthe new country when the household lacks access to credit. However, one would expect theeffects of credit constraints to diminish with duration of residence leading to a convergence ofthe immigrant and non-immigrant hours. This is not found in the estimation. It may be thatthis hours convergence is “masked” in the data by the desire to increase hours by immigrant3family members in response to the higher wage growth. The net effect might be a constanthours difference through time between immigrants and non-immigrants. An alternative explanation for the observed movements in the data is that immigrant family members have a lowerdisutility to work or lower wealth. These differences, coupled with a small response of thehours of married women to their wage growth, would explain the observed behaviour. Theseexplanations cannot be distinguished using reduced-form estimation.In Chapter 3 and Chapter 4, I develop a structural model of intertemporal labour supplyfor married couples which allows for uncertainty and the possibility that the household maybe credit-constrained in some time periods. The model extends the dynamic labour supplyliterature by relaxing the assumption of perfect capital markets. A procedure is developedwhich 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 credit-constraint based explanation of differences in labour supply patterns in immigrant versus non-immigrant families. Immigrant families place a lower value on the wife’s non-labour timerelative to the husband’s non-labour than do non-immigrant families. After controlling forall other factors, this would lead immigrant wives to work more hours than non-immigrantwives, and immigrant husbands to work fewer hours than non-immigrant husbands. Aftercontrolling for offered wages, immigrant family members are found to supply more labourin all periods due to either a lower disutility of work of its members, or lower wealth. The4results indicate that immigrant families are not more likely to be credit-constrained than nonimmigrant families. The empirical evidence supports the hypothesis that credit constraintsare an important determinant of hours of work in young families; however, after controllingfor age, immigrant families do not appear to be more likely to be credit-constrained than nonimmigrant families.5CHAPTER TWO2.1 IntroductionIn this chapter, the labour market behaviour of immigrant couples is compared to thebehaviour of non-immigrant couples through reduced-form estimation. Wage, hours and weeksof work of both immigrant spouses and the participation decision of the wife are studied andcompared to those of non-immigrant couples. These labour market outcomes will be used toevaluate the success of immigrants relative to non-immigrants in the labour market measuredat time of arrival and with years of residence in Canada.Immigrant husbands and wives are found to earn lower wages and work longer hours thannon-immigrant. husbands and wives. Over the 1980s, immigrant husbands and wives experiencehigher wage growth than their non-immigrant counterparts while their hours and weeks growthare roughly equal. These results are consistent with immigrant families being affected more bycredit constraints than non-immigrant families. Immigrant family members may work morehours in order to fund family consumption because they are unable to borrow against futureearnings. However, one would expect the effects of credit constraints to diminish with years ofresidence. The difference between the hours of immigrants and non-immigrants does not failwith years of residence. It is argued that the response of the immigrant family to the higherwage growth of its members may “mask” the credit constraint effect. This would explain theequal growth in hours of husbands and wives across immigrant and non-immigrants given thehigher growth in wages of immigrants. However, an alternative explanation is suggested. Itmay be that immigrant family members work more hours for lower wages than their non6immigrant counterparts due to a lower disutility to work or lower wealth. This along with alow response of hours to growth in wages over time would also explain differences by immigrantstatus found in the reduced-form estimation.2.2 Literature ReviewEconomic studies of immigrant labour market adjustment typically use labour market characteristics such as wages and earnings to measure how successful immigrants are relative tonon-immigrants. In particular, researchers have focused on how differences in wages and earnings 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 between immigrants and non- immigrants. Using a human capital earnings model, augmentedwith controls for immigrant status and years-since-migration, Chiswick estimates differences inearnings between immigrant and non-immigrant men using the 1970 U.S. Census. The resultsindicate that immigrant men with one year of residence in the U.S. have ten to fifteen percentlower annual earnings than otherwise similar non-immigrant men. This earnings differenceis smaller for immigrant men with more years of residence. The earnings of immigrant menwith 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 resultsas describing the path of the difference in earnings of immigrants versus non-immigrants as theyears of residence of the immigrants increases, after controffing for other factors. Figure 2.1demonstrates the Immigrant Adjustment Path (TAP) of earnings found by Chiswick. The TAP7is defined as the difference between the expected earnings of immigrants and non-immigrantsas years-since-migration rises. The slope of the TAP is interpreted as measuring the labourmarket adjustment or assimilation of immigrants.Consider the following version of Chiswick’s model:1mW = 7o+ X7 + XF7F +a50Y +a60Y + e (1)where mW is the natural logarithm of annual earnings, X is a vector of personal characteristicswhich does not contain a constant term, XF is a subset of these characteristics interactedwith an immigrant dummy variable, Y50 identifies immigrants who arrived before 1960, Y60identifies immigrants who arrived in the 1960s; 7° is the intercept, 7 and 7F are parametervectors, and e is an error term. The expected value of the log of earnings of a non-immigrantwith characteristics, xr, is:YrO,N=70+X7 (2)The expected value of the log of earnings of an immigrant from each cohort with the samecharacteristics is:2= 7o+ X7 + XF7F + Y6o (3)Y70,so= 70 + X7 + XF7F + QSO (4)Chiswick’s results indicate that Y70,N > flo,60 and fl0,50 > or a50 > a60. Given thatthe 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 variables used here. The specification of equation (1) is chosen to make it comparable to the specifications used inlater studies and in the analysis of this thesis.2The vector XF is set equal to X over the common set of characteristics in the two vectors.8to know whether or not 1%,50 > 7o,N If the crossover point were at ten years, then we couldinfer that Y70,5 > Y70,N.Borjas (1985) presents results from the same model estimated using both the U.S. Censusof 1970 and 1980. Borjas finds that Chiswick’s interpretation of his results is incorrect dueto the incorrect assumption that the immigrant adjustment paths of earnings are stationaryacross immigrant entry cohorts. Borjas argues that successive immigrant cohorts have hadlower unobserved ability due to a movement away from independent immigrants who are morerigorously selected on personal characteristics, and towards family class immigrants, who arechosen primarily because of being a relative of a U.S. citizen. He also argues that shiftingsource countries caused this drop in unobserved ability. Borjas’ results indicate that successiveimmigrant cohorts have had a larger earnings disadvantage at time of arrival in the U.S. Afteraccounting for these differences, Borja.s finds the slope of the lAP of each entry cohort to besmaller than what was found by Chiswick implying a much later earnings crossover point.Borjas’ method of identifying immigrant assimilation from differences across immigrantentry cohorts can be demonstrated using (1), Chiswick’s earnings equation.3 Let the followingequation explain the log of annual earnings of men in the 1980 U.S. Census:mW = 6 + X6 + XFbF + 050Y +860Y +070Y + u (5)where Y70 identifies immigrants who arrived in the 1970s; 6 is the intercept; 6 and 6F areparameter vectors; 7o, 6o, and °50 are parameters; and u is an error term.Predictions analogous to (2)-(4) can be derived from equation (5) for non-immigrants and3The following discussion is based closely on the discussion in Borjas (1985).9the three immigrant entry cohorts identified in the model:Ygo,N=60+X6 (6)= 6 +Xb +XFbF +070 (7)Ys0,60 = b + X6 + XF6F + 060 (8)Y30,5 = 6o + X6 + XFbF + (9)where Y80,N, ‘so,7o, l’so,6o, and o,so are the expected log earnings in1980 of individuals withcharacteristics, X, who are non- immigrants, immigrants who arrived in the1970s, immigrantswho arrived in the 1960s, and immigrants who arrived before 1960, respectively.Using the 1980 data, Chiswick’s cross-section-based measure of thedifference between thegrowth in earnings of immigrants who arrived in the 1960s and the growthin earnings of non-immigrants is:4(o,6o — Y8o,N) — Y80,N) = 060 — 07o(10)Borjas notes that this can be rewritten:060 — 07 = [Q9o,o — Y80,N) — (?7o,60 — Y70,N)} + [Qc0,60 — Y70,N) — (1>50,70 — Y80,N)] (11)The first term in square brackets gives the “within cohort” growth in earningsof immigrantswho arrived in the 1960s relative to the growth in earnings of the native-born. This measuresthe movement along the TAP of immigrants who arrived in the 1960s from having one to tenyears-since-migration to having eleven to twenty years-since-migration. Thesecond term insquare brackets gives the difference in the immigrant non-immigrant earnings differential of4This is the growth after controlling for age effects in X.10immigrants who arrived in the 1960s relative to those who arrived in the 1970s holding theYSM of each cohort at one to ten years. This term measures average differences in earningsacross the two cohorts due to differences in unobserved characteristics shortly after arrival inthe U.S., and is often referred to as the difference in earnings due to differences in unobservedability.5If immigrant cohorts differ in terms of unobserved ability then the TAP will be different foreach cohort. Borjas finds that successive immigrant cohorts have had lower unobserved abilityand 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 immigrantswho arrived in the 1960s, and this can be seen in the lower intercept of the TAP for the 1970scohort. Borjas assumes that rates of assimilation, or the slope of the TAP, for a given levelof YSM, is the same for all immigrant cohorts. Given the measured differences in unobservedability across immigrant entry cohorts, this implies that the TAP of immigrants who arrivedin the 1970s lies below the TAP of immigrants who arrived in the 1960s for all values of year-since-migration. Based on the specification of (6)-(8), O,7O — Yso,N is the average value ofthe TAP of immigrants who arrived in the 1970s over one to ten years of residence, whileY50,6— Yso,jv is the average value of the TAP of immigrants who arrived in the 1960s over therange of eleven to twenty years of residence. Chiswick’s measure of the slope of the TAP ispresented by the dotted line in Figure 2.2. The upward bias in the slope of the measured TAP51t would be preferable to have more narrowly defined immigrant arrival year cohorts in the data. The factthat the cohorts are defined in ten year blocks means that, instead of measuring differences in wages acrosscohorts in the first year after migration, we are measuring differences in average wages over the first ten yearsof residence. The data sets used in the estimation of this thesis only identifies immigrant arrival year in tenyear blocks; therefore, the discussion in the literature review wifi be restricted to this case.11is 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. Forexample, 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 ofimmigrants who arrived in the 1970s over one to ten years of residence is— Yso,N. Theaverage value of this group’s TAP from eleven to twenty years of residence is this numberplus 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 totwenty years of residence. It is possible to derive these ten year averages of the 1970s cohort’sTAP for increasingly larger values of YSM provided that enough earlier immigrant cohorts areidentified in the data.Latonde and Topel (1991) use the 1970 and 1980 U.S. Census data to analyze the sensitivityof Borjas’ results to the choice of comparison group. Instead of comparing immigrants to thetotal non-immigrant population, they compare immigrants to non-immigrants of the sameethnic group and to immigrants of the same ethnicity but with more years of residence. Theyfind that more recent immigrants have had lower average earnings, ceteris paribus, and thatthis is due solely to changes in the source countries of the immigrants. However, there appearsto be no drop in average “quality” within immigrant ethnic groups. They find that immigrantsassimilate quickly in the U.S. labour market with the initial earnings disadvantage overcomeafter ten years of U.S. experience. Immigrants with the lowest wages upon arrival experience12the highest rates of assimilation. They conclude that immigrants have lower initial earningsthan non-immigrants of the same ethnicity, but that their earnings quickly converge to thoseof the non-immigrants of their ethnic group.The different conclusions between Borjas (1985) and Lalonde and Topel (1991) are driven bythe choice of comparison group. If members of more recent immigrant cohorts are more likelyto be members of ethnic groups which face discrimination in the U.S. labour market than wereimmigrants from earlier cohorts, then the interpretation that more recent cohorts have lowerunobserved ability may be incorrect. In this case, using the total non-immigrant populationas the comparison group understates the unobserved ability of recent cohorts since differencesin 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 differencesin unobserved ability rather than discrimination then the correct comparison group is thetotal non-immigrant population. In this case, Latonde and Topel’s estimates of differences inwages between immigrants of recent cohorts at time of arrival and non-immigrants are biaseddownwards since the comparison group has lower unobserved ability than the rest of the nonimmigrant population.The data used in this thesis do not contain controls for ethnicity. Therefore, the comparison group used is the non- immigrant population. Differences in labour market outcomesacross cohorts will be attributed to either differences in ability or differences in discriminationexperienced in the labour market. The issue of testing between these competing explanations13of 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’ assumption that rates of assimllation, holding years-since-migration constant, are the same acrossimmigrant entry cohorts. The fact that LaLonde and Topel find that immigrants with lowerinitial earnings experience the highest rates of assimilation indicates that Borjas’ measuredTAP for recent cohorts may be biased. Figure 2.3 gives an example of the case where the TAPsof two immigrant cohorts differ both in terms of unobserved ability at arrival in the new country, and in terms of rates of assimilation. The cohort of immigrants who arrived in the 1970shas a larger initial earnings disadvantage relative to the non-immigrants than does the cohortof immigrants who arrived in the 1960s. However, the immigrants who arrived in the 1970sexperience a faster rate of assimilation than those of the earlier cohort, so that after ten yearsin the new labour market, there is only a small difference in the earnings of the two immigrantgroups. Tf the TAPs of successive immigrant cohorts have shifted in this manner, then the slopeof the TAP of recent cohorts, derived using Borjas’ procedure, is biased downwards. Considerthe case of the 1970s cohort. From the 1980 data, we can derive the average value of the TAPfor this group between one and ten years of residence. Following Borjas’ interpretation, wecan derive the average value of the TAP for this group from eleven to twenty years of residenceby adding the movement along the TAP for the 1960s cohort from one to ten years to elevento twenty years. This understates the expected movement along the TAP for the 1970s cohortbecause 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 the14Current Population Survey in the U.S. They find that immigrant cohorts with the lowest initialearnings also have the highest growth in earnings, or assimilation.In interpreting the empirical results of this thesis, I allow for the possibility that eachimmigrant entry cohort has a unique TAP. The TAPs of two immigrant cohorts may differ interms of the intercept and also the slope at each value of YSM, which measures the rate ofassimilation. Two cross section data sets are used; therefore, it is possible to derive two pointson the TAP of immigrant cohorts who arrived prior to the first survey, and one point on theTAP 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 incorrectassumptions.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 inCanada had thirty-three percent lower wages than non-immigrant men. However, this difference dropped to around zero for immigrants in earlier cohorts. Abbott and Beach (1993) usethe 1973 Canadian Job Mobility Survey to analyze differences between immigrant and nonimmigrant 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 thatcross-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 CanadianCensuses to analyze the issue. They find immigrant men’s earnings grow with time in Canada,15but at a low rate, implying a crossover point of thirteen to twenty- five years after arrival. Theyargue that the unobserved “quality” of immigrant men declined after changes in immigrationpolicies in 1974 leading to more family class immigrants.Baker and Benjamin (1992) extend this analysis using the 1971, 1981, and 1986 CanadianCensuses. They find the same drop in unobserved ability in successive immigrant cohortsobserved in Bloom and Gunderson (1991); however, they find lower growth rates of earningswith years of residence. Because they have three cross sections, they are able to test theassumption that the rates of assimilation holding YSM constant are the same across immigrantentry cohorts°, and do not reject this hypothesis. Baker and Benjamin analyze the importanceof the choice of comparison group in measuring immigrant earnings differences, as suggestedby LaLonde and Topel (1991). They compare new immigrants to non- immigrants and also toimmigrants with more years of residence. They also control for changes in the composition ofimmigrant cohorts in terms of source countries. In each case, rates of assimilation are foundto be low. This indicates that the estimates of the assimilation rates in the Canadian dataare less sensitive to the choice of comparison group than are the estimates of assimilation ofBorjas (1985) and Latonde and Topel (1991) using U.S. data.The economic literature on the labour market adjustment of immigrant women is less developed than the one for men. Long (1980) uses the 1970 U.S. Census to estimate Chiswick’smodel for immigrant women. The results indicate that immigrant women with one year of residence have over sixty percent higher earnings than non-immigrant women and this differentialis lower for immigrant women with more years of residence. Long interacts marital status6This implies that the lAP of each cohort has the same slope for a given value of YSM.16with the years-since-migration controls and finds that the negative earnings/YSM profile isflatter for single immigrant women than for married immigrant women. Annual hours of workfor immigrant women are found to decline with years of residence in the U.S. at a rate ofapproximately one and a half percent a year. Hours of work controls are not included in theearnings regression. It appears that at least part of the negative earnings/YSM relationship isdue to a negative hours/YSM relationship. In an attempt to reconcile the large differences inthese results compared to what was found for immigrant men, Long hypothesizes that, sinceimmigrant men may be perceived to be the principle earners, they may make human capitalinvestments after arriving in the new country. Given that it is difficult to borrow against future wage income, immigrant wives may need to work more hours or in occupations with highshort run earnings, but low growth in earnings, in order to fund family consumption. Once thehusband’s earnings begin to reflect the returns to the post-migration investments in humancapital, the wife reduces her labour supply or switches to an occupation with better careeropportunities. Subsequent researchers have referred to this explanation of the results as theFamily Investment Hypothesis (FIR).Beach and Worswick (1993) carry out a similar analysis using the 1973 Canadian JobMobility Survey. Highly educated immigrant women are found to have lower earnings thansimilarly educated non-immigrant women; however, foreign-born women with lower levels ofeducation 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 thesample; therefore, it is impossible to separate changes in labour supply from changes in market17wages.7 Beach and Worswick argue that the flat YSM path can be explained by the immigrantfamily being credit-constrained upon arrival in Canada and the wife responding by workingmore hours to support family consumption as was suggested by Long (1980). This wouldimply a negative relationship between the wife’s hours of work and her YSM. The observedflat earnings/YSM profile for women might be due to a combination of a negatively-slopedhours/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 immigrant entry cohorts cannot be distinguished in the observed patterns of earnings and hoursof work for different values of YSM. In the empirical work of this thesis, the importance ofassimilation relative to changes in unobservable characteristics across immigrant entry cohortswill be evaluated in determining the earnings and hours L&Ps of immigrant women.Few papers have studied immigrant adjustment while allowing for family objectives andadjustment strategies. Baker and Benjamin (1994) use data on married couples to test forfamily investment strategies. They use the 1986 and 1991 Canadian Survey of ConsumerFinances. They argue that immigrant women who are married to non-immigrant men areless likely to need to support their husband’s human capital acquisition than are immigrantwomen with immigrant husbands and; therefore, should have lower labour supplies upon arrival in Canada and have a steeper wage/YSM profile . Immigrant women with immigrant7Estimation of a log hours equation over the sample of womeu with reported hours of work indicates thathours are higher for women with fewer years of residence.they are more likely to make investments in their own human capital accumulation rather than thehuman capital accumulation of their husband.18husbands work more upon arrival and have lower wage assimilation than immigrant womenwith non-immigrant husbands. The evidence in favour of the FIR relies on the comparabilityof immigrant women with immigrant husbands versus those with non-immigrant husbands.However, the observed differences could also be explained by differences in preferences towardlabour supply and differences in expected lifetime wealth. Immigrant women with immigranthusbands may typically come from different source countries. This might lead to differentattitudes towards work.9 In a reduced-form model, it is not possible to distinguish between apreference- based explanation and a credit-constraint-based explanation for the different laboursupply patterns between the two groups of women.Duleep and Sanders (1993) use the 1980 U.S. Census to study the immigrant wife’s participation decision, and conclude that the results are consistent with a family strategy. They findthat immigrant women from home countries with high expected growth in immigrant men’searnings are more likely to participate. They argue that this is due to the husband participating in retraining programs and the wife having to work to support the family in the faceof constraints on borrowing. They also find that the labour force participation of immigrantwives is inversely associated with their husbands’ years of residence, after controlling for thewife’s years of residence. Since the study uses only one cross- section, it is not possible toseparate differences across immigrant entry cohorts from the effects of credit constraints. Theobserved behaviour which is attributed to an inability on the part of the family to borrowcould instead be due to different attitudes towards work across successive immigrant cohorts.2.3 Reduced Form Equations and Specification Issues9The SCF data used by Baker and Benjamin do not contain controls for country of origin.19In the empirical analysis of this chapter, immigrant married couples are compared to similarnon-immigrant couples in terms of wages, hours of work per week, and weeks of work peryear for both the husband and the wife. The focus will be on the magnitude of immigrantdifferences in these labour market outcomes: 1) at time of arrival in Canada, 2) with moreyears of residence, and 3) across immigrant entry cohorts.The data used come from two cross-sectional surveys, the 1981 and 1991 Census of CanadaFamily Microdata Files. The specification of the husband’s log wage equation, defined overthe pooled sample, has the following form:mW= /3o + X/3 + XFPF + /3rYR91 +X918’+4351Y + /361Y + /3Y71 +/391,5(YR91 * Y51) +/391,6(YR91 * Y61) +/391,7(YR91 * Y71)+i381Y + 13s6)f86 + /387Y + /388Y + /389Y + /390Y + e (12)where the vector X contains demographic characteristics of the husband, and XF contains asubset of these characteristics interacted with an immigrant dummy variable; YR91 indicatesthat the individual is from the 1991 survey; the vector X9’ contains age controls interactedwith the YR91 variable;’0 Y5, identifies immigrants who arrived before 1961; Y61 and Y7,identify immigrants who arrived between 1961 and 1970, and 1971 and 1980 respectively; Y8,identifies immigrants who arrived between 1981 and 1985; Y86,Y87,Y58,Y89, and Y90 identifyimmigrants who arrived in 1986, 1987, 1988, 1989 and 1990 respectively; /3 is the intercept;/3, 13F 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, 1F do not vary across time.20/88, /389, and flo are parameters; and e is an error term. The controls for the immigrantcohorts 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 alsoincluded as interactions with YR91. The coefficients on these interactions, 591,51, 591,61, and/391,71, measure the wage assimilation over the decade for each cohort.11To see this for the case of immigrants who arrived in the 1970s, first define the expectedwage in 1981 of a non- immigrant with characteristics 1K to be:Ygl,N=/30+X13 (13)The expected 1981 log wage of an immigrant who arrived in the 1970s with the same characteristics is:Ysi,71—/3o+X/3+XF/F+ 71 (14)The average value of the TAP over one to ten years of residence of an immigrant who arrivedin the 1970s with characteristics 7 is:Y81,7 Y81,N = XF/3F + 571 (15)In 1991, the expected log wages of a non-immigrant and an immigrant who arrived in the 1970swith these same characteristics are:Y91,N=/30+X/3+/3W +r’’ (16)Y91,7 = /3 +75 + /3g’ + XFI3F+ + Sn + 5i,i (17)‘1For example, #91,71 measures the average increase in the lAP for immigrants who arrived in the 1970s fromhaving one to ten years of residence to having eleven to twenty years of residence.21where X’ is the age control for this person after aging ten years.’2 The average value of theTAP of immigrants who arrived in the 1970s over eleven to twenty years of residence is:Y91,7— Y91,N = XFI3F+ 571 + 591,71 (18)The wage assimilation of this cohort over the ten year snrvey period is the movement alongthe TAP over the period:(1%,,7,—Y91,N)— (1,71 — Y81,N) = 591,71 (19)This analysis could be repeated to show that 591,61 and 5gj, measure the wage assimilationof 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 acrossbirth cohorts, holding age constant, are similar to the issues involved with measuring the TAPof each immigrant entry cohort, discussed above.Six birth cohorts are identified in the specification. In terms of their ages in 1981, the sixgroups 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 wageregression have the form:Xf3 + 5g1YR91 +x915’ = XNA/3N* YR81) +5,,35435 * YR81)* YR81) +3°1,45(A45 * YR81)‘2For example, if the age of a husband with characteristics X is forty in 1981, then X9’ indicates that he isfifty in 1991.22* YR81) + 13g’YR91+/31,40(A40 * YR91) +31,45(A45 * YR91)+f31,50(A50 * YR91) + i31,55(A 5 * YR91)+131,60(A60 * YR91) (20)where XNA are characteristics other than age; A30, .435, .440, .445, .450, .455, and .460 identifyindividuals age thirty to thirty-four, thirty-five to thirty- nine, forty to forty-four, forty-fiveto forty-nine, fifty to fifty-four, fifty-five to fifty-nine, and sixty to sixty-four at the time ofthe survey. The default category contains men age twenty-five to twenty-nine in 1981. Onecan see the wage/age cross section for 1981 using the parameters j3g130, i3g135, i3g140, i3g1,45and Each coefficient measures the percentage difference in average wages between theage cohort represented by the dummy variable and the default age cohort, after controffing forother characteristics. The coefficient 31 measures the growth in wages over the decade of thehusbands age twenty-five to twenty-nine in 1981. The specification allows for unique wage/agegrowth paths for each birth cohort. For example, husbands age forty to forty-four in 1981 havewage growth equal to /33’ + /35 —Age controls are not included in XF; therefore, immigrants and non-immigrants are assumed to have a common wage/age profile. The assimilation measured by the immigrantcohorts is then interpreted as the difference in returns to post-migration labour market experience as originally suggested by Chiswick (1978).The vector XNA contains five education dummy variables with the default group representing men with a high school diploma. Controls for region of residence are also included and the23default category contains husbands who live in Toronto. Controls for language fluency are alsoincluded 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 equation. The log weeks equation has the same specification, but also includes a dummy variableidentifying immigrants in the 1981 survey who arrived in 1980. The coefficient on this variablepicks up the difference in weeks of work for this group from the average weeks of work ofimmigrants in the 1981 survey who arrived between 1971 and 1979. Since the 1980 cohortarrive 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 characteristics replaced by the wife’s characteristics. Controls for the number of children ever born tothe 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 equationwith two exceptions. The controls for number of live births are not included. Instead, controlsfor presence of children in the household are included to control for demands placed on thewife’s non-labour time. The wife’s log weeks equation contains the same variables as the wife’shours equation along with a dummy variable identifying wives in the 1981 survey who arrivedin 1980. Since their weeks are likely truncated, this specification treats them separately in theanalysis.2.4 Empirical AnalysisIn order to study an immigrant family’s labour market adjustment, one would ideally use24panel data with a large number of immigrant families which follows each household from thetime of arrival through several years of residence in the new country. Unfortunately, this typeof 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 modeldescribed above. Instead, two cross-sectional data sets, with a ten year interval, are used. Eachcross-section is assumed to be a random sample of the Canadian population at each point intime. Therefore, movements in average labour market behaviour are estimates of the expectedlabour market movements of households over the period conditioning on family characteristicswhich are constant across time.The sample used in estimation is from the 1981 and 1991 Canadian Censuses. The Censusdata come from the Family Files which contain 94,745 census families from 1981 and 345,351census families from 1991. The data contain extensive information on income, hours and weeksof 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 arerepresentative 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-employmentincome are excluded from the estimation sample. In the 1981 data, households where eitherspouse 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 years13The 1981 Census Family File does not distinguish between households in Prince Edward Island from thosein the Yukon and the NorthWest Territories, subsequently, households from these three regions were excludedfrom both data sets.25of age are excluded from the 1991 sample.Households where one spouse was born outside Canada and the other spouse was Canadian-born are excluded from the analysis. Analysis of the labour market adjustment of immigrantsin these “mixed” households will be left for future work. The FIH is more likely to apply tohouseholds where both spouses are immigrants than to these mixed households. In the mixedhouseholds, the native-born spouse has domestic education credentials; therefore, borrowingis less-likely to be necessary. Also, the native-born spouse has family connections and is morelikely 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 bothare native-born.The labour supply measures used in the analysis of this chapter are the hours worked inthe reference week and the weeks worked in the reference year of the husband and the wife.’4Immigrants who arrived part way through the reference year would likely have a truncatedweeks of work for the year. To avoid this problem, a dummy variable is used to control forthis group in the weeks worked equations.Wage rates are constructed by dividing the product of the reference week hours variable andthe weeks worked per year variable into the individual’s annual earnings the previous year.15To do this, it was necessary to exclude from the sample households where either spouse had‘41n both Census data sets, the hours of work in the reference week variable is top-coded at one hundred.Households where at least one spouse reported hours of work of one hundred for the reference week were excludedfrom the analysis. After all other restrictions on the sample were made, this restriction only excluded 0.4 percentof households in the sample.15The annual earnings variable from the 1991 data is deflated using the GDP deflator for Canada into 1981dollars.26positive earnings and weeks the previous year, and zero hours in the reference week, or viceversa.All households in the 1981 sample where both spouses are immigrants and which meet theabove criteria were kept in the sample. Due to the large numbers of non-immigrant householdsin the two data sets, for both the 1981 and 1991 data, a twenty-five percent random sample ofnon-immigrant households is taken. As can be seen in Table 2.1, after these restrictions thereare 3688 foreign-born households from the 1981 Census, and 10472 households from the 1991Census. The total number of non-immigrant households from the 1981 Census is 3808, andfrom the 1991 Census there are 9815 remaining.Appendix 1 contains definitions for the variables listed in the tables. The year of arrivalinformation is more detailed in the 1981 Census than in 1991, therefore, arrival years aregrouped. It is possible to identify immigrants arriving between 1971-80, 1961-70, and before1961 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 forwhether the person can speak English but not French, French but not English, both Englishand French, and neither English nor French. Six age indicator variables are defined for eachspouse. 