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Social security and saving rates : a cohort analysis using Italian data Biagi, Federico 2000

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SOCIAL SECURITY AND SAVING RATES: A COHORT ANALYSIS USING ITALIAN DATA by Federico Biagi Laurea (Bachelor) in Law, Milan State University, Milan, Italy, 1990 M.A., New York University, 1993 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Economics) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 2000 © Federico Biagi, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Like other industrialized countries, Italy has recently experienced a substantial decrease in the fraction of total income saved by the private sector. Working with a repeated series of cross sections (Bank of Italy "Survey on Household Income and Wealth" for the period 1984-1995), this thesis verifies to which extent Social Security can explain the drop in aggregate saving rates observed in Italy after the mid 1980's. Since Social Security wealth is a cohort dependent variable and given the nature of our data, we generate a quasi-panel dataset by creating synthetic cohort measures (in terms of age, sector and education) for all the relevant variables, focusing on individuals between the ages of 20 and 60. Previous studies have tried to link savings and Social Security but very rarely they have specified a structural model where the estimated coefficients can be unambiguously interpreted. We reach such an objective using the simplest consumption model (finite lives, no uncertainty, perfect capital markets and selfish agents), whose implications are that-for given expectations on the Social Security regime-cohort consumption rates are an increasing function of their Social Security wealth to Permanent Income ratios We test our model under different assumptions on the expected prevailing regime (in 1992 Italy experienced a first reform of Social Security that affected the generosity of benefits for private and public sector workers and raised retirement age for the former group) and we find that only under the perfect foresight hypothesis and only for private sector workers, log consumption rates are positively and significantly correlated with Social Security wealth to Permanent Income ratios. This result, far away from reflecting an increasing generosity of Social Security, is due to the raise in retirement age introduced by the 1992 reform. We conclude that Social Security can be held responsible for declining saving rates only for the private sector and only when we consider retirement age provision, and hence that there likely are other common factors that drive the aggregate result. We investigate the role of bequests and we find that wealth allocation within the household could be responsible for the observed rise in consumption rates. i i Table of Contents Abstract ii Table of Contents i i i List of Tables vi List of Figures viii Acknowledgements x Dedication xi CHAPTER I Introduction 1 CHAPTER II Why did Italian aggregate saving rates decline? 7 2.1 Survey of the Literature 7 2.2 The Data 17 2.3 Aggregate facts and Micro data 16 2.4 Evidence from reduced form estimation 19 2.4.1 Public Sector Employees, Full sample 22 2.4.2 Private Sector Employees, Full sample 22 CHAPTER III The Theoretical Framework and the Explanatory Variables 24 3.0.3 The life-cycle model 24 3.0.4 The Consumption Function 25 3.1 Pension Legislation in Italy 33 3.2 Estimation of Pension Wealth and Human Wealth 36 3.2.1 Estimating life-cycle profiles for wages 36 3.2.2 Constructing Pension Wealth and Human Wealth Profiles 38 3.2.3 Private Sector Workers 40 3.2.4 Public Sector Workers 43 CHAPTER IV Estimation 45 Part I Perfect Foresight 46 4.1 The model 47 4.2 The Components of Old to Young Age Net Wealth Ratio 49 4.2.1 Public Sector 49 4.2.2 Private Sector 50 4.3 Estimation 52 4.4 Estimating the cohort fixed effects-Males Heads of Households 53 i i i 4.4.1 Public Sector Workers-Males Heads of Households 53 4.4.2 Private Sector Workers-Males Heads of Households 54 4.5 Explaining Fixed effects-Perfect Foresight-Males Heads of Households.. .54 4.6 Conclusions 56 Part II Complete Surprise 59 4.7 Explaining Fixed effects-Complete Surprise 60 4.7.1 Estimated Fixed Effects-Males Heads of Households 62 4.7.2 Fixed Effects on the explanatory variables-Males Head of Households 63 4.7.3 Conclusions 65 4.8 A control experiment 65 4.8.1 Males Head of Households 69 4.8.2 Households where the Head is married 69 4.8.3 Conclusions 69 CHAPTER V What have we learned about saving rates? 71 5.1 The Role of Assets 71 5.2 Implications for Aggregate Saving Rates 74 5.2.1 The role of Social Security Reform 75 5.2.2 The role of taxes 78 CHAPTER VI Conclusions 80 BIBLIOGRAPHY 83 APPENDIX A Pension Legislation in Italy 88 A . 1 Private Sector Employees 88 A. 1.1 The Pre Amato Regime 88 A. 1.2 Amato Reform 89 A. 2 Public Sector Employees 90 A.2.1 Pre Amato Regime 90 A.2.2 Amato Reform 91 APPENDIX B Wage estimation: Age and Cohort Effects 93 B. l Age profiles (Net Wages) 95 B. 2 Cohort Profiles (Net Wages) 97 APPENDIX C Perfect Foresight-Households where the Head is Married 101 C. l Estimation of the Fixed effects-Perfect Foresight-Households where the Head is married 101 C . l . l Private Sector 102 iv C. 1.2 Public Sector 102 C.2 Explaining the Fixed Effects-Perfect Foresight-Households where the Head is married 103 C. 3 Conclusions 103 APPENDIX D Complete Surprise-Households where the Head is Married.... 104 D. l Estimation of the Fixed effects-Complete Surprise-Households where the Head is married 104 D. l . l Private Sector 104 D.l .2 Public Sector 104 D.2 Explaining the Fixed Effects-Complete Surprise-Households where the Head is married 105 D.3 Conclusions 105 List of Tables Table 1 Saving Rates-Males Public Sector 106 Table 2 Saving Rates-Males Private Sector 107 Table 3 Log of Net Wages-Males Public Sector 108 Table 4 Log of Net Wages-Males Private Sector 109 Table 5 Estimation of Cohort Effects-Perfect Foresight Males Public Sector 110 Table 6 Estimation of Cohort Effects-Perfect Foresight Males Private Sector I l l Table 7 Cohort Effects on Explanatory Variables Males A l l Groups 112 Table 8 Cohort Effects on Explanatory Variables Perfect Foresight Males Private and Public Sector 113 Table 9 Estimation of Cohort Effects-Complete Surprise Males Public Sector 114 Table 10 Estimation of Cohort Effects-Complete Surprise Males Private Sector 115 Table 11 Cohort Effects on Explanatory Variables Complete Surprise Males A l l Groups 116 Table 12 Cohort Effects on Explanatory Variables Complete Surprise Males Private and Public Sector 117 Table 13 Differences in Log Consumption Rates (1993-1991) Complete Surprise-Males 118 Table 14 Differences in Log Consumption Rate (1993-1991) Complete Surprise-Males 119 Table 15 Estimation of Cohort Effects in Real Assets Males Public Sector 120 Table 16 Estimation of Cohort Effects in Real Assets Males Private Sector 121 vi Table 17 Fixed Effects on Explanatory Variables-Males 122 Table 18 Log Consumption Rate-All Groups-Perfect Foresight-Males 123 Table 19 Counterfactual Aggregate Saving Rates-Contributions by Sectors The Effect of Social Security 124 Table 20 Counterfactual Aggregate Saving Rates-Contributions by Sectors The Effect of Taxes Over the Life-Cycle 125 V l l List of Figures Figure 1 Saving and Growth, 1862-1990 126 Figure 2 Saving Components, 1862-1949 127 Figure 3 Inflation Adjusted Saving Rates, 1862-1949 128 Figure 4 Saving Components, 1950-1990 129 Figure 5 Inflation Adjusted Saving Rates, 1950-1990 130 Figure 6 Comparing Aggregate Saving Rates 131 Figure 7 Saving Rates in terms of Total and Labor Income Junior High School Graduates-Public Sector 132 Figure 8 Saving Rates in terms of Total and Labor Income High School Graduates-Public Sector 133 Figure 9 Saving Rates in terms of Total and Labor Income College Graduates-Public Sector 134 Figure 10 Saving Rates in terms of Total and Labor Income Junior High School Graduates-Private Sector 135 Figure 11 Saving Rates in terms of Total and Labor Income High School Graduates-Private Sector 136 Figure 12 Saving Rates in terms of Total and Labor Income College Graduates-Private Sector 137 Figure 13 Saving Rates in terms of Lifetime Resources Junior High School Graduates-Public Sector 138 Figure 14 Saving Rates in terms of Lifetime Resources High School Graduates-Public Sector 139 Figure 15 Saving Rates in terms of Lifetime Resources College Graduates-Public Sector 140 Figure 16 Saving Rates in terms of Lifetime Resources Junior High School Graduates-Private Sector 141 V l l l Figure 17 Saving Rates in terms of Lifetime Resources High School Graduates-Private Sector 142 Figure 18 Saving Rates in terms of Lifetime Resources College Graduates-Private Sector 143 Figure 19 Age Profiles-Saving Rates from Reduced Form Estimation-Males 144 Figure 20 Cohort Effects-Saving Rates from Reduced Form Estimation by Cohort-Males 145 i Figure 21 Cohort Profiles-Saving Rates from Reduced Form Estimation-Males. .146 Figure 22 Age Profiles for Net Wages-Males 147 Figure 23 Age Profiles for Net Wages-Females 148 Figure 24 Entry Net Wages, by Cohort-Males 149 Figure 25 Entry Net Wages, by Cohort-Females 150 Figure 26 Net Pension Wealth, by Cohort Perfect Foresight Versus Complete Surprise-Males 151 Figure 27 Human Wealth, by Cohort Perfect Foresight Versus Complete Surprise-Males 152 Figure 28 Ratio of Human Wealth after age 60 over Normalized Human Wealth, by Cohort-Males 153 Figure 29 Ratio of Net Pension Wealth over Normalized Human Wealth, by Cohort-Males 154 Figure 30 Ratio of Tax Rates over the Life-Cycle, by Cohort-Males 155 Figure 31 Generosity of Social Security, by Cohort-Males 156 Figure 32 Old to Young Age Net Wealth Ratio, by Cohort-Males. 157 Figure 33 Fixed Effects from Consumption Rates, by Cohort Perfect Foresight-Males 158 Figure 34 Old to Young Age Net Wealth Ratio, by Cohort Perfect Foresight Versus Complete Surprise 159 Figure 35 Fixed Effects from Consumption Rates, by Cohort ix Complete Surprise-Males 160 Figure 36 Ratio of Entry Assets over Normalized Human Wealth by Cohort-Males 161 Figure 37 Counterfactual Aggregate Saving Rates: Both Sectors 162 Figure 38 Counterfactual Aggregate Saving Rates: Private Sector 163 Figure 39 Counterfactual Aggregate Saving Rates: Public Sector 164 Acknowledgements I want to thank Paul Beaudry, Francisco Gonzalez Pineiro and David Green. They have taught me how to do research and this is a gift that I will never forgot. I also thank Roberto Artoni for constant support and the Cariplo Foundation for financing my research. I have also greatly benefited from discussions with Carlo Devillanova, Matteo Manera and Massimiliano Marcellino, all of them at Bocconi University and with Agar Brugiavini and Franco Mariuzzo at the University of Venice. Dedication My thesis is dedicated to all the people that made it possible: my grandparents Aldo and Bruna, my parents Bianca ed Enrico, my friends Ana, Carletto detto Puddu, Luisa, Hashmat, Nick, Patrick, Pino, Robertino i l Polaccazzo, Stefano and Samantha and, especially, to Rocio, my best friend and lover. xi Chapter 1 Introduction During the last 15 years many industrialized countries have experienced a decline in private saving rates. This stylized fact is particularly evident for Italy, whose private saving rate decreased from 17.7 during the 1960-1969 decade to 6.6 during the period 1990-1994. Binding credit constraints are a candidate explanation. Jappelli and Pagano (1989, 1994) show that a credit constrained economy exhibits higher saving rates and more reactivity to changes in the productivity rate when compared to a non constrained economy. This hypothesis has been tested with respect to Italy (see Maccan, Rossi and Visco (1994)) and the evidence points towards the relevance of binding credit constraints. An alternative explanation considers the importance of changes in the age pro-file for wages, such as those originating from a skill-biased technological change. Beaudry and Devereux (1996) show that a shift towards steeper age profiles for wages would induce agents to borrow (or reduce savings) in the first periods of their life, due to the increased profitability of education, hence shifting the bulk of wealth to a later part of their life. This could reduce the aggregate saving rate. In this paper we verify to which extent the drop in Italian private saving rates can be explained by changes in Social Security. Previous studies by Brugiavini (1987) and Jappelli (1995) find that between 10 and 20% of the decline in aggregate saving rates can be traced to the reduced accu-mulation induced by Social Security. The quantitative relevance of Social Security is amfirmed by the work of Rossi and Visco (1994, 1995)1. 1With reference to the U.S., Gokhale, Kotlikoff and Sabelhaus (1996) showed that a great deal of the decline in the aggregate saving rate can be accounted for by the large increase in the fraction of total wealth in the hands of older cohorts and by the fact that this wealth has been predominantly 1 In contrast with the findings of earlier literature, our results show that the direct effects of Social Security on Italian private saving rates are minor and that they are of the right sign only if we assume that agents are fully aware of all the aspects of Social Security legislation, including retirement age provision. In fact, we find that approximately 2% of the decline in aggregate private saving rates can be imputed to Social Security. This aggregate effect is not due to an increase in the generosity of pension legislation but to the increase in retirement age brought by the 1992 Amato reform. In empirical macroeconomics the choice of the appropriate unit of analysis (micro versus aggregate data) is very important. As far as Social Security is concerned, the Italian experience is full of examples of legislative changes that affected the value of pension benefits differently according to the cohort to which a worker belongs. For instance, the reform of the late 1960's benefited more those who at the time were about to retire, because it increased disproportionately their net pension wealth. Similarly, the reforms of the 1990's (the Amato reform of 1992 and the Dini reform of 1995) affected mostly young cohorts. The first input from our institutional knowl-edge is hence towards the importance of cohort effects. Moreover the reforms of the 1990's affected differently workers in the private and public sector and the changes produced different effects depending on the shape of the expected life-cycle profile for wages. This points towards the relevance of sector and education as relevant conditioning variables. Our approach, that bases the identification on between-sector and across-cohort variation, fits well with the available micro data coming from the Bank of Italy's Survey of Household Income and Wealth (SHIW) for the years 1984, 1986, 1987, 1989, 1991, 1993 and 1995. This is a repeated series of cross-sections (with a small panel component starting only from 1989). By conditioning on the proper set of variables (age, sector, education) we can generate observations relative to represen-tative sector-education specific cohorts and follow them through time. We choose the "dimension" of the cohort trying to balance the gain in representativeness with the loss in interesting information due to the averaging process. As for our theoretical framework, we work with a simple life-cycle consumption model, assuming finite lives, perfect capital markets, no uncertainty, selfish agents and homothetic preferences. Within our cohort approach, agents are those who belong to a given cohort, work in a given sector (private/public) and have a certain education (Junior High School, High School or College Graduates). This model annuitized (non transferable and hence non bequeathable), in the form of public pensions, Medicare or Medicaid payments. 2 predicts that cohort consumption rates are a function of Social Security wealth to Permanent Income ratios. Given the chosen conditioning variables (age, sector and education), the aggregate series can be obtained from the aggregation of the (optimal) consumption choices of the various sector and education specific age groups (cohorts). Within this framework, a decline in aggregate saving rates can be obtained -for a given age distribution in the population- only if the different cohorts are experiencing changes in the age profile for wealth. If we compare two cohorts with different age-wealth profiles, the one that has a steeper age profile for wealth, which amounts to saying the one that has more wealth towards the end of the life-cycle relative to its first part, will also have lower saving rates. To make the previous conclusion clearer we should add that wealth is an endogenous variable, linked to savings (the first difference of wealth is equal to saving). Hence when we refer to shifts in the age profile for wealth, we really mean shifts due to some exogenous factor that induce agents to react optimally by increasing wealth towards the end of the life-cycle. Focusing on our identification strategy, the hypothesis that Social Security is the driving force of the observed decline in private sector aggregate saving rates implies that -for a constant age composition- more recent cohorts benefited from a more generous Social Security system leading to an increase in net Social Security wealth and, potentially, in the Social Security wealth to Permanent Income ratio2. Our intuition is that, when focusing on Social Security (net) wealth, defined as the present value of expected pension benefits minus the present value of expected Social Security tax contributions, recent generations of Italians have not been treated more generously when compared to older cohorts and hence that Social Security is not a likely explanatory candidate for the fall in Italian aggregate private saving rates. This intuition is confirmed by our results. Only for private sector employ-ees and only under the assumption of Perfect Foresight, we obtain a positive and significant correlation between cohort consumption rates and cohort Social Security wealth to Permanent Income ratios. The positive correlation, far from reflecting an increase in the generosity of Social Security benefits, is due to the raise in retirement age introduced by the 1992 reform, which forces younger cohorts of private sector workers to substitute labor income for pension benefits (which are a fraction of labor income). On the contrary, under the hypothesis that agents forecasted their pension wealth according to the regime in place prior to 1992 and that they were completely sur-prised by that reform, we find that our model fails to explain the drop in cohort 2 This is the underlying intuition common to those who try to explain the aggregate phenomenon while keeping the basic life-cycle model. 3 saving rates. This result corresponds to the intuition that the pre-1992 Social Se-curity system was not becoming increasingly generous for younger cohorts, whose saving rates were still declining. Given that -within our model- Social Security does not seem able to explain consistently the behavior observed in both the private and the public sector, we investigate the role of other potentially relevant variables. Once again theory comes at hand. One of the implications of our model is that consumption rates are posi-tively correlated with the ratio of age-zero wealth (bequests) to Permanent Income. We compute this ratio and we find that it exhibits rising profiles for all the groups that show rising consumption rate profiles. Moreover, when we regress log consump-tion rates on a set of explanatory variables among which we have age, age-cohort interaction, household's characteristics, the ratio of age-zero wealth (bequests) to Permanent Income and the ratio of Social Security wealth to Permanent Income, we find that, after controlling for all the other factors affecting consumption rates, the ratio of age-zero wealth to Permanent Income is positively and significantly correlated with consumption rates for all the sector-education groups that exhibit significantly positive cohort effects in log consumption rates. Social Security wealth to Permanent Income ratios are positively correlated with log consumption rates (but there is a negative second order effect) only for the private sector3. This im-plies that we cannot exclude the empirical relevance of Social Security in explaining the drops in aggregate saving rates, but it reduces its quantitative relevance. In fact, when we verify the contribution of the various sector-education groups to aggregate saving rates, comparing the aggregate series obtained from the estimated consump-tion rates with the series that would have been obtained had the Amato reform not been implemented, we find that, on average, had the regime remained that observed before 1992, aggregate saving rates would have declined by a rate that is only 3 per-centage points lower (so that the drop rate would have been 2% smaller). This result depend on the fact that the Amato reform has opposite (and offsetting, according to our estimates) effects on the private and public sector. For both sectors it reduces the generosity of Social Security at constant retirement age, but at the same time it increases the latter for workers in the private sector. While the first effects would tend to decrease the value of the Social Security to Permanent Income Ratio, the second effect tend to increase the present value of the income stream received in old age (past age 60 in our normalization) relative to what is received prior to that age. 3We have some evidence that the Social Security wealth to Permanent Income ratio is positively and significantly correlated with consumption rates in the public sector as well, but such evidence is not very robust to the different specifications. 4 By forcing younger cohorts to work for a larger number of years, the 1992 Amato reform has the effect of increasing the normalized Social Security wealth to Perma-nent Income ratios, because the retirement age effect dominates over the reduction in benefits introduced by the same reform. These results also indicate a path for future research, which should explore how wealth is accumulated and distributed within the household, where the latter should be interpreted in a dynastic sense. Our work proceeds as follows. In Chapter 2 we briefly discuss the literature on the relationship between Social Security and private wealth, focusing mainly on those contributions that try to explain the drop in aggregate and individual saving rates with changes in Social Security. Then we present the data and discuss the relationship between aggregate and micro data. We compare the series of aggregate saving rates from National Accounts with the aggregate series constructed from the sub-sample of the SHIW dataset, adopting our cohort approach. Finally we present the results from a reduced form estimation, meant to provide evidence of systematic across-cohort differences in saving behavior. In Chapter 3 we develop the model used for estimation, relating the natural logarithm of consumption rates to the value of the Social Security wealth to Perma-nent Income ratio. Under the hypothesis (verified for most sex-age-sector-education groups) that the wage process can be separated into a cohort and an age profile4, we obtain that, for a given sector-education group, log consumption rates can be expressed in terms of a unique age profile for wages, cohort specific values for Social Security wealth to Permanent Income ratios, household's characteristics, a polyno-mial in age and age-cohort interaction. Moreover, we briefly review the rules gov-erning the Italian Social Security system, hence determining the content of the two alternative information sets considered in the estimation stage (Perfect Foresight5 versus Myopic Behavior). In Chapter 4 we go back to the theoretical model and derive the implications for our estimation procedure imposed by the institutional framework. We discuss the various components of the normalized Social Security wealth to Permanent Income ratio (named Old to Young Age Net Wealth ratio in our work) and, in Part I, we proceed to estimation under the Perfect Foresight assumption, while, in Part II, we 4The evidence of an age profile that is not cohort dependent seems to exclude the empirical relevance of the skill-biased technological change hypothesis (see Beaudry and Devereux (1996)). 5The Perfect Foresight hypothesis implies that each cohort forecasts his retirement regime ac-cording to the rules in place at the end of 1994 (or earlier if they retire before that date). For some cohorts (the older ones) this means retiring under the regime in place before 1992, while for the others it implies forecasting the effects of the 1992 reform. 5 estimate the model under the Complete Surprise hypothesis. We conclude that the theoretical model works well under the Perfect Foresight hypothesis and only for private sector workers. In Chapter 5 we compute age-zero wealth and we show that this variable exhibits rising cohort profiles. We also estimate the model including both the ratio of age-zero wealth (bequests) to Permanent Income and the ratio of Social Security wealth to Permanent Income. Using the estimated coefficients we verify the quantitative relevance, at the aggregate level, of changes in Social Security regimes and of changes in tax rates over the life-cycle. Chapter 6 concludes our work. 6 Chapter 2 Why did Italian aggregate saving rates decline? 2.1 Survey of the Literature Italy is characterized by having experienced extremely high aggregate saving rates during the 1960's and 1970's and a very rapid decrease in those rates during the 1980's and 1990's. Guiso, Jappelli and Terlizzese (1994) and Jappelli and Pagano (1998) document the time series of the Italian (Net of Depreciation) National, Government and private saving rate from 1950 to 19901. The picture2 that emerges (see Figs. 1 to 4) is one of rapidly declining Government saving rates starting from 1960, slowly rising private saving rate for the period 1965-1978 followed by a rapid drop thereafter, and a declining series of net national saving rates (derived from the two previous series) starting from 1966 (with the exception of the years from 1975 to 1978). One problem with this series is that it is not adjusted for the transfer of wealth from the private to the public sector caused by the reduction in the real value of nominal debt due to inflation. This problem was particularly evident in Italy during the 1970's and the 1980's. Once the series are adjusted for such a transfer (which leaves net national saving unaffected) Jappelli and Pagano find (see Fig.5) that the drop in Government saving rate is less pronounced while the drop in net private saving rate started earlier and was more evident3. 1Jappelli and Pagano (1998) actually report the whole series starting from the 1862, the year after the birth of the National State. 2Figures 1 to 5 are drawn using data provided by Jappelli and Pagano. 3Jappelli and Pagano (1998) find that the private sector saving rate for Italy is positively cor-related with the growth rate of GDP. Moreover they cannot reject the hypothesis that variation in 7 Comparing the Italian net national and private saving rate with those of the OECD or G10 and G7 countries, Guiso, Jappelli and Terlizzese (1994) and Jappelli and Pagano (1998) find that Italy has been characterized by higher than the average saving rates during all periods previous to the 1980's and faster decline during the 1980's, even after controlling for growth, government saving rates and per-capita GDP (which would be significant if preferences are not homothetic). In fact the average saving rate for the G10 countries was 10.5 during the 1960-1969 period (Italy had an average value of 17.7), which dropped to 8.8 during the following decade (11.3 for Italy), to become 7.5 during the period 1980-1989 (7.4 for Italy) and 7.4 during the period 1990-1994 (6.6 for Italy). These results have been interpreted by Jappelli and Pagano as a sign that growth and fiscal policy alone cannot account for the "abnormal" behavior of the Italian private sector saving rate. In a different paper (Jappelli and Pagano (1984)) the same authors show that, in a two period OLG economy with an exogenous credit constraint , "for any given growth rate the presence of borrowing constraints pro-duces a higher aggregate saving rate and it increases the sensitivity of the aggregate saving rate to changes in the growth rate". The hypothesis that credit constrained4 households have a higher saving rate has been tested by various authors with respect to Italy. Jappelli and Pagano (1988), splitting the 1984 SHrW sample between those who are likely to be credit constrained and those who are not, find that the group composed of liquidity constrained house-holds has a marginal propensity to save 10% higher than the control group (however the result is not independent from the sampling technique). Guiso, Jappelli and Ter-lizzese (1994) start from the simple intuition that mortgage market imperfections force Italian households to save more when young. By imposing the assumption that home owners are not credit constrained while renters are, they conclude that projected consumption of non-credit constrained renters would be higher than the observed one by a significant amount (around 14%). This approach suffers from the fact that home purchasing is an endogenous choice. Mariger (1986, 1987) developed an intertemporal consumption model in which binding credit constraints arise endogenously. The consumer maximizes over her life-cycle but in each period there is a minimum value of assets below which her wealth cannot drop if she wants to have access to credit. Once the assets go below that growth rates Granger-cause variation in saving rates. 