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 childrenin 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 immigrantand non-immigrant samples in each survey year. Immigrant women have a sixty-six percent27participation rate in the 1981 sample while the non-immigrant women’s participation rate isonly fifty-nine percent. Over the decade, the non-immigrant participation rate rose faster sothat, by 1991, seventy-four percent of immigrant women in the sample participate and seventythree percent of the non- immigrant women participate.The average wages of immigrant women are one dollar and thirty- seven cents lower thanthose of the non-immigrant women in 1981, but this wage gap has dropped to eighty-nine centsby 1991. Immigrant women work 2.2 hours more per week in 1981 and 1.85 more hours perweek in 1991. Immigrant women work a third of a week more on average in 1981 and less thanone week more in 1991. Immigrant women are over a year older in each year and have a moredispersed education distribution.Immigrant men have eighty-three cents lower wages in 1981, but by 1991 the differencehas decreased to twenty-five cents. Their mean hours per week and weeks per year patternsare very similar to the non-immigrant men. Immigrant men are roughly two years older thannon-immigrant men in each survey year, and like the immigrant women, have a more dispersededucation distribution.The means of the region of residence variables indicate that immigrant families are muchmore concentrated in Toronto than non-immigrant families. A higher percentage of immigrantfamilies reside in Vancouver than non-immigrant families.Table 2.2 contains results of OLS estimation of log wage, log hours and log weeks equationsover the sample of wives who work. The definitions of the variables are presented in Appendix1. The covariance matrix allows for heteroskedasticity of unknown form and is from White28(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 cross-section, women age twenty-five to twenty-nine have twelve to fifteen percent lower wages onaverage than older women. From the coefficient on YR91, we see that the growth in wages overthe decade for women of the youngest age cohort is sixteen percent. Older women experiencelower wage growth between the two surveys, so that by 1991, the youngest age cohort have nomore than six percent lower wages than older women.The wages of non-immigrant women are increasing in their level of education with a return of fifty-seven to sixty-eight percent to a university degree. Using the coefficients on theimmigrant-education interaction variables, we see that the wages of immigrant wives also risewith 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 wivesthan for non-immigrant wives, and a six to thirteen percent higher return to education belowa high school diploma than is the case for non-immigrant wives. This matches the result foundby both Long (1980) and Beach and Worswick (1993) that the returns to education are lowerfor immigrant women than for non-immigrant women.The coefficients on the controls for the number of live births of the wife are negativeimplying lower wages due to foregone work experience. There is a three percent drop in wagesassociated with each birth for non-immigrants, and this effect is statistically significant at the29five percent level.’6. For immigrants the drop in wages associated with the birth of each childis one percent lower than for non-immigrant wives; however, the difference is not statisticallysignificantThe coefficients on Y7180, Y6170 and YBEF61 indicate that the wages of non-immigrantsin 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 higherthan immigrants who arrived before 1961, ceteris paribus. Each of these wage differentialsare statistically significant.’8 The wage differentials describe the TAPs of the three cohortsover the relevant ranges of their years-since-migration. For example, the coefficient on Y7180implies that the average value of the TAP of the 1970s cohort is — .28 over one to ten yearsof residence. As was shown in section 2.3, the coefficients on the interactions between thecontrols for these three immigrant cohorts and Y1191 measure the wage assimilation over thedecade.19 The wages of immigrant women grow by eight to eleven percent more than the wagesof similar non-immigrant women, and these differences are statistically significant.2°This wageassimilation is larger for the more recent cohorts. Immigrant wives who arrived in the 1980shad twenty-nine to thirty-nine percent lower wages than similar non-immigrant wives with thelarger 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 have15The test statistic equals —4.77 and the prob-value of the test is less than .0001.7The test statistic equals .9, and the prob-value of the test is .37.‘8The test statistics are —6.00, —3.83, and —2.07 for the variables Y7180, Y6170, and YBEF61, respectively.The prob-values are less than .0001 for the first two coefficients and .04 for the coefficient on YBEF61.15For the case of the interaction of YR9I with Y7180, this is the change in the average value of the TAP fromhaving one to ten years-since-migration to having eleven to twenty years-since-migration.20The test statistics are 2.15, 2.67, and 3.26 for immigrant who arrived before 1961, between 1961 and 1970,and between 1971 and 1980, respectively; the prob-values of the individual tests are .030, .011, and .001,respectively.30lower wages upon entry into Canada than did earlier cohorts, after controffing for observablecharacteristics, can be tested by comparing the 1981 wages of immigrants who arrived in the1970s to the 1991 wages of immigrants who arrived in the 1980s.2’ The weighted average22 ofthe coefficients on the controls for immigrants who arrived in the 1980s equals — .3227. Thisimplies that the average 1991 wage of immigrant wives who arrived in the 1980s is four percentlower 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 equalsthe coefficient on Y7180 is not rejected.23 Therefore, recent cohorts of immigrant women donot appear to have significantly different wages at time of arrival than previous immigrantcohorts, 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 morehours than older women. From the coefficient on YR91 we see that the growth in hours overthe decade for the youngest cohort of women is zero. The growth in hours is negative forolder women. For example, women age fifty-five to fifty-nine in 1981, reduce their hours by sixpercent over the decade.Non-immigrant wives with a university education work four to ten percent more hours than21This tests the hypothesis that the average value of the lAP of the 1970s cohort over one to ten years-since-migration equals the average value of the lAP of the 1980s cohort over the same YSM range. It would bepreferable to test whether or not the intercept of the 1970s cohort’s lAP differed from the intercept of the 1980scohort’s lAP; however, that is not possible given the broadly defined immigrant arrival year categories in thedata.“The weight placed on each coefficient equalled the percentage share of immigrants who arrived between 1981and 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 onedegree of freedom and equals .9857. The prob-value of the test is greater than .25 and less than .5.31similar wives with a high school education. The increase in hours of work associated with auniversity education is smaller for immigrants. The increasing hours/education profile can beexplained by the increasing wage/education profile found in the wage equation. One wouldexpect women to respond to the higher wage rates by supplying more hours of work. Also, thefact that the hours/education profile is flatter for immigrant women than for non-immigrantwomen 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 ofwork of the wife.24 The effect is smaller for immigrant families, with all of the coefficients onthe interaction terms significant from zero except the coefficient on the K2PLUS interaction.25This result was also found in Long (1980) and Beach and Worswick (1993). It may be thatthe immigrant family is more likely to have extended family members present, who are ableto provide child care for young children26.Also, it may be the case that in immigrant familiesolder children are expected to provide greater care for young children than is the case innon-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 hoursthan similar non-immigrant wives. From the coefficients on the interactions terms of the threeearliest cohorts with the YR91 variable, we see that the hours assimilation of immigrant wiveswas not significantly different from zero for all three cohorts.27 Immigrant wives who arrived24The test statistics for the hypotheses that the coefficients on each control equals zero are —7.60, —7.17,—9.70, and —5.67 for KIDSOS, K1FLUS, KLDS614, and K2PLUS, respectively. The prob-values for thetests are less than .000 1 in each case.25The test statistics equal 2.85, 2.86, 3.32, and .73 for the interactions of the immigrant dummy variable withKJDSOS, K1PLUS, K1D5614, and K1PLUS, respectively. The prob-values are .004, .004, .001, and .465.26Unfortunately, the Census data does not include information on the presence of other adults in the home.27The test- statistics are —.28, —.15, and —.17; and the prob-values are .78, .88, and .87.32in the 1980s worked three to nine percent more hours in the 1991 reference week than similarnon-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 isthe 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 isfound to equal — .3023. Comparing this to the coefficient on Y7180 indicates that immigrantswho arrived in the 1980s worked two percent more hours in 1991 than immigrants who arrivedin the 1970s worked in 198128. The hypothesis that this weighted average equals the coefficienton Y7180 is not rejected.29 Therefore, recent immigrant cohorts do not appear to differ in termsof 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 the1981 cross section, weeks worked per year are found to be smaller for older women. The groupof wives age twenty-five to twenty-nine in 1981 increased their weeks per year over the decadeby eleven percent. The growth is much smaller for older women. For example, women ageforty-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 interactions of the immigrant dummy variable with the education variables, we see that theweeks/education profile is flatter for immigrant wives. This is consistent with the flatterhours/education profile and wage/education profile found above. The lower returns to education for immigrant women lead them to supply less labour both in terms of hours per week28The weights are the same as the ones listed in footnote 22.25The test statistic is distribnted asymptotically according to the Chi-square distribution with one degree offreedom; the prob-value of the test is between .25 and .5.33and weeks per year.The presence of children has a significant negative effect on the weeks worked of wives aswas the case in the hours equation.3° The only significant difference by immigrant status inthe response of the wife’s weeks to the presence of children is in the case of three or morechildren age six to fourteen present in the home.3’ Non-immigrant wives reduce their weeksby 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 1990and seventy-two percent fewer weeks in 1980. This is due to a bias caused by the wiveshaving arrived midway through the year. In the 1981 data, the weeks of work of wives ineach of the three immigrant cohorts are not significantly different from the weeks of similarnon- immigrant wives.32 The weeks assimilation of the earliest two cohorts is not significantfrom zero;33 however, the immigrant wives who arrived in the 1970s experience five percenthigher growth in weeks than similar non-immigrant wives, and this difference is statisticallysignificant.34 The wives who arrived in the 1980s work fewer weeks per year in general than thenon- 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 percentlower than the weeks of similar non-immigrant wives. The reference weeks hours for this groupdo not have the same pattern. It may be that these women have difficulty finding a job that30The test statistics are —5.09, —4.59, —7.39, and —6.49 for the variables KIDSO5, K1FLUS, KIDS614,and K2FLUS, respectively. The prob-values are less than .0001 in each test.31The test statistic is 3.11; and the prob-valne is .0018.82The test statistics are —1.48, .14, and —.62 for the variable Y7180, Y6170, and YBEF61. The prob-valuesare .14, .89, and .54, respectively.33The test statistics equal .12 for the coefficient on YBEF61 and —.52 for the coefficient on Y6170. Theprob-values are .90 and .60.54The test statistic equals 2.12; and the prob-value is .034.34suits their skills. If so, then this is not a difference in preferences over labour supply, butinstead a difference in the propensity to invest time in job search. The test of the hypothesisthat immigrant wives who arrived in the 1970s worked the same number of weeks in 1980 asimmigrant wives who arrived in the 1980s worked in 1990 is performed. A weighted average ofthe coefficients on the coefficient on the controls for immigrant arrival in the 1980s is calculatedand equals — .0727. This implies that the immigrant wives who arrived in the 1980s workedthree percent fewer weeks in 1990 than the immigrant wives who arrived in the 1970s workedin 1980. However, this difference is not significant.35The results of Table 2.2 indicate that immigrant wives generally have lower wages andwork more hours and weeks than similar non-immigrant wives. Immigrants wives experiencehigher wage growth than similar non-immigrant wives; however, their growths of hours andweeks 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, andweeks at time of arrival are not significant.These differences in labour market outcomes between immigrant and non-immigrant wivescan be explained by credit constraints having a larger impact on labour supply in immigrantfamilies than in non-immigrant families. The fact that immigrant wives work more hoursfor lower wages could be explained by the immigrant wife being unable to borrow againstfuture income in order to fund current consumption, and responding to this capital marketconstraint by working more hours. If the non- immigrant wife is able to borrow then she willnot need to work as many hours as the non-immigrant wife, ceteris paribus. One would expect35The Wald test statistic equals .9025, and the prob-vaine is greater than .25 and less than .5.35the effects of credit constraints to diminish with years of residence for immigrant families, assuggested by Long (1980). If that were the case, one would expect the hours of immigrantwomen 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 constantover the 1980s. It may be that the wife’s hours are not reduced because the higher growth inwages of immigrants over non-immigrants pushes her towards more hours of work. The desireto increase hours in response to the high growth in wages could “mask” the reduction in thecredit constraint effect.Table 2.3 contains the results of the log wage, log hours, and log weeks estimation for thehusbands. Definitions of the variables used in estimation are presented in Appendix 1. Thecoefficient estimates are distributed asymptotically according to the Normal distribution. Thecovariance matrix of the estimates allows for heteroskedasticity of unknown form and is fromWhite (1980). The first column lists the estimates from the log wage equation. Looking atthe age patterns in the 1981 sample, we see that the men age twenty-five to twenty- nine facesixteen to twenty-seven percent lower wages than older men. The growth in wages for theyoungest age cohort is twenty-two percent over the decade. Older men experience much lowerwage growth. For example, men age forty to forty-four in 1981 have average wage growth offour 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 seethat immigrant and non-immigrant men have similar wage/education profiles. This is inter36esting given the large differences in these profiles found in Table 2.2 for women. Given theproblems of having education credentials recognized after migration, one would expect lowerwage/education profiles for both immigrant men and immigrant women. This difference couldbe explained by the Family Investment Hypothesis. If the husband is perceived to be the mainearner, it may be that the family invests in job search and retraining for the husband so thathe can find a job that suits his skills, while the wife settles quickly in a job which may not suither skills but allows her to fund family consumption. However, this difference might also bedue to the family’s migration decision being more closely related to the husband’s career thanthe wife’s career.Immigrant men who arrived in the 1970s have twenty-eight percent lower wages in 1981than similar non-immigrant men, while those arriving earlier have twelve to sixteen percentlower wages. The wage assimilation of the earliest and the most recent of the cohorts was sevenpercent and was significant, while the wage assimilation of immigrant men who arrived in the1960s was not significant.37 The immigrant men who arrived in the late 1980s have forty-sevento sixty-four percent lower wages in 1991 than similar non-immigrant men. The hypothesisthat the 1981 wages of immigrant men who arrived in the 1970s equal the 1991 wages ofimmigrant men who arrived in the 1980s is tested. A weighted average of the coefficients onthe controls for immigrant arrival year in the 1980s is derived.38 The weighted average equals— .4379 and implies that the 1991 wages of immigrants who arrived in the 1980s are sixteen36The test statistic equals 2.58 for the coefficient on YBEF61 and 2.63 for the coefficient on Y7180; theprob-values are .010 and .009.37The test statistic is .92; and the prob-value is .36.35Each weight is the ratio of the number of immigrant men in the sample who have a value of one for thecohort 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, andY90, respectively.37percent lower than the 1981 wages of immigrants who arrived in the 1970s, after controllingfor observable characteristics. This difference is significant from zero.39 Therefore, the averagewages 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 Bakerand Benjamin (1994) for Canada. Immigrant men have significantly lower wages than non-immigrant men at time of arrival and experience low rates of wage assimilation. Also, morerecent 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. Menage 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 hoursof older men have lower growth in hours.In the 1981 data, immigrant men work uine to ten percent more hours than similar non-immigrant men, and these differences are statistically significant.4°The hours assimilation ofthe men who arrived in the 1970s is negative three percent over the decade and is significant.41The hours assimilation is not statistically significant for the two earlier cohorts.42 Immigrantmen who arrived after 1980 worked two to seven percent more hours per week than similarnon- immigrant men. The test of the hypothesis that immigrant husbands who arrived in the39The Wald test statistic is distributed asymptotically according to the Chi-square distribution with onedegree of freedom, and equals 22.89, and the prob-value is less than .005.40The test statistics are 5.13, 4.62, and 4.77 for the variables YBEF61, Y6170, and Y7180 respectively. Theprob-valnes are less than .0001 in each test.4tThe test statistic is 1.96; the prob-vaJue is .05.42The test statistic is —.16 and —1,08 for the coefficients on YBEF61 * YR91 and Y6170 * YR91 respectively;the prob-values are .87 and .28 respectively.381970s worked the same number of hours in the 1981 survey week as immigrant husbands whoarrived in the 1980s worked in the 1991 survey week is performed. A weighted average of thecoefficients on the controls for immigrant arrival in the 1980s is calculated and implies that the1980s cohort worked four percent fewer hours in the 1991 survey week than the 1970s cohortworked in the 1981 survey week. This difference is significant.”3The third column of Table 2.3 lists the results from the weeks equation. In the 1981 crosssection, men age twenty-five to twenty-nine work eleven to thirteen percent fewer weeks thanolder 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 in1981 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 fewerweeks that year. This is due to their having arrived, on average, midway through the year. Inthe 1981 cross-section, the immigrant men from each of the three earliest immigrant cohortsworked one to three percent more weeks than did similar non-immigrants; however, thesedifferences are not significantly different from zero.44 The weeks assimilation is not significantfor each of the three cohorts.45 The immigrants who arrived in 1989 have much lower weeksof work (twenty-three percent) than non-immigrants which is similar to the result found forimmigrant women. This may be picking up an increased likelihood of being unemployed in43The Wald test statistic is distributed asymptotically according to the Chi-square distribution with onedegree of freedom, and equals 8.14. The prob-value of the test is less than .005.44The test statistics for the individual tests are 1.16, 1.79, and .61 for the immigrants who arrived before1961, the immigrants who arrived in the 1960s, and the immigrants who arrived in the 1970s, respectively. Theprob- values for the three groups (in the same order) are .11, .07, and .54.45The test statistics are 1.54, .14, and .95 for the before 1961 cohort, the 1961-70 cohort, and the 1971-80cohort, respectively; the prob-values of the tests are .12, .89, and .34, respectively.39the first years after arriving. The immigrant men who arrived from 1981 to 1988 have verysimilar weeks of work to the non-immigrants, ceteris paribus. The hypothesis that the numberof weeks in 1990 of immigrant men who arrived in the 1980s equals the number of weeks in1980 of immigrant men who arrived in the 1970s is rejected. The weighted averaget6 of thecoefficients on the controls for immigrant arrival year in the 1980s implies that immigrant menwho arrived in the 1980s work four percent fewer weeks in 1990 than immigrant men whoarrived in the 1970s worked in 1980. However, this difference is not statistically significant.47The results of Table 2.3 indicate that immigrant men earn lower wages while working morehours and similar weeks in the year to non-immigrant men. Immigrant men experience higherwage growth, in general, over the 1980s than do non-immigrant men; however, their hours andwage growth are similar to those of non-immigrant men. As was suggested in interpreting theresults of Table 2.2 for women, these differences in labour market outcomes between immigrantsand non-immigrants can be explained by credit constraints being a more important determinantof labour supply in immigrant families than in non-immigrant families. This would explainthe 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 thanthe non-immigrant men given the higher wage growth over the 1980s. However, an alternativeexplanation is that immigrant men work more hours for lower wages than non-immigrantmen due to a lower disutility to work or a lower expected lifetime wealth. This along with a46The coefficient on Y90 was not included in the average to eliminate the truncation of weeks of that cohort.Therefore, the weights are .4892, .0736, .1457, .1551, and .1364 for the variables Y8185, Y86, Y87, Y88, andY89, respectively.47The Wald Test statistic is distributed asymptotically according to the Chi-square distribution with onedegree of freedom, and equals 5.22. The prob-va.lue of the test is greater than .25 and less than .5.40small hours response by immigrant men to a movement along their intertemporal wage pathcan also explain the observed differences in labour market outcomes between immigrant andnon-immigrant men.Next, differences in wages, hours and weeks for husbands and wives by immigrant statusare analyzed holding family characteristics at their mean values over the 1991 non- immigrantsample. The results of Table 2.2 and Table 2.3 indicate that there are important differencesacross immigrant and non-immigrant families in the way wages, hours and weeks respondto factors such as education, language fluency, and the presence of children. Evaluating theequations at these mean values allow us to look at differences between immigrant and non-immigrant families with “average” characteristics. Table 2.4 gives predicted differences betweenimmigrant wives and non-immigrant wives over the 1981 cross-section for each of the threereduced form equations; while Table 2.5 gives the analogous predictions over the 1991 cross-section. In each table, the predictions are evaluated at the 1991 non-immigrant wives’ samplemeans of the regressors.The patterns of wages, hours and weeks differences follow the patterns of coefficient estimates of the regressions in Table 2.2 very closely. In fact there is a simple relationship betweenthese predicted differences and the marginal effects of being in a particular cohort in a particular survey year in the regressions of Table 2.4 and Table 2.5. For example, consider thepredicted wage differential of Table 2.4 for immigrants who arrived in the 1970s. This impliestwenty-four percent lower wages for immigrants in this group than the non- immigrants in1981. In equation (14), an expression for this was derived in terms of the specification of the41regressions, (12):Y51,7— 81,N = XFI3F + P71 (21)Therefore, this differs from the coefficient estimate only by the value of the interaction termsevaluated at the 1991 non- immigrant sample means. Each predicted difference of the firstcolumn of Tables 2.4 and 2.5 differs from the marginal effect of being in that group measuredby the coefficients on the immigrant controls of the wage regression by XFJ3F. This termcan be measured by taking the difference between the predicted wage difference in Table 2.4for the 1971-80 group from the coefficient on Y7180 in the wage regression. The differenceequals .041, which implies that the 1981 wage difference between immigrants who arrived inthe 1970s and non-immigrants is four percentage points smaller when evaluated at the non-immigrant 1991 sample means than it is when characteristics are set at their default valuesin the wage regression. However, almost all of the predicted differences imply lower wages forimmigrants than non-immigrants in both Table 2.4 and Table 2.5. Therefore, the conclusionthat immigrant women generally earn lower wages than non-immigrant women still holds.”9Looking at the predicted differences in the second column of Table 2.4 and 2.5, we seethat immigrant women generally work more hours than non-immigrant women. The differencebetween the predicted hours difference for the 1971-80 cohort in Table 2.4 from the coefficienton Y7180 in the hours regression again equals the effect of the immigrant interaction terms in451n the discussion of the regression specification I focused on the hnsband’s wage equation. However, sincethe same general specification, is used in all of the regressions, one can easily think of (12) as representing thewage, hours or weeks equation for either spouse.49The one case where the predicted difference is positive is the case of women with the most years of residence,those in the 1991 survey who arrived before 1961. Their predicted wage is two percent higher than the predictedwage of the non-immigrants; however, the difference is not significant. The test statistic equals the ratio of thepredicted difference to its standard error and is distributed asymptotically according to the Normal distribution.The test statistic equals .69, and the prob-values equals .49.42the hours regression evaluated at the 1991 non-immigrant sample means, XFI3F. In this casethe difference is .0015. This implies that the hours differences by immigrant status are notvery 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 thecoefficient on Y7180 in the weeks equation equals .0408. This implies that when characteristicsare evaluated at the 1991 non-immigrant mean values rather than the default values of theregression, the difference between the weeks of the immigrants and the weeks of the non-immigrants rises by four percentage points. Therefore, this reinforces the conclusion thatimmigrant wives with five or more years of residence do not work fewer weeks than non-immigrant wives.Table 2.6 and Table 2.7 repeat the comparisons of Table 2.4 and Table 2.5 using theestimates and sample means for the husbands. The difference between the predicted wagedifference in Table 2.6 for the 1971-80 group from the coefficient on Y7180 in the wage regressionof Table 2.3 equals .068, This implies that the 1981 wage difference between immigrants whoarrived in the 1970s and non-immigrants is seven percentage points smaller when evaluated atthe non- immigrant 1991 sample means than it is when characteristics are set at their defaultvalues in the wage regression. However, aU of the predicted differences imply lower wages forimmigrant 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 that43immigrant husbands generally work more hours than non-immigrant women. The differencebetween the predicted hours difference for the 1971-80 cohort in Table 2.6 from the coefficient onY7180 in the hours regression equals .062. This implies that the hours differences by immigrantstatus are sensitive to the chosen values of personal characteristics. When characteristics areheld at the non-immigrant 1991 sample means, the difference between the immigrant and non-immigrant hours for each cohort in each year are six percentage points smaller. This leavesvery little difference between hours of work of immigrants and non- immigrants. The onlysignificant differences are for immigrants who arrived before 1981. The predicted differences inthe second column of Table 2.6 are all positive and significant implying three to four percentmore hours of work for immigrants.5°Also, the predicted hours differences for immigrantsarriving 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 thecoefficient on Y7180 in the husbands’ weeks equation of Table 2.3 equals .040. This impliesthat when characteristics are evaluated at the 1991 non-immigrant mean values rather thanthe default values of the regression, the difference between the weeks of the immigrant men andthe weeks of the non-immigrant men falls by four percentage points relative to the differenceswhen characteristics are held at the default values in the regression. The only differences inthe third column of Table 2.6 and 2.7 which are significantly different from zero are for the50The test statistics equal 2.52, 1.96, and 2.02 for the before 1961, 1961-70, and 1971-80 cohorts, respectively.The prob-values are .01, .05, and .04, respectively.51The test statistics equal 3.90 for the before 1961 group and 2.13 for the 1961-70 group. The prob-values areless than .0001 and .03, respectively.441988, 1989, and 1990 cohorts.52The results of the estimation indicate that immigrant husbands and wives face lower wagesimmediately alter arrival than non- immigrant husbands and wives. Successive immigrant cohorts of men have faced lower wages at entry, after controlling for observable characteristics;however, these differences across immigrant women’s cohorts are insignificant. Immigrant husbands 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 percenthours surplus which is striking when you consider that these women are earning one to thirty-five percent lower wages. For both husbands and wives these differences in hours remain moreor less constant with years of residence. The high hours and low wages are consistent withcredit 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 thenon-immigrant families in response to the higher wage growth of immigrants could also beexplained by credit constraints. As discussed above, a preference based explanation could alsobe 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 immigrants who work and the population of non-immigrants who work. In evaluating the success of52The test statistics are —2.43, —5.48, and —8.89, respectively. The prob-values are .02 for the 1988 cohort,and less than .0001 for the other two cohorts.45immigration policy and choosing immigrants who adapt well to the new labour market, it maybe preferable to compare the total population of immigrants and the total population of non-immigrants. This distinction is more likely to be an issue for women since their participationrate is lower. An example of how this distinction could be relevant in measuring differencesin unobserved ability between immigrant and non-immigrant wives is the foliowing. Considerthe extreme case where afl immigrant women choose to work but some non-immigrant womenchoose not to work. In particular, assume that non-immigrant women with high offered wagesare more likely to participate than those with low offered wages. Also, assume that the offered 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 ofimmigrant wives who work, although both groups share the same offered wage distribution. Ignoring the participation decision leads one to the conclusion that immigrant women have lowerunobserved ability than non-immigrant women, when the only difference between immigrantand 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 onthe 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 totake the form:lflWtzXw/3w+Ew (22)lnH=Xh/3h+eh (23)InWK Xwk/3w +Ewk (24)46where 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 inTable 2.2; 13h, and /9wk are parameter vectors; and E, ep,, and 8wk are error terms. Thewage equation explains the wage offered to each married woman on the market. The hours andweeks 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,, (26)lnH = Xh/3h + E{eh j e, : —Z/3} + Ch (27)1nWK = Xwk/3w + E{ewk I ep —Z/3} + Cwk (28)where E{x I e, —Z/3} is the expectation of x conditional on the wife working, for x =eh and ewk; and c, Ch, and Cwk are mean zero error terms over the sample of households wherethe wife works.It is assumed that the error terms e, e,,,, Eh, and Ek are jointly distributed according to47the Normal distribution with covariance matrix:L7 p,h p,wkCp,w f7, Uw,h w,wk2p,h ‘7w,h h h,wk2Cp,wk w,wk rJhwk tvkwhere is the variance of q for j = p, w, h, wk, and 0j,k is the covariance of &j with 6k forj,k=p,w,h,wk,wherej $ k.Equations (25)-(27) can be rewritten:mW = + f2f(Z) + c (29)UwlnH = Xh/3h + + cj (30)1nWK = Xj3w + “.(Z) + c (31)wkwhere (Z) is the inverse Mill’s ratio and is defined as (Z) E f(4.&)/F(), where f andF are the Standard Normal density function and distribution function, respectively.The first stage involves estimation of the determinants of the wife’s participation decisionusing the Probit estimator. The estimates of /3/a are used to derive a value of the inverseMill’s ratio, F(Z), over the sample of households where the wife works. The derived InverseMill’s ratio variable is then included as a regressor in the estimation of (28)-(30) over thesample 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 increasein the explanatory variable. The same set of controls are included as in the regressions of Table2.2. Controls for the husband’s age, education, and immigrant status were also included. This48is to make the results comparable to those of Duleep and Sanders (1993) and Baker andBenjamin (1994). Unlike the specification of the immigrant controls in the previous tables, thedefault group is no longer the non-immigrants, but instead couples with both spouses havingarrived in Canada in the 1980s.53 A dummy variable for non- immigrant households is includedin 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 resultsbecause there are controls for the characteristics of each spouse. Therefore, in order to simplifythe discussion, I will focus on the coefficients of the controls for the wife and husband’s arrivalcohort variables.The coefficient on the non-immigrant dummy variable, NB, measures the difference inthe wife’s participation probability between non-immigrant couples and immigrant coupleswhere both spouses arrived in the 1970s, after holding other characteristics at the defaultvalues. The coefficient is significant and implies a seven percent higher participation rate forthese immigrant wives.54 The coefficient on the interaction between the non-immigrant dummyvariable and the 1991 survey year dummy variable measures the change in this difference in thewife’s participation rate over the decade. The estimate implies a three percent higher growthin the non-immigrant participation rate than in the immigrant participation rate; however,this difference is not statistically significant.5553J could not include controls for the both the husband’s immigrant cohort and the wife’s immigrant cohortwhile having the default group being couples who are both native-born. The sum of the immigrant cohortcontrols 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 whoarrived in the 1970s.54The test statistic equals —2.39, and the prob-value is .017.55The test statistic equals 1.51, and the prob-value equals .13.49The coefficients on the dummy variables for the wife having arrived before 1961, and the wifehaving arrived in the 1960s indicate that these women have seven percent higher participationrates than do immigrant women who arrived in the 1970s.56 The coefficients on the interactionsof 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 ratesacross these immigrant cohorts change over the 1980s. In each case, the participation rate ofimmigrant women who arrived in the 1970s approaches the participation rate of the immigrantwives who arrived before 1970; however, these differences are not significant.57Therefore, 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 womenwho arrived in the 1970s. These differences in the wife’s participation rate do not changesignificantly over the 1980s.Using the coefficients on the controls for the husband’s immigrant status, we see themarginal 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 whoarrived in the 1970s. From the coefficients on the controls for the husband having arrivedbefore 1971, we see that immigrant wives with husbands from earlier cohorts are significantlyless likely to work.5856These differences are significant. The test statistics equal 2.00 for the coefficient on the first variable and2.70 for the coefficient on the second variable. The prob-va.lues are .042 and .007, respectively.57The test statistics are —1.28 for the coefficient on the variable for the before 1961 cohort, and —1.64 for thecoefficient on the variable for the 1961- 70 cohort. The prob-values are .20 and .10, respectively.55The test statistics are —4.93 for the control for the husband having arrived before 1961, and —4.06 for thecontrol for the husband having arrived in the 1960s —4.06. The prob-values are less than .0001 in each case.50The coefficients on the interactions between the husband’s arrival cohort with the dummyvariable for the 1991 survey year give the change in these relationships over the decade. Theyimply that these differences in participation rates do not change with time in Canada.59 Thismeans that the participation rate is higher for immigrant wives whose husbands are from morerecent immigrant cohorts, and the magnitude of these differences do not change significantlyover the 1980s.This could represent differences in the husband’s attitude towards the wife working acrossthe husband’s immigrant cohort. The husbands from the earliest cohorts may be less supportiveof the wife working.Table 2.9 contains estimates from the wage, hours, and weeks regressions for women aftercontrolling for the wife’s participation decision. The results are similar to the ones found inTable 2.2; therefore, I will focus the discussion on the coefficients on the controls for immigrantarrival cohort. The first column contains the result of the wage equation. The variable IMRat the end of the table is the inverse Mill’s ratio variable derived using the Probit estimatesof Table 2.8. The coefficient on IMR is positive and significant.6°From equation (28), this isan estimate of the ratio of the covariance of the error term in the wage equation and the errorterm in the participation index, over the standard error in the wage equation. The positivesign means that the covariance term is positive. Therefore, women with high offered wages aremore likely to work, after controlling for observable characteristics.The coefficients on the controls for the wife’s arrival cohort are generally smaller than59The test statistics are 1.87 for the before 1961 cohort of men, and 1.22 for the 1961-70 arrival cohort ofmen. The prob-values are .06 and .22, respectively.60The test statistic equals 7.00, and the prob-value is less than .0001.51those in the wage regression of Table 2.2. For example, the coefficient on Y7180 is .2588 in thewage regression of Table 2.9, and it is— .2821 in Table 2.2. The coefficient on the interactionsbetween the three earlier arrival cohorts with the 1991 survey dummy variable measure thewage assimilation for each cohort6’The assimilation is smaller in Table 2.9 than in Table 2.2,and it is now only significant for immigrants who arrived after 1960.62The second column contains the results from the selection corrected reference week hoursequation. The coefficient on IMR is negative and significant.63 This implies that the errorterm from the hours equation, (29), is negatively correlated with the error term from theparticipation index, (24). Therefore, women who participate work fewer hours than the womenwho choose not to participate would work if they were to participate. This relationship wasfound 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 alsofinds a negative relationship between the error term in the hours of work equation and theerror term in the wife’s participation index. In Chapter 4, the wife’s participation decision isanalyzed in more detail, within the context of a structural model of the wife’s participationdecision and labour supply.The coefficients on the controls for the immigrant wife’s arrival cohort are smaller in Table2.9 than in Table 2.2. However, the general pattern of the results is unchanged. In the 1981data, immigrant women who arrived after 1960 have significantly higher hours of work than61RecaJl that this is the difference between the growth in wages of each immigrant cohort from the growth inwages of the non-immigrants.82The test statistics are 1.75, 2.03 and 2.96 for the before 1961 cohort, the 1961-70 cohort, and the 1971-80cohort, respectively. The prob-valnes are .075, .042, and .003, respectively.63The test statistic equals 5.58, and the prob-value is less than .0001.52non-immigrant women.64 As was the case in Table 2.2, the coefficients on the interactionsbetween the wife’s arrival cohort and the dummy variable for the 1991 survey year are notstatistically significant.65 This means that the hours differences between immigrants of thesecohorts 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 theweeks 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 participatewould work if they were to participate.In the 1981 cross section, the coefficients on the controls for immigrant arrival year are verysimilar to those from the weeks equation of Table 2.2. In each case, the weeks of work are notsignificantly different between immigrant and non- immigrant women.67As was the case in Table 2.2, the weeks assimilation is not significant for immigrant wiveswho arrived before 1971.68 The weeks of immigrant wives who arrived in the 1970s grow bysix percent more than the growth in weeks for non-immigrants over the 19808.69Finally I derive the predicted differences in wages, hours, and weeks by immigrant arrival64The test statistics are 2.40 for the 1961-70 group and 1.99 for the 1971-80 group. The prob-values are .02and .05, respectively.65The test statistics are .02, —.75, and .37 for the before 1961 cohort, the 1961-70 cohort, and the 1971-80cohort, respectively. The prob-values are .98, .45, and .71, respectively.eeThe test statistic equals —3.99, and the prob-value is less than .0001.67The test statistics are —.06, —.32, and —1.77 for the controls for arrival cohort before 1961, between 1961and 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 yearin the 1960s. The prob-values are .94 and .74, respectively.69The coefficient on the interaction between the control for arrival in the 1960s and the 1991 survey yeardummy variable is significant. The test statistic equals 2.22 and the prob- value equals .03.53cohort of Table 2.4 and 2.5 using the new estimates. Table 2.10 and 2.22 contain these predicteddifferences after controlling for the wife’s participation decision.7° In general, there are onlysmall differences in Table 2.4 and 2.5 relative to Tables 2.10 and 2.11.2.5 Concluding RemarksThe results of the reduced form estimation indicate that immigrant men and women facelower 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-immigrantcounterparts. The wage/education profile of immigrant women is not as steep as that of non-immigrant women. This would reflect difficulties of international transferability of skills andcredentials. Interestingly, this difference is not apparent for men. It may be that immigrantwives take jobs that are readily available after migration which do not necessarily suit theirtraining so as to support family consumption while the husbands search for work or invests inretraining. However, an alternative explanation has been suggested. The family’s immigrationdecision may be tied more closely to the husband’s career prospects if he is perceived to bethe principal earner, than to the wife’s career prospects. This would lead to a better expectedreturn on the education of immigrant husband relative to the returns on the education of theimmigrant wife. A third possibility is that immigrant wives have difficulty finding trainingprograms which would assist them in having their foreign credentials and skills recognized inthe Canadian labour market. Beach and Worswick (1993) comment that most governmenttraining programs for recent immigrants are intended for men. It may be that new programsare needed to assist immigrant women in finding jobs suited to their education.70The variable 1MR is set to zero so that the predictions do not condition on the wife choosing to participate.54Recently arrived immigrant men and women work significantly fewer weeks in the yearthan do non-immigrants. It is likely that immigrants experience unemployment in the firstfew years after migration as they search for jobs suited to their skills. However, differencesbetween the weeks of immigrants with more than five years of residence and non-immigrantsare not significant.Immigrant wives work more hours per week than non-immigrant wives. Immigrant andnon-immigrant husbands work very similar hours. Hours growth over the decade is found tobe the same for immigrant and non-immigrants.The patterns in the data are consistent with the hypothesis that credit constraints areimportant determinants of the labour market adjustment of immigrants. Immigrants are foundto supply at least as many hours as non-immigrants while earning significantly lower wagesthan their non-immigrant counterparts. The high labour supply of immigrants given theirlow wages could be explained by the immigrant family being unable to borrow against futureearnings, and responding to this constraint by supplying more labour. If the effects of the creditconstraints 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-immigrantswith years of residence. However, given that immigrant men and women experience higherwage growth than similar non-immigrant men and women, it may be that the immigrant’sresponse to the higher wage rate in terms of increased hours of work “masks” the decline inhis/her hours due to the lessening of the credit constraint effect. An alternative explanationfor the hours and wage differences by immigrant status is that immigrant households work55more hours in all periods due to either a lower disutility to work or a lower expected lifetimewealth. This coupled with a lower responsiveness of immigrant hours of work to growth intheir wage rates over time would explain the movements found in the data. It is uot possibleto distinguish between these explanations using reduced form estimation.56CHAPTER THREE3.1 IntroductionIn this chapter, the hypothesis that credit constraints are important determinants of laboursupply decisions in immigrant families is explored within the context of a structural model ofintertemporal labour supply. The model extends the literature on dynamic labour supply ofwomen and men by allowing for the possibility that the household may be credit- constrainedin some periods. This extension of the existing dynamic labour supply models was needed inorder to separate differences by immigrant status in family preferences toward each spouse’slabour supply from differences in terms of access to credit.The results of the estimation of the structural model indicate that it is differences in familypreferences towards labour supply (and perhaps differences in lifetime wealth), and not creditconstraints, which explain the observed differences in hours of work in immigrant versus non-immigrant families. The marginal value placed on the wife’s non-labour time relative to thenon-labour time of the husband is smaller in immigrant families than in non-immigrant familieswhich would lead to more hours of work by immigrant women, ceteris paribus. After controllingfor differences in this marginal rate of substitution between the wife’s non-labour time and thehusband’s non-labour time, and differences in market wage rates, immigrant family memberswere found to work more hours in all periods due to either a lower disutility to work or a lowerexpected lifetime wealth of the household.573.2 The ModelThe following is an adaptation of a model of dynamic labour supply and consumption inthe presence of uncertainty and taxes developed in MaCurdy (1983). The model is extendedto allow for both the husband’s and the wife’s hours of work decisions and for the possibilitythat households may be credit-constrained in some time periods.The household chooses hours of work for both the husband and the wife and family consumption 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) +w2(r)hr) — p(r)c(r) r = 1, .., T (2)where r indexes future time periods, UQr) = U(cQr), hi(r),h2(r)) is the within period utilityof the family, p is the rate of time preference, p(r) is the price of the composite commodity,cQr) is family consumption; hi(r), h2Qr) and w1Qr), w2Qr) are the husband’s and the wife’shours and wage rates respectively; AQr) is non- human wealth held at the end of period r; andr(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 afterchoosing a level of assets to be held at the end of the period, A(r), then (2) is the constraint thehousehold 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 credit58constraint for period r is represented by a non-negativity constraint onA(r)O r=t,..,T (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 cannotborrow against future income.1Given an initial condition, A(O) = A0, and a terminal condition, A(T) = AT, this characterizes 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 consumptionover all periods, and satisfies the asset accumulation constraints and the asset non- negativityconstraints in all periods. The value function equals the present discounted value of householdutility over the remainder of the household’s T periods under the optimal choices of hours ofwork and consumption in each period.One can think of the household as maximizing:U(t) +1f,jEt{V(A(t),t + l)} +7Q)A(t)+AQt)[wi(t)hi(t) +w2(t)ht) + 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 amountwhich implies that they can aliow their non-human assets to become negative. In this case the constraint wouldbe of the form:A(r)+ll(Z(r))Owhere ll(Z(r)) represents the amount the household can hold as debt at the end of the period which dependson potentially time-varying exogenous household characteristics, ZQr). In particular, ll(Z(r)) may depend onthe immigrant status of the household.59multiplier for the period I asset non-negativity constraint. Therefore, the consumer maximizesthe above expression subject to (2) and (3).Assuming interior solutions for c(I), h1 (I), and h2(t), the necessary conditions are:2UQ) = )iQ)p(t) (5)Uh1 (I) = —A(I)wi(t) (6)Uh2(t) = —AQt)w2(t (7)where U1(t.) is the derivative of U(t) with respect to i, for i = c(I), hi(t),h2(I). Given theassumed additive separability of preferences across time, each condition is a function of variables observed at time t, utility parameters, and the latent variable, AQ). The effect of incomeearned outside the period in determining period I choices of hours and consumption enter thenecessary conditions through A(I), the marginal utility of wealth held at time I. Since it isunobserved, 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:______— wi(t)Uh2(t) — w2(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 theirwages. The equation describes how the family is prepared to trade fewer hours of work forone 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 credit-constrained in period I does not affect this condition. Credit constraints affect the family’s2The assumption of an interior solution for the wife’s hours of work will be relaxed in Chapter 4.60ability to trade more hours of work in the future for fewer hours of work in the present. Theabove MRS condition involves trading more hours of work in period t of one spouse for fewerhours of work in period t of the other spouse. The household does not need to use lendingmarkets in order to make these trades; therefore, the efficiency condition, (8), holds whetheror not the household is credit-constrained.The motion equation for the marginal utility of wealth, A(fl, is:3A(t)= 11E{A(t + 1)(1 + r(t + 1))} + 7(t) (9)If the household is credit-constrained in period t, ‘y(t) > 0, otherwise 7(t) = 0. In order tointerpret this condition, assume for the moment that the household is not credit-constrained inperiod t, which implies 7(t) = 0. In this case, the condition equates the expected present valueof 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 credit-constrained in period t, this marginal condition does not hold. The household would like to3To see this, differentiate the Bellman equation with respect to A(t):1 E ãV(A(t),t-i-1) At —o 0ÔA(t) ( )Define the Lagrangean:L = [(l+SI_1 +A(r){w1(t(r)+w2(ñh2(r1—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), h2(r), A(r), A1, A2, 7(r), and 6(r); r = t + 1, ..,T. At thesevalues, L = V(A(t), t + 1). Differentiating L with respect to A(t), and applying the envelope theorem, thentaking 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.4This description is taken from Altonji (1986).61lower 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 wouldchoose 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 ofwealth 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. Substituting (7) into (9) for A(t) and AQ + 1):—Ua2(t)— (1+r) f—Uft2(t+1)— +7(t) (10)w2(t) (l+p) i w2(t+1)When the household is not credit-constrained in period 1, j’(t) = 0, and (10) is the intertemporalMRS condition for the wife’s hours in period I and I + 1. The household chooses hours for thewife in each period, so that it is indifferent between marginal trades of hours of work in I forhours or work in I + 1 at the market interest rate, the period I wage rate, and the expectedperiod I + 1 wage rate for the wife. If the household is credit-constrained in period I, then itwould 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’tmake this trade because credit is rationed. Therefore, it chooses more hours in I so as toincrease consumption towards what it would be in the absence of the credit-constraint. To seethis in terms of equation (10), first note that the marginal utility of the wife’s hours in periodI, Uh2(I), is negative. I will refer to—Uh2(I) as the marginal disutility of the wife’s hours in Isince it is the drop in the household’s within period utility at time I due to a marginal increasein the wife’s hours. Given the concavity of the utility function, U(I), the marginal disutility62of the wife’s hours is increasing in her hours. Therefore, since the household chooses a largervalue of h2(t) when it is credit-constrained in t, this implies a larger value of—Uh2(t). Thismeans 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 ofher hours to her wage rate in t + 1, 9$}Et { }. Equation (10) will be referred to asthe Euler equation for the wife’s hours.Before proceeding I will give an outline of the estimation procedure. The first equation tobe estimated is (8), the within period MRS condition between the husband’s hours and thewife’s hours. These estimates reveal how the household adjusts the hours of work of each spouseto different offered wage rates. In particular, the estimation allows for differences in householdpreferences over the hours for the husband and wife between immigrant and non-immigrantfamilies. 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 1980sis observed in the data. Also, the growth of the wife’s hours is observed. Using the estimatesfrom the MRS condition, (8), the growth in the marginal disutility of the wife’s hours,—Uk2 (t),is derived.5 Using this information, equation (10) is estimated. From the estimates, we seewhether or not the growth in hours and wages is consistent with credit constraints having animportant effect on the hours patterns over time. In particular, we are interested in whetheror not differences by immigrant status in the parameter estimates of (10) are consistent withthe hypothesis that immigrant families are more likely to be credit-constrained than non5This is an oversimplification of the estimation procedure. Under the assumed functional form of the utilityfunction, it is not possible to derive all of the parameter estimates of —U,,, (t), from the estimation of (5). Theprocedure for estimating the remaining parameters is discussed below in Section 3.4.63immigrant families.In order to facilitate estimation, equation (10) is rewritten as:—UhJt)— (l+r)E f_Uh.,(t+l)lr(t) (11)w2(t)— (l+p) w2(i+1) jwhere Q) > 0 if the household is credit-constrained, and 1’Q) = 0 otherwise.6 The followingmultiplicative structure is assumed for the forecast error in (11):—Uh2(t+ 1)= e_1(t)(1 + p) (—Uh2t)’\ (1 + c(t+ 1)) (12)w2(t+ 1) (1+r) \. w(t) Iwhere c(t + 1) is a forecast error uncorrelated with (1 + p)/(l + r) and —Uh2(i)/w2(t).Taking the natural logarithm of both sides of (12) and rearranging:in(°t)— in (7) = — F(t) + iyQ + 1) (13)where b+1 = in(1+p)—in(1+r)+Et{in(1+cQt+1))}, and iì(t+1) is a forecast error uncorrelatedwith variables known by period t. Therefore, bt+i — Q) is the expected movement between tand t + 1 of the natural logarithm of the ratio of the marginal disutility of the wife’s hours toher wage rate.The results of Chapter 2 can be interpreted in terms of equation (13), the Euler equation forthe wife’s hours. Immigrant wives were found to have higher wage growth than non-immigrantwives. The effect of this difference, ceteris paribus, is a smaller value of the left hand sideof equation (13) for immigrant wives than for non-immigrant wives.7 The growth in hours6Multiplying by e’(t) scales up fl$}Ee { } until the equality holds.7Note that the left hand side of the equation can be rewritten ln(—Uh2(t+ 1)) — ln(—Uh2(t)) + ln(w2(t)) —In(w2(t + 1)). Since ln(w2(t)) — ln(w2(t + 1)) is smaller for immigrant wives, then holding the change in themarginal disutility of the wife’s hours the same between immigrant and non-immigrant families, this implies alower value of the left hand side of (13) for immigrant wives.64between immigrant wives and non-immigrant wives was found to be equal in Chapter 2. Itwas argued that the fact that the immigrant wives’ hours do not rise by more than the non-immigrant wives’ hours could be due to credit constraints. In terms of equation (13), thiswould mean that the differences in the left hand side of the equation by immigrant statusare explained by a larger value of the multiplier on the credit constraint, 1’Q), for immigrantfamilies. Since it appears as —I’(t) in (13) this could explain the lower value for immigrantfamilies of the left hand side of the equation due to the higher wage growth of immigrantwives. However, the fact that the growth in the wife’s hours is not significantly differentbetween immigrant and non-immigrant wives does not necessarily imply that the growth inthe family’s marginal disutility of her hours,—Uh2(1), is the same. It may be that the hours ofthe wife are not very responsive to increases in her wage. Therefore, a small difference in thehours of work of immigrant and non-immigrant women could imply a large difference in theirmarginal disutility of work,—Uh2Qt). This difference in the marginal disutility of the wife’shours, could offset the effect of the higher wage growth of immigrant wives in the left handside of (13).8 The estimation procedure allows us to derive estimates of the marginal disutilityof the wife’s hours from the estimation of the within-period MRS condition between the wife’shours and the husband’s hours, (8). Given these estimates, equation (13) can be estimated tosee 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 hypothesisthat immigrant families are more likely to be credit-constrained than non-immigrant families.8The larger growth in the marginaJ disutility of the wife’s hours for immigrant bmilies means a larger valueof in(—Uh2(t + 1)) — ln(—Uh2(t)) for immigrant &miies; therefore, this could offset the effect of the smallervalue of ln(w2(t))— ln(w2(t + 1)) leaving no difference in the left hand side of the Euler equation, (13), betweenimmigrant and non-immigrant Thmilies.65Differences by immigrant status in bt+i — FQ) could result from three sources which cannotbe distinguished in the estimation. First, credit constraints as represented by differences inr(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 preferencewhich appears in bt+i, could explain these differences. This variation would exist if the immigrant household’s preferences over work in the early years after migration relative to workin later years differed from the preferences of non-immigrant households. Finally, differencesin the distribution of the forecast error, cQ + 1), between the two groups, could explain thedifferences in bt+i — rQ).It will be assumed in the analysis that immigrant and non- immigrant households share thesame forecast error distribution. This implies that Et{ln(l+c(t+1))} is the same for immigrantand non-immigrant families. The assumption that this error distribution is homogeneous andexogenous is maintained in both the dynamic labour supply literature (MaCurdy (1983)) andin the dynamic consumption literature (Zeldes (1989) and Runkle (1991)). If immigrants havemore or less uncertainty about the future than do non- immigrants, then the variance of theforecast 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 endogenousvariables such as wages then the exogeneity assumption is violated. It is impossible to testthese assumptions without panel data. Therefore, these assumptions are maintained, and anexploration of their importance is left for future work.Differences by immigrant status in bt+i — F(t) will be attributed to either differences in66the rate of time preference, p, or differences in the credit constraint multiplier, T’(t). As theempirical results wili show, the value of bt+i — r(t) for immigrant families is not significantlysmafler than for non-immigrant families. This is evidence against the hypothesis that immigrant families are more likely to be credit-constrained than non- immigrant families. It ispossible that immigrant families are more likely to be credit-constrained than non-immigrantfamilies, implying a larger value of Q) for immigrant families, but the rate of time preferenceis also larger in immigrant families, implying a larger value of bt+1. This means that immigrantfamilies place a lower weight on future utility; therefore, they want the wife to work more inthe future. However, they are more likely to be credit- constrained; therefore, they are notable to substitute for fewer hours for the wife in the present at the expense of more hoursfor the wife in the future. While this is possible, it would not explain the differences in thereduced form results of Chapter 2. Since the difference in bt+i offsets the difference in r(t) thiscannot explain the fact that immigrant wives do not increase their hours by more than non-immigrant 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 betweenimmigrant and non-immigrant families can explain the observed patterns of hours and wagesof 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 LiteraturesMaCurdy (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 hoursof work and consumption over his lifetime. The husband is assumed to be able to borrow or67lend as much as he wishes at the market interest rate. As in section 3.2, the interest rate isassumed to be a constant. Also, he is assumed to have perfect foresight. In terms of (9), themotion 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 asa function of A(O):Uh1(t) =-A(O)w1(t (16)MaCurdy assumes that the within period utility function, UQ), is additively separable inthe husband’s hours and all other goods. Under the assumed functional form for utility, thecondition can be solved for the husband’s hours as a function of the marginal utility of wealthat time zero, A(O):h1(i) = h1 { [ Pj A(O), wiQ)} (17)MaCurdy refers to this as the lambda-constant labour supply function. It describes the movement 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 naturallogarithm of both sides of the equation, the log of A(O) appears additively. MaCurdy takes thefirst difference across time of the log hours equation and estimates this difference equation.68The marginal utility of wealth term, A(O), fails out of the difference equation since it is constantthrough time. Under the assumed functional forms, the coefficient on the change in log wagesin the log hours difference equation is an estimate of the intertemporal elasticity of substitutionfor hours. Using data from the PSID, MaCurdy estimates the hours difference equation andfinds 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 interestrate. MaCurdy takes the ratio of the marginal condition for the husband’s hours, (6), and themarginal condition for consumption, (5), to give:9Uh1(t) = wiQ)“18Uc(t) p(t)This is the condition that the household’s MRS between the hours of work of the husband andfamily consumption equals the real wage rate, in period 1. This MRS condition is estimatedusing instrumental variables methods to give consistent estimates of the parameters of thewithin period utility function, UQ).As in section 3.2, MaCurdy assumes that the interest rate is constant and known by thehousehold. 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 con9MaCurdy includes the after tax wage in place of the observed wage in this equation. In this thesis, taxissues are not addressed.69sumption, (5), and derives the Euler equation for consumption:UQt)— (l+r)E fU(t+1) (20)pQ) (l+p) tlp(t+l)Using the estimates from the first stage, the marginal utility of consumption is derived ineach period and then the Euler equation, (20), is estimated by instrumental variables methodstreating consumption in each period as endogenous. Using these estimates he is able to characterize the dynamic labour supply choices of married men. MaCurdy finds a greater degreeof 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 allowsfor the fact that the husband may be uncertain of his future wage path. Another advantageof this procedure is that the estimation of (18) takes advantage of the detailed information ineach cross-section of how the family trades more hours for the husband in order to have higherconsumption. This information is incorporated into the estimation of the Euler equation forconsumption, (20).Browning, Deaton, and Irish (1985) take the standard household intertemporal choicemodel and redefine it in terms of dual functions. They define profit functions for the household from which they are able to derive Frisch labour supply functions. The Frisch laboursupply function describes the individuals’ hours of work as a function of the period t pricesof all goods, and the marginal utility of wealth at time zero, A(0). The main advantage tothis procedure over the one used in MaCurdy (1981) is that it does not require that utilitybe additively separable in the husband’s hours and other goods. However, since the marginalutility of wealth, A(0), is not observed, a procedure must be developed to eliminate it from70the equation to be estimated. It is assumed that after taking the natural logarithm of theFrisch hours equation, the log of the marginal utility of wealth appears additively. Next thefirst difference of the equation is taken, eliminating the marginal utility of wealth. It is thisdifference equation which is then estimated. The difficulty with this is that strong assumptionsabout preferences are necessary in order for the log of the marginal utility of wealth to appearadditively in the log hours equation. In the empirical work, they focus on the hours of marriedmen and assume that preferences are additively separable between the husbands hours andother goods. In this case the Frisch labour supply function is the lambda-constant laboursupply function, (17), used by MaCurdy (1981).In the estimation, Browning, Deaton, and Irish (1985) use synthetic cohort data generatedfrom the U.K. Family Expenditure surveys. The annual cross sectional data sets from 1970through 1976 are used. Each cross section is treated as a random sample of the same populationat each point in time. They define sub-populations in terms of five year birth cohorts andwhether or not the person is a manual or a non- manual worker. They next define cohortsample 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 underlyingpopulation as manual workers who are nineteen to twenty-three in the 1971 survey. The dataused in estimating the hours difference equation are the means of the log hours and log wagesof these groups in each year, which they refer to as a “panel of cohort means”. The results ofthe estimation are not supportive of the life cycle model of labour supply for men. They findvery small responses of hours to changes in wages for men and suggest that the standard lifecycle model must be extended in order for it to be consistent with the results of the estimation.71The dynamic labour supply literature for married women is not as well developed as theliterature for men. Heckman and MaCurdy (1980) are the first to study the intertemporalhours choices of married women using panel data. They derive a lambda-constant leisuredemand function for married women and address the possibility that the wife may not workin some periods using a simple Tobit specification10. The estimation involves treating themarginal utility of wealth term, A(0), as an individual specific fixed effect. They find evidencein support of the life-cycle model for married women. They test for the effects of transitoryincome shocks on the wife’s labour supply, and find that spells of unemployment experiencedby the husband do not have a significant effect on the wife’s labour supply. Heckman andMaCurdy 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 coupleswithin the context of a life-cycle model. They use a single cross section from the U.K FamilyExpenditure Survey from 1980. Therefore, they are not measuring the intertemporal laboursupply behaviour of the couples. Instead, they are analyzing the hours of the husband andwife at a point in time using a model which is consistent with the household choosing thesehours in every period subject to a lifetime budget constraint. The model is equivalent to theone developed in Section 2.3 with the added assumption that the household is never credit-constrained. Their approach to modelling the household’s decisions is as a two-stage budgetingproblem. Instead of thinking of the household choosing hours of each spouse in each periodsubject to a lifetime budget constraint, the problem is reformulated as the choice of hours ineach 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 4.72leisure are chosen so that the household’s budget constraint for that period is satisfied. Theincome allocated to that period is endogenous to the problem. The household chooses hoursconditional on the income, and then the income is chosen optimally. The estimated hours ofwork equations condition on this income variable. The advantage to this approach is that youdo not have to make strong assumptions on within period preferences over the hours of thetwo spouses (the previous literature assumes additive separability of the wife’s hours and thehusband’s hours). However, the drawback is that the income allocated to that period is afunction of exogenous income which is difficult to measure in practice.Bernhardt and Backus (1990) use a theoretical model to study the effects of credit constraints on the labour supply and occupational choice in married couples. In an optimal controlframework, they derive predictions for a family which chooses consumption, labour supply, andoccupations for the husband and wife over the lifetime of the household. They find that creditconstraints will lead household members to supply more labour in periods when they are youngso as to increase consumption towards the level it would be if the family were able to borrowagainst future wage income. Bernhardt and Backus (1990) argue that specialization in terms ofoccupational choice allows the married couple to separate the borrowing and investing aspectsof occupational choice. One spouse enters an occupation with low human capital accumulationand a high current wage, and supports the other spouse’s entry into the occupation with a lowstarting wage, but high human capital accumulation.Empirical work on the existence of credit constraints on family behaviour has been restrictedprimarily to the consumption literature. Zeldes (1989) uses PSID data to estimate a dynamic73model of household consumption and tests for credit constraints. The test is based on theEuler equation for consumption. The equation used in estimation can be derived from theequations of section 2.3 by substituting the marginal condition for consumption, (5), into themotion equation for the marginal utility of wealth, (9):U(t) — (1+r) fUc(i+1)j 2p(t) - )Et p(t+1) j +7(0 (1)The test for credit constraints involves splitting the sample in terms of households with a highassets to income ratio and households with a low assets to income ratio. The first group areunlikely 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. Heconcludes 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 aggregate shocks and measurement error in consumption. Runkle finds that both aggregate shocksand measurement error are important issues in estimation.11 The results of his estimation donot 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 analysisand 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 estimating 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 sameway. The issue of measurement error wifi be addressed below in the discussion of the data.74and wage combinations of husbands and wives in each cross section. Also, MaCurdy’s methodof estimating an intertemporal MRS condition is conducive to incorporating credit constraintsinto the model in the same way as in the intertemporal consumption choice literature.3.4 Functional Forms and Estimating EquationsThe functional forms are chosen to suit the modelling of both spouse’s labour supplies andthe absence of consumption data.’2 The following functional form for the within period utilityfunction is used:’3(11t) = QQ) { [T —h1g(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 12(t) areage specific modifiers of taste and a and a2 are parameters.’5Using (22), equation (8), the within period MRS condition between the husband’s hoursand the wife’s hours, becomes:[7’ —h1(t)]@i’)— w,(t)23)— 21(t)](a2-l)— w21(t)‘21n what follows, consumption will be excluded from the notation.