4There is enough evidence that Italy has been characterized by tight credit up to the mid 1980's. This is true with respect to the financing of consumer durables (mainly homes and cars) and non-durables (Guiso, Jappelli and Terlizzese (1994), Jappelli and Pagano (1998)). 8 minimurn value, the life-cycle planning horizon is reduced to a single period problem. The advantage of such a procedure is that it determines endogenously the point in time (age) in which the consumption problem cease to be a multi period one and becomes a series of single period optimization problems. Applying this procedure to Italy Maccan, Rossi and Visco (1994) find that the incidence of liquidity constraints is higher in the older portion of the population (over 75) compared to households in their thirties and forties, hence casting some doubts on explanations that would base the explanation for falling saving rates on the intuition that in recent years the liberalization of insurance markets and the increased availability of credit have benefited only young households. Demographic change is another likely explanatory candidate for the changes in aggregate private saving rates. With reference to Italy, the issue has been explored by Cannari (1994) and Jappelli and Pagano (1998), adopting a decomposition of the aggregate consumption rate proposed by Bosworth, Burtless and Sabelhaus (1991) in which the aggregate variable is expressed as where G indexes the groups among which the population has been divided, wu represents the proportion of households in group i at time t (wu = yu is the ratio of average income in the i-th group compared to the overall average at time t t. Cannari5 considers two different SHIW surveys, the one of 1989 and the one of 1980. Then he imposes the weights wu observed in 1980 on the values for cru and yu computed with the 1989 survey and obtains a counterfactual aggregate consumption rate that would have been observed in 1989 had the demographic structure of the population remained that of 1980. The demographic factors that he considers are: age, the number of components of the households and the number of children (each factor considered one at a time). He finds that the only change that can account for a small portion of the rise in aggregate consumption rates is the change in the age structure, but it has only a small quantitative effect. He concludes that the rise in consumption rates has been fairly distributed across all groups and that the age profiles for consumption rates are fairly flat. A similar exercise is conducted by Jappelli and Pagano (1998) using the SHIW dataset for the period 1984-1993. The two authors allow for variation in each of 5The aggregate consumption rate refers to the aggregate that results from the two series and not the one that would correspond to national accounts. {Vit = t ^ ) and crit is the average propensity to consume of the i-th group at time 9 the three following factors (one at a time): the age distribution of the population, the propensity to consume of the various groups and their income share. They find that the changes in age distribution have reduced the aggregate saving rate by 7%, the changes in the income shares have increased it by 7% and the changes in the average propensities to save have reduced it by 6.6%. They conclude that the decline in productivity growth that characterizes younger generations cannot be held responsible for the decline in aggregate saving rates. In fact, the effects of the variation in the income share offset those of the variation in the age composition. What is driving the aggregate result is hence the rise in the average propensities to consume. We can try to interpret these results in terms of a simple model where the consumption rate function at the individual level can be separated into an intercept and an age profile and where the intercept is a function, among other things, of the growth rate of labor income through the life-cycle. Individuals belonging to younger cohorts have higher entry wages but, in the interpretation given by Jappelli and Pagano, they have lower productivity growth over the life cycle. This should then lead to lower consumption rates. If at the aggregate we observe the opposite is because there is something else that affects either the levels or the shape of the consumption rate function, whose effects dominate over the negative ones coming from the lower rates of productivity growth. One possible interpretation of these facts is that the intercept of the consumption rate function is rising across cohorts because more recent generations expect a more generous Social Security system, which has the effect of increasing the rate of growth of pension income for more recent cohorts. Several studies have explored the hypothesis that Social Security could be re-sponsible for the drops in private saving rates. To understand the differences among those studies, we need to briefly discuss the history of the Italian Social Security system. From 1952 to 1968 the Italian Social Security System faced both an increase in coverage and a movement from Fully Funded to Pay as You Go. Italy adopted the latter definitively in 1969. Pension benefits in the private sector were made proportional to the average earnings of the last three years prior to retirement (the last year for public sector workers) and to the number of years of contribution. Pensions were indexed to the cost of Jiving. Later, the number of years used to compute average earnings was extended to five and pension benefits were indexed to the earnings of workers in the manufacturing sector. The effects was a significant rise in the ratio of Social Security benefit to GDP. Retirement age in the private 10 sector was 55 for females and 60 for males (65 for males and females in the public sector). La 1992 a reform took place (Amato reform, from the Prime Minister in charge at that time). The purpose of the reform was to bring the regimes for the private and the public sector closer, to reduce the generosity of pension benefits and increase retirement age in the private sector. Moreover indexation of pension benefits to the earnings of workers in the manufacturing sector was abandoned in favor of indexation to the cost of living. The reform did not affect all generations in the same way. Those who could count on 15 years of contribution at the time of the reform were much less affected by it than those who had less than 15 years of working experience. The effects of such a reform on Social Security wealth (which we identify with pension wealth, given that private and corporate pension provision has not been very common in Italy up to very recent years) are quite obvious for public sector workers. Compared to what they would have obtained in the absence of the reform, they suffered a reduction in pension benefits. As for the private sector, the effects are more complex because they are a function of the years of contribution under the previous regime. Only three studies (Rossi and Visco (1994, 1995) and Attanasio and Brugiavini (1999)) directly relate saving rates to Social Security for Italy. Rossi and Visco (1994, 1995) focus on the pre-1992 scenario and identify the effects of Social Security on saving rates exploiting the (long run) steady state re-lationship6 between aggregate saving rates and the following variables: the real interest rate, the growth rate of real disposable income for the private sector, the ratio of non-human wealth (real and financial wealth) to net disposable income, the ratio of gross Social Security wealth to net disposable income and the social transfer to income ratio. Using a series from 1954 to 1992 (in Rossi and Visco (1994) the series goes from 1952 to 1990 and income is defined in a slightly different way) the authors7 find that until 1962 the rise in aggregate saving rates is the result of a rising non-human wealth to net disposable income ratio, with a negative effect com-ing from the rise in the gross Social Security wealth to net disposable income ratio. The increasing generosity of the Social Security system after the 1960's becomes a major determinant of the behavior of the aggregate saving rate, and Rossi and 6We focus on results for the estimation that uses time series evidence. Comparable results are obtained from the estimation that uses the 1991 SHIW cross-section. Notice that they consider the period up to the 1992 reform, for which a stable long run rela-tionship could be plausible. 11 Visco find that for the period 1980-1992 "slightly less than half of the entire fall of the private equilibrium saving rate appears to be due to the increased gross social security wealth to income ratio". At the same time they find that this negative effect is "partially offset by the direct effects of pension expenditures on disposable income", so that the net effect of Social Security on the equilibrium saving rate is greatly reduced. Attanasio and Brugiavini (1999) identify the relationship between Social Security and saving rates under the hypothesis that agents were surprised by the 1992 reform and that the observed variation in consumption rates between 1991 and 1993 can be explained by the variation in Social Security wealth brought by the 1992 reform. The two authors develop a simple life-cycle model without uncertainty, in which individual saving rates are a function of age, individual (or household) characteris-tics, the ratio of future to current earnings, the ratio of pension wealth to current earnings and the interaction between the last two variables with a polynomial in age. Attanasio and Brugiavini also control for cohort effects (including cohort dummies) and time effects (including a year dummy). The estimation is then conducted in three ways. First using individual data and OLS, then using individual data and Instrumental Variables for the ratio of future to current earnings and for the ratio of pension wealth to current earnings and finally using a difference in difference ap-proach using cohort averages. When they use OLS they find that pension wealth reduces private saving rates but the coefficient is quantitatively not very significant. When they use instrumental variables they find that the coefficient on the ratio of pension wealth to current income is actually positive. The most interesting part of their paper is the one in which they apply the method of difference in difference estimation. What they do is basically a regression of the changes in average saving rates between 1993 and 1991 for the groups that they identify as relevant8 on the changes in pension wealth, controlling for other factors that might influence the re-sult. Taking into account the fact that the changes in pension wealth should affect differently individuals at different stages in their lifetime, they interact the differ-ence in pension wealth with a polynomial in age. The results show that there is a negative average relationship between saving rates and pension wealth and that this effect is quantitatively larger than the one obtained with OLS. Moreover, Attanasio and Brugiavini show that the relationship between the two variables significantly depends on age. The age profile of the coefficient on the correlation between saving 8They choose to condition an characteristics like age and sector such that the effects of the Amato reform on pension wealth would be amplified. This is necessary to identify the relationship between changes in pension wealth and changes in saving rates. 12 rates and pension wealth shows a positive value up to age thirty, then it becomes negative and keeps dropping until age forty is reached. After that age its value rises and it becomes positive again at around sixty. Other papers (Brugiavini (1987) and Jappelli (1995)) have only indirectly studied the relationship between saving rates and Social Security, because they were aiming at estimating the degree by which Social Security wealth is a substitute for private wealth. Brugiavini (1987) and Jappelli (1995) share the same hypothesis regarding the functional form that links accumulated assets and Social Security wealth. This relationship, previously used by King and Dicks-Mireaux (1982, 1984) and Hubbard (1986) , originates from a basic life-cycle model. They define Total wealth (TW) as the sum of private wealth (W), Social Security wealth (SW) and private pension wealth (PW). They assume that the Total wealth (TW) to Permanent Income (Y) ratio is a function of age and hence they can express W/Y as a function of age, SW/Y and PW/Y. The coefficient that relates W/Y and SW/Y measures the degree of substitution between private and Social Security wealth. One problem with these studies is the construction of Permanent Income. This requires very strong assumptions regarding the shape of the age profiles. The prob-lem arises from the fact that both King and Dicks-Mireaux (1982) and Brugiavini (1987) use just one cross section. This implies that the estimated age profile cannot be separated from a cohort profile, meaning that the differences in wages due to age cannot be separately identified from differences in wages due to cohort effects. The second problem is the construction of Social Security wealth. This is un-observed and hence has to be constructed, imposing assumptions regarding some basic questions like: the expected age of retirement, the expected replacement rate between the first pension and the last wage, the expected indexation mechanism and other aspects that might affect its value (which depend on the institutional framework). The previous task is particularly complex for Italy, because there are numerous separate Funds and rules that govern the pensions of specific categories of self employed workers. Brugiavini (1987) estimates the previous model using the SHIW dataset for 1984 and finds that a one dollar increase in Social Security wealth induces a drop in private wealth of around 10 cents. This value is about one third of the one obtained by Hubbard (1986) for the U.S. and King and Dicks-Mireaux (1982) for Canada, using an almost identical procedure9. 9In the SHIW dataset it is not possible to match precisely every individual to his particular public pension fund and hence a good degree of approximation is present in the computation of 13 Given that the SHIW surveys for 1989 and 1991 report a question on the expected replacement rate between the first pension and the last wage and another one on the expected retirement age, Jappelli (1995) is able to avoid the second of the two above mentioned problems. Jappelli estimates the relationship between private and Social Security wealth using an equation analogous to the one used by Brugiavini and King and Dicks-Mireaux and finds that an increase in Social Security wealth causes a decrease in private wealth by a percentage between 11 and 20% (depending on the specification used). Moreover he finds that the offset is higher for households with higher values of PW/Y. The implications for saving rates is that "the development of Social Security system in the 1970s and 1980s explains about one-fifth of the fall in the Italian private saving rate in the last three decades". 2.2 The Data Our approach is based on two hypotheses that have to be separately analyzed. The first hypothesis is that an aggregate phenomenon can be understood and interpreted through the use of micro data (the Bank of Italy's Survey of Household Income and Wealth (SHIW)). While we cannot accept or reject such hypothesis, a minimum requirement for its credibility is that the aggregate series form National Accounts and the aggregate series obtained from the SHIW show the same trend. The same should hold if we focused on a sub-sample of the SHIW dataset. The second hypothesis is that there exists enough (statistically significant) across-cohort variation in saving rates to justify our cohort-based approach. We will address these two issues in order. The Bank of Italy's Survey of Household Income and Wealth reports information on individual and household variables. Data on individual labor and non labor income, wealth, consumption and savings are the main concern for this work. We also have information on the number of household's members and on the number of income recipients. Data on labor income are net of taxes and contributions to the Social Security system. These data have been collected since 1965, but only for the period after 1984 are we able to have information on the age of individuals. Because of a mistake by a collecting agency, the age variable prior to 1984 has been recorded only in classes of ten year intervals. Since we want a measure of cohorts shorter than that, we are forced to use only the dataset from 1984, 1986, 1987, 1989, 1991, 1993 and 1995. The data have been collected by different agencies in the different years and hence the sampling techniques and the definitions of the variables do not Social Security wealth. 14 always coincide. We have tried as much as possible to create comparable variables when this was necessary10. Given the sample provided by the Bank of Italy, we focus on a restricted sub-sample, formed by those who are employees in the private and public sector11. We choose to exclude self employed workers mainly for two reasons. The first one is based on the well known fact that individual income for this category of workers is under-reported. The second reason is related to the difficulties of computing pension wealth, since the Italian legislative landscape is full of specific rules and funds governing the pensions of the various types of self employed workers, while the data that we have do not allow us to identify the" type" of each worker clearly. We then split the sample by sex and by three education groups: (i) those with less than or completed Junior High School (the mandatory school level in Italy); (ii) those with completed High school; (iii) those with a completed Bachelor degree or postgraduate education. We focus only on agents (potentially) permanently attached to the labor market and hence only on agents that, in every given year, are older than 20 if they have post-secondary education or less and older than 25 if they are College Graduates, and younger than 60 if males and 55 if females. The exclusion of retirees is due to the fact that we do not have information on their wage path and hence we are not able to compare them with workers. By excluding retirees and self employed, we lose the tight relationship between our sub-sample and the aggregate data, but we gain in clarity in terms of the model used for estimation. Within the sub-sample we then proceed to create synthetic cohorts. When data refer to individuals we create sex-age-sector-education cells based on the character-istics of the individual. When dealing with variables defined only at the household level, we use the age, sector, education and sex of the head of the household to assign the variables of interest. Notice that the head of the household is always a male, unless the household is composed of a female that is a widow or a single. When imputing to individuals the variables defined only at the household level (consump-tion, saving, wealth, total income, family composition) we allow for Equivalence Scales, and hence we divide household variables by the square root of the number of household's members to obtain a satisfactory approximation to per-capita values. When relevant we construct real variables using the CPI index, with base year 1990. We then proceed to compute the average value for every relevant variable for each sex-age-sector-education cell. In order to obtain a sufficient number of observations we construct cohorts that have a five year interval. Hence we have 9 cohorts of 1 0For a description and analysis of the sampling procedure see Brandolini and Cannari (1994). 1 1 We exclude workers in the agricoltural sector. 15 College Graduates and 10 cohorts for the two groups with lower education. The oldest ones are the cohorts indexed by 1. They are: (a) High and Junior High School Graduates that entered the labor market at age 20 in the years between 1946 and 1951 and (b) College Graduates that entered the labor market at age 25 in the years between 1951 and 1956. When the highest bound of the age interval upon which the cohort is built is greater that 60 (or 55 if females) we drop the cohort. 2.3 Aggregate facts and Micro data As already mentioned, the first problem that we face is the reconciliation of the data obtained from the SHIW with those from National Accounts. As documented by Jappelli and Pagano (1998) and Brandolini and Cannari (1984), the two dataset in general do not match perfectly. The differences are due (see Brandolini and Cannari (1994)) to under reporting (in the SHIW) of income from self-employment, pensions and financial assets. For the periods we focus on (1984, 1986, 1987, 1989, 1991, 1993, 1995) the series of aggregate and "implied" aggregate data have a similar broad trend, but the timing of the changes does not match. In Fig.6 we report the series for aggregate saving rates coming from both National Accounts and OECD and we compare them to the series of "aggregate" data obtained from the sub-sample of the SHIW dataset previously described, using both total and labor income (agsrti refers to the saving rate in terms of total income while agsrli is expressed in terms of labor income). When we consider the aggregate series from National Accounts, the drop in saving rates between 1984 and 1995 is approximately 27% (six percentage points), while, for the same years, the "aggregate" series obtained from the SHIW sub-sample and using total income show a decline of approximately 21% (six percentage points). The differences between the true aggregate series and the constructed "aggregate" series are due to (1) sampling techniques for the SHIW; (2) our selection criteria in creating the quasi-panel; (3) the relative size of the various cohorts within our sub-sample. What most matter is that both series show a declining trend and an analogous drop in absolute terms. Hence we conclude that the sub-sample of the SHIW dataset we focus on is informative with respect to our objective. When we consider the "aggregate" series obtained from the SHIW sub-sample and using labor income we have a larger drop. The saving rate goes from 0.119 to -0.0004%, hence giving rise to a percentage reduction of approximately 100% (12 percentage points drop). This implies that in 1995, at the aggregate level, agents are consuming as much as they earn in terms of labor income. Given that the actual 16 saving rate is positive, they are saving out of non-labor income. But notice that this is just an aggregate result, which hides the fact that, even when denned in terms of labor income, the saving rate varies with age and shows across cohort-sector-education variation as well. In the remaining part of our thesis we focus on the saving rate defined in terms of labor income. A "strong" way to reconcile the aggregate and the micro data for the U.S. is the one followed by Gokhale, Kotlikoff and Sabelhaus (1996). They match National Income and Product Account (NIPA, the aggregate data) with Consumer Expen-diture Surveys (the micro data) to derive measures of cohort specific consumption and resources. Then, by recognizing that with homothetic preferences each cohort's consumption is proportional to the present value of its remaining lifetime resources, Gokhale et al. can perform counterfactual exercises by simply changing the amount of resources of the various cohorts (which include social security as well as the present value of Medicare and Medicaid services). A similar procedure could be followed focusing just on survey data by creating cohort averages and hence avoiding the matching between the two types of datasets. In this case it would be necessary to compute cohort averages for all the relevant variables (consumption rates, present value of future resources etc..) and analogous counterfactual exercises could be performed. This is the type of analysis conducted by Jappelli and Pagano (1998). At the present stage we just want to shed some light on the correctness of this type of exercise. Suppose that we focus on aggregate data obtained from survey data that are representative of the whole population of a country (such as the SHIW). As already mentioned, we can always decompose the aggregate saving rate in the following way g i=G i=G y = X) W i t y i t s r i t = 1 ~ WityitCTit f i=l i=l where G indexes the group over which we have taken the average consumption rate, wu represents the proportion of households in group i at time t (wu = 7^), yu is the ratio of average income in the i-th group compared to the overall average at time t (yu = and sru (crit) is the average propensity to save (consume) out of disposable income of the i-th group at time t. This decomposition is just an accounting exercise and, as such, should be used with care as far as policy conclusions are concerned. For instance, comparing the aggregate series of saving rates that would result from shifts in the distribution of income (keeping constant the age distribution and the average propensity to 17 save) is an acceptable exercise only as long as the income distribution is determined exogenously. Moreover this type of approach cannot help much when we want to test a causal relationship. For that we need to fully specify a consumption function. In Figures 7 to 12 we report the saving rate cohort profiles for the various groups (sector and education specific) computed for the years in which we observe them12. The picture shows a lot of variability. Following the same cohort through the various years, we notice that in some cases (and for some years) the profiles are rising while in others they are falling. This is someway expected, because the dynamics of the saving rate are a complex function of age, cohort, time effects and household characteristics which are possibly changing across the various groups. A step toward a more " structural" approach can be obtained if we assume that preferences are homothetic. In that case we know that era is proportional to the present value of lifetime wealth. The latter can be expressed both in terms of nor-malized age-zero values and in terms of the values that are computed with reference to the actual (average) age of group i in year t. The second approach is followed by Gokhale, Kotlikoff and Sabelhaus (1996). The problem with this approach arises from the fact that the present value of lifetime resources as of the actual age at time t includes the value of accumulated assets, which is an endogenous variable and hence would respond to changes in the exogenous variables (among which there is pension wealth). We prefer a different specification where consumption is expressed as a function of the present value of age zero lifetime wealth, which includes human and pension wealth. The previous decomposition can then be rewritten as St , f'?S rH(0)\ Rt(0) where ru(0) represents the present value (as of age zero) of the average lifetime wealth13 for cohort i at time i, rt(0) is the present value (as of age zero) of the average lifetime wealth at time t (r^ (0) = Rffi), where Rt(0) is the present value of total life time wealth (as of normalized age zero) at time t and Nt is the size of the population at time t, Yt is the value of total income (resulting from the aggregation of cohort average income at time £), and a# is the average propensity to consume out of lifetime wealth of cohort i at time t. 12Notice that srittot refers to saving rates computed using total income, while sritlab to saving rates computed using labor income. 1 3We have indexed this variable by t because we allow for time variation, for instance due to unexpected shocks to human or pension wealth. 18 In Figures 13 to 18 we show the behavior of the average propensity to save out of lifetime resources computed as of age zero (the variable is named sritrit, which corresponds to (1 — an)) for each cohort (and each sector and education group) in the various years in which we observe it. As we can see the pattern is consistent: in all groups for which we have more than one observation we observe declining profiles (with the exception of cohort 10 for Junior High School Graduates in the public sector and cohort 9 for College Graduates in the private sector). Still this picture is not sufficiently informative because we have not specified an explicit solution for the consumption function. If we do that, as in Chapter 3, it will appear that (even in a simple no uncertainty case) an is a function of many parameters and variables: the intertemporal elasticity of substitution, age, the interest rate(s), the discount factor(s), household's characteristics and possible interaction between those variables. What this means is that the behavior of an can be the result of age, cohort and time effects (besides their interaction) and household's characteristics. Before we perform counterfactual exercises (in which, for instance, we compare the aggregate profiles obtained under two different values of pension wealth), we should verify that such a consumption model is actually appropriate. Moreover we should be careful in extrapolating the results to periods that do not share the same information set. In the next chapters we specify a functional form for the consumption function, derive an equation for consumption rates that permits to separate age and cohort effects under the assumption that changes in pension wealth affect only the levels of consumption rates of the various cohorts (and not the age profile) and finally verify the hypothesis that pension wealth can explain the variation in consumption rates observed across cohorts. 