‘3The restriction that within period utility is additively separable in consumption is required since the datasets employed do not contain measures of consumption. It is common in both the labour supply and theconsumption demand literature to assume that utility is additively separable in hours and consumption. To theauthor’s knowledge there has been no research using dynamic household models which uses both labour supplyand consumption analysis; therefore, it is impossible to say whether or not this assumption imposes importantrestrictions 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 hedoes not report the results of tests of the separability assumption.14n the estimation, 2’ is set at 5252 hours. Other values were used with only small changes in the results.‘5While the utillty function assumed is restrictive, it does nest commonly used utility functions such as theCES and Cobb-Douglas. This type of utility function has been used in Heckman and MaCurdy (1980), MaCurdy(1981), and Altonji (1988).75The following functional forms for the taste-shifters, Q1(t) and it1(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 areparameter vectors; and a(t) and e1(t) are error terms.The effect of the demographic characteristics, XQ), in tc1Q) is to shift the weight placed onthe wife’s non-labour time in period t relative to the weight placed on the husband’s period tnon-labour time in the household utility function. This difference appears in the MRS functionbetween the husband’s hours and the wife’s hours in period t, (23). Changes in n1(t) shift theslope of the family’s indifference curve between the wife’s hours and the husband’s hours in agiven period.The effect of X1(t) in Q1(t) is to shift the weight placed on the utility the family receivesfrom 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 thewife and husband, but it does appear in the Euler equation, (13). For example, if the householdplaces a higher weight on periods where young children are present then the household willincrease the non-labour hours of both spouses in those periods.76Taking the natural logarithm of both sides of (23) and rearranging:’6in[T — h2(t)] = X(t)/3* + cx,in[T — h,(t)] + 4{ln(wi(t)) — in(w2(t))] + e’(t) (26)where 3* —/3/(c24), a = (ai—1)/(a2— ), a = —1/(a21), and E(t) = —e(t)/(c2l).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’swage, in(wi:(t)) — in(w2(t)).Using the assumed functional forms, the Euler equation, (13), can be rewritten:(iq(t + 1)[T — h2(t + 1)](a2_1) \ (ic(t)[T —h2(t)](a2—l) —in i i — in I i——) w2(t) )—(X1(t + 1) —+c(t + 1) (27)where c(t+1) a(t)—a(t+1)+ii(t+1) is an error term. Since (t) falls out of the withinperiod MRS condition, (26), the parameter vector 4 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 ratioof the marginal disutility of the wife’s hours to her wage rate when the weight placed on periodt utility, Q(t), does not change between t and t + i.’ The expression (X1t + 1) — X(t))q161n the model, the variables tn[T —h2(t)] and ln[T —h1(t)] are endogenous. In the econometric framework,{ln(w(t))— ln(w2(t))] is also treated as an endogenous variable due to the concern that the method of derivingthe wage rates creates a statistical endogeneity. Therefore, one could solve the equation placing any of thesethree variables as the left hand side variable. This specification was chosen based upon a comparison of theresults of regressing each of the endogenous variable on all of the exogenous variables. The value of the R2 waslowest in the regressions with ln[T — h2(t)] as the dependent variable. Therefore, this was chosen as the lefthand side variable, since the instruments appear to be better at explaining the other two endogenous variables.‘The weight on period t utility, p1(t), changes only when the household characteristics, X(t), change. If77appears on the right hand side of the equation. This represents the part of the change inthe log of the marginal disutility of the wife’s hours, in(—Uh2(t)), between t and t + 1, whichis due to changes in household characteristics over the period. Changes in these householdcharacteristics shift the weight, 2(t), placed on utility from period t compared with the utilityfrom period t + 1 in the family’s lifetime utility function, (1). Therefore, b+1 — T’(t) equalsthe net change in the log of the ratio of the marginal disutility of the wife’s hours to her wagerate between t and t + 1.In order to simplify the notation, define:Yj(r) = in (tt1r)[T —h21(r)](a2_l) (28)where r = t, t + 1. Therefore, Y1Qr) is the log of the ratio of the marginal disutility of the wife’shours to her wage rate, for the case where the weight placed on period t utility, (11t), equalsone. Therefore, equation (27) can be rewritten:Yj(t + 1) — YQ) = — — (X1Q + 1) — X1Q)) + c(t + 1) (29)Equation (26) can be estimated by two-stage least squares (2SLS) treating both spouseshours and wages as endogenous. If panel data were available, one could estimate (29) by 2SLStreating hours and wages as endogenous. However, the data used in estimation will be fromtwo cross-sections. In estimating (29) using this data, one cannot compare the same householdat two points in time.Next, I will outline the procedure used to estimate (29). Each cross section is treated as ahousehold 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.78random sample of the same population at two points in time, 1981 and 1991. The results fromthe estimation of (26) are used to derive estimates of a2 and ic(t).’5 Given these estimateswe can derive values of Y(t) for the household’s in the 1981 cross section and l’(t + 1) forhouseholds in the 1991 cross section. Equation (29) is estimated over the 1981 cross-section.The derived values of Y1Q) are used in (29) in place of the true values. Predictions of Yj(t + 1)and X1Q + 1), derived using households in the 1991 cross section, are used in (29) in place ofthe actual values of Yj(t + 1) and X1(t + 1).Let Z1 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) = Zf3h2 + V1l2 (30)XQ + 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 Z1, and we have consistent estimates of /3h2 and/3x1, thenwe can derive consistent predictions of this household’s 1991, or t + 1, values of Y1Qt + 1) andX(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:— Yj(t) =— T’(t)— (Zj/3x÷1 — XQ)))-.- u(t + 1) (32)where u1Q +1) = q (t + 1)— — vf’ ‘. The true value of Y1(t+1) is replaced by the expectedvalue, Z/3h2 in the left hand side of (32). Also, the true values of X(t + 1) are replaced on‘5The derived value of n(t) is k(t)=249 where &t and Lt2 are the derived values of atand a2 from the estimation of (26).79h X1the right hand side of (32) by their expected values, Zd3x.1. The error terms 2 and v1are absorbed into u1Q + 1).Using the observed values of X(t) and Z1, the derived values of Yj(t) and consistent estimates of 43h2 and ,8x÷1 one could estimate (32) over the 1981 sample. However, due to theconcern that the household characteristics, X(t), may contain stochastic components whichare correlated with c7Q + 1), it was decided to treat X1(t) as a set of endogenous variables.The following equations are assumed to determine the household characteristics, X1(t):= Z/3x + vft (33)The assumed form of (33) enables us to replace the set of endogenous variables X(t) inequation (32), with consistent predictions of these variables using the estimates of and theexogenous family characteristics, Z. Substituting (33) into (32) gives the following expressionfor the Euler equation:— YQ) = — I’Q)— (Zj(/3x+,—i3x)) + u(t + 1) (34)where u7Qt + 1) = u(t + 1) + vftqsThe estimation involves three steps. First, the MRS condition between the husband’s hoursand the wife’s hours, (26), is estimated by 25115 over both the 1981 and 1991 cross sectionstreating 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 Y1Q + 1) using (28), overthe 1991 sample. Second, equations (30) and (31) are estimated by OLS over the 1991 crosssection using the predictions described above and the observed values of X1(t + 1). This gives80consistent estimates of /3j, and/3x+1. Also, equation (33) is estimated over the 1981 samplegiving us consistent estimates of[3x. In the final stage of estimation, 12(t) is derived over the1981 sample using the estimates from the first stage and equation (28). The Euler equationfor the wife’s hours, (34), is then estimated over the 1981 sample, by OLS, using the estimatesof 13h2,I3x÷1 and j3x from the second stage. Under the assumptions, this estimation yieldsconsistent 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) —Y1(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 X1(t + 1) — X(t), the change in householdcharacteristics between I and I + 1. Next, the predictions of Yj(t + 1) — Yj(t) are regressed onthe predictions of XQt + 1) — X1(t) and controls for age and immigrant arrival year,19 overthe 1981 sample. The procedure creates a synthetic panel by creating predictions of the 1991behaviour 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 estimates 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 pointsin 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‘91n the estimation, b+1 — F1(t) is assumed to be a function of age and immigrant arrival year.81thirty-six distinct groups in the data defined in terms of time-constant characteristics. Norestrictions are placed on variation in the conditional mean of the dependent variable acrossthese thirty-six groups, in each equation of (30), (31) and (33); however, the conditional meanof 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 panelof cohort sample means is that the final estimation is over households rather than sub-samplemeans. Using this procedure, the error term in the Euler equation contains the error term inthe Euler equation if one were to estimate using panel data. The error term also includes theprediction error terms resulting from using predicted values. Therefore, the cost of using thisprocedure as opposed to using panel data is only a loss of efficiency.3.5 Empirical AnalysisThe sample used in estimation is from the 1981 and 1991 Canadian Censuses. The sampleselection 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 excludedfrom the analysis. The labour supply measure used in this analysis is the annual hours of workof the husband and the wife. Annual hours is constructed by multiplying the annual weeks ofwork in the previous year by the hours of work in the reference week. This measure of annualhours will contain measurement error. This is addressed in the estimation by treating thehours of each spouse as endogenous. However, the hours of the husband and the wife appear82in the equations as the log of the non- labour hours of each spouse, which is a non-lineartransformation of the hours variables. Therefore, the effect of measurement error in hours onthe results will depend on the choice of T, potential hours of work. In the estimation, differentvalues of T were employed with only small changes in the results.Immigrants who arrived part way through the reference year likely have a truncated annualhours of work. To avoid this problem, immigrant families where at least one spouse arrived in1980 are excluded from the 1981 data. In the 1991 data, immigrants who had arrived in 1980cannot be distinguished from those who arrived between 1971 and 1979. Therefore, in theanalysis that follows, immigrants in 1981 who arrived between 1971 and 1979 are compared toimmigrants in 1991 who arrived between 1971 and 1980.20Wage rates are constructed by dividing the hours measure into the individual’s annualearnings the previous year. The resulting measure of the wage rate contains noise and maycontain division bias. However, instrumental variables techniques are used to address thisissue.As in Chapter 2, all households in the 1981 sample where both spouses are immigrantsand which meet the above criteria are kept in the sample. Due to the large numbers of non-immigrant households in the two data sets, a twenty-five percent random sample is taken ofnon-immigrant households. As can be seen in Table 3.1, after the restrictions there are 2372foreign- 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 the20A comparison of the 1981 sample means for demographic characteristics and wage rates for the 1971 to 1979cohort versus the 1979 cohort implied relatively small differences in these two groups.831991 Census there are 7194 remaining.2’Sample selection issues are not addressed in this chapter. Handling the endogeneity of thewife’s participation might lead to different predictions from this model. However, it is commonin the immigration literature to restrict the sample to individuals who work in the referenceperiod. The studies on immigrant men typically restrict the sample to individuals who workfull-time and for more than forty weeks in the reference year. Baker and Benjamin (1994) andDuleep and Sanders (1993) are the first studies to look at the effect of the wife’s participationdecision on her earnings and labour supply. In Chapter 4, a method is developed to incorporatethe wife’s labour force participation decision into the analysis.Table 3.1 lists sample means of selected variables used in estimation.22 Average hours ofwork for wives in immigrant families are 103 hours higher in 1981 and 110 hours higher in1991 than for non-immigrant wives. The mean hours for immigrant and non-immigrant menare almost identical in both years. The wages of the non-immigrant women are one dollar andthirty cents higher in 1981 but by 1991 the difference has dropped to sixty-three cents. For theimmigrant men, their wages are thirty-two cents lower in 1981; however, by 1991 their wageshave caught up to the wages of the non-immigrant men. Immigrant men and women in thesample are one to three years older in each cross-section, and have a more dispersed educationdistribution. Immigrant families are more likely to have children present in 1981; however, by211n Table 2.1, immigrant wives have a higher participation rate in 1981 than non-immigrant wives; however,the non-immigrant wives participation grows at a faster rate over the decade. The effects of this on the sampleselected are evident in the sample counts in this Chapter. The random sampling should lead to roughly fiftypercent of both the 1981 sample and the 1991 sample being foreign-born. However, the fraction is 51.8 percentin 1981 and 47.3 percent in 1991. This is due to the differences in participation rates between the two groupsin each year. The importance of ignoring these differences will be analyzed in Chapter 4.22The definitions of the variables are presented in Appendix 1.841991 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 andwife’s hours at time t, are presented in Table 3.2.23 The log of the husband’s non-labour timeand the difference in the log of the husband’s wage from the log of the wife’s wage are treatedas 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 birthsof the wife are also used. These instruments are fully interacted with a dummy variable forimmigrant status. The covariance matrix used allows for heteroskedasticity of unknown formand is from White (1980). The parameter estimates are distributed asymptotically accordingto the Normal distribution. The asymptotic standard errors are listed in parentheses.The coefficient estimates on the controls for household characteristics measure the effectof the household characteristics on the log of the non-labour time of the wife ln[T — h2Qt)j,holding the non-labour time of the husband, ln[T—h11(t)], and the difference in the spouses’ logwages, ln(wi1Q))— ln(w2Qt)), constant. The household characteristics vector, X1(t), includescontrols for immigrant status, immigrant arrival year, the age of each spouse, and the presenceof children in the household. The specification is very similar to the one used in the wife’sparticipation index from Chapter 2.24Controls for presence of children are included on their own and as interactions with theimmigrant dummy variable. This allows for separate effects of the presence of children onhousehold preferences over the labour supply of the wife relative to the husband.23The estimates of the reduced form equations for the difference in the log wages of the husband and the wifeand the log leisure of the husband are included in Appendix 2.24To compare the specifications, see Table 2.8.85The specification of the immigrant cohort controls is the same as the one used in the wife’sparticipation index of Chapter 2 after accounting for the fact that immigrants who arrived after1980 have been excluded from the sample used in this chapter. The default group containsimmigrant couples who arrived in the 1970s. A dummy variable indicating that the householdis from the 1991 survey is included. Its coefficient measures the percent change in the non-labour hours of wives in the default group over the 1980s holding the husband’s non-labour timeand 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-immigrantfamilies compared to those in the default group for given values of the husband’s hours and themarket wages of both spouses. An interaction of the non- immigrant dummy variable with thedummy 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 ofnon- immigrant wives over the 1980s, ceteris paribus. Controls for the immigrant wife havingarrived in the 1960s and before 1961 are also included on their own and as interactions with the1991 survey year variable, YR91. From these coefficients we see differences in the non-labourhours of wives who arrived before 1971 relative to those who arrived after 1971. Controls forthe immigrant husband having arrived in the 1960s and before 1961 are also included on theirown and as interactions with the YR91 variable. From these coefficients, we see the marginalchange in the immigrant family’s preferences over the non-labour hours of the wife when thehusband is from an earlier arrival cohort.The age controls are identical to the ones used in the wife’s participation index of Chapter2. Age controls are included for both the husband and the wife. Therefore, it is possible86to see the non-labour hours of the wife for each combination of the wife’s birth cohort, andthe husband’s birth cohort, holding the husband’s non-labour time and both spouses wagesconstant. Also, for each of the possible combinations of the husband’s and the wife’s birthcohorts, we can derive the change in the non-labour time of the wife over the 1980s, ceterisparibus.The estimate of the coefficient on the difference between the log of the husband’s wage andthe log of the wife’s wage implies that a2, the curvature parameter on the wife’s non-labourhours in the utility function, is —10.49. Using this estimate and the coefficient on the log of thehusband’s non-labour hours, one can impute a value of 0.8783 for a1, the curvature parameteron the husband’s non-labour hours. The estimates imply that the husband’s hours are moreresponsive to movements along his wage profile than are the wife’s hours to movements alongher wage profile. To see how the MRS between the husband’s hours and the wife’s hours varieswith the hours of the husband and wife consider the case where both the husband and wifesupply 2000 hours of work in period t. Using (23) and the parameter estimates we can seethat the MRS in this case is .7023. Therefore, the household places a higher marginal valueon the wife’s non- labour time than the husband’s non-labour time. However, as we decreasethe hours of work of the wife and husband while holding them equal, h11(t) = h2(t), we seethat the relative value placed on the wife’s non-labour time decreases relative to the husband’ssince a2 < a1. Evaluating both the husband’s hours and the wife’s hours at the immigrantwives’ 1981 sample mean of 1538 hours, the MRS has risen to 3.041, meaning that the relativemarginal value that the household places on the wife’s non-labour time is now lower than thatof the husband.87The presence of children in the household leads the non- immigrant wife to increase hernon-labour hours by three to thirteen percent for given values of the husband’s non-labour timeand the offered wages. These effects are significant at the five percent level.25 The effect ofchildren is smaller in immigrant families, and these differences are in general significant at thefive percent level.26 Therefore, family preferences are such that the immigrant wife lowers herhours 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 equationsof Chapter 2.The coefficient on NB indicates that non-immigrant wives have three percent more non-labour hours, ceteris paribus, than wives in immigrant couples where both spouses arrived inthe 1970s, and this difference is significant.27 From the coefficient on the 1991 survey yeardummy variable, YR91, we see that the non-labour hours of immigrant wives who arrived inthe 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 thenon-labour hours of the wife over the 1980s between non- immigrant wives and the defaultgroup, immigrant wives who arrived in the 1970s. This coefficient is not significant.29 Theseresults are consistent with the general trend in the Canadian economy over the 1980s towardsfull-time work for married women. All of the coefficients on the controls for the wife’s and25The test statistic in each case is the ratio of the coefficient estimate to the estimate of its standard error.The test statistics are distributed asymptotically according to the Standard Normal distribution, and equal9.76, 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.26The test statistics are —2.44, —2.46, —2.23, and —1.18, for the variables ED * KIDSO5 ED * KO5PLUS,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 .004.26The test statistic equals —3.38, and the prob-value equals .001.29The test statistic equals 1.27, and the prob-value equals .20.88husband’s immigrant arrival cohort, and the interactions of these variables with the 1991 surveyyear variable are not individually significant at the five percent level.30 Therefore, the resultsindicate that immigrant families prefer the wife to work more hours than do non-immigrantfamilies for a given value of the husband’s hours and the offered wages, and this difference doesnot change significantly over the decade.The coefficients on the age controls for the husband and the wife are not significant at thefive percent level except for the coefficients on the following variables for the wife: .44044 *YR91, .44549 * YR91, .45054 * YR91, .45559 * YR91, and .46064 * YR91.31 The fact that allof the age interactions with the 1981 survey year dummy variable, YR81, are not significantfrom zero means that the non-labour hours of the wife, ceteris paribus, are the same acrossthe six age cohorts in the 1981 survey. However, the growth in the non-labour hours of thewife, holding the husband’s hours and the offered wages constant, is not equal across theseage cohorts. Women under forty see their non- labour hours drop by five percent over thedecade. Older women reduce their non-labour hours by less. For example, wives who are fiftyto 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 non-labour hours constant throughout. A more interesting comparison would be between the choiceof hours of work of the wife and husband in immigrant versus non- immigrant families whenfacing the same constraints. In Figure 3.1 an experiment is carried out which demonstrates the30The test statistics equal —.31, .77, .24, .26, —.87, .63, 1.19, and .37 for the variables Y6170, YBEF61,Y6170 * YR91, YBEF61 * YR9I for the wife and Y6170, YBEF61, Y6170 * YR91, YBEF61 * YR91 for thehusband. The prob-values are .76, .44, .81, .79, .38, .53, .23, and .71, respectively.31The test statistics for these variables are 2.45, 3.29, 3.53, 5.78, and 3.24,respectively. The prob-values are.01 for the variable A4044 * YR91 and less than .0001 for the other variables.89importance of the observed differences by immigrant status in the family preferences towardslabour supply found in the MRS function. For expositional purposes, assumptions are madewhich translate the dynamic household problem into a static problem of choosing the husband’shours and the wife’s hours, in period t, subject to an artificial constraint. One can think of thisartificial constraint as a requirement that each household consume Cb dollars worth of theconsumption good given that their savings are zero at the beginning of the period and theycannot borrow against future income. The households choose the wife’s and the husband’shours in period t so as to fund Cno consumption. Each household is assumed to face thesame wage rate for the husband’s hours and the same wage rate for the wife’s hours. Theexperiment holds everything constant across the immigrant and non-immigrant families, exceptthe estimated differences in the MRS function. This is meant to highlight the importance ofthese differences in preferences in terms of hours of work.32The artificial constraint is:— {v1Q) + iu2(t)JT — CNB — — h2(t)]7’— hi(t)— (35)where uii(t), i1(t), iv2(t), and )2(t) are the sample means of the hours and wages of thehusbands and wives in the 1981 sub-sample of non-immigrant households where both spouseswork; and CNB 2{w1(t)7t)+zii]. This constraint is meant to approximate the “typ32Alternatively, one can think of the hours choices of each household in the experiment as the solution to thehours choices for period t in the household’s dynamic problem under the following assumptions. Assume thatthe immigrant family is constrained to have the same hours and consumption choices, and the same access tocredit, in all future periods as the native-born families have along their optimal program. Also, the savingswhich 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-immigrantfamily. Finally, the level of family consumption in period t in immigrant families is constrained to equal theconsumption in non-immigrant families. Under these assumptions, the dynamic problem reduces to the staticproblem of choosing hours of work of the husband and the wife in period t subject to the artificial budgetconstraint.90ical” constraint faced by non-immigrant families at time t, as they choose hours combinationsfor period t which are consistent with the family’s lifetime optimal program. The exerciseforces an immigrant and non- immigrant family with identical characteristics (eg. ages andcomposition of children present) to choose their optimal hours combinations subject to thisconstraint.In Figure 3.1, the optimal hours of the husband and the wife in immigrant and non-immigrant families are shown as the tangency of the relevant indifference curve to the artificialconstraint, (35).33 The indifference curves are derived using the parameter estimates from theMRS estimation and are for the case where no children are present in the household, and boththe wife and husband are age forty to forty-four. The immigrant family’s preferences are forthe 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’shours using the MRS condition to derive the associated husband’s hours and choosing theoptimal combination of hours which satisfies the budget constraint.34 For the immigrantfamily this was found to be T — h1(t) = 3468 and T— h2(t) = 3471. For the non-immigrantfamily T — hi(t) = 3392 and T — h2(t) = 3568.As can be seen in the figure, the immigrant family’s indifference curve is flatter than theindifference curve of the non-immigrant family. This leads the foreign-born household to choose33Non-labour time of spouse j is defined as?’— h1Qt) for j = 1,2 and 7’ = 5252.34The functional form for U(t) as defined in (22) permits a closed form solution for leisure demand functionsin the static case only when ai(t) = 2(t) which is the case of a CES utility function. Given the parameterestimates, it was necessary to use this grid search method. Given that the utility function is strictly concaveand increasing in the non-labour time of the husband and the wife, there exists a unique hours combinationwhich satisfies the MRS condition and which satisfies the budget constraint.91to have the wife work ninety-seven more hours and the husband work seventy-six fewer hoursthan is the case in the native-born family. This serves to explain in part the reduced formresults 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, implyingjust under one hundred more hours of work per year for the wife in immigrant versus non-immigrant families under the experiment of Figure 3.1.In Figure 3.2, immigrant families face an artificial constraint based on their own meanbehaviour. The new constraint incorporates into the analysis: 1) differences by immigrantstatus in the ratio of the husband’s wage and the wife’s wage (captured by the slope of theconstraint), and 2) differences by immigrant status in either the household’s disutility to workor 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 isdefined in the same way, but using the 1981 sample means of the hours and wages of husbandsand wives in immigrant families. As in Figure 3.1, the optimal hours combinations for non-immigrant families were derived using the MRS condition and the budget constraint. Theexercise was repeated for the immigrant family using the immigrant family’s MRS conditionand an analogous artificial constraint based on the sample means of hours and wages of thehusband and wife in immigrant families from the 1981 sub-sample. Indifference curves areplotted 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 the92husband’s wage in immigrant families versus non-immigrant families can be seen in the flatterconstraint for the immigrant family. This tends to push the immigrant family towards morehours of work for the husband rather than the wife due to the higher relative returns to hislabour. However, the magnitude of this effect appears to be small relative to the differencesin the MRS function. The fact that the FB artificial constraint lies below the NB constraintis due to either the immigrant household having a lower disutility to the labour supplies ofits members,35 or the immigrant family’s wealth at time t being lower than in non-immigrantfamilies.36 These two explanations cannot be distinguished using the data at hand.So far, the results from the structural model indicate that the value of the wife’s non-labourtime 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 thewife’s non-labour time in immigrant families to the same extent as it does in non-immigrantfamilies. 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 timerelative to the husband’s non-labour time in immigrant families does not necessarily implythat the immigrant wife places a lower value on her non-labour time than the non-immigrantwife does. The family utility function should be interpreted as a summary of the family decisionmaking process. The observed differences in family preferences toward the wife’s labour supplybetween immigrants and non-immigrants could be explained by the immigrant wife having a35This would appear iu (6) and (7) as a time-iuvariaut component of £1(t), the weight placed on period tutility in the lifetime utility function.36This difference would appear in A(t) in (6) and (7). Since A(t) is the marginal utility of wealth held at timet, an increase in wealth at time t leads to a lower value of A(t).93lower 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 inschooling which make his non-labour market time relatively more valuable than the non-labourmarket time of the wife, ceteris paribus. An evaluation of these alternative explanations willbe left for future work.Table 3.3 contains estimates from the Euler equation for the wife’s hours, (34). Thirty-six sub-groups within the sample are defined based on the wife’s characteristics:37immigrantstatus, the three entry cohort categories, three age categories (age twenty-five to thirty-fourin 1981, age thirty-five to forty-four in 1981, and age forty-five to fifty-four in 1981), andthree education categories (below a high school diploma, a high school diploma, and abovea high school diploma).38 Indicator variables are defined for thirty-five of the subgroups andare included along with an intercept in the estimation of equations (30), (31), and (33).39Predictions are generated from this estimation over the 1981 sample and equation (34) isestimated using these predictions. In the estimation of (34), b+i — I’(t) is assumed to be afunction of the wife’s age and arrival cohort. The household characteristics, X1(t), are controlsfor the presence of children in the household. These controls are interacted with an immigrantdummy variable.40 This allows for the estimation of separate effects by immigrant status of371t would be preferable to sample on both the husband’s and the wife’s characteristics. However, birth yearand immigrant arrival year are highly correlated between husbands and wives; therefore, one would have tochoose 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.35Education may be time-varying, but for most people, the education levels are determined before startingworh. Since the sample has been restricted to individuals who were older than twenty-five in 1981, it is unlikelythat the education of many of the women in the sample would change between 1981 and 1991.39The results of the estimation are presented in Appendix 34°ln the specification of the utility function, (22), the demographic characteristics X1(t) enter into both 12(t)and n(t). The demographic characteristics enter into the MRS equation through ,c(t), while they enter intothe estimation of the Euler equation through 91(t). I include only a subset of the household characteristicsused in the estimation of the MRS equation in the estimation of the Euler equation. Since panel data is not94the presence of children on the weight placed on period t utility in the family’s lifetime utilityfunction.The default category contains households where the wife is native-born and age thirty-fiveto forty-four in 1981. The intercept gives the value of b+i — T’(t) for this group. Recall that thisis the change over the 1980s of the log of the ratio of the marginal disutility of the wife’s hoursto her wage rate. The estimate is negative and significant from zero,41 implying an annualvalue of b+i — F(t) of — .56. This means that their marginal disutility of hours of the wife is notgrowing as quickly as the wage rate. The wage rate causes the ratio of the marginal disutility ofthe wife’s hours to fall. Since the marginal disutility of the wife’ hours rises with her hours, thewife’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 wifeis 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 in1981 is negative and significant.”3 This means that the value of b2+i — I’(t) is smaller for thisgroup. Given that young households typically face steeper wage profiles and own little in theway of assets relative to older households, it is reasonable to think that they are more likely tobe credit- constralned than households where the wife is older. Therefore, it is likely that thisdifference in b,+1 — I’(t) between these households and the default group of households, wherethe wife is ten years older, is due to the effects of credit constraints. Also consistent with thisavailable, and I am conditioning on the wife’s characteristics in the estimation of the Euler equation, it is notfeasible to control for many other household characteristics (such as the husband’s age and immigrant arrivalcohort information) in the estimation of the Euler equation.41The test statistic equals —6.95, and the prob-value is less than .0001.42MaGurdy interprets this number as b+1, since, in his model, it is assumed that the household is nevercredit-constrained; therefore, 1(t) = 0, for all t.43The test statistic equals —3.08, and the prob-value equals .002.95argument is that fact that households where the wife is forty- five to fifty-four in 1981 have asignificantly larger value of bt+i — r(t) than do the households in the default group, where thewife 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 1991in the Euler equation represents the change in 12(t), the weight on period t utility in thefamily’s lifetime utility function, over the 1980s. The estimates listed are of the parametersof the vector from equation (24). One would expect households to place a higher weighton periods when young children are present, which would imply a positive value of qS. Thiswas found in MaCurdy (1983). The results of Table 3.3 indicate that this is generally thecase for non-immigrant households. The estimates of the parameter of the vector for thedifference in the dummy variable, KIDSO5, between 1981 and 1991 is the wrong sign but is notsignificant.45 The coefficient on the change in the dummy variables KO5PLUS and KIDS614are positive and significant implying that non-immigrant families place a higher weight in thelifetime utility function on periods when two or more children under the age of six are present inthe 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 1980sis negative and significant, implying that non-immigrant households place a lower weight onperiods where three or more children age six to fourteen are present in the household.47 Thismay be picking up a credit constraint effect. Having at least three children in the household44The test statistic equals 5.93, and the prob-value is less than .0001.45The test statistic equals —.32; the prob-value equals .75.46The test statistics are 6.79 and 5.23, respectively. The prob-values are less than .0001.47The test statistic equals —2.93, and the prob-value equals .003.96is unlikely to force the wife to stay at home since the children would be attending full-timeschool. However, the household must make large expenditures on food and clothing for thesechildren. The household may wish to borrow against labour income in the future when thechildren are adults and no longer living at home. If households typically cannot borrow againstfuture 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 thesecontrols for the change in the presence of children variables over the decade are significant.48Adding the coefficient on each interaction with the coefficient on the analogous variable givesthe change in X(t)q5 for immigrant families. The effect of additional children present in thehousehold is to increase the weight placed on that period in the immigrant family’s lifetimeutility function.49 In particular, unlike what was found for non- immigrants, a higher weightis 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 interestingthat this effect does not show up for immigrant families. It may not be present for immigrantfamilies because children in this age group are expected to care for younger children afterschool in immigrant families compared with non-immigrant families. This supervision mightfree up more time for the wife to supply to the market.The controls for immigrant status and entry cohort do not support the hypothesis thatimmigrant families are more likely to be credit-constrained than non-immigrant families, ceteris45The test statistics equal 5.18, —6.27, —4.99, aud 2.86, for the KIDSO5, KO5PLUS, K1D5614, andK614PLUS interactions, respectively. The prob-values are less thau .0001 for the first three variables, andis .004 for the K614FLUS variable.49The only exception to this rule is the effect of one to two children present age six to fourteen. This has asmall negative effect on the weight placed on that period.97paribus. 