2.4 Evidence from reduced form estimation We have already shown that the aggregate series obtained from the SHIW dataset (after having conditioned on the appropriate variables) is not inconsistent with the behavior of the aggregate series from National Accounts or OECD. It is likely that the same forces that tend to drive down cohort saving rates would also affect the aggregate series. To motivate empirically the choice of a cohort framework or, put differently, to show that there are (statistically) significant differences across cohorts, we regress cohort saving rates, one sector-education group at a time, on a cubic in age, cohort dummies, interactions between the cohort dummies and age (when significant) and the deviation of the unemployment rate from its trend (used to 19 capture cyclical components) according to src,g,t = S0 + F^g * 81 + ageCigttPi + (agec^t)232 + (agec^tf (3Z +1? * ut + ec>g>t (2.1) and src,g,t = 60 + F^g *61 + agecg^ + (agec,g<t)2f32 + (ageCtg>t)3/33 + (2.2) (Fc,g * a9ec,g,t) *6 + tf*ut + €Cjgtt where g refers to groups (defined in terms of sector and educational attainment) and c indexes the cohort within the group. FCt9 is a vector of cohort dummies that are also group specific and ut is the deviation of the unemployment rate from its trend, assumed to be affecting all cohorts in the same way. We consider two different functional forms because we allow for cohort-group specific age profiles. Notice that individuals are defined both in terms of groups and cohorts. The dependent variable is the saving rate, defined as the inverse of the average propensity to consume out of income where income is either net total income or net labor income. An analogous definition of saving rate has been used in empirical work by At-tanasio (1994) and Attanasio and Brugiavini (1999). Having consumption and not income at the denominator makes it less variable across individuals (since consump-tion is less variable than income), and hence less dependent on extreme values. When estimating the age and cohort profiles for the different groups the first problem we face concerns age, cohort and time effects. When, in different years, we observe an individual specific variable, being it the saving rate or the wage, we do not know whether its behavior can be explained by ageing, by time or by specific effects that can operate at the cohort level. In many studies of the labor market it is believed that cohort effects matter, but the problem is how to identify them. The reason is simple: time (measured in years) is the sum of the age of an individual and the year in which he\she was born (his\her cohort). There is a perfect collinearity between the three variables. If we observed different individuals in a given year (hence "fixing" time) and we were trying to estimate the effect of ageing on saving rates, we would not be able to know whether the observed differences between individuals of different ages were due to ageing itself or to the fact that those individuals belong to different cohorts. If instead we wanted to follow the same individual though time (hence "fixing" the cohort) we would not know whether the changes in his\her saving rate are due to ageing or to time effects. 20 In our case we assume that the only time effects affecting all cohorts of a given group are cyclical effects (ut), and hence we interpret the differences in saving rates intercept as cohort effects14. One final note on the unit of analysis. Potentially we can think of either the in-dividual or the household as the basic unit of analysis. In the first case we pick the head of the household as our representative individual and we construct Equivalent Scale values for the variables that are defined only at the household level. Alterna-tively, we can think that the household is the reference agent. In the second case we would have to split the sample into singles and married couples and concentrate on the latter because ageing and marriage are related and if we did not separate the two groups we would have even more difficulties for separating age and cohort effects. Focusing on married couples has the drawback that it works only if the couples remain married forever. On the other hand, when we focus on individuals and construct (equivalent) consumption rates we let the Equivalent Scale mechanism take into account the changes in the household composition. We have conducted the estimation for both samples: (1) male head of households (full sample) and (2) households were the head is married (married couples). Here we present the results only for the larger sample. For each particular group, where the group is defined in terms of sector (pri-vate/public) and education (Junior High, High School and College Graduate), we pool together the observations of all the cohorts for all the years, and then we run the regression separately for each group. The results show that there are consistent patterns and differences across groups. We also find that the behavior of saving rates out of labor income follows closely the behavior of saving rates denned in terms of total income. For this reason we report only the graphs and the results that refer to the former. In Fig. 19 we report the estimated age profiles for the private and public sector (for the case when we do not allow for age-cohort interaction), while in Fig.20 we report the estimated cohort profiles for "Entry Saving Rates" denned as the value of saving rates at the time of entry in the labor market (for the cases in which we do not allow for age-cohort interaction). In Fig 21 we report the estimated cohort life-cycle profiles (referring to the ages for which we have observations) for the various cohorts (again not allowing for age-cohort interaction). Notice that in every figure the oldest cohorts are the ones on the right. 1 4We do not claim that we are actually identifying time, age and cohort effects. Under the assumption that the only common effect is a cyclical one, we interpret the cohort dummies as cohort effects. 21 To summarize the results (see Tables 1 and 2 for estimation when we do not allow for age-cohort interaction), we find the following. 2.4.1 Public Sector Employees, Full sample • College education: for none of the cohorts we find significant cohort effects, under none of the specification and for none of the definition of saving rates. • High school education: under (2.1) we find that the constant and the coef-ficients on the cohort dummies are negative and significant (a part from cohort 3) and they imply falling cohort profiles for "Entry Saving Rates", while under (2.2) we find that none of the coefficients on either the cohort dummies or on the interaction terms is significant. • Junior High school education: under (2.1) we find that the coefficients on the cohort dummies are significant only for cohort 6 and 7 (but there is almost significant evidence for three other cohorts), while under (2.2) we find that none of the coefficients on either the cohort dummies or on the interaction terms is significant. The significant coefficients on the cohort dummies are negative and imply declining cohort profiles for " Entry Saving Rates". 2.4.2 Private Sector Employees, Full sample • College education: for none of the cohorts do we find significant cohort effects, under any of the specification and for any of the definition of saving rates. When we allow for age-cohort interaction we find some evidence of declining Entry Saving Rates for the younger cohorts (but not significant at the customary level of confidence). • High school education: under (2.1) we find that the coefficients on the constant and on the cohort dummies are significant (a part from cohort 3 and 4) , while under (2.2) we find that the constant, the coefficients on all the cohort dummies and on all the interaction terms are (highly) significant. In both cases the significant coefficients on the cohort dummies are negative (implying falling cohort profiles for "Entry Saving Rates") while the coefficients on the interaction between cohort dummies and age are positive. • Junior High school education: under (2.1) we find that the constant and the coefficients on the cohort dummies are significant, while under (2.2) we find that the coefficients on all the cohort dummies are significant while only for 22 cohort 4 the coefficient on the interaction term is significant. In both cases the significant coefficients on the cohort dummies are negative and imply falling cohort profiles for " Entry Saving Rates", while the coefficient on the interaction between cohort dummies and age (for cohort 4) is positive. It appears that the statistical significancy of the decline in saving rate profiles across cohorts is concentrated in households where the head is a High or a Junior High School Graduate, and is particularly strong for workers in the private sector. Notice that we find evidence of age-cohort interaction only for High School Graduates that work in the private sector. One final note regarding the interpretation of the reduced form estimation. The purpose of this paragraph was to show that the cohort approach is an interesting and empirically solid way to look at the problem. In the remaining part of the thesis we will substantiate and interpret these findings in light of economic theory. 23 Chapter 3 The Theoretical Framework and the Explanatory Variables 3.0.3 The life-cycle model In this paragraph we present the life-cycle model used as the basis for the empirical analysis. It is a model widely used in the literature, for studying both consumption and labor supply in a dynamic context. The life-cycle model, in its deterministic framework, has been first fully developed by Modigliani and Brumberg in the 50's (Modigliani and Brumberg (1954)). It is mainly a model created to explain individual behavior. In its simplest form it assumes that agents have finite lives and that they face no uncertainty. Moreover, the certainty assumption is often coupled with the perfectly competitive markets assumption. This means that there are no credit constraints and hence that the per-period budget constraints can be summarized in a single life-time budget constraint where the present value of consumption is equal to the present value of the flow of future income plus initial wealth1. One of the reasons for such a widespread fortune of the deterministic approach with perfect capital markets is that, under homothetic preferences, consumption at a given age is a fraction of the present value of the income stream that a person will receive in his life. In subsequent years the model has been extended and developed in stochastic and infinite life environment, to study the behavior under uncertainty and/or the time series of aggregate data2. 1If we introduced credit constraints, there would no longer be a unique budget constraint and, depending on the form of the imperfection in the capital market, we would have to specify the optimizing problem in a more complicated fashion. 2See Deaton (1992) for a detailed survey over consumption. 24 In our analysis we maintain the assumptions of finite lives, complete certainty and absence of credit constraints but we think of the model as applying to cohorts. In the next paragraph we present formally the model and discuss its implications for the analysis of saving rates. 3.0.4 The Consumption Function We choose to present the solution to the agent's optimization problem in terms of consumption and not in terms of either assets or saving rates. Those can be immediately obtained once we have the solution for consumption. Agents (cohorts belonging to the different sector-education groups) live T + 1 periods and have the following preferences with Ubc>g(t),CCt9(t)) = 7 c J t ) ^ ^ where a < 1 and 7Cje(i) is a cohort-group specific taste snifter at time t. The intertemporal budget constraint is given by ^ ( o ) + E ^ ( o ) = $>cClff(i) o o where St = 1/ [(1 + n) (1 + r2) (1 + rt)\ and ACi9(0) represents initial as-sets. Ln terms of our problem, we can think of Yc<g(t) as being either labor or pension income. For instance, in a three period model where agents work for the first two periods and retire in the third one, the lifetime budget constraint would be Ac,g(0) + YCi9(0) + SiYCt9(l) + S2Pc,g{2) = ACig(0) + HWc,g(0) + PWc<g(0), where HWCt9(0) = YCtg(0) + SiYCtg(l) represents human wealth and PWc<g(0) = S2YCig(2) refers to Social Security (pension) wealth3. Notice that WCtg(0) = HWCig(0)+PWc>g(0) + ACtg(0) represents the present value of lifetime wealth as seen from age zero. Given our assumptions we can solve the problem in more than one way. We could choose to characterize the solution in terms of Frisch Demand functions or we could just express it in term of all the explanatory variables (among which we have the present value of lifetime wealth). The choice in general depends on the 3Note that we are using real values. 25 question asked. If we are interested in studying the profiles for consumption levels, the Frisch Demand function approach is more elegant, while the reverse is true if we are interested in studying consumption or saving rates. Given our objective we use the second approach. Still, this allows us to represent the solution at least in two ways4. • In terms of the Present Value of lifetime wealth as of age zero. The first order optimality condition for consumption at age at in year t is given by (T^yU'(CCt9(at)) = \c>9(0)St where AC j e(0) (the Lagrange multiplier) represents the marginal utility of wealth as of age zero for cohort c and group g and is hence a function of parameters and of the factors affecting the present value of lifetime wealth. By substituting the first order conditions in the budget constraint we can express CCj9(at) as a function (besides other variables) of WCt9(0). • In terms of the Present Value of lifetime wealth as of age u>, where u> is the age at which individuals optimize. The first order conditions are / 1 \at-ut [Y^P) U'(Cc,g(at)) = XCt9(ut)St As in the previous case we could substitute the first order conditions into the lifetime budget constraint (expressed from age at onwards) and we would have CCt9 as a function (besides other variables) of Wc^(ust), the present value of remaining lifetime wealth as seen from age u>t (which would include accumulated assets). Notice that, with constant real interest rates, we have the following relationship between AC ) 9(0) and Xc,9(uJt) for the same cohort: The Lagrange multipner as of age s (s = 0, u>t) is a function of the assets existing at time s and of the stream of labor income and pension benefits5. To compare 4Prom now on we will think of time as age and hence use a instead of t when indexing variables that have an age representation. Real interest rates will be still indexed by t because they are common to everybody in the same year (they will affect differently individuals depending on their age) 5The more an individual ages and the more (1) he faces a lower present value of human wealth (just because he has less working years) and (2) he faces higher values of net pension wealth (because he approaches retirement). 26 across cohorts the intercept and the coefficient(s) on the slope of the consumption rate profiles, we have to make a normalization of the age at which we operate such a comparison. Notice that Xiig(u>t) and Xjtg(0) are not directly comparable across cohorts zand j (even within the same group) and neither are WiiQ{ut) and Wj)9(0), because they refer to lifetime wealth as seen from different ages. We choose to normalize everything as of age zero6 (s = 0), where age zero is de-fined as the age at which the various sector-education groups enter the labor market (20 for Junior High and High School Graduates and 25 for College Graduates). By substituting the first order conditions into the lifetime budget constraint we obtain the following expression for consumption by a representative individual belonging to cohort c of group g at age at CCAAT) = {^M) ^ ^ *^(0)^(0) {3A) Notice that we have imposed the condition that all the cohorts share the same discount rate. While this is someway arbitrary, we have to remember that: (1) we cannot directly identify the discount factor from other cohort related effects and (2) the challenging economic problem is to be able to explain cohort differences in terms of observables. The variable ^ ^(O) is a function of the real interest rate, the discount rate, the parameter a affecting the curvature of the Utility function and the sequence of taste shifters ^ycg(0)....'yc>g(Dfj, where D is the age of (expected) death. The consumption rate is obtained dividing the left and the right sides of the equation by the value of income at age at. We express consumption rates in terms of net labor income w^g(at) (in order to avoid the endogeneity problems that would arise if we considered the return on assets) and so, after taking logs, we obtain In 'CCig(aty 1 - a In i + i ^ K r r £ ) . at+ln*Ci9(0)+ln Wc,(0) wc,g(at) (3.2) The main result of our theoretical model is that we can express consumption rates in terms of age, cohort dummies, household's characteristics, the interaction between age and household's characteristics and the ratio of lifetime wealth to the 6Notice that the choice of the reference age does not imply assuming that individuals choose all the path for consumption as of age zero and never change it thereafter. It is only a reference point and agents are allowed to re-optimize if new informations are delivered to them. 27 real net wage received at age at. We now look more thoroughly at the various elements of the previous expression. • The term In (^c , g^) refers to household's characteristics at age at (in year t) relative to those at age zero (we interpret this as normalized household's characteristics). The term lis m ( a * P^c^s UP * n e l i n e a r contribution of age. • The term In \PC)9({)) is a function of r, a, p and the sequence (~/cg(0)....'ycg(D)Sj . Potentially this term hides cohort-age interaction if the relevant household's characteristics show a cohort dependent age profile. • The term In W°'l^ refers to the ratio of the present value of lifetime wealth to the value of net labor income at age at. This term as well could exhibit cohort-age interaction, in the event that the age profiles observed in the labor market were cohort dependent. The latter is a fundamental point which deserves a thorough treatment. Suppose that, focusing on a group at a time, we can write the (net) wage as a multiplicative process between an age function and a cohort effect (both specific for that group), analogously to7 wc,g(at) = »c,g*9g(at) where ficg is a (group dependent) cohort effect and gg(at) is a group specific poly-nomial in age. Then, the value of net human wealth for cohort c belonging to group g (as of age zero), defined as NHWCig(0) (equal to the present value of lifetime net wages under the assumption of a discount factor equal to zero), could be written as k=R NHWc,g(0) = / i C ) f l * £ gng{ak) where Jf? refers to retirement age. As for pension wealth, suppose that we compute the value of the first gross pension benefit that applies to cohort c of group g (PCyg(R + 1)). Then we can 7Analogous results hold if we adopt a functional form where the log of wages is separated into cohort effects and a polynomial in age. In both cases we are able to express human wealth as a combination of two separate age and cohort profiles. 28 express (implicitly) the replacement rate between the first pension and the last wage as in the following equation8 PCig(R + l) = 6Ci9*wl(R) (where 6Cig is the replacement rate and w^(R) is the gross wage received in the last working period prior to retirement). If we assume that retirement age does not change across either cohorts or groups, different cohorts of the same group will experience different values of 5c>g either if the rules determining pension benefits change or if the age profile for wages varies across cohorts. For instance, let's suppose that, within the same group, two different cohorts experience the same value for the wage cohort effect ( C^tg) but the younger one has a higher age profile for the first four of the last five years before retirement (so that the two cohorts share the same final wage). If the pension benefit is based on an average of the last five years, the younger cohort will have a replacement rate higher than the older one. Symmetrically, if two cohorts (of the same group) share the same cohort effects and the same age profiles for wages, but the younger one experiences a more generous pension system, we would observe that the younger cohort has a higher replacement rate. This means that (within the same group) differences across cohorts in the values of 8c,g can be traced directly to differences in pension legislation or indirectly to differences in the labor market performance. It is then clear that, when comparing across cohorts (and groups) the generosity of the Social Security system, we cannot completely separate the latter from the performance in the labor market. The two are linked because the generosity of the pension system is defined given a particular life-cycle profile for wages9. The attempts to separate the effects of changes in pension legislation from those arising in the labor market are greatly simplified if we can show that the cohorts' wage profiles can be separated into a cohort and an age effect10. In this case we exclude one source of variation in the value of <5Ci9, since we impose the condition that all the cohorts within a group share the same age profile. 8This approach is very natural when the law itself, in determining pension benefits, refers to an average of past wages (as in the Pre Amato and Amato regimes). But it can be adopted also when the formula used to compute the pension benefit is based on past contributions. 'However, notice that, for the same cohort, we can always compare the generosity of the Social Security system under alternative regimes (assuming that the performance in the labor market is not altered). 10Notice that two are the relevant wage processes. The first one is for net wages (relevant for the computation of net human wealth), while the second one is for gross wages (relevant -at least for Italy- when computing gross pension wealth). 29 Assiiming that such a separation is confirmed by the data11, we can write net pension wealth (as of age zero) as NPWCtg(0)= £ NPc,g(kt) = 6c,9*(l-Tc,g)* E <,(*) = k=R+l fc=fl+l = Sc,g * (1 - rc,g) * vc,g *(D-R)* g$(R) (3.3) where uCt9 is the group specific cohort effect for gross wages (which normally differs from fJ-c<g), (1 — rc > f l) is the average income tax rate on pension benefits and g^(R) is the age component for gross wages computed for the year of retirement. This expression summarizes the different forces affecting the value of pension wealth: the generosity of the system in computing pension benefits, conditional on a given wage path (Sc<g); income taxation after retirement (1 — rC)<,); the wage path (vc,g * 9g(R))', the time interval between retirement and (expected) death (D — R). We are now able to express total wealth (as of age zero)12 as Wc<g(0) = NHWc>g(0) + NPWc,g(0) = k=R = M c , 9 * £ 9ng(k) + 6c,g * (1 - rc,g) * vCt9 *(D-R)*gl(R) (3.4) fc=0 so that the total wealth to labor income ratio becomes ^k=R V o ^ y . i u - T c < g ) * i/c<g Mco 9n(at) < > t ) 9n(at) (l-TCtg)*vCig 6c>g*(D-R)*gl(R) lc,g (Gg + BC>g) (3.5) where represents the age profile for net human wealth (which is common across cohorts of the same group but differs across groups), and _ (1 -Tc,g)*vc,g c,g * (Sc,g *(D-R)* (fgiR)) Bc.a = is the cohort-age profile for pension wealth (which differs both across cohorts and groups). Notice how Bcg depends on ^1~T c'g^*1 / c , g which is the ratio of the (group n This assumption is confirmed for most groups. See Appendix A. Note that at this stage we are excluding age-zero assets because we want to explore at full lenght the issue of pension wealth. Assets will be considered in Section 10. 30 specific) cohort effects for gross and net wages, multiplied by one minus the average tax rate paid on pension benefits. This variable captures how income taxation affects cohorts over the life-cycle. In fact, given the proposed wage process, we can write Vc,g = (1 - Kg) * vc,g where tCj9 is the average income tax rate for cohort c belonging to group g at the beginning of his working life. This leads us to write (1 ~ Tcj) * vc,g = (1 - T C | g ) Vc,g (1 - Kg) which describes how (on average) income taxation is distributed over the life-cycle. Given (3.5) we can rewrite (3.2) as l n f ^ 4 U l n G 0 + l n ,wc,g(at)j 1 + Gg + In _ l _ a - n . ~, i (3-6) This result is important because, under the assumption that we can separate out a cohort and an age profile for wages, we obtain that the effects of Social Security on consumption rates operate through the ratio -Q 3-- This is the ratio between pension wealth and human wealth, both computed as of age zero. We will explore more in depth in the next chapter how to make this variable comparable across groups and cohorts that experience different retirement ages, but the important result is that the distribution of wealth over the life cycle affects (log) consumption rates only at the intercept. The possibility of expressing in just one number the distribution of wealth over the life cycle is very appealing because we would have a multicollinearity problem in trying to estimate separately the marginal effects of net human and pension wealth. The two variables are in fact very highly correlated, due to the method used to compute the first pension (which is an average of past wages). This result also implies that when we estimate the equation for consumption rates one group at a time, regressing the natural log of consumption rates on cohort dummies, an age profile, cohort-age interaction and household characteristics, we can interpret the estimated coefficient on the cohort dummies as potentially explainable by the ratios of net pension to human wealth. Notice that by estimating the previous equation one group at a time we lose one source of variation but we gain in simplicity because the differences across cohorts should be explained by differences in the ratio of Old to Young Age Wealth 31 The choice of the reference age does not imply assuming that individuals choose all the path for consumption as of time zero and never change it thereafter. It is only a reference point and agents are allowed to re-optimize if new information are delivered to them. We can always represent their choice from the standpoint of age zero or of any other age. What is important is that in the estimation we use only the years in which the information set is the same. For instance, say that we compare the fixed effects of the same cohort before and after a reform affecting pension wealth has taken place. We observe this cohort for four consecutive years, three of them before the change and one after. The assumptions about the information set drive the estimation procedure. If we assume that the cohort has perfect foresight and hence that, at every observation in all the four years, it knows exactly the actual value of pension wealth, we can use all the four years and estimate the fixed effects at one time. Instead, if we believe that the cohort was completely surprised by the changes that occurred at the end of the third year, we have to estimate separately the fixed effects before and after the reform. The fixed effects before the reform will be estimated using only the observations pertaining to the period prior to the reform (the first three years) while the fixed effects relative to consumption chosen after the reform has taken place will be estimated using only the dataset pertaining to the period following the legislative changes (the fourth year). In both cases we can estimate cohort fixed effects as of age zero. But they would reflect different information sets. The model presented, per se, just implies absence of credit constraints and no uncertainty. It does not tell us anything about the information set. We consider two alternative cases: Perfect Foresight and Complete Surprise. Under the Perfect Foresight hypothesis, agents, when choosing consumption, know (the means) of all the relevant variables, which in our case are: the wage profile, the pension profile, the structure of the household etc.13 Under the Complete Surprise assumption, agents assume that what they observe will go on forever. If there is a change in the environment, they immediately adapt their information set and assume once again that the new environment goes on forever14. 1 3We do not introduce general equilibrium conseguences of Social Security. 