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 disutilityof the wife’s hours to her wage rate, is larger in immigrant families than in non- immigrantfamilies. This means that after accounting for differences in wage growth over the 1980s,51and after accounting for differences in the marginal disutility function of the wife’s hours,52the movements of the wife’s hours in immigrant and non-immigrant families indicate thatimmigrant 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 equationfor the husband’s hours. The MRS coudition between the husband’s hours and the wife’shours, as represented by equation (23), can be rearranged to give:—h2(fl](a2_i)— [7’— h11(t)] (aj—i) (36)w21(t)— w1(t)The left hand side of this equation is the log of the ratio of the marginal disutility of the wife’shours to her wage rate, when the weight, Q(t), placed on period I utility in the lifetime utilityfunction equals one. This expression appears in equation (27), the Euler equation for the wife’shours. Substituting (36) into (27) gives:([7’— h11(t + 1)](al—1)”\ ([T —h11(t)](a1—1)\ —In, i—in, i—wi(t+l) J wj(t) J—(X1Q + 1)—+c(t + 1) (37)50The test statistics equal 2.82, 3.18, and 5.35, for the variables Y7180, Y6170, YBEF61, respectively. Theprob-valnes are .005, .001, and .0001, respectively.5tWhich appear in the denominator of the ratio.52Using the estimates from the MRS equation, and by controffing for changes in the presence of children inthe household in the estimation.98the Euler equation for the husband’s hours. Next redefine:(FT— h tr1(0i1Y\Yj(r)=ln(1 “s I (38)wij(r) jwhere r = t, t + 1. Given this definition of Y4(r) one could then proceed with the derivationinvolved in equations (29) through (34). The only difference is that the dependent variable isnow the change in the log of the ratio of the marginal disutility of the husband’s hours to hiswage rate, holding household characteristics constant, rather than the change in the log of theratio 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, thevector 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 afunction of the husband’s age and immigrant arrival cohort. This is to make it consistent withthe 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 inTable 3.4. The coefficient estimates are very different from those of Table 3.3. In principle, thiscould be due to the fact that I am conditioning on the husband’s characteristics rather thanthe wife’s characteristics in the estimation. It may be that bt+i — Q) is a function of bothspouses’ characteristics. Investigating this possibility would require including both spouses53As discussed above, since age and immigrant arrival year information are highly correlated between husband’s and wives, it is impossible to define sub-samples in the data based on both spouses characteristics withoutending up with no households in some sub-samples. This is the “curse of dimensionality” which arises in thenon-parametric econometrics literature.99characteristics in the vector Z. As discussed above, this is not feasible. It is also possible thatthe wife’s characteristics are better explanatory variables for the presence of children in thehousehold than are the husband’s variables. This is supported by the higher values of the fl2in the results from the estimation of equations (31) and (33) for women (found in Appendix3) than for men (found in Appendix 4). If the husband’s characteristics are not as effective atexplaining the presence of children, then the predictions of changes in the presence of childrenin the household over the 1980s will not be as good in the Euler equation for the husband asthey 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 correlatedwith the husband’s values of these variables. Therefore, it is a concern that the results aredifferent. Panel data would be needed in order to investigate the causes of the differences in thetwo Euler equations. Given the data limitations, an investigation of the possible explanationsis left for future research.In the discussion of the results of Table 3.4, I will focus on the controls for the husband’sarrival cohort. Unlike in Table 3.3, the coefficients on the arrival cohorts are all negativeimplying a smaller value of b+1 — I’(t) for immigrant families; however, in each case, thesedifferences are small in magnitude and not statistically significant at the five percent level.54Therefore, we still reject the hypothesis that immigrant families are more likely to be credit-constrained than non-immigrant families.54The test statistics are —1.61, —1.10, and —1.12, for the variables Y7180, Y6170, and YBEF61, respectively.The prob-values are .11, .27, and .26.100In the remainder of the discussion of this chapter, I will focus on interpreting the resultsof Table 3.3. Since Long (1980) first suggested that credit constraints may be important indetermining the wife’s hours of work, it seems reasonable to focus on the results of the Eulerequation for the wife.Next, three experiments are carried out which are similar to the ones generating Figure 3.1and Figure 3.2. An artificial constraint is defined which reduces the family’s dynamic probleminto a choice of the wife’s hours in 1981 and 1991 subject to this constraint. In Figure 3.3and 3.4, the wife in the immigrant and non-immigrant households faces wages equal to thesub-sample means for non-immigrant women in 1981 and 1991. The wife’s hours choices in1981 and 1991 must generate income equal the income the wife earns at those wages whenworking the mean hours of wives in the 1981 and 1991 non- immigrant sub-samples. In Figure3.3, the immigrant families preferences over intertemporal labour supply when children arepresent will be constrained to be the same as those in the non-immigrant family. In Figure3.4, the immigrant family’s preferences over children will be allowed to differ from those of thenon-immigrant family. In Figure 3.5, the non-immigrant family will solve the same problem asin 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 the1981 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 ratioof the marginal disutility of the wife’s hours to her wage rate, will be attributed to variation101in p, the rate of time preference. Therefore, in the diagrams, the indifference curves will betangent to the artificial constraints, rather than crossing the constraints, as would be the caseif the household were credit-constrained. This avoids the problem of choosing a value of prelative to the value of r, the interest rate, while still highlighting the differences in hours ofthe immigrant and non-immigrant families implied by the results of the Euler equation.In Figure 3.3, the focus is on the differences in —F1(i) by immigrant status. Immigranthouseholds are forced to have the non-immigrant responses to the presence of children55 andthe intertemporal MRS is defined as the non-immigrant sample means for the changes in thepresence of children variables. Each spouse is age forty to forty-four. Equal probability isplaced on the immigrant husband and wife being from each of the entry cohorts. As in Figure3.1, an artificial constraint based on the non-immigrant family’s dynamic problem is defined.The constraint can be written:T — h2Qt + 1) = [iu2Q) + ui2Q + 1)JT — CNBQ, t + 1) — — h2(t)] (39)w2Q+ 1)where uJ2(t), 1i2(t), iu2(t + 1), and i2(t + 1) are the mean wages and hours of non-immigrantwives in 1981 and 1991; and CNB(1, t + 1) Eui2(t)Et) + 1z72(t + 1)E2(t + 1). The immigrantand non-immigrant families choose the hours of the wife in 1981 and 1991 subject to thisconstraint.The steeper immigrant indifference curve leads the immigrant wife to work three hundredand sixteen fewer hours in 1981 and two hundred and seventy-two more hours in 1991 thannon- immigrant wives. This is opposite to what would be expected under the hypothesis that55This was done by ignoring the coefficients on the interaction terms in Table 3.3.102immigrant families are more likely to be credit-constrained. In that case, the wife would workmore in 1981 so as to increase consumption since the family is unable to borrow against thelabour income in 1991.In Figure 3.4, the combined effect of differences in b+1 —r1Q) due to immigrant status anddifferences due to immigrant status in Q1(t), the weight placed on utility in periods when youngchildren are present, are analyzed. Using the same constraint as in Figure 3.3, the household’sproblem is solved for immigrant and non-immigrant households. The non-immigrant household’s intertemporal MRS is the same as in Figure 3.3. For the immigrant household, thecoefficients on the interaction of immigrant status with the presence of children variables fromTable 3.3 are used. This allows for different responses between immigrant and non- immigrantfamilies to the changes in the composition of children present over the decade. In determiningthe immigrant MRS, the sample means for changes in presence of children in the immigrantsample are used. As can be seen in Figure 3.4, the immigrant indifference curve is now flatterthan the non-immigrant curve. Immigrant women work one hundred hours more in 1981 andeighty-five fewer hours in 1991.In the within period MRS estimation of Table 3.2, differences in the intercept by immigrantstatus and differences in family responses to the presence of children in the household workin the same direction. With no children present, immigrant households place a lower weighton the wife’s hours relative to the husband’s hours than do non-immigrant households. Ifchildren are present, this difference grows. The effect of children means the household placesan even higher weight on the wife’s hours relative to the husband’s hours, and this effect is103more pronounced for non-immigrant families than for immigrant families.In contrast, differences in the intercept of the Euler equation, or —1(t), by immigrantstatus and differences by immigrant status in the weight placed on the period if children arepresent work in the opposite direction. The intercept differences imply that immigrant womenare more likely to work in later years than the non-immigrant women (either due to a higherrate of time preference or a smaller effect of credit constraints). The higher weight placed onperiods where children are present by non-immigrant families than immigrant families, andthe fact that average number of children present in the home under each age category is higherin 1981 than in 1991, means that immigrant wives work more hours in earlier years since theyrestrict their hours less when children are present.In Figure 3.5, an artificial constraint is defined for immigrant families, in an analogousfashion to the non- immigrant constraint, (39), but using sample means over immigrant families. Next the optimal choices of the wife’s hours in each period were derived and plottedas tangencies between the immigrant intertemporal indifference curve and the immigrant artificial constraint. The same MRS functions were used as those in Figure 3.4. As in Figure3.2, the immigrant constraint lies below and to the left of the non-immigrant constraint. Thisimplies 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 flatterimmigrant indifference curve is apparent. As in Figure 3.4, the fact that the immigrant wife’shours 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 slightly104flatter artificial constraint. This would encourage the immigrant women to supply relativelymore hours in 1991 than in 1981 compared to non-immigrant women. However, this effectappears to be small.Five key differences between immigrant and non-immigrant families are apparent in Figures3.1-3.5. First, immigrant families have a larger MRS between the husband’s hours and thewife’s hours, in a given period. Second, the ratio of the husband’s wage to the wife’s wage islarger in immigrant families; however, the effect of this on differences in hours by immigrantstatus 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 non-immigrants in the 1980s does not appear to be an important determinant in the differencesin their hours of work. Fifth, when immigrant and non-immigrant households are forced toplace the same weight on periods when young children are present and when the compositionof children in the household over the decade is forced to be the same, immigrant wives workfewer hours in the current period and more hours in the future relative to non- immigrantwives. It is this measured tendency for immigrant wives to work fewer hours in the currentperiod and more hours in future periods, ceteris paribus, that is the reason why we cannotreject the hypothesis that immigrant families are equally likely to be credit-constrained asnon-immigrant families.3.6 Concluding RemarksThe results from the estimation of the structural model indicate that the marginal rate105of substitution between the husband’s hours and the wife’s hours, in a given period, is largerin immigrant households than in non-immigrant households implying a higher labour supplyfor immigrant women than for non-immigrant women, ceteris paribus. This difference is morepronounced when young children are present. Also, the results indicate that immigrant husbands and wives supply more labour than non-immigrant husbands and wives, after controffingfor the difference in the marginal rate of substitution, and the market wage rates. This is attributed to either a lower disutility to the labour supply of family members or to a lower valueof lifetime wealth in immigrant families. Finally, the empirical evidence indicates that youngfamilies are more likely to be credit-constrained; however, after controlling for age, immigrantfamilies are not more likely to be credit-constrained.106CHAPTER FOUR4.1 IntroductionIn this chapter, the model of Chapter 3 is extended to allow for the possibility that the wifesupplies zero hours of work in a given time period. In creating the synthetic panel of Chapter3, it was assumed that each cross section data set was a random sample of the same populationat the two points in time. If the wife’s participation decision is endogenous then the sampleof married couples where the wife works is not a random sample of the population of marriedcouples. In the sample means of Table 2.1, we see that the participation rate of non-immigrantwomen 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 dynamiclabour market behaviour of non-immigrant and immigrant families to different extents. Thiscould lead to biased results in Chapter 3.The results of the estimation of this Chapter support the conclusions from Chapter 3. TheMRS estimates indicate that the wife’s hours are less responsive to changes in the ratio of thehusband’s wage to the wife’s wage than was the case in Chapter 3. Immigrant families arefound to place a lower value on the wife’s time relative to the husband’s time compared withnon-immigrant families; however, this difference is smaller than what was found in Chapter3. Differences in the Euler equation estimates support the conclusions of Chapter 3, thatimmigrant families do not appear more likely to be credit-constrained than non-immigrantfamilies.1074.2 Approaches to Modelling the Participation DecisionIn their analysis of the intertemporal labour supply decisions of married women, Heckmanand MaCurdy (1980) model the wife’s participation decision using the simple Tobit specification. Blundell and Walker (1986) also use this specification of the wife’s participation decisionin their analysis of the labour supply decision of married couples. In the simple Tobit specification, the woman does not work if the marginal disutility she receives from the first hourof 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 doesnot work in period t:—Uh2(t) > A(t)w2(t .In the static labour supply literature, researchers have found that the simple Tobit specification does not fit the data as well as other models. Zabel (1993) compares four differentstatic models of married women’s labour force participation and labour supply and finds thesimple 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 thewoman must pay a fixed cost in order to work. The fixed cost is independent of the numberof hours of work she chooses that period. The version of the model considered here is one inwhich there is a monetary cost to working, but no costs in terms of time associated with thejob other than hours paid for at the market wage rate. The fixed cost could be thought ofas a cost of organizing childcare which is independent of the number of hours of work. Thewoman’s problem is to maximize the utility function: U(c, h) where c is consumption and h is108hours 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 equalsone if h> 0 and zero otherwise.The budget constraint is represented by the line ABC in Figure 4.1 and Figure 4.2. Thewife has exogenous income of 1000 dollars. Total hours in the period, T, is set at 1000. Thewife faces the offered wage of one dollar, and must pay a 500 dollar fixed cost of work. Figure4.1 shows the case of a non-worker. The woman works zero hours and consumes 500 dollarsworth of the consumption good. In Figure 4.2, the woman chooses to work 800 hours andconsume 1300 dollars worth of the consumption good.In this chapter, the fixed cost of work model is incorporated into the dynamic laboursupply model of Chapter 3. This is a significant extension of the intertemporal labour supplyliterature for women. Analogous conditions to the within period MRS condition between thehusband’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 endogeneityof the wife’s participation decision.4.3 The ModelThe household chooses hours of work for both the husband and the wife and family consumption so as to maximize the expected value of discounted life-time family utility:U(t)+ 1 } (2)109where r indexes future time periods, pis the rate of time preference, and U(T) = U(c(T), h,(r),h2(r))is the within period utility of the family which is assumed to be strictly concave and twicecontinuously differentiable, c(T) is family consumption; and h, (T), h2(r) are the hours of workof the husband and the wife, respectively.The household is assumed to face a fixed cost, F(t), which it must pay each period beforethe wife can work. This can be thought of as a cost of arranging chuldcare or some other costassociated 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— 1)(1 + r(r)) = w,(r)h,(r) +w2(T)h) — F(t)d() —p(r)c(r) r = t,..4 (3)where d(t) = 1 if the wife works in period t, and zero otherwise; p(r) is the price of the composite commodity; w,(r) and w2(T) are the husband’s and the wife’s wage rates, respectively;A(T) 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 thefact 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 givenvalue of assets held at the beginning of the period, A(r— 1)(1 +r(r)), and after choosing a levelof assets to be held at the end of the period, A(T), then (3) is the constraint the householdfaces 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 associatedwith his work are not modelled.110As in Chapter 3, the credit constraints are a set of non- negativity constraints onA(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:h2(r)O r=t,..,T (5)The household will choose zero hours of work for the wife in period t if the returns to workinga positive number of hours do not cover both the fixed cost of work that period, FQt), and thedisutility the family receives from having the wife work.Given an initial condition for assets, A(O) = A0, and a terminal condition for assets,A(T) A7, this characterizes the household’s problem. The value function for the household’sproblem 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 allperiods, and satisfies the asset accumulation constraints, and both the asset non- negativityconstraints and the wife’s hours non-negativity constraints, in all periods. The value functionequals the present discounted value of household utility over the remainder of the household’speriods under the optimal choices of hours of work and consumption in each period.111One can think of the household as maximizing:U(t) + + 1)} + -y(t)A(t) + 5(t)h2(+Ap(t)[wj(t)h1( )+w2(t)ht)— F(t) + A(t—1)(1 + r(t))— A(t) — p(t)c(t)j+AN(t)[Wl(t)hl(t) + AQ — 1)(1 + r(t)) — A(t)— p(t)c(t)]where Ap(t) is the multiplier for the period t asset accumulation constraint when the wifeparticipates in the labour market in period t and AAT(t) is the multiplier for the period t assetaccumulation constraint when the wife does not work in period t; 7(t) is the multiplier forthe period t asset non-negativity constraint; and (t) is the multiplier on the non-negativityconstraint 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) andA(t). The first constraint defines the downward sloping part of the budget constraint,2whilethe second constraint defines the budget constraint at zero hours of work for the wife.3Under the strict concavity of the utility function, either )pQ) or AN(t) equals zero. Theonly instance when both versions of the asset accumulation savings constraint could bind wouldbe when the household chooses h2(t) = F(t)/w2( . This would only occur if the householdhad Leontief preferences which is ruled out by the strict concavity of the utility function.The necessary conditions are:=[Apt) + .XN(t)]p(t) (7)Uh1(t) = —[.kp(t) + )N(t)]w1(t) (8)Uh(t) —Ap(t)w2(t— 6(t) (9)2The analogue in the static case is the line AB of Figure 4.1 and Figure 4.2.3This is equivalent to point C of Figure 4.1 and 4.2 in the static case.112where U(t) is the derivative of U(t) with respect to i, i = c(t),h1(t),h2(t). The expressionAp(t) + )N(t) is the marginal utility of wealth held at time t for the household.4 If the wifeworks in period t then the marginal utility of wealth equals ,\p(t + 1); otherwise, the marginalutility 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 utilityto the household from period t onward when the wife works zero hours in period t and thehousehold chooses all other levels of hours and consumption given this restriction and initialassets, A(t — 1). Let Vp(A(t— 1),t) be the value of utility from t onward when the wife paysF(t) and works5 and the family then chooses the hours of both spouses and consumption fromt onward subject to this constraint and the initial assets A(t — 1). The wife’s participation4To see this, first define assets held at the beginning of period t to be A*(t) A(t— 1)(1 + r(t)). Next definethe Lagrangean:U = E(i + p(T){wi(T)hi(r) +w2(r)hr) — F(r)—p(r)c(r) + A*(T)— A(r)}+AN(T){’wI(T)hl (i-) — p(r)c(r) + A*(T)— A(r)}+7(T)A(T) + 6(r)h2(r ]Evaluate U at the optimal values of c(T), hl(T), h2(r), A(r), .Xp(T), .)iN(T), y(r), and 5(T); r = t,..,. Atthese values, U equals the present value of utility that the household receives from period t forward under itsoptimal 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.5This is not quite correct. The budget set is not closed. Consider the case where the wife would prefer towork 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 thenany point on the budget line to the left of B. This is the case of nonparticipation in the simple Tobit model. Toensure that, in period 1, Vp(A(— 1), t) is defined, assume that the wife has to pay the fixed cost whether ornot she works. The household then chooses the hours for both spouses and consumption in all periods subjectto this constraint, and initial assets.113index is defined to be:1(t) Vp(A(t— 1),t)— VN(A(t — 1),t) (10)The wife works if 1(t) 0 and does not work otherwise. It is easy to see the effect ofthe fixed cost on the participation decision. Increasing F(t) lowers Vp(A(t— 1), t) since thehousehold must now pay more in order for the wife to work in period t, but this has no effecton Vj(A(t — 1), t) since the wife does not work in period t. Therefore, as the fixed cost ofworking 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 berewritten:Uh1 (t) = —Ap(t)w1(t (11)Uh2(t) = —Ap(t)w2(t (12)Taking the ratio of (11) and (12), over the sample where both spouses work, gives the MRScondition from Chapter 3:Uh1(t) — wi(t) (13)Uh2(t) — w2(t)This is the within period MRS condition between the husband’s hours and the wife’s hoursin period t, which was used in the estimation of Chapter 3. It states that in equilibrium thehousehold sets its MRS between the hours of the husband and the hours of the wife equal tothe ratio of their wages. The equation describes how the family is prepared to trade fewerhours of work for one spouse at the expense (in terms of utility) of higher hours of work forthe other spouse, at different offered wages. As in Chapter 3, the MRS condition between thehusband’s hours and the wife’s hours is the first equation estimated. A procedure is developed114to address the fact that this condition is only defined over the subsample of households wherethe wife works in period t.The motion equation for the marginal utility of wealth, )‘p(t) + Aiv(t), is:6\p(t) + AN(t)= 1 Et{[(t + 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 iscredit-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 utilityfrom another unit of wealth in period t + 1, -E{[)p(t + 1) + )N(t + 1)j(1 + r(t + 1))}, to thecost in terms of the decrease in utility in period t, ).p(t) + AN(t). If the household is credit-constrained in period t, this marginal condition does not hold. The household would like tolower 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 would6To 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)hi(r)+w2( )r -F( )T=t+1—p(r)c(r) + A(i-—1)(1 + r(r))— A(T)}+AN(T){wl(T)hl(T) — p(r)c(r) + A(T— 1)(1 + r(T))—A(r)}7(r)A(r) + 5(r)h2(r ]Evaluate L at the optimal values of c(T), hj(r), h2(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 kp(t) + AN(t) when credit constraints exist.115choose 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 oneunit less of wealth in period t + 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 motionequation for AQ). When the wife does not work, this condition does not hold. The procedureused in this chapter is to substitute for )p(r) in (14) from (12) for households where the wifeworks, for i- = t, t + 1. For households where the wife does not work in T, i\p(r) = 0, and wesubstitute into (14) for ).N(r) using (8), the marginal condition for the husband’s hours, forT = t, t + 1. Under this procedure, the following expression can be derived:—U (t) d(t) —U (t) (1—d(t))Ap(t) + N(t)= { w2(t)] { w1(t)] MU(t) (15)This allows us to express the marginal utility of wealth at time t as a function of the marginaldisutility 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) = theratio of the marginal disutility of the wife’s hours to her wage rate. If the wife does not workin t then MU(t) = the ratio of the marginal disutility of the husband’s hours to hiswage rate.It is assumed that r(t + 1) = r and r is known. Substituting (15) into (14) for Ap(t) + )N(t)and \p(t + 1) + AN(t + 1) gives:MU(t) = E{MU(t + 1)} + 7(t) (16)Before proceeding I will give an outline of the estimation procedure. The first equation116to be estimated is (13), the within period MRS condition between the husband’s hours andthe wife’s hours. This condition is estimated over the sample of households where the wifeworks. A procedure similar to the one in Section 2.5, is employed to address the fact that thisis not a random sample of the population of married women. The estimation yields consistentestimates of the parameters of the within period utility function, U(t).7 These estimates revealhow 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 hoursfor the husband and wife between immigrant and non-immigrant families. The procedure forestimating the effects of credit constraints on household labour suppiy can be thought of inthe following way. The wages and hours of husbands and wives are observed in the 1981 andthe 1991 cross sections. Using this information and the estimates from the MRS estimation,—U (t)an estimate of the ratio of the marginal disutility of the wife s hours to her wage rate,w2(t)is derived for households where the wife works in the survey period. If the wife does not workin the survey period, an estimate of the ratio of the marginal disutility of the husband’s hoursto his wage rate, is derived. Using this information and equation (15), we derive avalue of the marginal utility of wealth at t, MU(t), for each household in the sample. Bycomparing households with similar time-constant characteristics in the two data sets we canderive an estimate of the change in MU(t) over the 1980s. From this comparison, we seewhether or not the growth in hours and wages of husbands and wives is consistent with creditconstraints having an important effect on the hours patterns over time. In particular, we areinterested in whether or not differences by immigrant status in the parameter estimates are7As in Chapter 3, this description is an oversimplification of the procedure. Not all of the parameters of theutility function can be derived from this estimation. In particular, the parameters of the weight, j(t), placedon period t, utility in the lifetime utility function, (2), must be estimated in the second stage of estimation.117consistent with the hypothesis that immigrant families are more likely to be credit-constrainedthan non-immigrant families.In order to facilitate estimation, equation (16) is rewritten:MU(t) = + E{MU(t+ 1)}eF(t) (17)where I’(t) > 0 if the household is credit-constrained, and f(t) = 0 otherwise. The followingmultiplicative 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 timet.Taking the natural logarithm of (18):ln(.lvIU(t + 1)) — ln(MU(t)) = b+1 — P(t) + (t + 1) (19)where b+1 = ln(1 + p) — ln(1 + r) + Et{lri(1 + c(t + 1))}, and ?7(t + 1) is a forecast erroruncorrelated with variables known by period t. In Chapter 3, bt1 — P(t) was the change inthe log of the ratio of the marginal disutility of the wife’s hours to her wage rate from t tot + 1. Since we have relaxed the assumption that the wife works in every period, this is nolonger correct. In the subsequent discussion, I will refer to bt+1 — F(t) as the change in the logof the marginal utility of wealth from t to t + 1. Also, I will refer to equation (19) as the Eulerequation for the wife’s hours.88Referring to (19) as the motion equation for the log of the marginal utility of wealth would be more accurate.However, I will refer to (19) as the Euler equation for the wife’s hours so as to make it easier to compare to theestimation procedure of Chapter 3.1184.4 Functional Forms and Estimating EquationsThe same functional forms are used as in Chapter 3:U(t) = c2(t) { [T hQ)]a1 + k(t) [T - Q)]a2} (20)where T is the maximum number of hours a person can work in a year, ii(t) and (t) are agespecific modifiers of taste and and c2 are parameters.The following functional forms for the taste-shifters, Q(t) and i(t), are assumed:= exp-fX(t) + a(t)} (21)ic(t) = exp{X(t)/3 + (t)} (22)where X(t) is a vector of exogenous characteristics which includes age controls; and areparameter vectors; and a(t) and E(t) are error terms.The effect of the demographic characteristics, X(t), in itj(t) is to shift the weight placed onthe wife’s non-labour time in period t relative to the weight placed on the husband’s non-labourtime in the household utility function. This difference appears in the MRS function betweenthe husband’s hours and the wife’s hours in period t, (13). Changes in ic(t) shift the slopeof the family’s indifference curve between the wife’s hours and the husband’s hours in a givenperiod.The effect of X(t) in Q(t) is to shift the weight placed on the utility the family receivesfrom 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).119For example, if the household places a higher weight on periods where young children arepresent 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, canbe rewritten using the functional forms as:[T—— w11(t) (23)—— w2(t)Taking the natural logarithm of both sides of (19) and rearranging:ln[T — h2(t)] = X(t),8* + aln[T — k1(t)] + a[ln(w1(t)) — ln(w2(t))] +e2(t) (24)where/*= —i3/(a21), c = (ai—1)/(a2— ), a = —1/(a21), andr2(t) =It should be noted that (24) is only defined for households where both spouses work. The errorterm, 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 entersinto this part of the model. If this conditional mean is non-zero then, conditional on the otherexplanatory 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:a1, a’2, and ij(t). The procedure is similar to the one used in section 2.5. Let W(t) be avector of all exogenous characteristics of the household at time t. The following equations areassumed to explain the husband’s non-labour hours and the difference between the log of thehusband’s wage and the log of the wife’s wage, for all households in the sample:9ln[T — h1(t)] = W(t)i31 + Ei(t) (25)9ldentification of the model requires that the vector W(t) contains variables not included in X(t).120ln[wi(t)) — ln(w2(t)] = T’V(t)i3 + e(t) (26)where ,6 and are parameter vectors; and Ei(t) and E(t) are error terms. These areequivalent to the first stage equations estimated in the 2SLS estimation of the MRS conditionfor 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— h2(t)] = X(t),3* + 4[T’Vi(t)/31+ 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 theexogenous variables in period t:I(t) W(t)/3 + E(t) (28)where f3J3 is a parameter vector and Ej(t) is an error term.10 Over the sample of householdswhere the wife works, equations (25)-(27) can be rewritten:ln[T— h1(t)J = T’Vj(t)/31 + Et{ei(t) I ei(t) —T’V(t)3} + c1(t) (29)ln[w1(t))— ln(w2(t)1 = Wj(t)i3 + .Et{E(t) I piQ) —T’Vj(t)i3} +c0(t) (30)ln[T — h2(t)] = X(t)/3* + a[T’V(t)/31+ Et{Ei(t) 1,(t) > —T’V(t)3}]+4[W(t)i3 + E{(t) I E,j(t) > —WQ)/3}]+Et{e2(t) I e(t) —WQ)/31,}+ c(t) (31)10J Cogan (1981), the participation index relates the hours chosen by the wife to a reservation hours functionwhich is the hours the wife would work when facing her reservation wage, the lowest wage rate which inducesher to work. There does not exist a simple analogue to Cogan’s index in the dynamic context, since it relies ona static uncompensated labour supply function.121where Et{x I e(t) —w(t)j3} is the expectation of x conditional on the wife working, forx = Ei(t), &(t) and E2(t); and ci(t), c(t), and c2(t) are mean zero error terms over thesample of households where the wife works; and c(t) = c4ci(t) + cci(t) +c2(t).Assume that £1(t), E(t), e2(t) and E7,(t) are distributed according to the joint Normaldistribution with covariance matrix:a12ai 2w ptvl2 a2 2walp apw 2wwhere a is the variance of E(t) for j 1,2, w,p, and Ujk is the covariance of e(t) with EkQ)for j = 1,2, w,p, where j k. The three equations to be estimated can be rewritten as:ln[T — h12(t)] = I’Vj(t),di + +c1(t) (32)ln[w1(t))— ln(w2(t)j = W(t)/3 + (t) + c(t) (33)ln[T-h2(t)] = X(t)/* + a[W(t)/31++c4[T’Vi(t)i30+ + + c(t) (34)where (t) = is the inverse Mill’s ratio, and f and F are the StandardNormal density function and distribution function.The estimation involves a multiple step procedure similar to the two step procedure firstsuggested 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 estimatedusing the Probit estimator over the entire sample. The estimates of are used to deriveestimates of (t) which are used in the estimation of (32) and (33). This yields consistent122estimates 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 boththe endogeneity of the wife’s participation decision and the endogeneity of the husband’s hoursand 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(—Uh2(t)) — ln(w2(t))} + (1— dQ)){lm(—Uh(t)) — ln(wi(t))} (35)Under the assumed functional forms, this can be rewritten:ln(JVIU(t)) = d(t){X(t)j3 + E(t) + (a2 — 1)ln(T — !i2(t)) — ln(w2Q))}+(1 — d(t)){(a1— 1)ln(T — h1(t)) — ln(w11(t))} + X(t)q + a(t) (36)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 distributionof the error terms it is possible to derive an expression for its conditional mean. Using thedefinition ofE2(t),1’ j(t) can be expressed as:= —(a2— 1)E[s2(t) I d(t) = 1] — (a2 — 1)c2(t)over the sample of households where the wife works. Recall that from equation (31), c2(t) ismean zero over the sample of households where the wife works. Under the assumed distribution“The definition is found below equation (24).123of the error terms, this can be rewritten:= —(a2 — 1)(t)— (a2— (37)U2Substituting this expression into (36) for e(t) gives:ln(MU(t)) = d(t){X(t)— (a2 — 1)(t)— (a2 — 1)c2(t)U2+(a2 — 1)ln(T — h2(t))— ln(w2(t))}+(1 — d(t)){(ai — 1)lrt(T— hi(t)) — ln(w1(t))} + X(t) + a(t) (38)Next, define:Yj(r) d(r){X1( )— (a2 — 1)(r) + (a2 — 1)ln[T —h2(r)] — ln(w2(r))}— d(r)){(a1— 1)ln[T— h1(r)1 — ln(wi(r))} (39)for r = t, t + 1. Therefore, MU(r) = Yj(r) — (a2 — 1)d(r)c2(r + X(r)ql + a(r). We can nowderive consistent predictions of Y(r) for each household in the sample using the parameterestimates from the MRS estimation, the hours and wage information of each spouse, theparticipation decision of the wife, and the household characteristics.Therefore, equation (19) can be rewritten:1’(t + 1) — 1’(t) = — r(t) — (XQ + 1) — x(t)) + c(t + 1) (40)where c(t + 1) = (a2 — 1)[d(t + 1)c2(t+ 1)—d1(t)c2Q 1 + [a(t) — a(t + 1)] + (t + 1). Recallthat c21(t) is mean zero over the sample of households where the wife works; therefore, c(t+ 1)is mean zero over all households in the sample.124The 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, andeducation). Assume the following relationships exist:Yj(t+1) = Zj3h2 +V2 (41)X(t + 1) = Z[3x1 + (42)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 /3h2 andi3x11, thenwe can derive consistent predictions of this household’s 1991, or t + 1, values of Yj(t + 1) andX(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:— Y(t) = b+1 — I(t)— (Z/3y+1 —X1(t)))q5 + u2(t + 1) (43)where u(t + 1) = c’(t + 1) — V2 — v’’ . The true value of Y(t + 1) is replaced by the expectedvalue, Z,I3h2 in the left hand side of (43). Also, the true values of X(t + 1) are replaced onthe right hand side of (43) by their expected values, Zx1. The error terms 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 estimates of /3h2 and 5x1 one could estimate (43) over the 1981 sample. However, due to theconcern that the household characteristics, X(t), may contain stochastic components whichare correlated with u(t + 1), it was decided to treat X(t) as a set of endogenous variables.125The following equations are assumed to determine the household characteristics, X2(t):X1(t) = ZjJ3x + (44)The assumed form of (44) enables us to replace the set of endogenous variables X(t) inequation (43), with consistent predictions of these variables using the estimates of /3x and theexogenous family characteristics, Z2. Substituting (44) into (43) gives the following expressionfor the Euler equation:Z2/3h — Y2(t) = b+1 — I’(t)— (Zj(/3xt+1—i3x)) + u’(t + 1) (45)where u(t + 1) = u(t + 1) + VftbThe estimation involves three steps. First, the MRS condition between the husband’s hoursand the wife’s hours, (34), is estimated by the procedure discussed above over both the 1981and 1991 cross sections. This gives consistent estimates of , a, a, , and (t). Theseestimates 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 predictionsof Yj(t + 1) and the observed values of X(t + 1). This gives consistent estimates of /3h2 andI3x11. Also, equation (44) is estimated over the 1981 sample giving us consistent estimates ofI3x. In the final stage of estimation, Y(t) is derived over the 1981 sample using the estimatesfrom the first stage and equation (39). The Euler equation for the wife’s hours, (45), is thenestimated over the 1981 sample, by OLS, using the estimates of /3h,,/3x+1 and !3x from thesecond 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) —126Yj(t). Also, for each household a predicted value is derived of XQ + 1) — X(t), the changein household characteristics between t and t + 1. Next, the predictions of Y(t + 1) — Yj(t) areregressed on the predictions of X2(t + 1) — X(t) and controls for age and immigrant arrivalyear,’2 over the 1981 sample. The procedure creates a synthetic panel by creating predictionsof 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 estimates 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 pointsin 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 representingthirty-six distinct groups in the data defined in terms of time-constant characteristics. Norestrictions are placed on variation in the conditional mean of the dependent variable acrossthese thirty-six groups, in each equation of (41), (42) and (44); however, the conditional meanof the dependent variable is assumed to be the same within each of these groups.4.5 Empirical AnalysisThe sample used in estimation contains the data used in Chapter 3 and also includeshouseholds where the wife does not work in the reference year and the survey week. Table 4.1lists sample means of variables used in estimation.’3 Average hours and wages for the wivesare calculated over the sample of workers. Therefore, they are equal to the sample means in12J the estimation, b+1—F(t) is assumed to be a function of age and immigrant arrival year.13The variables are defined in Appendix 1.127Table 3.1. Sixty-six percent of immigrant women work in 1981 while fifty-nine percent of non-immigrant women work. Both participation rates rise over the 1980s with the non- immigrantrate growing by more. In 1991, both non-immigrant and immigrant women have averageparticipation rates of seventy-three percent. Comparing the education distribution for womento the one in Table 3.1 we see that more women are in the lowest education groups in Table 4.1indicating that these women are more likely to be out of the labour market. The distributionof children present in the home is very similar between immigrant and non-immigrant familiesin 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 inTable 4.2. The estimates are of the change in the probability of the wife working for a unitincrease in the regressor. The specification of the participation index, (28), is the same asthe one used in Chapter 2 with two differences. Since immigrant households where at leastone spouse arrived in Canada after 1980 are excluded from the sample, controls for immigrantarrival year are for arrival before 1981. Also, controls for the husband’s occupation and industryare included. Due to the large number of variables included in the estimation, I will focus onthe 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 negativeimplying a lower probability of working for non-immigrant wives than for wives in the defaultcategory, wives in immigrant households where both the wife and the husband arrived inthe 1970s. However, the coefficient estimate is not significant.’4 The coefficient on YR91 ispositive indicating an increase in the participation rate of the wives in the default category‘4The test statistic equals —.61, and the prob-value equals .54.128over the decade, but again this coefficient estimate is not significant.’5 The coefficient on thevariable NB * YR91 is close to zero indicating that the growth in the participation rate ofnon- 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 immigrantwives who arrived before 1971 are five percent more likely to work than those who arrivedafter 1970.16 The coefficients on the interactions of these controls with the 1991 survey yeardummy variable, YR91, are not significant from zero.17 The coefficients on the controls forthe husband’s arrival cohort indicate that an immigrant wife whose husband is a member ofan earlier arrival cohort is significantly less likely to work than one whose husband is from arecent arrival cohort.’8 From the coefficients on the interactions of these variables with the1991 survey year variable, we see that immigrant wives with husbands from earlier arrivalcohorts experience a higher growth in the participation rate over the 1980s than do wiveswhose husbands are from recent cohorts.’9Results 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 asendogenous variables. The variables used as instruments are the age, education, and languagefluency of each spouse. Controls for number of live births of the wife are also used. Controlsfor the occupation and industry for the husband are included. The analogous variables forthe wife are not included since they are only defined for women who work. The instruments‘5The test statistic equals 1.02. The prob-value equals .31.‘6The test statistics are 1.86 and 1.39, respectively. The prob- values are .07 and .16, respectively.‘7The test statistics are — .95 and — .64, respectively. The prob-values are .34 and .52, respectively.‘8The test statistics equal —4.35 and —5.41 for the variables Y6170 and YBEF61 for the husband. Theprob-value is less than .0001 in each case.‘9The test statistics equals 1.51 and 2.15 for Y6170 and YBEF61, respectively. The prob-values are .13 and.03, respectively.129are fully interacted with a dummy variable for immigrant status. The age controls and thecontrols for immigrant arrival cohort are also interacted with a dummy variable for being inthe 1991 sample. The parameter estimates are distributed asymptotically according to theNormal distribution. The asymptotic standard errors are in parentheses.The MRS specification includes the same demographic controls as were used in the MRSestimation of Chapter 3. Controls for presence of children are included and interacted withthe immigrant dummy variable. The default category contains immigrant households in 1981where both spouses arrived in the 1970’s, both are age twenty-five to twenty-nine, and nochildren are present. A control for native-born households is included and interacted withthe year 1991 dummy variable. Controls for membership in the two earlier immigrant cohortsfor both the husband and the wife are also included, and are interacted with the year 1991variable.20The estimate of the coefficient on the difference between the log of the husband’s wage andthe log of the wife’s wage implies that a2, the curvature parameter on the wife’s hours in theutility function is —21.44, which is almost twice as large in absolute value as the value foundin the analysis of Chapter 3. This is similar to the result found by Cogan (1981). Once theparticipation index is allowed to differ from the hours of work equation, the effect of a changein the wife’s wage on her hours of work is smaller. Cogan argues that this implies that most ofthe variation in hours for married women involves movement in and out of the labour marketand not changes in hours of work of women in the labour market. Using this estimate of a2,one can impute a value of 0.7931 for ai, the curvature parameter on the husband’s hours in20Appendix 5 contains the results of the first stage estimation of equations (32) and (33).130the utility function. This value is smaller than the value found in Chapter 3. To see how theMRS function varies with the hours of the husband and the wife, consider the case where boththe husband and wife supply 2000 hours of work in period t. Using (23) we can see that theMRS in this case is .35. Therefore, the household places a higher marginal value on the wife’snon-labour time than the husband’s non- labour time. However, as we decrease the hoursof work of the wife and husband while maintaining hi(t) = h2(t), we see that the relativevalue of the wife’s non-labour time decreases relative to the husband’s since a2 < a1. Whenwe evaluate both the husband’s hours and the wife’s hours at the sample mean of hours ofimmigrant 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’snon- labour time.When children are present, the non-immigrant household chooses five to eight percent morenon-labour hours for the wife for given values of the husband’s non-labour time and the offeredwages. These effects are significant at the five percent level.2’ In immigrant families, the effectof children is smaller, and these differences are in general significant at the five percent level.22Therefore, family preferences are such that the immigrant wife lowers her hours of work byless than the non-immigrant wife when children are present in the household. This matchesthe results found in the estimation of the structural model of Chapter 3 and the reduced-formestimation of Chapter 2.21The test statistic in each case is the ratio of the coefficient estimate to the estimate of its standard error.The test statistics are distributed asymptotically according to the Standard Normal distribution, and equal5.97, 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.22The test statistics are —2.25, —1.92, —1.98, and —1.30, for the variables FB * KIDSO5 FB * KOSFLUS,FB * KIDS614, and FB * K614PLUS, respectively. The prob-values are .02, .05, .05, and .19, respectively.131From the coefficient on NB, we see that non-immigrant wives have three percent morenon-labour hours, ceteris paribus, than wives in immigrant couples where both spouses arrivedin the 1970s; however, this difference is not significant.23 From the coefficient on the 1991survey year dummy variable, YR91, the non-labour hours of immigrant wives who arrived inthe 1970s fall by five percent over the 1980s, ceteris paribus, and this change is significant.24From the coefficient on the variable NB * YR91 we see that the decrease in the non-labourhours of the wife over the 1980s in non-immigrant families is two percent smaller than thedecrease in immigrant families.25 All of the coefficients on the controls for the wife’s andhusband’s immigrant arrival cohort, and the interactions of these variables with the 1991survey year variable are not individually significant at the five percent level.26 Therefore, theresults indicate that the 1981 non-labour hours of wives are the same in immigrant and non-immigrant 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-labourhours 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 tothe relationships found in the estimation of Chapter 3. The coefficients on the age controls forthe husband and the wife are not significant at the five percent level except for the coefficientson the following variables for the wife: A4549 * YR91, A5054 * YR91, and A5559 * YR91 27 The23The test statistic equals 1.23, and the prob-value equals .22.24The test statistic equals —3.47, and the prob-value equals .001.25The test statistic equals 2.00, and the prob-value equals .05.26The test statistics equal —.09, .83, —.02, —.10, —1.47, —.35, 1.60, and .94 for the variables Y6170, YBEF61,Y6170 * YR91, YBEF61 * YR91 for the wife and 16l70, YBEF61, 16l70 * YR91, YBEF61 * YR91 for thehusband. The prob-values are .93, .41, .98, .92, .14, .73, .11, and .35, respectively.27The test statistics for these variables are 2.04, 1.97, and 3.00,respectively. The prob-values are .04, .05 and.003, respectively.132fact that all of the age interactions with the 1981 survey year dummy variable, YR81, are notsignificant from zero means that the non-labour hours of the wife, ceteris paribus, is the sameacross the six age cohorts in the 1981 survey. However, the growth in the non-labour hours ofthe wife, holding the husband’s hours and the offered wages constant, is not equal across theseage cohorts. Women under forty-five see their non-labour hours drop by five percent over thedecade. 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 ispositive and significant implying u2, > 0, from (34). Therefore, households where there is apreference for the wife to work longer hours (due to a small value of2(t)), tend to be thehouseholds where the wife is less likely to work (due to a small value of ,j(t)). This can beexplained by the households with the preference for the wife to work long hours also being thehouseholds which face a large value of the fixed cost of work, F(t). This would be the case ifwomen who work very few hours have an easier time arranging childcare than do women whowork longer hours. The fact that this result was found supports using a fixed cost model overthe simple Tobit model. In the Tobit model, the decision to work and the number of hoursworked are identical. Therefore, this negative correlation between the decision to work andthe hours worked given that the wife works is not possible.The importance of the observed differences in family preferences found in the MRS estimates 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 thehusband’s hours and the wife’s hours, in period t, subject to an artificial constraint. The ar133tificial constraint requires the household to consume C1, dollars worth of consumption when:1) savings are zero, 2) the household is unable to borrow, and 3) both immigrant and non-immigrant households face the mean non- immigrant wages of husbands and wives in the 1981sample of Table 3.1.28 The experiment holds everything constant across the immigrant andnon-immigrant families, except the estimated differences in the MRS function.The artificial constraint is defined as in Chapter 3:T— h1(t) = [n1(t) +2(t)]T — GNB —i2(t)[T — h2(t)] (46)1(t)where 1(t), i1(t), Y2(t), and i2(t) are the sample means of the hours and wages of thehusbands and wives in the 1981 sub-sample of non-immigrant households where both spouseswork; and CNB E1(t) +i2(t)].In Figure 4.3, the optimal hours of the husband and the wife in immigrant and non-immigrant families are shown as the tangency of the relevant indifference curve to the artificialconstraint, (46). The indifference curves are derived using the parameter estimates from theMRS estimation and are for the case where no children are present in the household, and boththe wife and husband are age forty to forty-four. The immigrant curves are for immigrantfamilies where both spouses arrived in Canada in the 1970s.The immigrant family’s indifference curve is flatter than the indifference curve of the nonimmigrant family. Therefore, the foreign-born household will choose to have the wife workforty-two more hours and the husband work thirty-nine fewer hours than is the case in thenative-born family. These differences are smaller than those found in Figure 3.1 reflecting the28These are used in order to make the budget constraint the same as the one used in Figure 3.1.134smaller 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 artificialconstraint is defined for immigrants and their optimal hours are chosen subject to this constraint. The new constraint incorporates into the analysis: 1) differences by immigrant statusin 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 wealthat 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. Theimmigrant constraint is defined using the 1981 means of the hours and wages of husbands andwives over the sample of immigrant families where both spouses work. The results are similarto those found in Chapter 3. The indifference curve for immigrant families is”flatter” thanthat of non-immigrant families. The lower ratio of the wife’s wage to the husband’s wage inimmigrant families versus non-immigrant families can be seen in the flatter artificial constraintfor the immigrant family. The fact that the FB artificial constraint lies below the NB constraintis due to either the immigrant household having a lower disutility to the labour supplies ofits members, or the immigrant family’s wealth being lower than the wealth of non- immigrantfamilies.The results of the MRS estimation when the endogeneity of the wife’s participation decisionis modelled are similar to those found in the previous chapter. The value of the wife’s nonlabour time relative to the husband’s non-labour time is smaller in immigrant families than innon-immigrant families. Also, the presence of children does not increase the relative value of135the wife’s non-labour time in immigrant families to the same extent as it does in non-immigrantfamilies. The main difference is that the wife’s hours are less responsive to the ratio of theirwages after controlling for the husband’s hours.Next the Euler equation for the wife’s hours, (45), is estimated to see if modelling thewife’s participation decision changes the results of Chapter 3. Table 4.4 contains estimatesfrom the Euler equation estimation.29 The default category contains households where thewife 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 themarginal utility of wealth, ?p(t) + AN(t). The estimate is negative and significant from zero,30implying an annual value of bt+i — F(t) of —1.25, which is larger in magnitude than the valuefound in Chapter 3. Differences in the Euler equation by age have the same pattern as inChapter 3. The coefficient on the dummy variable for wives age twenty-five to thirty-four in1981 is negative and significant.31 This means that the value of b+i — I’(t) is smaller for thisgroup. Given that young households typically face steeper wage profiles and own little in theway of assets relative to older households, it is reasonable to think that they are more likelyto be credit-constrained than households where the wife is older. As was found in Chapter3, the value of bt+1 — I’(t) is significantly larger for where the wife is forty-five to fifty-fourin 1981.32 In both cases these age effects are strongly significant. Therefore, the empiricalevidence supports the hypothesis that credit constraint effects decrease with age.29The results of the estimation of equations (41), (42), and (44) are presented in Appendix 6.30The test statistic equals —8.25, and the prob-value is less than .0001.The test statistic equals —3.37, and the prob-value equals .001.32The test statistic equals 6.62, and the prob-value is less than .0001.136The effect of changes in the presence of children in the household between 1981 and 1991in the Euler equation represents the change in c(t), the weight on period t utility in thefamily’s lifetime utility function, over the 1980s. The estimates listed are of the parametersof the vector from equation (45). The estimates of the parameter of the vector q for thedifference in the dummy variable, KIDSO5, between 1981 and 1991 is the wrong sign and issignificant.33 The coefficient on the change in the dummy variables KO5PLUS and KID S614are positive and significant implying that non-immigrant families place a higher weight in thelifetime utility function on periods when two or more childreu under the age of six are present inthe household and when one or two children age six to fourteen are present in the household.34The estimate of the parameter from q.’ on the change in the variable K614PLUS over the 1980sis negative and significant, implying that non- immigrant households place a lower weight onperiods where three or more children age six to fourteen are present in the household.35 Aswas discussed in Chapter 3, this may be picking up a credit constraint effect. Having at leastthree children in the household is unlikely to force the wife to stay at home since the childrenwould be attending full-time school. However, the household must make large expenditureson food and clothing for these children. The household may wish to borrow against labourincome in the future when the children are adults and no longer living at home. If householdstypically cannot borrow against future earnings, then this variable may be proxying a creditconstraint effect.As was found in Chapter 3, the coefficients on all of the interactions of the immigrant33The test statistic equals —8.37; the prob-value is less than .0001.34The test statistics are 8.30 and 8.21, respectively. The prob-values are less than .0001.35The test statistic equals —3.48, and the prob-value equals .001.137dummy variable, FB, with these controls for the change in the presence of children variablesover the decade are significant.3°Adding the coefficient on each interaction with the coefficienton the analogous variable gives the change in X(t)4 for immigrant families. The effect ofadditional children present in the household is to increase the weight placed on that period inthe immigrant family’s lifetime utility function.37 As in Chapter 3, a higher weight is placedon periods when three or more children age six to fourteen are present in the home. The effectof the presence of these children in non-immigrant families is a significantly lower weight beingplaced on those periods. It was suggested above that this may be proxying a credit constrainteffect. It is interesting that this effect does not show up for immigrant families. It may not bepresent for immigrant families because children in this age group are more likely to be expectedto care for younger children after school in immigrant families compared with non-immigrantfamilies. 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 thatimmigrant families are more likely to be credit-constrained than non-immigrant families, ceterisparibus. The coefficients on all of the immigrant cohort controls are positive and significant.38Therefore, the estimate of bt+i — T’(t), the change in the log of the marginal utility of wealthis larger in immigrant families than in non-immigrant families. Therefore, the movement ofhours and wages in immigrant versus non-immigrant families over the l980s is not consistentwith the immigrant families being more likely to be credit-constrained than the non-immigrant35The test statistics equal 7.67, —7.90, —8.21, and 3.56, for the KIDSOS, KO5PLUS, KIDS614, andK614PLUS 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 asmall negative effect on the weight placed on that period.35The test statistics equal 5.86, 5.43, and 7.62, for the variables Y7180, Y6170, YBEF61, respectively. Theprob-values are less than .0001.138families.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 forthe husband’s hours, (8), we see that the marginal utility of wealth, ApQ) + ;\N(t) equals the—Uh(t)ratio of the marginal utility of the husband s hours to his wage rate, , as was the case inChapter 3. In fact the Euler equation for the husband’s hours derived in Chapter 3 holds overthe sample being analyzed in this chapter. The only difference is that in Chapter 3 the Eulerequation for the husband’s hours was estimated over the sample of households where the wifeworks, and in this chapter the estimation is over all households.Redefine equation (39) as:Y(r) = lrt[T — h1(r)] — ln(w1(r)) (47)where r = t, t + 1. Given this definition of Y(r) one can proceed with the derivation involvedin equations (40) through (45). The only difference is that the dependent variable is now thechange 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 vectornow 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 functionof the husband’s age and immigrant arrival cohort. This is to make it consistent with theuse of the husband’s characteristics in Z?. The estimates of equations (41), (42) and (44) are139reported in Appendix 7.The results of the estimation of the Euler equation for the husband’s hours are reported inTable 4.5. The coefficient estimates are very different from those of Table 4.4. As discussed inChapter 3, there are a number of explanations for these differences. An exploration of theseexplanations 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’sarrival cohort. Unlike in Table 4.4, the coefficients on the arrival cohorts all imply a smallervalue of b+1 — F(t) for immigrant familles; however, in each case, these differences are small inmagnitude and not statistically significant at the five percent level.39 Therefore, the hypothesisthat immigrant faniilles are more likely to be credit-constrained than non-immigrant famillesis rejected.Next, the three experiments from Chapter 3 are repeated using the MRS and Euler estimates. An artificial constraint is defined which reduces the family’s dynamic problem intoa choice of the wife’s hours in 1981 and 1991 subject to this constraint. In Figures 4.5 and4.6, the wife in the immigrant and non-immigrant households faces wages equal to the subsample means for non-immigrant women in 1981 and 1991. The wife must work enough hoursin 1981 and 1991 to support consumption equal to the income the wife earns at those wageswhen working the mean hours of wives in the 1981 and 1991 non- immigrant sub-samples. InFigure 4.5, the immigrant families preferences over intertemporal labour supply when childrenare present will be constrained to be the same as those in the non-immigrant family. In Figure39The test statistics are —.92, —.96, and —1.90, for the variables 1’7180, Y6170, and YBEF61, respectively.The prob-values are .36, .34, and .06.1404.6, the immigrant family’s preferences over children will be allowed to differ from those of thenon-immigrant family. In Figure 4.7, the non-immigrant family will solve the same problemas in Figure 4.6; however, the immigrant family will face a different constraint. The constraintwill be defined by the wages of the immigrant women in the 1981 and 1991 data, and theincome required will equal the income earned at those wages when the wife works the 1981and 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. Immigranthouseholds are forced to have the non-immigrant responses to the presence of children4°andthe intertemporal MRS is defined at the non-immigrant sample means for the changes in thepresence of children variables. Each spouse is age forty to forty-four. Equal probability is placedon the immigrant husband and wife being from each of the entry cohorts. The constraint canbe written:T— h2(t + 1) = [u2(t) + ii2(t + 1)]T — CNB(t,t + 1) — — h2(t)] (48)w2(t + 1)where 2(t),i2(t), w2(t + 1), and h2(t + 1) are the mean wages and hours of non-immigrantwivesin 1981 and 1991’; and CNB(t,t+ 1)2(t)]t)+tzY+1)2(t+ 1).As can be seen in Figure 4.5, the differences in hours are even larger than those of Chapter3. In Figure 3.3, the immigrant wife works 363 fewer hours in 1981 and 272 more hours in1991. In Figure 4.5, the immigrant wife works 519 fewer hours in 1981 and 456 more hoursin 1991.42 These large differences are due to the wife’s hours being less responsive to changes40This was done by ignoring the coefficients on the interaction terms in Table 4.4.411n the diagram, these are the sample means of the hours and wages of non-immigrant women in 1981 and1991 from Table 3.1 so as to make the figure comparable to Figure 3.3.42The non-immigrant family’s tangency is to the left of the range of the graph.141in her wages43 than in Chapter 3, and the fact that immigrant families in general respondless to the presence of children than do non-immigrant families. In this experiment, we areforcing the immigrant family to respond to the presence of children in the same way that thenon-immigrant family responds. As was the case in Chapter 3, there is evidence against thehypothesis that immigrant families are more likely to be credit-constrained than non-immigrantfamilies. The estimates indicate that wives in immigrant families work more in later years andless in earlier years than do non-immigrant wives, after controlling for their wage paths, anddifference in the within period MRS function.In Figure 4.6, the combined effect of differences due to immigrant status in b+i — I’(t) ofthe Euler equation for the wife’s hours and differences due to immigrant status in the weightplaced on periods where young children are present are analyzed. Using the same constraint asin 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 Figure4.5. For the immigrant household, the coefficients on the interaction of immigrant status withthe presence of children variables from Table 4.4 are used. This allows for different responsesbetween immigrant and non-immigrant families to the changes in the composition of childrenpresent over the decade. In determining the immigrant MRS, the sample means for changesin presence of children in the immigrant sample were used. As can be seen in Figure 4.6, theimmigrant indifference curve is much flatter than in Figure 4.5 and is now only slightly steeperthan the non-immigrant curve. Immigrant women work one hundred hours more in 1981 andeighty-five hours fewer in 1991.43Due to the larger value for the curvature parameter a’2.142As discussed in Chapter 3, intercept differences in the within period MRS estimation ofTable 4.3 by immigrant status, and differences in family responses to the presence of childrenin the household worked in the same direction. With no children present, immigrant households placed a lower weight on the wife’s hours relative to the husband’s hours than did non-immigrant households. If children were present, this difference grew. The effect of children wasthat the household placed an even higher weight on the wife’s hours relative to the husband’shours, and this effect was more pronounced for non-immigrant families than for immigrantfamilies.In contrast, differences in the intercept, bt+1 — P(t) of the Euler equation by immigrantstatus and differences by immigrant status in the weight placed on the period if children arepresent work in the opposite direction. The intercept differences imply that immigrant womenare more likely to work in later years than the non-immigrant women (either due to a higherrate of time preference or a smaller effect of credit constraints). The higher weight placed onperiods where children are present by non-immigrant families than immigrant families, andthe fact that average number of children present in the home under each age category is higherin 1981 than in 1991, means that immigrant wives work more hours in earlier years since theyrestrict their hours less when children are present.In Figure 4.7, an artificial constraint is defined for immigrant families, in an analogousfashion to the non- immigrant constraint, (48), but using sample means over immigrant families. Next the optimal choices of the wife’s hours in each period were derived and plotted astangencies between the immigrant intertemporal indifference curve and the immigrant artificial143constraint. The same MRS functions were used as those in Figure 4.6. As in Figure 4.4, theimmigrant constraint lies below and to the left of the non-immigrant constraint. This impliesthat, either due to a lower disutility to work, or due to lower life-time wealth, immigrant womensupply more labour in each period than non- immigrant women. The higher growth rate inimmigrant 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 in1981 compared to non-immigrant women. However, this effect appears to be small.4.6 Concluding RemarksThe empirical results from the estimation of the model accounting for the wife’s endogenousparticipation decision reinforce the conclusion of Chapter 3. Immigrant families place a lowervalue on the wife’s non-labour time relative to the husband’s non-labour time compared withnon-immigrant families. Immigrant families are less responsive to the presence of children interms of the hours of work for the wife for given hours of work of the husband and marketwage rates of both spouses. The results do not support the hypothesis that immigrant familiesare more likely to be credit constrained than non-immigrant families. There is evidence insupport of credit constraints being important determinants of the hours of work of youngwomen; however, after controliing for this effect, immigrant families do not appear to be morelikely to be credit-constrained than non- immigrant families.144CHAPTER FIVEConclusionsThis thesis has analyzed the labour market adjustment of immigrant families. The empiricalevidence indicates that the labour market adjustment of immigrants is difficult in the first yearsafter migration. However, with time in Canada, the labour market performance of immigrantmen and women compares favourably to the performance of non-immigrants. Immigrant menand women face much lower wages than non-immigrant men and women in the first yearsafter 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 thisinitial differential is overcome with years of residence.Immigrant men and women with less than five years of residence work significantly fewerweeks in the year than non-immigrants. This appears to be due to higher unemploymentover this period. After the first five years, the weeks of work of the immigrant husbandsand wives are similar to those of the non-immigrant husbands and wives. A similar patternemerges in the probability of the wife working. Immigrant women with fewer than five yearsof experience are less likely to participate than non-immigrant women. However, immigrantwomen with more years of residence are significantly more likely to work than non-immigrantwomen. Immigrant husbands and wives work more hours per week than non- immigrants foralmost every immigrant cohort.145The economic literature on labour market adjustment has focused almost exclusively onwage rates and whether or not immigrants are of poorer “quality” than the pre-existing population. 