1 4The relevance of these two approaches will become clearer when we talk about the changes in pension legislation that were carried out in Italy in the early 1990's. 32 3.1 Pension Legislation in Italy Italy has recently witnessed some major changes in the rules governing the public pension system. In this paragraph we summarize the most important ones. For a more detailed description see Appendix A. Public pension systems can be organized according to two basic principles: Pay As You Go and Fully Funded. According to the PAYG structure, an individual pays taxes when working and receives a benefit when retired. Pension benefits of retirees are financed by the payroll contributions of current workers. It is the law that specifies the way in which pensions have to be computed. They can reflect past wages, past contributions or just basic needs. The choice of defining the functions of pensions in a PAYG system is mainly political and it could be difficult to interpret such a system in pure individualistic terms. It is not obvious that workers perceive payroll contributions as forced saving, the returns of which (plus the capital) is given back at the time of retirement. Workers know how much they are contributing and have certain expectations about how much they will receive at the time of retirement, but those expectations are expectations about the behavior of the Government. At the end it is the Government that guarantees the inter-generational contract implicit in a PAYG system. Typically, two kinds of rules have been followed by Governments when choosing the value of pensions within a PAYG system. The first one is an earnings based method (metodo retributivo), according to which the (first) pension is a function of past wages and years of contribution. This rule stresses more the income smoothing function of Social Security, according to which the main function of pensions is to guarantee an income stream that is not too different from the one experienced during working life. The second (metodo contributivo or "contribution based method") stresses the insurance component of Social Security, linking benefits to contributions, which could be real or fictitious. It is not (necessarily) the case that the present value of benefits is equal to the capitalized value of all payroll contributions paid by the individual during his work-life, but there is a closer relationship between what is paid and what is received. In both cases the total amount of resources to be transferred to the elderly are given by the total amount of payroll contributions collected from those who work. Hence both suffer from adverse demographic or economic trends. Conversely, in a Fully Funded system, an individual is forced (if the system is compulsory) to save a certain fraction of his wage, which is administered by a fund 33 and then given back (principal plus returns) at the moment of retirement (it is paid out as an annuity over the years after retirement). The relationship between contributions and benefits is clear and perceived as such by individuals. It is also obvious that there is only one way to determine the value of (annual) pensions in this system. They are equal to the principal (past contributions to the system) plus interests, divided by the life expectancy at the time of retirement. From 1969 to 1992 Italy was characterized by a Pay as You Go regime using an earnings based method, that we call Pre-Amato. In 1992 a first reform was implemented (the Amato reform), changing slightly some rules governing retirement but still maintaining the basic Pay as You Go structure and the earnings based method. In 1995 a second reform, the so called Dini reform was implemented. The Dini reform changed the way in which pension benefits are computed, from an earnings based to a contribution based method, however maintaining the Pay As You Go structure. Both reforms provide a temporary regime whose logic is the following: the longer an individual has worked under the previous legislation, the less his/her pension will be far away from the one he/she would have received under the old regime. We will now review the basic rules governing retirement under the Pre Amato and the Amato regimes15, focusing exclusively on Old Age Pensions (Pensione di Vecchiaia). Most private sector pensions are managed by the Istituto Nazionale di Previdenza Sociale (INPS), and, within the latter, by a fund called Fondo Pensioni Lavoratori Dipendenti (FPLD). There are some differences between occupations (pertaining more to the tax side) but the rules governing pensions are basically the same for the whole private sector. As for public sector employees, there are two major differences. The pensions of State employees are managed (and partly governed) by the Treasury, while those of the other employees (local public sector employees) are managed (and partly governed) by an independent Institute (INPDAP). The rules governing pensions in the two funds are slightly different. Under the Pre-Amato regime, retirement age was 60 for males in the private sector, 55 for females in the private sector, 65 for males and females in the public sector. The Amato reform raised the retirement age for workers in the private sector to 65 for males and 60 for females, to be realized starting from 1993 by increasing it by one year every two calendar years. The Dini reform confirmed the raise but allowed flexibility between a minimum (57) and a maximum age (65). People retiring 15See Appendix B and the Thesis for a more elaborate discussion of the rules governing retirement in Italy. 34 earlier would just be getting lower pensions. The Pre-Amato regime guaranteed high replacement rates between the last wage and the first pension (with a maximum of 80% if a worker had contributed for 40 years). It also benefited workers that experienced a steep wage profile at the end of their working life because of the method used to compute the average of past wages (the Retribuzione Pensionabile). This was obvious in the case of public sector workers. The Retribuzione Pensionabile was the last wage, augmented by 18%. But also for private sector workers the averaging, being only on the last five years before retirement, ended up favoring the steepest careers. The positive relationship between the steepness of the wage profile and pension benefits was only partially offset by the fact that the coefficients used to compute the first pension were decreasing in the value of the Retribuzione Pensionabile. As for indexation, the Pre-Amato regime guaranteed indexation to prices and to real growth in the manufacturing sector, but it protected low more than high pensions. The Amato reform affected the value of the Retribuzione Pensionabile extending the number of years over which the average had to be taken. The change was stronger for younger workers (those who had less than 15 years of work experience as of 31/12/1992). It also limited indexation to inflation only. The Dini reform confirmed the rules introduced by the Amato for the oldest generations (those who had more than 18 years of experience as of 31/12/1995). It also reduced the value of pension benefits for those who would start working in 1996. As for those who had already started working as of 31/12/1995 but had less than 18 years of experience, it introduced a mixed system in which elements of both the earnings and the contribution based method live together. 35 3.2 Estimation of Pension Wealth and Human Wealth The estimation of the present value of net labor income for each cohort requires knowledge of future and past wages for each representative agent and group. We have data for seven years and information only on net annual wages at the individual level. To compute the Retribuzione Pensionabile we need gross (of income and social security taxes) wages. In the next paragraph we explain how we construct the entire life profile for (net and gross) wages, starting from the observed value for an individual in a given year. It is important to notice that the results obtained at this stage will drive all the subsequent steps. The present value of net labor income and the present value of pension income can be obtained only if we know the age profile for wages (net and gross) for each individual agents (or cohort). 3.2.1 Estimating life-cycle profiles for wages For wages16 we have the same problem that we had for saving rates. Cohort, age and time are perfectly colunear. Given this basic identification problem, we make the assumption that the only time effect common to all cohorts is cyclical and it is captured by the deviation of the unemployment rate from its trend. Hence we interpret the coefficients on the cohort dummies as "Entry Wages". In the estimation we use two strategies. According to the first one, we take the individual observations and we use them directly in the wage regression. The second strategy utilizes individual observations to create cohort averages and then runs the wage regression on the latter. Given that the number of observation is not very large, especially for College Graduates and for women, when we use cohort average wages we cannot condition on many variables. For instance, it would be interesting to follow the wage of (representative) College females working in the public sector as white collars and living in the South. We simply do not have enough observations to do that. When we use individual data we have more freedom because we can allow for occupational (White-Blue Collar for workers with High and Junior High School education and Manager for workers with a College degree) and area dummies (five areas for North-West, North-East, Center, South and Islands) that are not year-dependent (which is not possible in the representative worker framework). Hence we estimate a (log annual) wage regression for each sector-education group with the following explanatory variables: a cubic in age, cohort dummies, a dummy for the 1 6 In our framework wages coincide with yearly labor income. 36 type of occupation, four dummies for the area and the deviation of the unemployment rate from its trend to capture cyclical effects. In both cases we run the regression separately for each group (where the group is defined in terms of sex, sector and education) and we test whether there is evidence of cohort specific age profiles17. The results obtained using cohort averages show signs of significant age-cohort interaction for male Junior High and High School Graduates in the public sector, for male Junior High Graduates in the private sector and for female Junior High and High School Graduates in the private sector. When we use individual data, we find significant evidence of age-cohort interac-tion only for male College Graduates in the public sector, for most cohorts of male Junior High School Graduates in the private sector, for very few cohorts of female Junior High and High School Graduates in the private sector and for most cohorts of female College Graduates in the private sector. The coefficient on age-cohort interaction is negative in all cases but the one for female College Graduates in the private sector, for which the sign is positive18. We also verify that when we drop the age-cohort interaction term the explanatory power of the regressions is affected in only a minor way. These results, and particularly those that refer to individual data, make us quite confident in constructing life-cycle profiles using the age coefficients obtained from the estimation that does not include age-cohort interaction. The results from log (annual) net wage19 estimation at the individual level are reported in Tables 3 and 4. The estimated cohort Entry Wages and age profiles (for the various groups) are reported in Figs. 22 to 25. To compute human wealth we need to construct the full life-cycle profile for wages for any individual starting from its observed wage in any given year. This means that we first have to find the coefficients that describe the evolution of wages as an individual ages. Once we have those we can go back to the wage observed in a give year and, for each individual, we can compute the series of future and past wages from starting age to retirement. If wages are a function of a cubic in age, cohort dummies, a dummy for the type of occupation, four dummies for the area and the deviation of the unemployment rate from its trend, the full life-cycle profile can 1 7We have conducted estimation for both net and gross real wages (relevant when computing pension benefits), using the CPI as our deflator. The reference year is 1990. A negative coefficient means that for more recent cohorts an extra year of experience increases labor income by less. 19These Tables refer to net wages. Analogous Tables referring to gross wages can be obtained form the author upon request. 37 be obtained with a recursive model that starts from the observed wage (after having controlled for the year effect) and computes the next element of the (backward or forward) recursion by applying the estimated age coefficients on the change in age, age squared and age cube lnwjt±i = Inwjt + 8X * (ajt±1 - ajt) +{33* (o 2 t ± 1 - a?jt) + /?4 * (a3jt±l - a%) The retirement age at which we end the process depends upon the assumptions made with respect to forecasting at the individual level20. Hence we compute the wage profiles under different assumptions. First under the assumption that agents know exactly the retirement age at which they will actually retire under the regime that will apply to them. Then we have assumed that agents are myopic and computed the human wealth profile as if retirement age were the one prevailing under the Pre-Amato regime. The normalized age chosen to estimate the fixed effects has to be the same one that we use when we fix the first element of the individual age profile. For instance, if we assume that fixed effects should be computed as if agents maximized from the standpoint of a 40 year old, than the value of human wealth should be computed as of the standpoint of a 40 year old as well. Given that we choose to normalize at the age of entry in the labor market21, human wealth and pension wealth should be computed as seen from that age as well. 3.2.2 Constructing Pension Wealth and Human Wealth Profiles The results that we present in the next paragraphs are based on the estimation that uses individual data. Once we have obtained the whole life-cycle profile for each individual (under the two different assumptions regarding retirement age), the task of computing the variable human wealth (as of age zero) is quite simple because we just take the present value of the whole series (for each individual) applying a discount rate (that we fix at 10%). The computation of pension wealth is a complex task. The first problem arises from the fact that the Retribuzione Pensionabile used to determine the first pension is based on gross wages, which are not available in our dataset. Hence we construct them doing a sort of reversed income tax computation. The major problem at this 2 0In the previous paragraph we have described how changes in the legislation affected retirement age of private sector workers (retirement age for public sector workers has not changed). 2 1 Normalized age-zero corresponds to age 20 for High School and Junior High Graduates and to age 25 for College Graduates. 