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 recentimmigrants may never have wages that are on average equal to similar non-immigrants. However, the evidence on other labour market traits of these individuals indicates that they areprepared 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 labourmarket.The hypothesis that credit constraints are important determinants of hours of work inimmigrant families has been explored. In the reduced-form estimation of Chapter 2, immigrantfamily members were found to work more hours than non-immigrants. These differences donot vary through time in spite of larger wage growth experienced by the immigrants. Sincethe credit constraint eases with years of residence, it was argued that this may be due tothe immigrant household not increasing their hours of work by more than the non-immigrantfamily in response to the higher wage growth.A preference-based argument was also put forward. It may be that immigrant families havea lower disutility to its members labour or a lower expected lifetime wealth. Combined with alower responsiveness of immigrants to movements along their lifetime wage proffle, this wouldalso explain the movements in the data.146In Chapter 3, a structural model of household labour supply allowing for uncertainty andcredit constraints was developed. The estimation procedure allowed for the estimation ofstructural labour supply equations using multiple cross sections of data rather than paneldata, and may be of use in other applications where panel data is not available, but multiplecross section data sets are available. The results of the estimation indicate that immigrantfamilies place a lower value on the wife’s non-labour time relative to the non-labour time of thehusband than is the case in non-immigrant families. This difference would explain in part thehigher hours of immigrant wives than non-immigrant wives despite their lower wages. Aftercontrolling for offered wages, immigrants were found to work more hours than non- immigrantsdue to a lower disutility to work or lower wealth. The results do not support the hypothesisthat 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 tobe endogenous. The model is a significant extension of the dynamic labour supply literaturefor 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 periodin order for the wife to work that period, as suggested by Cogan (1981) in the static laboursupply model. After accounting for the participation decision, the wife’s hours are found tobe less responsive to movements along her lifetime wage path. The results of the estimation ofthe Euler equation for the wife’s hours support the conclusions of Chapter 3. After controllingfor age, immigrant families do not appear to be more likely to be credit- constrained thannon-immigrant families.147The assumption that immigrant families are more likely to be credit-constrained thannon- immigrant families is critical to the Family Investment Hypothesis, which predicts thatimmigrant married women will work long hours in the first years after migration when thefamily is unable to borrow and then reduce their hours after years of residence in the newcountry when the need to borrow has diminished. The results of this thesis are strong evidenceagainst the FIR. Immigrant family members do not appear to distort their hours of work in thefirst years after migration in order to fund family consumption. In particular, the immigrantwives 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 3and Chapter 4 indicate that the hours of immgirant wives are consistent with immigrantfamilies being less likely to be credit-constrained than non-immigrant families. Under theFIR, immigrant wives are predicted to bear the brunt of the distortion on family labour supplydecisions. 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 generating incomes for their families which are comparable to those of non-immigrant familieswithin ten years of residence in Canada. This is strong support for recent Canadian immigration policy. There does not appear to be an economic rational for adjusting either the sizeof the immigrant inflow or the current policies aimed at assisting immigrants adjust to theCanadian labour market.Future research should analyze the determinants of the higher hours of work of immigrantsafter controlling for offered wages. It may be possible to distinguish the preference-based148explanation from the explanation based on lower wealth of immigrants. A study of the weeksof work of immigrants in the first five years after migration would also be interesting given thelower weeks worked for these immigrants for both men and women. Finally, further researchshould focus on the causes of the differential rates of return on the education of immigrantversus non-immigrant women.149CD b b dFICUE2.1mmgrantAdjustmentPathforEornngsIIIIIYEARS—SINCE—MICRATIONEn z En C00 0 0 0 CD 0 CD000——lAPEqualEarningsLineIIIII48121620242832FIGURE2.2YEARS—SINCE—MIGRATIONImmigrantAdjustmentPathsandCohortDifferences(0 b b (0 c 0 0 0 0 co R 0m z01C m U C——IIIIIII•II_IIIII,IIIIII,,I11111IIIIIII‘‘I0’———————————————————————-.——(0.II00481216lAPfor1 960scohort———lAPfor1 970scohort——lAPunderstationarityassumptionEqualEarningsLine20242832FIGURE2.3ImmigrantAdjustmentPathsDifferencesinAssimilationRates0IIII000•(0 0——-——jirilill—IIrIIILJ.JIIIIllzLN—Ic_fl-.‘III—-0111,1111111——— mI-i’’’—0 blAPfor1 960scohort———APfor1 970scohortEqualEarningsLine0IIII48121620242832YEARS—SINCE—MIGRATIONTable 2.1Sample Means for Selected VariablesWife’s FB 1981, FB 1991, NB 1981, NB 1991,Variables N=3688 N=10472 N=3808 N=9815PART .6551 .7357 .5885 .7330WAGE* 8.00 10.03 9.37 10.92HOURS* 34.67 35.47 32.47 33.64WEEKS* 43.37 46.71 43.04 46.11AGE 38.01 46.32 36.77 44.74EDO8 .2400 .2042 .1253 .1110BD913NG .1883 .1621 .2661 .1960EDHSGRAD .1280 .1598 .1895 .1372EDPS .3364 .3346 .3364 .3933EDBACH .0848 .1038 .0734 .1185EDGRAD .0225 .0355 .0093 .0440KIDSO5 .2208 .0835 .1911 .0731K1PLUS .1008 .0171 .1016 .0184KIDS614 .7028 .5025 .6265 .4988K2PLUS .0589 .0324 .0466 .0338BIRTHS 2.200 2.391 2.218 2.293BIRTH9 .0018 .1234 .0050 .1237ENGOFF .7981 .8151 .6102 .6208FREOFF .0354 .0358 . .2009 .1967BILOFF .0996 .0940 .1884 .1820OTHOFF .0669 .0551 .0005 .0005* The mean is calculated over the sample of women who worked. For Immigrantfamilies the sample size is 2372 in 1981 and 6400 in 1991. For non-immigrantfamilies the sample size is 2244 in 1981 and 7194 in 1991.153Table 2.1 cont.Husband’s FB 1981, FB 1991, NB 1981, NB 1991,Variables N=3688 N=10472 N=3808 N9815WAGE 11.36 13.29 12.09 13.54HOURS 42.87 42.07 42.69 42.31WEEKS 47.56 48.25 48.26 48.38AGE 41.04 49.35 38.90 46.90EDO8 .1956 .1748 .1322 .1110ED913NG .1261 .1309 .1988 .1960EDHSGRAD .0576 .0885 .1238 .1372EDPS .4431 .3965 .3994 .3933EDBACH .1099 .1277 .1099 .1185EDGRAD .0677 .0816 .0359 .0440ENGOFF .8525 .8627 .6065 .5213FREOFF .0284 .0289 .1475 .1967BILOFF .1191 .1084 .2460 .2820OTHOFF .035 1 .0360 .0003 .0005ATL .0078 .0099 .1077 .1037QUENM .0075 .0086 .1896 .1889MONT .1247 .1134 .1278 .1148TOR .3808 .3961 .0773 .0830ONTNT .2170 .2001 .2408 .2410PRAIR .1228 .1210 .1613 .1636BCNV .0482 .0413 .0592 .0616VANC .0915 .1096 .0363 .0434154Table 2.2Results from Estimation of Wage,Hours, and Weeks Equations for Wives1nWAGE 1nHOURS 1nWEEKSIntercept 1.914 3.560 3.787(.037) (.027) (.027)YR91 .1598 .0001 .1139(.029) (.020) (.022)ATL -.2559 .0203 -.1183(.033) (.023) (.023)QUENM -.1123 -.0386 .0028(.040) (.029) (.027)MONT -.0581 -.0475 .0323(.039) (.028) (.025)ONTNT -.1411 -.0384 .0077(.028) (.020) (.017)PRAIR -.1493 -.0297 - .0025(.031) (.022) (.018)BCNV -.1274 -.0879 -.0592(.044) (.029) (.025)VANC .0332 -.0570 -.0024(.044) (.033) (.028)A3034*YR81.1216 -.0476 .0360(.032) (.023) (.026)A3539*YR81.1524 -.0777 .0413(.033) (.025) (.029)A4044*YR81.1275 -.1082 .0638(.035) (.025) (.027)A4549*YR81.1523 -.1403 .0641(.040) (.031) (.030)A5054*YR8I.1388 -.1589 .0865(.049) (.036) (.034)A4044*YR9I.0035 -.0389 -.0134(.018) (.011) (.010)155Table 2.2 cont.InWAGE 1nHOURS [ 1nWEEKSA4549*YR91.0614 -.0763 -.0123(.018) (.012) (.011)A5054*YR91.0240 -.1259 -.0240(.023) (.015) (.013)p.5559*yR91.0577 -.1890 -.0540(.028) (.020) (.016)A6064*Y981-.0074 -.1532 -.0499(.055) (.033) (.026)EDO8 -.2679 -.022 1 -.1329(.041) (.026) (.026)ED913NG -.0998 .0083 -.0555(.024) (.016) (.015)EDPS .1901 -.0084 .0097(.021) (.014) (.012)EDBACH .5699 .0421 .0153(.027) (.020) (.018)EDGRAD .6774 .1012 .0552(.043) (.036) (.022)FREOFF -.0480 .0047 -.0729(.037) (.026) (.025)BILOFF .0366 .0449 -.0399(.027) (.019) (.019)OTHOFF .5790 -.3554 .3228(.332) (.434) (.032)BIRTHS -.0334(.007)BLRTH9 -.0113(.026)KIDSO5 -.1520 -.1017(.020) (.020)KIPLUS -.3153 -.2020(.044) (.044)156Table 2.2 cont.InWAGE InHOURS 1nWEEKSKIDS614 -.0776 -M517(.008) (.007)K2PLUS -.1815 -.2401(.032) (.037)YBEF61 -.1036 .0202 -.0206(.050) (.036) (.033)Y6170 -.1802 .0987 .0046(.047) (.033) (.032)Y7180 -.2821 .0914 -.0472(.047) (.032) (.032)Y80 -.7219(.123)YBEF61*YR91 .0838 -.0085 .0032(.039) (.030) (.027)Y6170*YR91 .0908 -.0037 -.0125(.034) (.024) (.024)Y7180*YR91 .1142 -.0038 .0508(.035) (.023) (.024)Y8185 -.2930 .0901 -.0097(.054) (.03 1) (.027)Y86 -.2869 .0824 -.1027(.103) (.058) (.051)Y87 -.3380 .0611 -.0728(.087) (.046) (.044)Y88 -.3845 .0672 -.1330(.082) (.037) (.047)Y89 -.3238 .0263 -.2506(.085) (.048) (.061)Y90 -.3935 .0316 -.6097(.105) (.058) (.081)FB*ATL .0576 -.0552 .0573(.094) (.055) (.049)157Table 2.2 cont.InWAGE IriHOURS 1nWEEKSFB*QUENM-.0929 .0952 -.0674(.139) (.063) (.069)FB*MONT-.0121 .0158 -.0848(.052) (.034) (.03 1)FB*ONTNT .0223 -.0672 -.0444(.036) (.024) (.020)FB*PRAIR .0430 -.0768 -.0559(.040) (.027) (.023)FB*BCNV .0704 - .0750 - .0744(.059) (.041) (.035)FB*VANC-.0412 -.0489 -.077 1(.051) (.036) (.032)FB*EDO8 .1266 .0398 .0952(.051) (.031) (.031)FB*ED913NG .0556 -.0252 .0261(.038) (.023) (.022)FB*EDPS-.0190 -.0199 -.0182(.032) (.020) (.019)FB*EDBACH-.1356 -.0399 .0127(.042) (.028) (.025)FB*EDGRAD-.0688 -.0764 -.0345(.058) (.044) (.03 1)FB*FREOFF-.0485 -.0257 -.0026(.066) (.038) (.043)FB*BILOFF-.0500 -.0818 .0326. (.043) (.027) (.025)FB*OTHOFF-.7180 .3764 -.3934(.335) (.434) (.041)FB*BIRTHS.0090(.010)FB*BIRTH9-.059 1(.038)158Table 2.2 cont.InWAGE [ InHOURS InWEEKSFB*KIDSO5 .0742 .0152(.026) (.027)FB*K1PLUS .1604 .0374(.056) (.054)FB*KIDS614 .0332 .0157(.010) (.009)FB*K2PLUS .0312 .1400(.043) (.045)R2 .0983 .0369 .0558F 32.29 12.26 18.59N 19 558 19 558 19 558* Standard errors are in parentheses.159Table 2.3Estimates from Wage, Hours and WeeksRegressions for HusbandsVariable ln(WAGE) ln(HOURS) ln(WEEKS)Intercept 2.139 3.616 3.735(.034) (.018) (.020)A3034*YR81.1625 .0605 .1193(.027) (.014) (.019)A3539*YR81 .2263 .0750 .1337(.028) (.015) (.019)A4044*YR81 .2448 .0567 .1251(.030) (.016) (.020)A4549*YR81 .2724 .0319 .1063(.030) (.015) (.020)A5054*YR81 .2645 .0384 .1266(.031) (.017) (.021)YR91 .2183 .0558 .1114(.027) (.014) (.018)A4044*YR91 .0436 .0037 .0105(.018) (.007) (.007)A4549*YR91 .0772 .0010 .0138(.018) (.007) (.007)A5054*YR91.0665 -.0200 .0084(.020) (.008) (.008)A5559*YR9I.0160 -.0379 .0023(.021) (.009) (.008)A6064*YR91 .0210 -.0945 -.0216(.026) (.012) (.011)ATL -.2198 .0330 -.0480(.026) (.013) (.012)QUENM -.1481 .0067 .0204(.031) (.015) (.013)MONT -.0612 -.0005 .0458(.030) (.015) (.013)160Table 2.3 cont.Variable ln(WAGE) ln(HOURS) ln(WEEKS)ONTNT -.1135 .0408 .0279(.024) (.012) (.008)PRAIR -.1700 .0650 .0094(.027) (.013) (.010)BCNV -.0592 .0197 -.0190(.034) (.016) (.012)VANC -.0003 .0502 .0155(.037) (.017) (.017)FB*ATL .3076 -.0394 .0685(.066) (.043) (.020)FB*QUENM-.0674 .0030 -.1147(.097) (.044) (.043)FB*MONT-.1237 -.0358 -.0735(.042) (.019) (.018)FB*ONTNT .0964 -.0134 -.0334(.029) (.013) (.011)FB*PRAIR.0634 -.0365 -.0304(.034) (.015) (.013)FB*BCNV.0203 -.0540 -.0363(.048) (.022) (.019)FB*VANC-.0790 -.0565 -.0456(.043) (.020) (.019)EDO8 -.1508 .0161 -.0818(.026) (.011) (.011)ED913NG -.0354 .0238 -0166(.022) (.009) (.009)EDPS .1140 .0181 .0137(.019) (.008) (.008)EDBACH .4328 .0067 .0455(.023) (.011) (.009)EDGRAD .4848 .0365 .0138(.030) (.015) (.013)161Table 2.3 cont. -Variable ln(WAGE) ln(HOURS) ln(WEEKS)FB*EDO8.0677 -.0558 .0168(.039) (.015) (.017)FB*ED913NG-.0305 -.0485 -.0033(.037) (.014) (.015)FB*EDPS .0409 -.0392 -.0168(.031) (.012) (.013)FB*EDBACH-.0793 -.0470 -.0215(037) (.016) (.015)FB*EDGRAD.0555 -.0481 .0322(.042) (.019) (.018)FREOFF -.0423 .0098 -.0593(.027) (.013) (.014)BILOFF .0204 .0101 -.0222(.020) (.0 10) (.009)OTHOFF -.2593 -.0282 .1410(.107) (.030) (.021)FB*FREOFF.0634 -.0060 .0 133(.053) (.022) (.027)FB*BILOFF.0412 .0029 .0199(.032) (.015) (.014)FB*OTHOFF .1419 .0117 -.2059(.114) (.034) (.030)YBEF61 -.1594 .0975 .0305(.042) (.019) (.019)Y6170 -.1231 .0877 .0305(.040) (.019) (.017)Y7180 -.2803 .0906 .0116(.042) (.019) (.019)Y80 -.5531(.094)YBEF61*YR91.0723 -.0051 .0215(.028) (.013) (.014)162Table 2.3 cont.Variable ln(WAGE) ln(HOURS) ln(WEEKS)Y6170*YR91.0230 -.0130 .0017(.025) (.012) (.012)Y7180*YR91 .0735 -.0254 .0133(.028) (.013) (.014)Y8185 -.3707 .0629 .0176(.047) (.019) (.019)Y86 -.3876 .0724 -.0259(.080) (.033) (.046)Y87 -.3985 .0544 .0084(.070) (.027) (.026)Y88 -.6353 .0319 -.0234(.081) (.029) (.027)Y89 -.4679 .0201 -.2284(.069) (.028) (.050)Y90 -.5134 .0335 -.5432(.084) (.037) (.066)R2FN 27 783 27 783 27 783* Standard errors are in parentheses.163Table 2.41981 Predicted Differences in Wages, Hours,and Weeks of Wives by Immigrant Status1nWAGE 1nHOURS InWEEKSBefore 1961 -.0625 .0187 .0202(.039) (.022) (.024)1961-70 -.1392 .0973 .0455(.035) (.021) (.022)1971-80 -.2411 .0899 -.0064(.039) (.022) (.024)Table 2.51991 Predicted Differences in Wages, Hours,and Weeks of Wives by Inuuigrant Status1nWAGE 1nHOURS ( 1nWEEKSBefore 1961 .0213 .0102 .0234(.031) (.018) (.016)1961-70 -.0484 .0607 .0329(.028) (.015) (.015)1971-80 -.1269 .0861 .0444(.027) (.015) (.013)1981-85 -.2520 .0886 .0311(.042) (.020) (.018)1986 -.2459 .0810 -.0619(.095) (.052) (.047)1987 -.2970 .0596 -.0319(.079) (.040) (.038)1988 -.3435 .0658 -.0922(.074) (.030) (.042)1989 -.2828 .0249 -.2097(.076) (.041) (.057)1990 -.3525 .0301 -.5689(.099) (.054) (078)* Standard errors are in parentheses.164Table 2.61981 Predicted Differences in Wages, Hours,and Weeks of Husbands by Immigrant Status1nWAGE 1nHOURS [ InWEEKSBefore 1961 -.0912 .0353 -.0095(.029) (.014) (.014)1961-70 -.0549 .0254 -.0095(.026) (.013) (.013)1971-80 -.2121 .0283 -.0283(.030) (.014) (.015)Table 2.71991 Predicted Differences in Wages, Hours,and Weeks of Husbands by Immigrant Status1nWAGE 1nHOURSBefore 1961 -.0298 .0390 .0172(.024) (.010) (.009)1961-70 -.0428 .0213 -.0027(.022) (.010) (.009)1971-80 -.1495 .0119 -.0100(.023) (.0 10) (.009)1981-85 -.3134 .0095 -.0173(.036) (.014) (.015)1986 -.3303 .0191 -.0608(.074) (.031) (.044)1987 -.3413 .0011 -.0264(.061) (.024) (.024)1988 -.5780 -.0215 -.0582(.076) (.026) (.024)1989 -4107 -.0332 -.2632(.063) (.025) (.048)1990 -.4562 -.0199 -.5781(.078) (.035) (.065)* Standard errors are in parentheses.165Table 28Results from Probit Estimationon Wife’s ParticipationVARIABLEYR9I .0428(.266)NB -.0740(.03 1)NB*YR9I .0302(.020)YBEF6I (WIFE) .0651(.032)Y6170 (WIFE) .0728(.027)YBEF6I*YR9I-.0485(WIFE) (.03 8)Y6170*YR9I-.0526(WIFE) (.032)Y8185 (WIFE) .0031(.032)Y86 (WIFE) -.0495(.071)Y87 (WIFE) -.03 06(.063)Y88 (WIFE) -.1148(.069)Y89 (WIFE) -.1844(.079)Y90 (WIFE) -.2868(.083)YBEF61 -.1578(HUSBAND) (.032)Y6170 (HUSBAND) -.1097(.027)VARIABLEFB*QUENM.0271(.05 1)FB*MONT.0165(.030)FB*ONTNT-.03 52(.020)FB*PRAIR.0129(.022)FB*VANC.0293(.028)FB*BCNV.0118(.029)EDO8 (WIFE) -.1864(.0 16)ED913NG (WIFE) -.0749(.012)EDPS (WIFE) .1246(.0 11)EDBACH .2215(WIFE) (.019)EDGRAD .3201(WIFE) (.044)FB*EDO8 (WIFE) .0833(.022)FB*ED9I3NG.0259(WIFE) (.019)FB*EDPS (WIFE) -.0504(.0 17)FB*EDBACH-.0541(WIFE) (.027)166Table 2.8 cont.VARIABLEYBEF61*YR91 .0711(HUSBAND) (.03 8)Y6170*YR91 .0402(HUSBAND) (.033)Y8185 (HUSBAND) -.0114(.033)Y86 (HUSBAND) .0109(.071)Y87 (HUSBAND) -.0230(.063)Y88 (HUSBAND) .0571(.072)Y89 (HUSBAND) .0048(.082)Y90 (HUSBAND) .0458(.033)A3034*YR8I-.0089(WIFE) (.019)A3539*YR81-.0261(WiFE) (.023)A4044*YRSI-.0508(WIFE) (.027)A4549*YR8I-.1462(WIFE) (.031)A5054*YR8 1 -.2399(WIFE) (.03 5)A3034*YR81-.0586(HUSBAND) (.023)A3539*YR8I-.0720(HUSBAND) (.026)A4044*YR8I-.0582(HUSBAND) (.029)VARIABLEFB*EDGRAD-.0556(WIFE) (.054)EDO8 (HUSBAND) -.0242(.0 17)ED9I3NG .0082(HUSBAND) (.015)EDPS (HUSBAND) -.0401(.0 13)EDBACH -.0757(HUSBAND) (.017)EDGRAD -.1234(HUSBAND) (.024)FB*EDO8.0252(HUSBAND) (.025)FB*ED9I3NG.0246(HUSBAND) (.024)FB*EDPS .0349(HUSBAND) (.02 1)FB*EDBACH.0348(HUSBAND) (.026)FB*EDGRAD-.0245(HUSBAND) (.033)BIRTHS -.0091(.003)BIRTH9 -.0256(.0 15)FB*BIRTHS-.0039(.005)FB*BIRTH9-.0089(.022)KIDSO5 -.1957(.013)167Table 2.8 cont._VARIABLEA4549*YR81-.0489(HUSBAND) (.032)A5054*YR81-.0434(HUSBAND) (.03 5)A4044*YR91-.0490(WIFE) (.011)A4549*YR9I-.0779(WIFE) (.014)A5054*YR91-.1361(WIFE) (.017)A5559*YR9-.2560(WIFE) (.019)A6064*YR9I-.3891(WIFE) (.024)A4044*YR9I-.00002(HUSBAND) (.013)A4549*YR9I-.0457(HUSBAND) (.0 15)A5054*YR9I-.0592(HTJSBAND) (.0 17)A5559*YR91-.0805(HUSBAND) (.019)A6064*YR91-.0934(HUSBAND) (.022)ATL -.0979(.019)QUENM -.1015(.025)MONT -.0943(.024)ONTNT -.0289(.0 17)VARIABLE I__________KIPLUS -.4219(.02 1)KIDS6I4 -.0629(.006)K2PLUS -.1916(.022)FB*KIDSO5.0027(.0 18)FB*KIPLUS.0718(.028)FB*K6I4PLUS.0174(.008)FB*K2PLUS.0464(.029)FREOFF (WIFE) -.03 06(.024)BILOFF (WIFE) .0485(.0 18)OTHOFF (WIFE) .0529(.228)FB*FREOFF (WIFE) .0304(.039)FB*BILOFF (WIFE) .0029(.026)FB*OTHOFF-.1269(WIFE) (.229)FREOFF -.0085(HUSBAND) (.024)BILOFF -.0141(HUSBAND) (.018)OTHOFF -.1551(1{USBAND) (.301)168Table 2.8 cont.VARIABLEPRAIR .0103(.018)VANC -.0527(.025)BCNV -.0781(.022)FB*ATL-.0056(.044)R2 .2083LR 4401N 27783* Standard errors are in parentheses.VARIABLEFB*FREOFF .0184(HUSBAND) (.04 1)FB*BILOFF-.0157(HUSBAND) (.025)FB*OTHOFF.2144(HUSBAND) (.3 02)169Table 2.9Results from Estimation of Wage, Hoursand Weeks Equations for Wives afterControlling for Participation DecisionInWAGE InHOURS 1nWEEKSIntercept 1.7834 3.638 3.847(.047) (.031) (.035)A3034*YR81.1058 -.0329 .0228(.036) (.023) (.026)A3539*YR81.1513 -.0538 .0347(.038) (.024) (.028)A4044*YR81 .1504 -.0791 .0605(.039) (.025) (.029)A4549*YR8I.1460 -.0742 .0857(.043) (.030) (.033)A5054*YR81.0925 -.0527 .1464(.056) (.040) (.043)YR91 .2195 -.0326 .0879(.033) (.021) (.025)A4044*YR91.0062 -.0153 .0006(.017) (.012) (.015)A4549*YR91.0602 -.0343 .0 134(.019) (.0125 (.018)A5054*YR91.0009 -.0571 .0211(.022) (.020) (.022)A5559*YR91-.0279 -.0615 .0356(.03 1) (.030) (.033)A6064*YR91-.1750 .0463 .0941(.052) (.046) (.049)ATL -.2916 .0542 -.0920(.038) (.024) (.028)QUENM -.1526 -.0042 .0295(.047) (.030) (.035)MONT -.0953 -.0149 .0575(.045) (.029) (.034)170Table 2.9 cont.1nWAGE 1nHOURS [ 1nWEEKSONTNT -.1491 -.0297 -.0194(.031) (.020) (.024)PRAIR -.1454 -.0290 -.0411(.033) (.021) (.025)BCNV -.1536 -.0616 -.0682(.042) (.027) (.032)VANC .0113 -.0407 -.0360(.047) (.030) (.035)FB*ATL .0458 -.0203 .0913(.092) (.058) (.067)FB*QUENM-.0922 .0972 -.0652(.104) (.066) (.076)FB*MONT.0 129 .0440 -.054 1(.057) (.036) (.041)FB*ONTNT.0023 -.0250 -.0044(.038) (.024) (.029)FB*PRAIR .0437 -.0425 -.0184(.041) (.026) (.031)FB*BCNV .0646 -.0321 -.0292(.059) (.037) (.043)FB*VANC- .0290 -.0060 -.0293(.054) (.034) (.040)EDO8 -.3664 .0714 -.0604(.041) (.029) (.031)ED9I3NG -.1302 .0372 -.033 1(.026) (.017) (.019)EDPS .2282 -.0471 -.0397(.023) (.016) (.018)EDBACH .6216 -.1730 -.0308(.032) (.022) (.026)EDGRAD .7482 .0251 -.0038(.061) (.041) (.050)171Table 2.9 cont.InWAGE 1nHOURSFB*EDO8.1796 .0082 .0760(.049) (.03 1) (.034)FB*ED913NG .07 12 -.0 120 .0442(.038) (.024) (.027)FB*EDPS-.0352 .0197 .0194(.032) (.021) (.024)FB*EDBACH-.1540 -.00001 .0494(.044) (.028) (.033)FB*EDGRAD-.0943 -.0305 .0066(.075) (.048) (.059)FREOFF -.0670 .0207 -.0605(.041) (.026) (.030)BILOFF .0509 .0324 -.0590(.029) (.018) (.021)OTHOFF .5256 -.3127 .3512(.541) (.335) (.306)*FPOFF-.0246 -.0272 .0009(.068) (.043) (.049)p,3*BILOFF-.0530 -.0683 .0464(.042) (.027) (.03 1)FB*OTHOFF-.6891 .3534 -.4028(.542) (.336) (.307)BIRTHS -.0474(.007)BIRTH9 -.0257(.029)FB*BIRTHS.0080(.009)FB*BLRTH9-.0645(.040)KIDSO5 -.0792 -.0452(.022) (.025)172Table 2.9 cont.1nWAGE 1nHOURS 1nWEEKSK1PLUS -.1373 -.0639(.046) (.049)KIDS614 -.0554 -.0344(.008) (.010)K2PLUS -.1064 -.1818(M32) (.036)FB*KIDSO5 .0704 .0123(.024) (.027)FB*KIPLUS .1208 .0066(.046) (.047)FB*KIDS614 .0270 .0109(.010) (.012)FB*K2PLUS .0143 .1267(.039) (.044)YBEF61 -.0940 .0143 -.0251(.056) (.034) (.039)Y6170 -.1578 .0769 -.0 123(.052) (.032) (.038)Y7180 -.2588 .0652 -.0672(.052) (.033) (.038)Y80 -.7281(.074)YBEF61*YR91.0751 .0004 .0101(.043) (.027) (.031)Y6170*YR91 .0750 -.0181 .0018(.037) (.024) (.027)Y7180*YR91.1097 .0084 .0600(.037) (.023) (.027)Y8185 -.2812 .0761 -.0205(.055) (.033) (.039)Y86 -.2774 .0788 -.1055,(.100) (.062) (.073)173Table 2.9 cont._____________InWAGE InHOURS InWEEKSY87 -.3364 .0629 -.0713(.078) (.048) (.057)Y88 -.3828 .0711 -.1300(.073) (.045) (.053)Y89 -.3684 .0708 -.2161(.081) (.050) (.057)Y90 -.4491 .0868 -.5669(.092) (.058) (.065)IM.R .3078 -.2676 -.2076(.044) (.048) (.052)R2 .1006 .0386 .0570F 37.60 12.61 18.69N 19 558 19 558 19 558* Standard errors are in parentheses.174Table 2.101981 Predicted Differences in Wages, Hours,and Weeks of Wives by Immigrant Status afterCorrecting for the Participation SelectionInWAGE InHOURS InWEEKSBefore 1961 -.0602 .0141 .0167(.040) (.025) (.028)1961-70 -.1241 .0767 .0295(.035) (.023) (.026)1971-80 -.2250 .0650 -.0254(.036) (.023) (.027)* Standard errors are in parentheses.175Table 2.111991 Predicted Differences in Wages, Hours,and Weeks of Wives by Immigrant Status afterCorrecting for the Participation SelectionJnWAGE 1nFIOURSBefore 1961 .0149 .0145 .0268(.028) (.018) (.020)1961-70 -.0490 .0586 .0313(.024) (.015) (.018)1971-80 -.1153 .0734 .0346(.015) (.023) (.017)1981-85 -.2475 .0760 .02 13(.035) (.022) (;026)1986 -.2436 .0786 -.0637(.090) (.057) (.067)1987 -.3026 .0628 -.0295(.066) (.042) (.049)1988 -.3491 .0709 -.0882(.060) (.038) (.045)1989 -.3346 .0706 -.1742(.069) (.044) (.050)1990 -.4153 .0866 -.525 1(.082) (.053) (.059)* Standard errors are in parentheses.176Table 3.1Sample Means for Selected VariablesWife’s PB 1981, FB 1991, NB 1981, NB 1991,Variables N=2372 N=6400 N=2244 N =7194AHOURS 1537 1692 1434 1582WAGE 8.07 10.29 9.37 10.92AGE 37.91 46.02 36.30 43.81EDO8 2105 .1602 .0777 .0496ED913NG .1770 .1527 .2392 .1896EDHSGRAD .1248 .1170 .1699 .2127EDPS .3610 .3684 .3982 .4166EDBACH .0992 .1170 .1015 .1093EDGRAD .0275 .0361 .0135 .0222KJDSO5 .2065 .0623 .1643 .0708KO5PLUS .0691 .0075 .0574 .0132KIDS614 .6760 .5192 .5700 .5257K614PLUS .0542 .0280 .0391 .03 14Y7180 .3568 .4169Y6170 .3799 .3597YBEF61 .2633 .2234177Table 3.1 cont.Husband’s FB 1981, FB 1991, NB 1981, NB 1991,Variables N=2372 N=6400 N=2244 N7194AHOURS 2057 2088 2060 2071WAGE 11.04 13.31 11.88 13.28AGE 40.87 49.15 38.43 46.08EDO8 .1804 .1491 .1039 .0865ED9I3NG .1244 .1283 .2139 .1909EDHSGRAD .0604 .0816 .1182 .1442EDPS .4555 .4245 .4083 .4042EDBACH .1145 A359 .1171 .1275EDGRAD .0647 .0775 .0383 .0467Y7180 .3423 .3983Y6170 .3628 .3534YBEF61 .2950 .2483178- Table 3.2Results from Estimation of the FamilyMarginal Rate of Substitution FunctionVARIABLEIntercept 8.036(.062)LNTHRS .0106(.008)WDIFF .0871(.006)KIDSO5 .0781(.008)KO5PLUS .1332(.015)KIDS614 .0321(.003)K614PLUS .0906(.012)FB*KIDSO5-.0268(.011)FB*KO5PLUS-.0516(.021)FB*KIDS614-.0089(.004)FB*K614PLUS-.0200(.017)NB .0287(.010)YR91 -.0473(.0 14)NB*YR91.0127(.010)Y6170 (WIFE) -.0046(.015)VARIABLEYBEF61*YR91.0077(HUSBAND) (.021)A3034*YR81-.0066(WIFE) (.011)A3539*YR81.0020(WIFE) (.014)A4044*YR81.0019(WIFE) (.016)A4549*YR81.0 100(WIFE) (.018)A5054*YR81.0161(WIFE) (.021)A4044*YR91.0147(WIFE) (.006)A4549*YR91.0230(WIFE) (.007)A5054*YR91.03 18(WIFE) (.009)A5559*YR91.0636(WIFE) (.011)A6064*YR9I.0518(WIFE) (.016)A3034*YR81.0061(HUSBAND) (.0 13)A3539*YR81.0077(HUSBAND) (.015)A4044*YR81.0064(HUSBAND) (.016)A4549*YR81.0 140(HUSBAND) (.018)179Table 3.2 cont.VARIABLEYBEF61 .0139(WIFE) (.018)Y6170*YR91 .0044(WIFE) (.017)YBEF61*YR91 .0054(WIFE) (.021)Y6170 -.0131(HUSBAND) (.015)YBEF6I .0114(HUSBAND) (.018)Y6170*YR91 .0214(HUSBAND) (.0 18)R2 .069F 20.21N 18210* Standard errors are in parentheses.VARIABLEA5054*YR81 .0050(HUSBAND) (.020)A4044*YR91-.00534(HUSBAND) (.008)A4549*YR91-.0053(HUSBAND) (.008)A5054*YR91 .0075(HUSBAND) (.009)A5559*YR91 .0090(HUSBAND) (.010)A6064*YR91 .0036(HUSBAND) (.012)180cv E :3 0oDC 0 z (I)-D C 0 (I) :3 I0 0 OD V)0 0 N 0 0 (0 r) 0 0 LI) 0 0 0 0 0 0FIGURE3.11981Non—LabourTimeforImmigrantandNon—ImmigrantFamiliesGivenNon—ImmigrantWagesandArtificialConstraint0 03300340035003600370038003900Wife’sNon—LabourTimeFIGURE3.21981Non—LabourTimeforImmigrantandNon—ImmigrantFamiliesGivenMarketWagesandArtificialConstraint0 0 OD‘II‘IIE0(00%%II0.__111111,11I—o--_______FBConstraint(I)IO——NBConstraintI-FBIndifferenceCurve—NBIndifferenceCurve0 0IIIII03300340035003600370038003900Wife’sNon—LabourTimeTable 3.3Results from Estimation of the Euler Equation for the Wife’s HoursVARIABLEIntercept -5.559(.800)A2534 (WIFE) -3.020(.979)A4554 (WIFE) 2.478(.418)Y7180 (WIFE) 1.804(.639)Y6170 (WIFE) 2.193(.690)YBEF61 (WIFE) 3.560(.665)KIDSO5 (1991) - KIDSO5 (1981) -.58 15(1.812)KO5PLUS (1991) - KO5PLUS (1981) 118.8(17.5)KIDS614 (1991) - KIDS614 (1981) 7.536(1.44)K614PLUS (1991) - K614PLUS (1981) -23.32(7.96)FB*[KTDSO5 (1991) - KIDSO5 (1981)] 18.54(3.58)FB*[KO5PLUS (1991) -KO5PLUS -105.4(1981)] (16.8)FB*[KIDS614 (1991) - KTDS614 -7.786(1981)] (1.56)FB*[K614PLUS (1991) - K614PLUS 24.00(1981)1 (8.38)R2 .0344F 20.26N 4616* Standard errors are in parentheses.183Table 3.4Results from Estimation of the Euler Equation for the Husband’s HoursVARIABLEIntercept -.1280(.082)A2534 (HUSBAND) - .0273(.118)A4554 (HUSBAND) . 1693(.043)Y7180 (HUSBAND) -.1177(.073)Y6170 (HUSBAND) -.0691(.063)YBEF61 (HUSBAND) -.0671(.060)KIDSO5 (1991) - KIDO5 (1981) .6905(.373)KO5PLUS (1991) - KO5PLUS (1981) 1.268(1.04)KIDS614 (1991) - KIDS6I4 (1981) .1095(.202)K614PLUS (1991) - K6I4PLUS (1981) -1.312(1.03)FB*[KIDSO5 (1991) - KIDSO5 (1981)1 .9457(.42 1)FB*[KO5PLUS (1991) -KO5PLUS -2.387(1981)] (1.18)FB*[KIDS6I4 (1991) - KIDS614 -.1760(1981)1 (.159)FB*[K614PLUS (1991) - K614PLUS .7478(1981)] (1.12)R2 .0236F 13.76N 4616* Standard errors are in parentheses.184FIGURE3.3HoursofImmigrantandNon—ImmigrantWivesOverTime(I) 0 :3 0ui_J C 0 z 0) 0) U)ci)11111111111111111IINBConstraintNBIndifferenceCurve——FBIndifferenceCurveGivenNon—ImmigrantWagesandArtificialConstraint0 0 0 0 0 0 0 0 0 Co N) 0 0___3700I I ‘I‘4380039004000410042004300Wife’s1981Non—LabourHoursFIGURE3.4HoursofImmigrantandNon—ImmigrantWivesOverTimeGivenNon—ImmigrantWagesandArtificial0 0 0 0 0 0 0 0 0 0) r)IIIIIIIIConstraint(I) L. :3 0 :3 0coO 0 z0 0 aD— 0)0“-‘0 N)0-0(°0 0 LI)—IIIII-NBConstraintINBIndifferenceCurve——FBIndifferenceCurve355036003650370037503800385039003950Wife’s1981Non—LabourHours(I) :5 0 I :3 0 C 0 z 0) 0) (I) 0FIGURE3.5HoursofImmigrantandNon—ImmigrantWivesOverGivenMarketWagesandArtificialConstraintsTimeIIIII0 0 0 0 0) V) 0 0 0 0 LI) 0 0z111111111111111NBConstraint•—FBConstraintNBIndifferenceCurve——FBIndifferenceCurveIIIIII360036503700375038003850390039504000Wife’s1981Non—LabourHoursC 0co-I--’ E 15 C/) C 0 C)0 0 co 0 0 0 0 0 0 0 (0 0 0 CN 0FIGURE4.1TheCaseofaNon—workerintheFixedCostofWorkModelStatic02004006008001000120014001600Wife’sNon—LabourTime,-0D-i-’ E :5 (I) C 0 00 0 0 0 0 0 0 0 0 (D 0 0 (N 0FIGURE4.2TheCaseofaWorkerintheStaticFixedCostofWorkModel02004006008001000120014001600Wife’sNon—LabourTimeTable 4.1Sample MeaiisWife’s FB 1981, FB 1991, NB 1981, NB 1991,Variables N=3593 N=8730 N=3808 N=9815PART .6601 .7331 .5885 .7330WAGE* 8.07 10.29 9.37 10.92AHOURS* 1537 1692 1434 1582AGE 38.15 47.04 36.77 44.74EDO8 .2423 .2137 .1253 .1110ED913NG .1866 .1658 .2661 .1960EDHSGRAD .1267 .1631 .1895 .1372EDPS .3406 .3301 .3364 .3933EDBACH .0823 .0979 .0734 .1185EDGRAD .0215 .0293 .0093 .0440KIDSO5 - .2206 .0645 .1911 .0731K1PLUS .0998 .0100 .1016 .0184KIDS614 .7074 .4723 .6265 .4988K2PLUS .0598 .0290 .0466 .0338BIRTHS 2.217 2.404 2.218 2.293BIRTH9 .0016 .1144 .0050 .123-7ENGOFF .7983 .8298 .6102 .6208FREOFF .0358 .0334 .2009 .1967BILOFF .1014 .0961 .1884 .1820OTHOFF .0646 .0405 .0005 .0005* The mean is calculated over the sample of women who worked. For Immigrantfamilies the sample size is 2372 in 1981 and 6400 in 1991. For non-immigrantfamilies the sample size is 2244 in 1981 and 7194 in 1991.190Table 4.1 cont.Husband’s FB 1981, PB 1991, NB 1981, NB 1991,Variables N=3593 N=8730 N=3808 N=9815WAGE 11.45 13.61 12.09 13.54AHOURS 2057 2061 2065 2055AGE 41.18 50.10 38.90 46.90EDO8 .1978 .1864 .1322 .1110ED913NG .1247 .1322 .1988 .1960EDHSGRAD .0573 .0885 .1238 .1372EDPS .4445 .4026 .3994 .3933EDBACH .1090 .1200 .1099 .1185EDGRAD .0667 .0739 .0359 .0440ENGOFF .8188 .8367 .6065 .5213FREOFF .0289 .0271 .1475 .1967BILOFF .1195 .1123 .2460 .2820OTHOFF .0328 .0239 .0003 .0005ATh .0080 .0101 .1077 .1037QUENM .0077 .0082 .1896 .1889MONT .1258 .1126 .1278 .1148TOR .3796 .3908 .0773 .0830ONTNT .2189 .2143 .2408 .2410PRA.IR .1199 .1165 .1613 .1636BCNV .0920 .0436 .0592 .06 16VANC .0481 .1037 .0363 .0434191Table 4.2Results from Probit Estimationon Wife’s ParticipationVARIABLEYR91 .0450NB -.0354(.057)NB*YR91.0017(.052)Y6170 (WIFE) .0521(.028)YBEF61 (WIFE) .0458(.033)Y6170*YR91-.0313(WIFE) (.033)YBEF6 1 *YR9 1 -.0248(WIFE) (.039)Y6170 (HUSBAND) -.1217(.028)YBEF61 -.1784(HUSBAND) (.033)Y6170*YR91.0512(HUSBAND) (.034)YBEF61*YR91.0858(HUSBAND) (.040)A3034*YR81-.0258(WIFE) (.027)j\3539*-.0697(WIFE) (.033)A4044*YR81-.0741(WIFE) (.040)A4549*YR81-.1849(WIFE) (.045)VARIABLEFREOFF (WIFE) -.0284(.024)BILOFF (WIFE) -.0501(.018)OTHOFF (WIFE) .1061(.235)FB*FREOFF.0072(WIFE) (.041)FB*BILOFF (WIFE) -.0041(.027)FB*OTHOFF-.2119(WIFE) (.236)FREOFF -.0066(HUSBAND) (.024)BILOFF -.0131(HUSBAND) (.018)OTHOFF .1833(HUSBAND) (.3 18)FB*FREOFF.0210(HUSBAND) (.044)FB*BILOFF-.0061(HUSBAND) (.026)FB*OTHOFF.2184(HUSBAND) (.3 19)KIDSO5 -.2154(.015)K1PLUS -.4523(.022)KIDS614 -.0686(.007)192Table 4.2 cont.VARIABLEA5054*YR81-.3012(WIFE) (.052)A4044*YR9 1 -.0708(WIFE) (.016)A4549*YR91-.1060(WIFE) (.021)A5054*YR9I-.1583(WIFE) (.025)A5559*YR91-.2840(WIFE) (.029)A6064*YR9 1 -.4674(WIFE) (.037)FB*A3034*YR8 1 .0097(WIFE) (.040)FB*A3539*YR81.0536(WIFE) (.048)FB*A4044*YR81.0190(WIFE) (.056)FB*A4549*YR8 1 .0499(WIFE) (.063)FB*A5054*YR81.0833(WIFE) (.072)FB*A4044*YR91.0382(WIFE) (.025)FB*A4549*YR9 1 .0495(WIFE) (.03 1)FB*A5054*YR91.0427(WIFE) (.036)FB*A5559*YR91.0508(WIFE) (.041)FB*A6064*YR91.1202(WIFE) (.051)VARIABLEK2PLUS - .2087(.023)FB*KIDSO5.0276(.021)FB*K1PLUS.0767(.034)FB*KIDS614.0245(.0 10)FB*K2PLUS.0708(.034)BIRTHS -.005 1(.003)BIRTH9 -.0219(.0 16)FB*BIRTHS-.0119(.005)*BIRTH9-.0210(.023)ATL -.0934(.019)QUENM -.1054(.025)MONT -.0983(.024)ONTNT -.0259(.017)PRAIR .0063(.018)VANC -.0541(.023)BCNV -.0653(.023)193Table 4.2 cont.VARIABLEA3034*YR81-.0758(HUSBAND) (.030)ft..3539*YR81-.0754(HUSBAND) (.035)A4044*YR81-.0721(HUSBAND) (.041)A4549*YR81-.0662(HUSBAND) (.045)A5054*YR81-.06 14(HUSBAND) (.050)A4044*YR91 .0043(HUSBAND) (.0 17)A4549*YR91-.0427(HUSBAND) (.020)A5054*YR91-.0638(HUSBAND) (.024)M559*Y1-.0939(HUSBAND) (.027)A6064*YR91-.0871(HUSBAND) (.033)FB*A3034*YR8 1 .05 15(HUSBAND) (.05 1)FB*A3539*YR81.0348(HUSBAND) (.057)FB*A4044*YR8 1 .0486(HUSBAND) (.063)F*A4549*YR81.0532(HUSBAND) (.068)FB*A5054*YR81.0530(HUSBAND) (.074)*A4J44*YR91-.0216(HUSBAND) (.03 1)VARIABLEFB*ATL-.0554(.047)FB*QUENM.0260(.055)FB*MONT.0 124(.031)FB*ONTNT-.0419(.021)FB*PRAIR M204(.024)FB*VANC.0188(.028)FB*BCNV.0215(.029)PRIM -.1695(.024)MANUF -.076 1(.017)CONSTR -.0244(.022)TRANSP -.0910(.019)TRADE -.0322(.018)FINANCE -.04 15(.023)PUBLIC -.0468(.018)OTHIND -.0307(.020)FB*AGRIC.1154(.06 1)194VARIABLETable 4.2 cont.FB*A4549*YR91-.0341(HUSBAND) (.035)FB*A5054*YR91-.0146(HUSBAND) (.039)FB*A5559*YR91-.0077(HUSBAND) (.043)FB*A6064*YR91-X472(HUSBAND) (.049)EDO8 (WIFE) -.1801(.016)ED913NG -.0734(WIFE) (.012)EDPS (WIFE) .1233(.011)EDBACH (WIFE) .2 177(.0 19)EDGRAD .3090(WIFE) (.044)FB*EDO8 (WIFE) .0721(.023)FB*ED913NG .0259(WIFE) (.020)FB*EDPS (WIFE) -.0487(.018)3*EDBACH-.0269(WIFE) (.029)FB*EDGRAD-.0236(WIFE) (.057)EDO8 (HUSBAND) -.0053(.017)ED913NG .0145(HUSBAND) (.0 15)VARIABLEFB*PRIM-.0699(.042)FB*MANUF.0 145(.024)FB*CONSTR-.07 17(.03 1)FB*TRANSP.0282(.027)FB*TRADE-.0103(.025)FB*FINANCE-.0007(.034)FB*PUBLIC.0015(.029)FB*OTHIND.0029(.028)AGRIC .0211(.038)OSCI .0367(.166)OTEACH .0539(.025)OCLER .0630(.020)OSSERV .0082(.0 14)OPRPROC -.0071(.014)OCONSTR - .0507(.0 18)OTROTH -.0222(.015)195Table 4.2 cont.VARIABLEEDPS (HUSBAND) -.0394(.013)EDBACH -.1127(HUSBAND) (.019)EDGRAD -.1628(HUSBAND) (.026)FB*EDO8 .0291(HUSBAND) (.027)FB*ED913NG .0172(HUSBAND) (.026)FB*EDPS .0368(HUSBAND) (.022)3*EDBACH .0633(HUSBAND) (.029)FB*EDGRAD -.0004(HUSBAND) (.037)R2 .2309LR 4605N 25946* Standard errors are in parentheses.VARIABLEFB*OSCI -.0229(.024)FB*OTEACH -.0277(.037)FB*OCLER .0190(.030)FB*OSSERV .0262(.022)FB*OPRPROC M053(.020)FB*OCONSTR .0 175(.027)FB*OTROTH .0161(.024)196Table 4.3Results from Estimation of the FamilyMarginal Rate of SubstitutionVARIABLE VARIABLEIntercept 8.058(.072)LNTHRS .0092(.009)WDIFF .0446(.009)KIDSO5 .0537(.009)KO5PLUS .078 1(.017)KIDS614 .026 1(.003)K614PLUS .0778(.013)FB*KJDSO5-.0248(.011)FB*KO5PLUS-.0404(.021)FB*KIDS614-.0079(.004)FB*K614PLUS- .0234(.018)NB .0123(.0 10)YR91 -.0486(.014)NB*YR91 .0220(.0 11)A4549*YR91 .0143(WIFE) (.007)Y6170 (WIFE) -.0013(.015)YBEF61 (WIFE) .0157(.019)Y6170*YR9I-.0004(WIFE) (.018)YBEF61*YR91-.0022(WIFE) (.022)Y6170 -.0221(HUSBAND) (.015)YBEF61 -.0067(HUSBAND) (.019)Y6I70*YR9I .0288(HUSBAND) (.018)YBEF61*YR91 .0207(HUSBAND) (.022)A3034*YR81-.0077(WIFE) (.011)A3539*YR81-.0026(WIFE) (.014)A4044*YR81 -.0022(WIFE) (.016)A4549*YR81-.0060(WIFE) (.018)A5054*YR81-.0106(WIFE) (.022)A4044*YR91 .0096(WIFE) (.006)A4549*YR8I .0082(HUSBAND) (.018)197Table 4.3 cont.VARIABLEA5054*YR91.0 177(WIFE) (.009)A5559*YR91 .0360(WIFE) (.012)A6064*YR91 .0056(WIFE) (.017)A3034*YR81 .0006(HUSBAND) (.013)A3539*YR81 .0009(HUSBAND) (.015)A4044*YR81 .0013(HUSBAND) (.0 17)IMR .0772(.011)R2 .042F 18.9N 18210* Standard errors are in parentheses.VARIABLEA5054*YR8 1 .0006(HUSBAND) (.020)A4044*YR91-.0058(HUSBAND) (.007)A4549*YR9I-.0086(HUSBAND) (.008)A5054*YR91.0012(HUSBAND) (.009)A5559*YR91-.0029(HUSBAND) (.0 10)A6064*YR91-.0114(HUSBAND) (.013)1980 0 OD 0 0 N 0 0 Co r-o 0 0 LI)0 0 0 0 N)0 o CN V) 0 03300FIGURE4.31981Non—LabourTimeforImmigrantandNon—ImmigrantFamiliesGivenNon—ImmigrantWagesandArtificialConstraintci) E :5 0D0ø—J C 0 z (I)-D 0 0 C’)340035003600370038003900Wife’sNon—LabourTimeFIGURE4.41961Non—LabourTimeforImmigrantandNon—ImmigrantFamiliesGivenMarketWagesandArtificialConstraint0 0 aDIIIIII0)(D ri-)0I—I———I—I—lii11111111111111,,,,0 C)CNFBConstraintCl)I’O——NBConstraint-•IFBIndifferenceCurve—INBIndifferenceCurve0 0IIII03.300.340035003600370038003900Wife’sNon—LabourTimeTable 4.4Results from Estimation of the Euler Equation for the Wife’s HoursVARIABLEIntercept -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 (1991) - KO5PLUS 237.4(1981) (28.6)KIDS614 (1991) - KIDS614 21.60(1981) (2.63)K614PLUS (1991) - -26.86K6I4PLUS (1981) (7.72)FB*[KIDSO5 (1991) - KIDSO5 121.1(1981)] (15.9)FB*[KO5PLUS (1991) - -226.0KO5PLUS (1981)] (28.6)FB*[KIDS614 (1991) - -22.42KIDS614 (1981)] (2.73)FB*[K614PLUS (1991) - 36.34K614PLUS (1981)] (10.2)R2 .0344F 20.26N 7401* Standard errors are in parentheses.201Table 4.5Results from Estimation of the Euler Equation for the Husband’s HoursVARIABLEIntercept -.1823(.094)A2534 (HUSBAND) .0486(.125)A4554 (HUSBAND) .1726(.048)Y7180 (HUSBAND) -.0708(.077)Y6170 (HUSBAND) -.0642(.067)YBEF61 (HUSBAND) -.1220(.064)KIDSO5 (1991) - KIDO5 (1981) -.9198(.438)KO5PLUS (1991) - KO5PLUS (1981) .8520(.897)KIDS614 (1991) - KIDS614 (1981) .0924(.251)K614PLUS (1991) - K614PLUS (1981) -1.245(1.11)FB*[KIDSO5 (1991) - KIDSO5 (1981)] 1.089(.480)FB*[KO5PLUS (1991) -KO5PLUS -1.531(198 1)1 (.933)f*[}(JDS614 (1991) - KIDS614 -.2824(1981)] (.198)FB*[K6I4PLUS (1991) - K614PLUS 1.045(1981)] (1.20)R2 .0176F 10.17N 7401* Standard errors are in parentheses.202FIGURE4.5HoursofImmigrantandNon—ImmigrantWivesOverTimeGivenNon—ImmigrantWagesandArtificialConstraint0 0 CNIIIIIIIDOl00N)Co—JI_*.)liii11111111111111IIIIii1111111111111IIIIIIllillillIiiIIII111111IIIIIIIIIIIIliii0C(00N)z—00)00)‘—0G)0-IndifferenceCurveN)IndifferenceCurve0 0IIIIII0408041204160420042404280432043604400Wife’s1981Non—LabourHoursC,):5 0 0-oMO C 0 z 0) C’) 00 0 0 0 0 0) 0 0 OD 0 0 N V) 0 0 (0FIGURE4.6HoursofImmigrantandNon—ImmigrantWivesOverTimeGivenNon—ImmigrantWagesandArtificialConstraint360036403680372037603800384038803920Wife’s1981Non—LabourHoursFIGURE4.7HoursofImmigrantandNon—ImmigrantWivesOverTimeGivenMarketWagesandArtificialIIIIIConstraints(I) D 0 :5 0L’JC uiJ C 0 cY) 0) (I)a a a a O) 0 a N a a LI) 0 a___N)rr3500111111111,1—aaII36003700——NBconstraint—FBconstraintNBIndifferenceCurve——FBIndifferenceCurve3800390040004100Wife’s1981Non—LabourHoursREFERENCESAbbott, M. and C. 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Includes professional degrees.11) ED - Graduated from High School and may have a university degree or other post-secondaryeducation.12) NB - Non-immigrant family.20913) Y90 - Immigrant who arrived in 1990.14) Y89 - Immigrant who arrived in 1989.15) Y88 - Immigrant who arrived in 1988.16) Y87 - Immigrant who arrived in 1987.17) Y86 - Immigrant who arrived in 1986.18) Y8185 - Immigrant who arrived 1981-85.19) Y80 - Immigrant who arrived in 1980.20) Y7180- Immigrant who arrived 1971-80.21) Y6170 - Immigrant who arrived 1961-70.22) YBEF61- Immigrant who arrived before 1961.23) KIDSO5- One child present under six years of age.24) KO5PLUS- More than one child present under six years of age.25) K10S614- Number of children present between six and fourteen years of age, up to amaximum of two.26) K614PLUS- More than two children present between the ages of six and fourteen.27) A3034 - Age thirty to thirty-four.28) A3539- Age thirty-five to thirty-nine.21029) A4044 - Age forty to forty-four.30) A4549 - Age forty-five to forty-nine.31) A5054 - Age fifty to fifty-four.32) A5559 - Age fifty-five to fifty-nine.33) A6064 - Age sixty to sixty-four in 1981.34) A2534 - Age twenty-five to thirty-four in 1981.35) A4554 - Age forty-five to fifty-four in 1981.36) YR91 - Household from the 1991 sample.37) Y1t81 - Household from the 1981 sample.38) ATTJ - Household resides in Newfoundland, New Brunswick, Nova Scotia, or PEI.39) QUENM - Household resides in Quebec outside of Montreal.40) MONT - Household resides in Montreal.41) ONTNT - Household resides in Ontario outside Toronto.42) PItAIR - Household resides in Manitoba, Saskatchewan, or Alberta.43) VANC - Household resides in Vancouver.44) BCNV - Household resides in British Columbia outside Vancouver.45) FREOFF - Individual’s official language is French.21146) BILOFF - Individual speaks both official languages.47) OTHOFF - Individual speaks neither official language.48) OSCI - managerial, science, medical, and related occupations.49) OTEACH- teaching and related occupations.50) OCIJER - clerical and related occupations.51) OSSERV - sales and services occupations.52) OPRPROC- primary, processing, machining, and related occupations.53) OCONSTR - construction trades and occupations54) OTROTH - transport equipment operating, related occupations, and other occupations.55) AGRIC - Agricultural industry.56) PRIM - other primary industry.57) MANUF- manufacturing.58) CONSTR- construction.59) TRANSP- transportation and storage.60) TRADE- wholesale trade and related industries.61) FINANCE- finance, insurance, and real estate.62) PUBLIC- public administration and defense.21263) OTHIND - other industries.213Appendix 2First Stage Estimates for Two StageLeast Squares Estimation of MRS FunctionDIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorati -0.0193 0.0403 0.0297 0.0112quenm -0.1116 0.0527 0.0066 0.0146mont -0.0841 0.0504 0.0103 0.0139ontnt -0.0186 0.0340 -0.0038 0.0094prair -0.0755 0.0358 -0.0218 0.0099vane -0.0866 0,0488 -0.0047 0.0135bcnv -0.0090 0.0466 0.0048 0.0129wa3034*yr8l-0.0110 0.0616 -0.0064 0.0170wa3539*yr8l-0.1469 0.0794 -0.0325 0.0220wa4044*yr8l-0.0146 0.0936 -0.0381 0.0259wa4549*yr8l-0.0844 0.1077 -0.0195 0.0298wa5054*yr8l-0.0372 0.1284 -0.0447 0.0356a3034*yr8l 0.0506 0.0648 -0.0168 0.0179a3539*yr8l 0.1274 0.0784 -0.0255 0.0217a4044*yr8l 0,1501 0.0924 0.0107 0.0256a4549*yr8l 0.0870 0.1034 0.0128 0.0286a5054*yr8l 0.0832 0.1164 0.0076 0.0322wa4044*yr9l-0.0013 0.0301 -0.0106 0.0083wa4549*yr9l 0,0109 0.0391 -0.0045 0.0108214Appendix 2 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorwa5054*yr9l-0.0186 0.0503 -0.0179 0.0139wa5559*yr9l-0.0214 0.0655 -0.0006 0.0181wa6064*yr9l 0.0134 0.1011 -0.0117 0.0280a4044*yr9l 0.0084 0.0319 -0.0038 0.0088a4549*yr9l 0.0175 0.0386 -0.0057 0.0107a5054*yr9l-0.0405 0.0463 0.0170 0.0128a5559*91-0.0530 0.0569 0.0140 0.0157a6064*yr9l-0.0795 0.0757 0.0560 0.0210births 0.0213 0.0080 -0.0033 0.0022birth9 -0.0345 0.0308 -0.0091 0.0085edO8 -0.1139 0.0399 0.0099 0.0110ed9l3ng -0.0516 0.0317 0.0061 0.0088edps 0.0103 0.0276 -0.0023 0.0076edbach 0.1394 0.0390 -0.0194 0.0108edgrad 0.2655 0.0528 -0.0342 0.0146wed08 0.1076 0.0447 0.0110 0.0124wed9l3ng 0.0812 0.0288 -0.0014 0.0080wedps -0.0934 0.0249 -0.0153 0.0069wedbach -0.2778 0.0399 -0.0127 0.0111wedgrad -0.4360 0,0687 -0.0064 0.0190kids05 -0.1328 0.0325 -0.0042 0.0090215Appendix 2 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorkiplus -0.2130 0.0603 -0.0170 0.0167k2plus 0.0852 0.0533 -0.0132 0.0148kids6l4 -0.0123 0.0143 -0.0043 0.0040freoff 0.0341 0.0525 0.0148 0.0145biloff 0.0127 0.0360 0.0021 0.0100othoff 0.6363 1.1801 -0.0579 0.3267wfreoff 0.0235 0.0518 0.0263 0.0144wbiloff 0.0265 0.0359 0.0135 0.0099wothoff -1.0124 0.8351 0.0536 0.2312osci -0.0432 0.0334 0.0513 0.0092oteach 0.1776 0.0485 0.0933 0.0134ocler -0.2319 0.0399 0.0673 0.0110osserv -0.1815 0.0293 0.0289 0.0081oprproc -0.1281 0.0308 0.0620 0.0085oconstr -0.0902 0.0403 0.0709 0.0112otroth -0.1730 0.0343 0.0436 0.0095agric -0.6176 0,0814 -0.2817 0.0225prim 0.3528 0.0545 0.0112 0.0151manuf 0.2171 0.0367 -0.0049 0.0102constr 0.1196 0.0479 0.0332 0.0133transp 0,2829 0.0398 -0.0218 0.0110216Appendix 2 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errortrade -0.0221 0.0373 -0.0374 0.0103finance 0.1594 0.0480 -0.0057 0.0133public 0.2484 0.0373 0.0250 0.0103othind -0.0244 0.0420 0.0140 0.01 16wosci -0.0524 0.0371 0.0035 0.0103woteach -0.0376 0.0441 0.0115 0.0122wocler 0.1667 0.0305 0.0026 0.0085wosserv 0.3261 0.0346 0.0076 0.0096woprproc 0.2067 0.0532 0.0032 0.0147wotroth 0.1934 0.0614 -0.0287 0.0170wagric 0.1634 0.0926 -0.1514 0.0257wprman -0.0624 0.0387 0.0046 0.0107wconstr -0.3124 0.0683 -0.1169 0.0189wtransp -0.1184 0.0444 -0.0171 0.0123wtrade 0.1263 0.0315 -0.0240 0.0087wfinance 0.0189 0.0382 -0.0070 0.0106wpublic -0.0709 0.0378 0.0146 0.0105wothind 0.0692 0.0300 0.0068 0.0083yr9l 0.0012 0.085 1 -0.0052 0.0236nb 0.0247 0.1193 0.0893 0.0330nyr9l 0.0351 0.1000 -0.0168 0.0277217Appendix 2 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errory6l7O 0.0661 0.0609-0.0320 0.0169ybef6l -0.0443 0.0740 -0.0227 0.0205wy6170 -0.0778 0.0604 0.0097 0.0167wybef6l -0.0911 0.0748 -0.0052 0.0207y6170*yr9l 0.0176 0.0709 0.0263 0.0196ybef6l*yr9l 0.1094 0.0856 0.0126 0.0237wy6170*yr9l 0.0070 0.0703 -0.0126 0.0195wybef6l*yr9l-0.0758 0.0860 -0.0147 0.0238flJ*atl 0.9138 0.1065 -0.0804 0.0295fb*quenm-0.0872 0. 1207 0.0139 0.0334fl,*mont-0.0546 0.0658 0.0064 0.0182flJ*ontnt 0.0908 0.0422 -0.0062 0.01 17fij*prajr 0.0442 0.0465 -0.0068 0.01290,0148 0.0592 0.0165 0.0164fl,*bcnv-0.0046 0.0620 -0.0092 0.0172flJ*wa3034*yr81 0.0824 0.0900 -0.0099 0,0249flJ*wa3539*yrgl 0.2203 0.1108 0.0241 0.0307fl*wa4O44*yr81 0.1309 0.1281 0.0390 0.0355flJ*wa4549*yr8l 0,1902 0.1462 0.0030 0.0405fIJ*wa5O54*yi.81 0.0752 0.1730 0.0146 0.0479fb*a3034*yr8l-0.0584 0.1061 0.0245 0.0294218Appendix 2 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*a3539*yr8l-0.1455 0.1210 0.0241 0.0335fIJ*a4044*yrgl-0.1478 0.1362 -0.0123 0.0377fb*a4549*yr8l-0.0432 0.1488 0.0012 0.0412fb*a5054*yr8l 0.0328 0.1655 0.0151 0.0458fb*wa4044*yr9l-0.0077 0.0465 -0.0026 0.0129fb*wa4549*yr9l-0.0780 0.0581 -0.0132 0.0161flj*wa5054*yij.91 0.0094 0.0710 0.0026 0.0197fb*wa5559*yr9l 0.0312 0.0894 0.0032 0.0247flJ*wa6064*yr91-0.0057 0.1318 0.0168 0.0365fb*a4044*yr9l 0.0770 0.0563 0.0049 0.0156fl,*a4549*yj91 0.0436 0.0640 0.0054 0.0177fb*a5054*yij.91 0.1196 0.0724 -0.0063 0.0201fb*a5559*yr9l 0.0522 0.0840 0.0056 0.0233fb*a6064*yr9l 0.0914 0.1045 -0.0088 0.0289fl,*bjfths 0.0099 0.0120 -0.0026 0.0033fl*bih9 0.0595 0.0463 0.0169 0.0128fjJ*edO8 0.1100 0.0611 0.0308 0.0169fb*ed913 0.0490 0.0540 0.0118 0.0150fIJ*edps 0.0826 0.0454 0.0125 0.0126fl,*edbach-0.0018 0.0596 0.0249 0.0165fb*edgrad 0.0458 0.0761 0.0091 0.0211219Appendix 2 cont,DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*wed08-0.0999 0.0599 -0.0236 0.0166f13*wed913-0.1089 0.0453 -0.0175 0.0126ffi*wedps-0.0230 0.0380 -0.0017 0.0105fIJ*wedbach 0.0029 0.0572 0.0028 0.0158fb*wedgrad 0.0561 0.0929 -0.0233 0.0257fl*kidsO5 0.0481 0,0468 0.0125 0.0130flJ*klplus 0.1957 0.0877 0.0127 0.0243fb*k2plus-0.0558 0.0763 0.0184 0.0211fl,*kjds614 0.0083 0.0209 -0.0009 0.0058fIJ*freoff-0.0513 0.0986 -0.0317 0.0273f13*bioff 0.0068 0.0534 -0,0223 0.0148fb*othoff-0.6492 1.1826 0.0941 0.3274flj*wfreoff 0.1067 0.0941 0.0218 0.0260fb*wbjloff 0.1074 0.0535 0.0026 0.0148fb*wothoff 0.9452 0.8376 -0.0566 0.2319fb*oscj 0.0841 0.0476 0.0284 0.0132fb*oteach-0.0238 0.073 1 0.0264 0.0202fb*ocler-0.0013 0.0591 0.0308 0.0164fb*osserv-0.0302 0.0444 0.0024 0.0123fla*oprproc 0.0521 0.0441 0.0096 0.0122fb*oconstr 0.1692 0.0605 0.0356 0.0168220Appendix 2 cont,DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*otroth 0.0454 0.0518 0.0284 0.01430.4559 0.1367 0.1967 0.0378flJ*pñm 0.1659 0.1012 0.0449 0.0280flJ*manuf-0.0793 0.0494 0.0273 0.0137flJ*constr-0,0044 0.0685 0.0202 0.0190fIJ*transp-0.0966 0.0572 0.0514 0.0158flo*trarje-0.0257 0.0522 0.0187 0,0145fl*finance-0.1424 0.0680 0.0177 0.0188fb*public-0.0690 0.0591 0.0320 0.0164fb*othind 0.0041 0.0572 0.0056 0.0158f1*j 0.0621 0.0549 0.0358 0.0152flJ*woteach 0.0289 0.0687 0.0435 0.0190fIJ*wocler-0.0061 0.0458 0.0306 0.0127flJ*wossep,r-0.0432 0.0506 0.0223 0.0140flj*woprp-0.0300 0.0695 0.0440 0.0192fIJ*wotroth 0.0005 0.0826 0.0685 0.0229-0.2344 0.1432 -0.0074 0.0396flJ*wpan 0.0779 0.0531 0.0007 0.0147fjj*wconstr-0.0435 0.1006 0.0563 0.0278-0.0426 0.0709 0.0131 0.0196-0.0539 0.0457 0.0185 0.0126221Appendix 2 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorflj*wfinance-0.0224 0.0547 0.0410 0.0152fl,*wpublic-0.0630 0.0618 0.0361 0.0171fl,*wothjfld-0.0849 0.043 1 0.0175 0.0119intercept 0.1641 0.0928 7.9542 0.0257.0921 .0817F 9.494 10.83N 18 210 18 210* Variable names preceded by the letter w are the wife’s variables.222Appendix3ResultsfromEstimationofEquationsUsedtoGenerateWife’sEulerEquationData1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)Intercept-3.2620.069.0101.6985.0289(.097)(.009)(.004)(.023)(.006)A2534*HS*NB-.0142.0044.0024.0861.0136(.123)(.012)(.005)(.031)(.008)A2534*AHS*NB-.1151.0737.0187.1351.0326(.110)(.010)(.004)(.027)(.007)A3544*BHS*NB.0254-.0606-.0101-.6205-.0289(.145)(.012)(.005)(.033)(.009)A3544*HS*NB-.1075-.0648-.0101-.5826-.0289(.141)(.014)(.006)(.038)(.010)A3544*AHS*NB-.0844-.0581-.0084-.4953-.0238(.132)(.011)(.005)(.030)(.008)A4554*BHS*NB-.0367-.0691-.0101-.6940-.0289(.222)(.018)(.008)(.050)(.013)A4554*HS*NB-.1272-.0691-.0101-.6985-.0289(.306)(.026)(.011)(.070)(.018)A4554*AHS*NB-.3298-.0691-.0101-.6849-.0289(.223)(.018)(.008)(.050)(.013)Appendix3cont.“31991MUKIDSO5K1PLUSKJDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*BHS*Y7180.0532.0515-.0025.2186.0339(.150)(.015)(.006)(.040)(.010)A2534*HS*Y7180.0350.0376.0029.2153.0380(.191)(.017)(.007)(.046)(.012)A2534*AHS*Y7180.0670.0306-.0080.1588.0029(.102)(.009)(.004)(.024)(.006)A3544*BHS*Y7180.0422-.0086.0000.2499.0122(.202)(.018)(.008)(.048)(.012)A3544*HS*Y7180.0475-.0043.0000.1029.0000(.261)(.024)(.010)(.065)(.017)A3544*AHS*Y7180.0341.0043-.0017.2020.0058(.167)(.013)(.006)(.036)(.009)A4554*BHS*Y7180-.0774.0000-.0000.0431-.0000(.432)(.041)(.017)(.110)(.028)A4554*HS*Y7180-.3143.0000-.0000-.0000-.0000(.580)(.057)(.024)(.154)(.028)A4554*AHS*Y7180.1154.0000.0000.0410.0000(.393)(.036)(.015)(.099)(.025)A2534*BHS*Y6170-.1285-.0288-.0064-.0648.0041(.206)(.017)(.007)(.046)(.012)A2534*HS*Y6170-.2260.0390.0063.0340-.0300(.187)(.021)(.009)(.056)(.015)Appendix3cont.1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*AHS*Y6170-.0543-.0088-.0020.0116-.0169(.141)(.014)(.006)(.038)(.010)A3544*BHS*Y6170.0604-.0009-.0000.0794-.0000(.187)(.015)(.006)(.041)(.010)A3544*HS*Y6170.0900.0073.0000.1225.0058(.213)(.022)(.009)(.058)(.015)A3544*AHS*Y6170-.1873-.0026-.0003.1166.0033(.144)(.011)(.005)(.031)(.008)A4554*BHS*Y6170.4853.0000-.0000.0057-.0000(.296)(.029)(.012)(.079)(.020)A4554*HS*Y6170.1220.0000-.0000-.0000-.0000(.540)(.047)(.020)(.126)(.032)A4554*AHS*Y6170.1010.0000.0000.0123.0000(.318)(.028)(.012)(.075)(.019)A2534*BHS*YBEF61.5603-.0464-.0101-.0508-.0175(.495)(.027)(.011)(.073)(.019)A2534*HS*YBEF61-.1708.0124.0032-.0347-.0591(.244)(.023)(.010)(.062)(.016)534*AHS*YBEf61-.2906.0051-.0157.0403-.0180(.182)(.017)(.007)(.045)(.016)A3544*BHS*YBEF61.1463-.0085.0000-.0011.0000(.216)(.017)(.007)(.047)(.012)t\J I’)UiAppendix3cont.1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A3544*HS*YBEF61.0580-.0043.0000.0037.0000(.368)(.028)(.012)(.075)(.019)A3544*AHS*YBEF61-.1991-.0110-.0017-.0416-.0051(.204)(.017)(.007)(.047)(.012)A4554*BHS*YBEF61.4670.0000-.0000-.0046-.0000(.315)(.024)(.010)(.065)(.017)A4554*HS*YBEF61-.0158.0000-.0000-.0000-.0000(.407)(.040)(.017)(.107)(.027)A4554*AHS*YBEF61-.4083.0000.0000.0006.0000(.291)(.026)(.011)(.071)(.018)R2.0026.0785.0220.2515.0320F1.36245.0211.89177.717.46N1395413954139541395413954M t\J*Standarderrorsareinparentheses.Appendix3cont.I\)KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)Intercept.2989.0931.7828.0779(.024)(.015)(.047)(.014)A2534*HS*NB.0742-.0023-.2363-.0481(.035)(.023)(.070)(.020)A2534*AHS*NB-.0387.0286-.3939-.0535(.028)(.018)(.056)(.016)A3544*BHS*NB-.2640-.0867-.0665-.0209(.032)(.021)(.064)(.018)A3544*HS*NB-.2211-.0774.0896-.0474(.040)(.026)(.080)(.023)A3544*AHS*NB-.1916-.0698.0226-.0058(.031)(.020)(.061)(.017)A4554*BHS*NB-.2896-.0931-.5009-.0725(.036)(.023)(.072)(.021)A4554*HS*NB-.2989-.0931-.5078-.0779(.057)(.037)(.114)(.032)A4554*AHS*NB-.2989-.0931-.3909-.0723(.036)(.024)(.073)(.021)A2534*BHS*Y7180.0458.1489-.1303.0030(.039)(.025)(.078)(.022)A2534*HS*Y7180.0133.1009-.0734.0119(.050)(.033)(.101)(.029)Appendix3cont.N)N)KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A2534*AHS*Y7180.1285.0284-.0068.0068(.026)(.017)(.052)(.015)A3544*BHS*Y7180.1863.0536.1578.1151(.042)(.027)(.085)(.024)A3544*HS*Y7180.2036-.0157.1328.0656(.072)(.047)(.145)(.041)A3544*AHS*Y7180.0771.0551.231.0107(.035)(.023)(.070)(.020)A4554*BHS*Y7180.0479.0000.3124.0280(.070)(.045)(.140)(.040)A4554*HS*Y7180.0000.0000.2304.0000(.156)(.101)(.313)(.089)A4554*AHS*Y7180.0000.0000.0333-.0056(.083)(.054)(.167)(.048)A2534*BHS*Y6170.1374-.0353.4022-.0105(.043)(.028)(.086)(.025)A2534*HS*Y6170.0231.0485.2037-.0298(.066)(.042)(.131)1(.038)A2534*AHS*Y6170.1705-.0535.3471-.0051(.039)(.025)(.078)(.022)A3544*BHS*Y6170.0889.0078.1247.0657(.033)(.021)(.066)(.019)Appendix3cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A3544*HS*Y6170.0337.0234.0046.0276(.060)(.039)(.121)(.034)A3544*AHS*Y6170.0922.0296.1334-.0282(.030)(.020)(.060)(.017)A4554*BHS*Y6170-.0093-.0000.0140.0124(.057)(.037)(.113)(.032)A4554*HS*Y6170.1177.0000.0305.0399(.091)(.059)(.182)(.052)A4554*AHS*Y6170.0515.0000-.0256-.0056(.049)(.032)(.098)(.028)A2534*BHS*YBEF61.0118-.0578.0762.1599(.072)(.047)(.144)(.041)A2534*HS*YBEF61-.0113.1411-.0552.1117(.082)(.053)(.164)(.047)A2534*AHS*YBEF61-.0326.0479.0083.0390(.048)(.031)(.096)(.027)A3544*BHS*YBEF61.0122-.0064.1126-.0405(.040)(.026)(.079)(.023)A3544*HS*YBEF61-.0447-.0157.0388.0351(.073)(.047)(.146)(.042)A3544*AHS*YBEF61-.0072-.0002.0011-.0376(.043)(.028)(.087)(.025)Appendix3cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A4554*BHS*YBEF61.0075-.0000-.0086.0018(.041)(.026)(.081)(.023)A4554*HS*YBEF61.0000.0000-.1076.0000(.089)(.058)(.179)(.051)A4554*AHS*YBEF61.0090.0000-.0910-.0056(.045)(.029)(.090)(.026)R2.1335.1042.1050.0346F52.7339.8140.1612.25N4616461646164616w C*Standarderrorsareinparentheses.Appendix4wResultsfromEstimationofReducedFormEquationsUsedtoGenerateMen’sEulerEquationData1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)Intercept-3.125.0863.0086.8144.0289(.031)(.009)(.004)(.025)(.006)A2534*HS*NB-.0532.0204.0171.0631.0147(.048)(.014)(.006)(.038)(.010)A2534*AHS*NB-.2941.0695.0243.0728.0407(.034)(.010)(.004)(.029)(.007)A3544*BHS*NB-.0540-.0745-.0075-.6052-.0241(.040)(.012)(.005)(.034)(.009)A3544*HS*NB-.2128-.0690-.0062-.5174-.0189(.046)(.015)(.006)(.041)(.010)A3544*AHS*NB-.3828-.0644-.0073-.4991-.0152(.035)(.011)(.005)(.030)(.008)A4554*BHS*NB.0154-.0797-.0086-.7747-.0266(.047)(.015)(.006)(.040)(.010)A4554*HS*NB-.0642-.0863-.0086-.7988-.0288(.075)(.023)(.010)(.063)(.016)A4554*AHS*NB-.2774-.0863-.0086-.7554-.024 1(.049)(.015)(.006)(.040)(.010)Appendix4cont.(\J1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*BHS*Y7180.2133.0508.0179.2210.0243(.075)(.018)(.008)(.050)(.013)A2534*HS*Y7180-.0355.0418-.0059.0928.0555(.092)(.026)(.011)(.072)(.018)A2534*AHS*Y7180.0182.0376-.0066.1929.0049(.030)(.010)(.004)(.026)(.007)A3544*BHS*Y7180.1023.0252.0035.3140.0138(.060)(.018)(.008)(.050)(.013)A3544*HS*Y7180.0945.0223-.0025.1386.0099(.078)(.027)(.011)(.073)(.019)A3544*AHS*Y7180.1523.0108.0000.2365.0140(.034)(.011)(.004)(.029)(.007)A4554*BHS*Y7180.3593-.0066.0000.1492-.0022(.104)(.028)(.012)(.076)(.019)A4554*HS*Y7180.1649.0000.0000.0558.0000(.129)(.050)(.021)(.137)(.035)A4554*AHS*Y7180.1353.0000.0000.0744-.0047(.065)(.023)(.010)(.062)(.016)A2534*BHS*Y6170-.0456.0240-.0086.1562.0153(.067)(.023)(.009)(.062)(.016)A2534*HS*Y6170.0758.0711-.0035-.0108.0676(.132)(.037)(.016)(.102)(.026)Appendix4cont.1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*AHS*Y6170-.0633.0073-.0075.0005-.0223(.040)(.015)(.006)(.042)(.011)A3544*BHS*Y6170.0582.0006-.0012.1490.0046(.061)(.016)(.007)(.043)(.011)A3544*HS*Y6170.1043-.0063-.0025.0546.0121(.070)(.028)(.012)(.076)(.019)A3544*AHS*Y6170-.0023.0077.0010.1244.0001(.028)(.010)(.004)(.028)(.007)A4554*BHS*Y6170.0687-.0009.0000.0400.0092(.082)(.021)(.009)(.058)(.015)A4554*HS*Y6170-.0628-.0000-.0000.1120-.0000(.110)(.041)(.017)(.112)(.029)A4554*AHS*Y6170-.0513.0103.0000.0541-.0047(.063)(.018)(.008)(.050)(.013)A2534*BHS*YBEF61-.2266.0618-.0086.1486.0823(.181)(.047)(.020)(.129)(.033)A2534*HS*YBEF61.0077.0223-.0257.2193-.0112(.166)(.044)(.019)(.122)(.031)&534*ft.J{S*YBEF61-.1078.0119-.0143.0507.0175(.038)(.020)(.008)(.054)(.014)A3544*BHS*YBEF61-.0814-.0028-.0012.0520-.0002(.054)(.018)(.008)(.050)(.013)r’JLJ (JJAppendix4cont.N)1991MUKIDSO5K1PLUSKJDS614K2PLUSExpression(1991)(1991)(1991)(1991)A3544*HS*YBEF61-.0235.0090-.0025.0714-.0099(.077)(.041)(.017)(.111)(.028)A3544*AHS*YBEF61.1913-.0063.0050.0223-.0042(.054)(.015)(.006)(.040)(.010)A4554*BHS*YBEF61-.0113-.0066.0000.0047-.0022(.056)(.017)(.007)(.046)(.012)A4554*HS*YBEF61-.0244.0000.0000.0177.0000(.111)(.038)(.016)(.103)(.026)A4554*AHS*YBEF61.0775.0027-.0000-.0075-.0047(.054)(.017)(.007)(.047)(.012)R2.0026.0730.0165.2177.0276F1.36230.536.51107.811.0N1395413954139541395413954*Standarderrorsareinparentheses.Appendix4cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)Intercept.2747.1065.6493.0563(.028)(.018)(.055)(.016)&534*HS*NB.0730-.0132-.2245-.0563(.046)(.029)(.090)(.026)A2534*AHS*NB-.0049.0192-.2808-.0407(.032)(.020)(.063)(.018)A3544*BHS*NB-.1699-.0923.1478.0261(.036)(.023)(.071)(.020)A3544*HS*NB-.1376-.0870.1935-.0281(.046)(.029)(.090)(.026)A3544*AHS*NB-.1044-.0570.2088.0166(.033)(.021)(.065)(.019)A4554*BHS*NB-.2400-.0992-.2259-.0381(.036)(.023)(.071)(.020)A4554*HS*NB-.2423-.1065-.3390-.0563(.056)(.036)(.110)(.031)A4554*AHS*NB-.2579-.1065-.2430-.0273(.036)(.023)(.071)(.020)A2534*BHS*Y7180.0816.1515-.1751.0248(.053)(.034)(.105)(.030)A2534*HS*Y7180.2239.0479-.1394.0375(.078)(.050)(.155)(.044)(\jC.)UiAppendix4cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A2534*AHS*Y7180.1228.0371-.0463-.0015(.027)(.017)(.054)(.015)A3544*BHS*Y7180.1732.1088.1615.0154(.047)(.030)(.093)(.027)A3544*HS*Y7180.1804-.0195.1041.1600(.087)(.056)(.172)(.049)A3544*AHS*Y7180.0941.0519.0900.0455(.030)(.019)(.059)(.017)A4554*BHS*Y7180.1089.0127.1317.1402(.058)(.038)(.116)(.033)A4554*HS*Y7180-.0324.1104.3595.0000(.133)(.085)(.263)(.075)A4554*AHS*Y7180.0196.0194.2792-.0290(.055)(.035)(.109)(.031)&534*BHS*Y617O.2534.0247.2012.0229(.065)(.042)(.130)(.037)P534*HS*Y6170.2788-.0933.4752.0000(.119)(.076)(.235)(.067)4534*pJS*Y6170.1097-.0085.1412-.0036(.043)(.028)(.085)(.024)A3544*BHS*Y6170.1036.0321.2463.0643(.040)(.026)(.079)(.022)(%j(jAppendix4cont.M wKIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A3544*HS*Y6170.0692-.0195.5317-.0283(.087)(.056)(.173)(.049)A3544*AHS*Y6170.0615.0166.0248-.0179(.027)(.018)(.054)(.015)A4554*BHS*Y6170.0263.0113.0451.0183(.043)(.027)(.085)(.024)A4554*HS*Y6170.0866.0000.0439.0000(.105)(.068)(.209)(.059)A4554*AHS*Y6170.0532.0065.1892.0028(.037)(.024)(.074)(.021)A2534*BHS*YBEF61-.0302.1403-.1389.1882(.187)(.120)(.370)(.105)A2534*HS*YBEF61.0963.0312-.0007.0000(.145)(.093)(.287)(.081)A2534*AHS*YBEF61.0285.0384.1567-.0157(.055)(.035)(.109)(.031)A3544*BHS*YBEF61.0144.0028.2746.0915(.051)(.033)(.102)(.029)A3544*HS*YBEF61.1417.0707-.2030-.0283(.117)(.075)(.232)(.066)A3544*AHS*YBEF61-.0109-.0238.1670-.0294(.038)(.025)(.076)(.022)Appendix4cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A4554*BHS*YBEF61.0144.0029.0468-.0077(.034)(.022)(.068)(.019)A4554*HS*YBEF61-.0324.0000-.0369.0517(.097)(.062)(.192)(.055)A4554*AHS*YBEF61.0104.0045.0349-.0162(.033)(.021)(.065)(.019)R2.1086.0573.1068.0401F15.98.015.65.5N4616461646164616*Standarderrorsareinparentheses.Appendix 5First Stage Estimates Corrected forParticipation Selection, for the Two StageLeast Squares Estimation of MRS FunctionDIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorati -0.01 17 0.0438 0.0266 0.0120quenm -0.1163 0.0561 0.0015 0.0154mont -0.0861 0.0535 0.0037 0.0147ontnt -0.0160 0.0345 -0.0042 0.0095prair -0.0559 0,0361 -0.0206 0.0099vanc -0.0748 0.0502 -0.0078 0.0138bcnv 0.0100 0.0483 0.0015 0.0133wa3034*yr8l-0.0230 0.0624 -0.0082 0.0172wa3539*yr8l-0.1722 0.0811 -0.0360 0.0223wa4044*yr8l-0.0466 0.0952 -0.0400 0.0262wa4549*yr8l-0.1321 0.1136 -0.0286 0.0312wa.5054*yr8l-0.1048 0.1419 -0.0628 0.0390a3034*yr8l 0.0475 0.0670 -0.0225 0.0184a3539*yr8l 0.1259 0.0805 -0.0328 0.0221a4044*yr8l 0.1517 0,0944 0.0039 0.0259a4549*yr8l 0.1020 0.1052 0.0067 0.0289a5054*yr8l 0.1047 0.1182 0.0046 0.0325wa4044*yr9l-0.0142 0.0325 -0.0137 0.0089wa4549*yr9l-0.0095 0,0428 -0.0081 0,0118239Appendix 5 cont,DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorwa5054*yr9l-0.0394 0.0570 -0.0255 0.0157wa5559*yr9l-0.0552 0.0854 -0.0174 0.0235wa6064*yr9l-0.0260 0.1427 -0.0405 0.0392a4044*yr9l 0.0098 0.0323 -0.0033 0.0089a4549*yr9l 0.0175 0.0398 -0.0077 0.0109a5054*yr9l-0.0422 0.0480 0.0134 0.0132a5559*yr9l-0.0504 0.0599 0.0089 0.0165a6064*yr9l-0.0990 0.0781 0.0545 0.0215births 0.0296 0.0081 -0.0043 0.0022birth9 -0.0383 0.03 14 -0.0112 0.0086edO8 -0.1277 0.0403 0.0092 0.0111ed9l3ng -0.0559 0.0322 0.0075 0.0089edps 0.0001 0.0289 -0.0059 0.0079edbach 0.1180 0.0438 -0,0256 0.0120edgrad 0.2352 0.0597 -0.0429 0,0164wed08 0.1291 0.0635 -0.0023 0.0175wed9l3ng 0.0980 0.0325 -0.0084 0.0089wedps -0.1469 0.0324 -0.0033 0.0089wedbach -0.4118 0,0498 0.0075 0,0137wedgrad -0.5741 0.0810 0.0170 0.0223240Appendix 5 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorkids05 -0.1618 0.0504 -0.0156 0.0139kiplus -0.2871 0.1104 -0.0436 0.0303k2plus 0.0670 0.0652 -0.0223 0.0179kids6l4 -0.0238 0.0185 -0.0072 0.0051freoff 0.0582 0.053 1 0.0155 0.0146biloff 0.0268 0.0365 0.0023 0.0100othoff 0.5669 1.1939 -0.1111 0.3283wfreoff 0.0092 0.0529 0.0260 0.0145wbiloff 0.0107 0,0371 0.0182 0.0102wothoff -0.8900 0.8450 0.0813 0.2323osci -0.0451 0.0341 0.0544 0.0094oteach 0. 1715 0.0497 0.0977 0.0137ocler -0.2196 0.0416 0.0710 0.0114osserv -0.1473 0.0295 0.0309 0.0081oprproc -0.1126 0.0311 0.0643 0.0085oconstr -0.0763 0.0418 0.0698 0.0115otroth -0.1458 0.0346 0.0423 0,0095agric -0.5580 0.0766 -0.3336 0.0211prim 0.3474 0.0633 -0.0008 0.0174manuf 0.2170 0.0388 -0.0109 0.0107241Appendix 5 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorconstr 0.0837 0.0474 0.0150 0.0130transp 0.2703 0.0428 -0.0309 0.0118trade 0.0113 0.0375 -0.0446 0.0103finance 0.1699 0.0484 -0.0090 0.0133public 0.2367 0.0380 0.0231 0.0105othind -0.0104 0.0421 0.0147 0.0116yr9l -0.0325 0.0864 -0.0036 0.0238nb 0.0026 0.1122 0.0523 0.0308nyr9l 0.0696 0.1009 -0.0175 0.0277y6l7O 0.0574 0.0658 -0.0375 0.0181ybef6l -0.0420 0.0821 -0.0318 0.0226wy6170 -0.0888 0.0620 0.0125 0.0170wybef6l -0.1208 0.0760 -0.0054 0.0209y6l7O*yr9l 0.0322 0.0727 0.0255 0.0200ybef6l*yr9l 0.1111 0.0885 0.0130 0.0243wy6170*yr9l 0.0045 0.0714 -0.0111 0.0196wybef6l*yr9l-0.0730 0.0871 -0.0143 0.0239fb*atl 0.3037 0.1081 -0.0859 0.0297fl,*quepm-0.0749 0.1220 0.0077 0.0335fb*mont-0.0576 0.0663 0.0087 0.0182242Appendix 5 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*ontnt 0.0920 0.0432 -0.0132 0.0119fb*prair 0.0399 0.0469 -0.0064 0.01290.0155 0.0597 0.0158 0.0164fb*bcnv-0.0029 0.0625 -0.0120 0.0172flJ*wa3O34*yi.81 0.0752 0.0910 -0.0097 0.0250fb*wa3539*yr8l 0.2221 0.1126 0.0275 0.0310fb*wa4044*yr8l 0.1355 0.1295 0.0401 0.0356flj*wa4549*yr8l 0.1971 0.1480 0.0078 0.0407fb*wa5054*yr8l 0.0853 0.1757 0.0260 0.0483fb*a3034*yrgl-0.0603 0.1080 0.0315 0.0297fb*a3539*yr8l-0.1473 0.1227 0.0285 0.0337fb*a4044*yr8l-0.1540 0.1382 -0.0081 0.0380fb*a4549*yr8l-0.0541 0.1510 0.0063 0.0415fl3*a5054*yr81 0.0249 0.1679 0.0147 0.0462flJ*wa4044*yr91-0.0155 0.0473 0.0026 0,0130fb*wa4549*yr9l-0.0953 0.0590 -0.0088 0.0162fIJ*wa5O54*yj91-0.0091 0.0719 0.0088 0.0198fb*wa5559*yr91 0.0202 0.0907 0.0109 0.0249flj*wa6O64*yj91-0.0321 0.1353 0.0269 0.0372fl,*a4044*yr91 0.0798 0.0570 0.0008 0.0157243Appendix 5 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*a4549*yr9l 0.0557 0.0648 0.0018 0.0178fIJ*a5054*yj.91 0.1413 0.0732 -0.0087 0.0201fb*a5559*yr91 0.0743 0.0849 0.0031 0.0234fl,*a6o64*yj91 0.1191 0.1060 -0.0183 0.0291fb*births-0.0162 0.0123 -0.0030 0.0034fb*birth9 0.0606 0.0470 0.0159 0.0129fl,*edO8 0.1401 0.0621 0.0339 0.0171fIJ*ed913 0.0634 0.0547 0.0145 0.0150fb*edps 0.0989 0.0464 0.0169 0.0128fIJ*edbach 0.0185 0.0611 0.0296 0.0168lb*edgrad 0.0643 0.0769 0.0103 0.0212flJ*wed08-0.1012 0.0633 -0.0159 0.0174fIJ*wed9l3-0.1163 0.0458 -0.0152 0.0126fIJ*wedps-0.0066 0.0386 -0.0056 0.0106fb*wedbach 0.0612 0.0540 -0.0031 0.0148fb*wedgrad 0.1064 0.0914 -0,0268 0.0251fb*kidsO5 0.0506 0.0476 0.0163 0.0131fb*klplus 0.2092 0.0906 0.0160 0.0249fb*k2plus-0.0587 0.0781 0.0242 0.0215fb*kids6l4 0.0118 0.0215 0.0010 0.0059244Appendix 5 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*freoff-0.0642 0.0998 -0.03 10 0.0274fb*biloff-0.0049 0.0540 -0.0242 0.0148fb*othoff-0.5604 1.1966 0.1536 0.3290fb*wfreoff 0.1142 0.0950 0.0251 0.0261fb*wbiloff 0.1123 0.0540 -0.0004 0.0149fl*wothoff 0.8 158 0.8480 -0.0897 0.2332fl*cj 0.0827 0.0480 0.0323 0.0132fIJ*oteach-0.022 1 0.0734 0.0337 0.0202fb*ocler 0.0021 0.0595 0.0410 0.0164fl,*ossep,r-0.0141 0.0447 0.0084 0.0123flJ*oprproc 0.0619 0.0441 0.0168 0.0121flJ*oconstr 0.1849 0.0610 0.0455 0.0168fl,*otroth 0.0461 0.0520 0.0374 0.01430.3286 0.1214 0.1620 0.0334fb*prim 0.1615 0.1031 0,0429 0.0284flJ*manuf-0.0799 0.0493 0,0309 0.0136flJ*constr-0.0290 0.0689 0.0247 0,0189fb*transp-0.1029 0.0574 0.0567 0.0158flJ*trje-0.0379 0.0518 0.0203 0.0142flj*finance-0.1676 0.0677 0.0262 0.0186245Appendix 5 cont.DIFF LNTHRSVariable* Coefficient Standard Coefficient StandardError Errorfb*publjc-0.0863 0.0591 0.0401 0.0163fb*othjnd-0.0239 0.0567 0.0121 0.0156imr 0.0702 0.1364 0.0414 0.0375intercept 0.3308 0.0881 7.9859 0.0242R2 .0686 .0710F 9.377 9.718N 18 210 18 210* Variable names preceded by the letter w are the wife’s variables.246Appendix6ResultsfromEstimationofEquationsUsedtoGenerateWife’sEulerEquationData1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)Intercept-3.8950.0804.01330.7289.0923(.119)(.005)(.003)(.014)(.008)A2534*HS*NB-.0510.0193.0043.0860-.0644(.169)(.007)(.004)(.019)(.012)A2534*AHS*NB-.2306.0782.0344.1139-.0656(.144)(.006)(.003)(.016)(.010)A3544*BHS*NB.0498-.0746-.0133-.6305-.0274(.167)(.008)(.004)(.020)(.011)A3544*HS*NB-.2113-.0772-.0133-.6035-.0439(.182)(.009)(.004)(.024)(.014)A3544*AHS*NB-.2221-.0699-.0119-.5194-.0023(.183)(.007)(.004)(.019)(.011)A4554*BHS*NB-.0011-.0787-.0133-.7186-.0834(.183)(.009)(.005)(.024)(.011)A4554*HS*NB-.3186-.0804-.0133-.7289-.0923(.298)(.014)(.007)(.037)(.019)A4554*AHS*NB-.5607-.0778-.0133-.7157-.0850(.241)(.011)(.005)(.028)(.013)tJ—1Appendix6cont.1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*BHS*Y7180.0014.0908.0013.2402-.0370(.190)(.010)(.005)(.025)(.014)A2534*HS*Y7180-.0081.0366.0158.1549.0219(.272)(.011)(.006)(.030)(.019)A2534*AHS*Y7180.1179.0302-.0205.1556.0014(.161)(.006)(.003)(.016)(.011)A3544*BHS*Y7180.0137.0001.0029.2262.0922(.244)(.011)(.006)(.029)(.017)A3544*HS*Y7180-.0176-.0032-.0000.0783.0764(.372)(.016)(.008)(.042)(.029)A3544*AHS*Y7180.0530.0047.0005.2055.0018(.267)(.009)(.005)(.025)(.014)A4554*BHS*Y7180-.0270.0017-.0000.0388.0323(.335)(.020)(.010)(.051)(.026)A4554*HS*Y7180-.4474-.0000-.0000-.0000.0000(.604)(.034)(.016)(.088)(.053)A4554*AHS*Y7180-.0852-.0026.0000.0285.0303(.526)(.024)(.012)(.061)(.035)534*BHS*Y617O.1467-.0111-.0083-.0977-.0153(.252)(.012)(.005)(.027)(.015)&,2534*HS*y617O-.4251.0378.0036.0053.0107(.276)(.014)(.007)(.037)(.026)(‘JAppendix6cont.1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*AHS*Y6170-.0798-.0128-.0068-.0039.0034(.221)(.010)(.005)(.026)(.015)A3544*BHS*Y6170.1131-.0010.0000.0654.0755(.212)(.009)(.004)(.024)(.012)A3544*HS*Y6170.0588.0054-.0000.1117.0047(.278)(.014)(.007)(.037)(.023)A3544*AHS*Y6170-.2632-.0011-.0002.1014-.0292(.227)(.008)(.004)(.021)(.012)A4554*BHS*Y6170.3136-.0017-.0000.0022.0000(.217)(.014)(.007)(.037)(.019)A4554*HS*Y6170.2944-.0000-.0000-.0000.0260(.532)(.026)(.013)(.068)(.033)A4554*AHS*Y6170.1062-.0026.0000.0045.0023(.375)(.017)(.008)(.044)(.020)A2534*BHS*YBEF61.7167-.0201-.0047-.0651.1412(.700)(.018)(.009)(.047)(.025)&.534*HS*yBEF61-.3167.0058.0041-.0095.0626(.372)(.016)(.008)(.041)(.027)p.,534*,}IS*yBEF61-.4403.0125-.0215.0187.0217(.291)(.012)(.006)(.031)(.020)A3544*BHS*YBEF61.0625-.0058.0000-.023 1-.0287(.237)(.010)(.005)(.026)(.015)I’JAppendix6cont.1991MUKIDSO5K1PLUSKJDS614K2PLUSExpression(1991)(1991)(1991)(1991)A3544*HS*YBEF61.1487-.0032-.0000.0185.0943(.454)(.017)(.008)(.045)(.027)A3544*AHS*YBEF61-.3705-.0106-.0014-.0614-.0256(.310)(.012)(.006)(.031)(.017)A4554*BHS*YBEF61.3121.0004-.0000-.0040-.0020(.223)(.011)(.006)(.029)(.013)A4554*HS*YBEF61-.0467-.0000-.0000-.0000-.0000(.380)(.022)(.010)(.056)(.030)A4554*AHS*YBEF61.4086-.0026.0000-.0046-.0014(.310)(.015)(.007)(.040)(.018)R2 F N1395413954139541395413954N)()1 C*Standarderrorsareinparentheses.Appendix6cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)Intercept.3468.1780.8204.0931(.013)(.010)(.026)(.015)&534*HS*NB.0527.0346-.1880-.0023(.020)(.015)(.039)(.023)A2534*AHS*NB-.0533.0217-.3913.0286(.017)(.013)(.033)(.018)A3544*BHS*NB-.2592-.1616-.0104-.0867(.018)(.014)(.036)(.021)A3544*HS*NB-.2260-.1350.0670-.0774(.024)(.018)(.046)(.026)A3544*AHS*NB-.2106-.1237.0622-.0698(.019)(.014)(.037)(.020)A4554*BHS*NB-.3374-.1780-.5095-.0931(.019)(.015)(.038)(.023)A4554*HS*NB-.3368-.1780-.4836-.0931(.033)(.025)(.064)(.037)A4554*AHS*NB-.3444-.1780-.4244-.0931(.023)(.017)(.045)(.024)A2534*BHS*Y7180.05384.1464-.1307.1489(.023)(.018)(.045)(.025)A2534*HS*Y7180-.0109.0500-.1719.1009(.033)(.025)(.065)(.033)r\.) LiiAppendix6cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A&534*AHS*Y718O.0988.0346-.0423.0284(.018)(.014)(.035)(.017)A3544*BHS*Y7180.1184.0645.0685.0536(.029)(.022)(.056)(.027)A3544*HS*Y7180.1232-.0179.0189-.0157(.050)(.038)(.099)(.047)A3544*AHS*Y7180.1018.0367.1490.0551(.024)(.018)(.047)(.023)A4554*BHS*Y7180.0561.0000.2835.0000(.044)(.033)(.087)(.045)A4554*HS*Y7180-.0100.0000-.0807.0000(.091)(.068)(.178)(.101)A4554*AHS*Y7180-.0024-.0000-.0354.0000(.060)(.045)(.117)(.054)A534*BHS*y617O.0698-.0358.3455-.0353(.026)(.020)(.051)(.028)A2534*HS*Y6170.0487-.0321.1314.0485(.044)(.033)(.087)(.042)A2534*AHS*Y6170.1657-.0770.3441-.0535(.026)(.020)(.052)(.025)A3544*BHS*Y6170.0870.0034.1113.0078(.021)(.016)(.041)(.021)L”JAppendix6cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A3544*HS*Y6170-.0033-.0032.0841.0234(.039)(.030)(.077)(.039)A3544*AHS*Y6170.0898.0031.1017.0296(.021)(.016)(.041)(.020)A4554*BHS*Y6170.0102.0000.0736-.0000(.032)(.024)(.063)(.037)A4554*HS*Y6170.0669.0000-.0069.0000(.057)(.043)(.112)(.059)A4554*AHS*Y6170.0469-.0000.0248.0000(.034)(.026)(.067)(.032)A2534*BHS*YBEF61-.0205.0083-.0018-.0578(.042)(.032)(.082)(.047)A2534*HS*YBEF61-.0667.1267.1004.1411(.046)(.035)(.091)(.053)&.534*jJ{S*yBEF61.0005-.0210.0578.0479(.034)(.026)(.067)(.031)A3544*BHS*YBEF61.0048-.0056.0569-.0064(.025)(.019)(.049)(.026)A3544*HS*YBEF61-.0420-.0231-.1266-.0157(.046)(.035)(.091)(.047)A3544*AHS*YBEF61-.0304-.0065-.0058-.0002(.030)(.023)(.059)(.028)I’J1-flAppendix6cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A4554*BHS*YBEF61.0049.0000.0630-.0000(.023)(.017)(.045)(.026)A4554*HS*YBEF61-.0100.0000-.1454.0000(.052)(.039)(.102)(.058)A4554*AHS*YBEF61.0036-.0000.0271.0000(.030)(.023)(.059)(.029)R2 F N4616461646164616I’J*Standarderrorsareinparentheses.Appendix7ResultsfromEstimationofEquationsUsedtoGenerateHusband’sEulerEquationData1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)Intercept-3.819.0996.0134.8121.0436(.027)(.006)(.003)(.016)(.004)534*HS*NB-.0561.0158.0198.0726.0101(.043)(.010)(.005)(.025)(.007)A2534*AHS*NB-.2988.0736.0371.0961.0343(.034)(.007)(.003)(.019)(.005)A3544*BHS*NB-.0633-.0843-.0110-.6039-.0057(.034)(.008)(.004)(.021)(.006)A3544*HS*NB-.2171-.0960-.0115-.5225-.0320(.040)(.010)(.005)(.027)(.007)A3544*AHS*NB-.3977-.0754-.0104-.4911-.0300(.031)(.007)(.004)(.019)(.005)A4554*BHS*NB-.0259-.0938-.0134-.7721-.0413(.038)(.009)(.004)(.023)(.006)A4554*HS*NB-.1503-.0945-.0134-.7866-.0436(.058)(.015)(.007)(.038)(.010)A4554*AHS*NB-.3633-.0968-.0134-.7561-.0409(.041)(.009)(.004)(.024)(.007)A2534*BHS*Y7180.1267.0921.0214.2541.0156(.066)(.013)(.006)(.033)(.009)U’Appendix7cont.1991MUKIDSO5K1PLUSKJDS614K2PLUSExpression(1991)(1991)(1991)(1991)A2534*HS*Y7180-.0584.0847.0002.1570.0380(.082)(.018)(.009)(.048)(.013)A2534*AHS*Y7180.0039.0416-.0152.1713.0034(.027)(.007)(.003)(.018)(.005)A3544*BHS*Y7180.1309.0246.0042.3267.0160(.050)(.012)(.006)(.031)(.008)A3544*HS*Y7180.1069.0615-.0019.1438.0384(.068)(.019)(.009)(.049)(.013)A3544*AHS*Y7180.1498.0172.0037.2444.0177(.030)(.007)(.004)(.019)(.005)A4554*BHS*Y7180.3406.0011.0000.1312-.0023(.090)(.016)(.008)(.043)(.012)A4554*HS*Y7180.1416-.0051.0000.0233.0000(.104)(.032)(.015)(.083)(.022)A4554*AHS*Y7180.1517-.0027.0000.0622-.0027(.060)(.015)(.007)(.038)(.010)&,534*BHS*Y617O-.0426.0116-.0023.1546.0175(.064)(.015)(.007)(.039)(.011)p.534*Hs*y617o.0469.0542-.0162-.0372.0819(.109)(.025)(.012)(.066)(.018)A2534*AHS*Y6170-.0847.0005-.0176-.0129-.0211(.040)(.011)(.005)(.028)(.008)UiAppendix7cont.1991MUKIDSO5K1PLUSKIDS614K2PLUSExpression(1991)(1991)(1991)(1991)A3544*BHS*Y6170.0518.0116-.0003.1417.0093(.052)(.010)(.005)(.026)(.007)A3544*HS*Y6170.0613-.0057-.0019.0776.0119(.059)(.018)(.009)(.048)(.013)A3544*AHS*Y6170-.0106.0118-.0012.1220.0030(.024)(.007)(.003)(.018)(.005)A4554*BHS*Y6170.0945-.0025.0000.0367.0073(.057)(.012)(.006)(.032)(.009)A4554*HS*Y6170.0973-.0051.0000.0872.0000(.098)(.026)(.012)(.067)(.018)A4554*AHS*Y6170-.0043.0064.0000.0380-.0004(.050)(.011)(.005)(.029)(.008)A2534*BHS*YBEF61-.2123.0393-.0134.1046.0675(.147)(.031)(.015)(.082)(.022)-.0268.0059-.0029.2365-.0234(.161)(.033)(.016)(.086)(.023)-.1554.0006-.0137.0129.0168(.039)(.014)(.007)(.036)(.010)A3544*BHS*YBEF61-.0781-.0058-.0024.0172-.0041(.048)(.012)(.006)(.030)(.008)A3544*HS*YBEF61.0678.0326-.0019.0489-.0116(.114)(.024)(.012)(.063)(.017)I’.jUIAppendix7cont.1991MUKIDSO5K1PLUSKJDS614K2PLUSExpression(1991)(1991)(1991)(1991)A3544*AHS*YBEF61.1682-.0005.0041-.0042-.0017(.044)(.010)(.005)(.026)(.007)A4554*BHS*YBEF61-.0113-.0043.0000-.0011-.0009(.041)(.009)(.005)(.024)(.007)A4554*HS*YBEF61.0047-.0051.0096.0130.0000(.079)(.022)(.010)(.058)(.016)A4554*AHS*YBEF61.0862-.0012.0000-.0174-.0027(.043)(.010)(.005)(.026)(.007)R2.2161.0560.6235.0982F252.954.5151999.9NN) (ii*Standarderrorsareinparentheses.Appendix7cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)Intercept-3.783.1726.7072.0704(.037)(.013)(.034)(.010)A2534*HS*NB-.0299.0557-.2062-.0591(.052)(.021)(.054)(.016)A2534*AHS*NB-.1606.0580-.2770-.0458(.042)(.015)(.039)(.012)A3544*BHS*NB-.0784-.1308.1544.0209(.048)(.017)(.044)(.013)A3544*HS*NB-.2004-.1333.2094-.0095(.056)(.021)(.055)(.016)A3544*AHS*NB-.3694-.0944.2378.0081(.044)(.015)(.040)(.013)A4554*BHS*NB-.0737-.1655-.2847-.0464(.045)(.016)(.042)(.013)A4554*HS*NB-.2364-.1726-.3590-.0704(.074)(.026)(.068)(.020)A4554*AHS*NB-.3517-.1663-.2726-.0471(.047)(.017)(.043)(.013)A2534*BHS*Y7180.0509.1926-.1830-.0166(.070)(.026)(.067)(.020)&534*HS*Y718O.2664-.0025-.1965.0419(.127)(.039)(.102)(.030)t\.)Ui‘.0Appendix7cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A2534*AHS*Y7180.0671.0177-.0968-.0140(.036)(.014)(.036)(.011)A3544*BHS*Y7180.1548.1092.1340.0036(.070)(.024)(.064)(.019)A3544*HS*Y7180.5150-.0393.0092.0919(.148)(.046)(.120)(.036)A3544*AHS*Y7180.2350.0500-.0462.0502(.048)(.015)(.039)(.012)A4554*BHS*Y7180.3324.0093.1996.1236(.130)(.031)(.081)(.024)A4554*HS*Y7180.4072.0994.2554.0000(.152)(.075)(.195)(.058)A4554*AHS*Y7180.1287.0063.1463.0132(.100)(.027)(.070)(.021)A2534*BHS*Y6170-.1591.0690.2213-.0230(.074)(.031)(.080)(.024)A2534*HS*Y6170.2340-.0155.3358-.0113(.235)(.054)(.140)(.042)&534*AHS*y617O-.0109-.0101.1263.0011(.056)(.022)(.056)(.017)A3544*BHS*Y6170.0261.0255.1851.0533(.052)(.019)(.049)(.015)(“jCAppendix7cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A3544*HS*Y6170.1810.0393.2290-.0071(.138)(.041)(.107)(.032)A3544*AHS*Y6170.0806.0188.0023-.0062(.036)(.013)(.034)(.010)A4554*BHS*Y6170.0593.0118.0902.0229(.056)(.021)(.054)(.016)A4554*HS*Y6170.1567.0000.2755.0466(.114)(.054)(.139)(.041)A4554*AHS*Y6170-.0475.0028.1937.0076(.051)(.018)(.048)(.014)L&.2534*BHS*YBEF61-.0026.2637.1109.0534(.126)(.057)(.148)(.044)b534*HS*yBEF61-.0144-.1038-.0769-.0113(.107)(.087)(.225)(.067)ft534*AHS*yBEF61.0621-.0484.1555-.0246(.114)(.026)(.068)(.020)A3544*BHS*YBEF61.2007.0073.1682.0978(.090)(.024)(.063)(.019)A3544*HS*YBEF61.0132.0762.0152-.0609(.098)(.057)(.148)(.044)A3544*AHS*YBEF61.1191-.0292.0906-.0004(.051)(.019)(.048)(.014)Appendix7cont.KIDSO5K1PLUSKIDS614K2PLUS(1981)(1981)(1981)(1981)A4554*BHS*YBEF61.0179.0040.1109-.0071(.044)(.015)(.040)(.012)A4554*HS*YBEF61-.0596.0000.0512.0634(.105)(.046)(.119)(.036)A4554*AHS*YBEF61.0837-.0007.0767-.0078(.042)(.016)(.040)(.012)R2.1127.1009.0993.0340F43.538.437.712.0NI’J*Standarderrorsareinparentheses.

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