38 stage comes from the fact that the Italian income tax schedule is progressive, and hence that the average tax rate is not independent from the (observed) net wage22. To assign individuals to their actual income tax bracket, for every year and every individual, we start from the declared net income and assign the individual to the tax bracket that would be appropriate if net and gross income coincide. Then, using the information on the household, we compute the resulting due tax and net income. If net income resulting from this computation is different from the observed net income we reassign the individual to a higher tax bracket. This goes on until the computed gross income is consistent with the observed net income and the tax schedule. Then, to compute gross annual wages net of Social Security taxes we just divide the observed net annual wage by one minus the average income tax rate. Finally we take account of social security taxes and we obtain gross wages. With these at hand we do the same as for net wages. We estimate an equation for log gross wages using individual and cohort data. Then we apply the (estimated) coefficients for the age polynomial to the gross wage (constructed) for each individual in the dataset and we obtain the whole life path for each individual. This is then used to compute the first pension. Once we have the first pension we apply the indexation mechanisms and the rules that fix a maximum and a minimum to pension benefits and we get the whole series of pension benefits up to expected death. Then we take the present value of such a series using a discount rate of 10% per year and we obtain pension wealth (as of age zero). The choice of doing these computations at the individual level rather than at the cohort level is due to the presence of non linearities in the formula used to compute pensions. Allowing the greatest amount of diversification among individuals can be useful in the identification process. Once we have the value for pension and human wealth for each year and every individual, we put together all the years in which a cohort appears and compute the average value for each sex-age-sector-education group (using sample weights). We focus only on the sample made of male head of households because only by looking at them we can really understand the changes at the individual level following from the reform of the pension system. 2 2If this were not the case than we would simply divide the observed net income by (1-average tax rate) and we would get gross income. 39 3.2.3 Private Sector Workers Pension Wealth Similarly to what we do for wages, we first compute the value of pension wealth at the individual level and then we compute its average value for every sex-age-sector-education group. We take the standpoint of a deterministic model and hence we assign to individuals the expected age of death as given by the Italian Statistic Institute (74 years for men and 80 years for women). We do not allow for across cohort differences in expected life-span. This might slightly underestimate pension wealth for more recent cohorts, if their life will turn out to be longer. We have computed pension wealth under different assumptions. In Fig.26 we compare the cohort profiles for the present value of pension benefits obtained under the assumption of, respectively, Perfect Foresight and Complete Surprise. • Identification Assumption: individuals forecast according to the Perfect Foresight Hypothesis (which include the Amato regime for those who retire after 1993) Under this assumption, for those who retire prior to 1992 we estimate pension wealth according to the Pre-Amato regime, while, for those who retire after that year, we apply the temporary and permanent regimes introduced by the 1992 Amato reform. We do not consider the possibility that agents forecast according to the second reform that took place in 1995 (the Dini reform), given that the last dataset was collected in 1995. • Identification Assumption: individuals forecast on the basis of the existing regime: Pre Amato from 1984 to 1991 and Amato in 1993, and they are surprised by the 1992 reform (Complete Surprise) The real issue is whether in 1984, 1986, 1987, 1989 and 1991 agents are able to forecast changes that occur in 1992. Hence we compute pension wealth under the no-reform scenario as well. This is useful when we estimate the model under the assumption of myopic behavior, which means that from 1984 to 1991 agents forecast pension wealth according to the Pre-Amato regime and they are completely surprised by the Amato reform of 1992. In this case we have to use only the years to which the identification assumption refers: 1984-1991 for the Pre-Amato period, 1993 for the Amato reform. We want to stress the differences between pension wealth as estimated according to the Pre-Amato regime (agents do not forecast the reform) and pension wealth as 40 estimated according to the combination of Pre-Amato and Amato regimes (agents forecast taking into account the reform). For the private sector, pension wealth, as computed according to the Pre-Amato regime (npwnoref, corresponding to the Complete Surprise hypothesis), is always higher than pension wealth computed according to the combination of Pre-Amato and Amato (npwamato, corresponding to the Perfect Foresight assumption). This is due to various factors: (1) for the private sector retirement age is higher under the Amato regime and hence the number of years during which an individual receives the pension is lower23. The effect is higher for younger cohorts because they are the one that will retire at 65; (2) the formula used to compute the Retribuzione Pensionabile is more generous under the Pre-Amato regime24. Then, within the Amato regime, it is more generous for older cohorts (more than 15 years of working experience as of 31/12/1992); (3) indexation is more generous under the Pre-Amato regime. The fact that retirement age in the private sector is increased by the reforms and that the Retribuzione Pensionabile is lowered also explain the declining portion of the cohort profiles when we assume Perfect Foresight. In fact we see that the profiles for pension wealth have a convex shape. This is due to the fact that for more recent cohorts retirement age has reached the upper limit and -keeping this constant- younger cohorts are more productive than older ones. The gain in productivity is quite evident when we observe the cohort profiles under the Pre-Amato regime. For each individual the " Retribuzione Pensionabile" is just a weighted average of past wages and hence it reflects the estimated age and cohort profiles for wages. Since we estimate those profiles assuming that for each sex-sector-education group there is a unique age profile, under the assumption of constant legislation pension wealth differs across cohorts basically only in the value of "Entry Wages" experienced by the different generations. For the Junior High Graduates group, pension wealth profiles raise smoothly and, given that there are no changes in legislation, this is due to higher productivity 23Note that the Amato reform increased retirement age by one year every two calendar years starting from 1995. 2 4This is true if real wages are monotonically rising through the life-cycle, because the Amato reform extends the number of past wages to use in the computation of the Retribuzione Pensionabile. If real wages were declining towards the end of the life-cycle, as it is for Junior High School Graduates in the private sector, then the Retribuzione Pensionabile under the Amato Regime could end up being higher than the one computed under the pre-Amato regime. Even in this case we could observe a lower value for Pension Wealth under the reform just because of the change in the indexation mechanism (a part from the retirement age effect). 41 which is then translated into higher wages25 and hence higher pensions. For workers in the private sector that have completed High School we can ob-serve that the cohort profile under the Pre-Amato regime is not smoothly rising. Particularly we can see that cohort 4, 5 and 6 show a very small decline in pension wealth (compared to previous cohorts). As for College workers, we have more variability, still with an overall raise of the cohort profile under the Pre-Amato regime. The wider variability in this case is mostly due to the lower number of observations in each year. Human Wealth We constructed the profiles for this variable according to the same identification as-sumptions used for pension wealth: Perfect foresight and Complete surprise (Fig.27). By comparing Fig.2726 to Fig.24, we can see how cohort effects estimated at the level of net wages are translated into the shape of the cohort profiles for human wealth. For Junior High Graduates we find significant and positive cohort effects for all generations (except for the last), which imply a growing "Entry Wage" cohort profile (excluding the last cohort) that is matched by the shape of the "human wealth" cohort profile. We also find evidence of a decline in entry wages (compared to the previous generation) for cohorts 4, 5 and 6, and this is confirmed as well in our "human wealth" cohort profile. When we compare the values for the Net Human Wealth profiles under the two identification assumptions, we see that the retirement age effect shows up (and hence raises the human wealth cohort profiles) but less than in the case of pension wealth. This is due to the fact that an increase from 40 to 45 as the relevant years of working experience is less, in percentage term, than a decrease from 14 to 9 (the number of years spent as retirees under the two regimes). We observe that the human wealth cohort profiles under the Complete Sur-prise assumption (hcnoref) are below the profiles obtained under Perfect Foresight (hcamato), for every cohort (but the first one, which is not affected by the Amato reform), irrespectively to the education attained. 2 5 According to our estimation of gross wages that uses individual data. 2 6In Fig.27 the triangles refer to the present value of wages under the "complete surprise" iden-tification assumption, under which there are no changes in retirement age between 1984 and 1991. 42 3.2.4 Public Sector Workers The Amato reform did not affect retirement age in the public sector, which remains constant at 65 for both males and females. It is true that in this sector there have been incentives and ways to obtain early retirement, but we choose to stick to the general rule for Old Age Pension. The absence of a retirement age effect is such that, at the individual level, the stream of pension benefits tend to follow closely the life path for wages. And this is particularly true for the oldest cohorts because the Pre-Amato regime based the computation of the first pension on just the last wage. Pension Wealth Under the assumption that agents forecasted according to the perfect foresight hy-pothesis we find that (npwamato in Fig.26), for High and Junior High School Gradu-ates, the "pension wealth" cohort profiles are rising. There is no evidence of a convex shape, as it was for private sector workers, because retirement age is not affected by the reform. The positive cohort effects obtained in the estimation for gross wages for most recent generations are confirmed by the rising "pension wealth" profile. As for College Graduates, the results seem to point towards a rising "pension wealth" cohort profile, but there is more variation, confirmed also in the results obtained from gross wage estimation. This is probably due to the smaller sample that characterizes this particular group. When we compare the profiles obtained under Perfect Foresight with those cor-responding to myopic expectations (Pre-Amato scenario), we find that the Amato reform had the effect of lowering the value of pension wealth for all the cohorts to which it applied. For a constant retirement age, all cohorts would be better off under the Pre-Amato regime. The spread between the two is a function of the steepness of the wage age-profile. The steeper is the latter and the more effective is the drop coming from having to use an average of past wages as opposed to just the last wage. Within each education group the effect is stronger for more recent cohorts because for them the average is taken over a longer period27. Taking into account all this, we can conclude that under both scenarios we have a clear pattern of rising pension wealth, for every education group. 2 7This seems to be contradicted by the graph for Junior High School, where for recent cohorts the spread is reduced. But this is due to a year effect and not to the reform. We have to remember that the two series are used using different years. For the perfect foresight case we used all the years in the dataset. For the complete surprise case we used only the years from 1984 to 1991, given that the Amato reform was implemented in 1992. 43 Human wealth Given that retirement age does not change and that we think in terms of partial equilibrium, the human wealth profiles are not affected by the reforms. This means that under both types of assumptions regarding the way in which expectations are formed we have the same human wealth cohort profile (see Fig.27). Human wealth cohort profiles are raising for the lowest education groups. The only cohorts that do not seem to do better than the immediately preceding ones are cohort 9 for Junior High, and cohort 2 and 5 for High School. Before we enter the stage of estimation of the fixed effects we have to notice two things that are important in our identification strategy. • Under perfect foresight the path of pension wealth for public sector workers has a shape that resembles very much the shape of the human wealth profile. This causes collinearity and would make extremely difficult to disentangle the effects of the two variables on the cohort effects. For private sector workers (combined with the assumption of perfect foresight) the Amato Reform affects the two variables in opposite ways, reducing pension wealth and increasing human wealth. • Under complete surprise, for public sector workers, the only effect of the Amato reform is to decrease the value of pension wealth. This can help in explaining the variation of age zero cohort fixed effects between 1991 and 1993 (before and after the reform). 44 Chapter 4 Estimation Part I Perfect Foresight 46 4.1 The model The estimation strategy depends on the identification assumptions. First we will concentrate on the perfect foresight case and then explore the complete surprise one. The starting point is the optimization process described in Chapter 3, which allows us to describe the natural logarithm of the consumption rate for any given cohort c belonging to group g at age at at time t as in (3.6), where, upon separating age and cohort effects in the wage process, pension wealth affects consumption and saving rates only through the ratio Our model implies that we can estimate the equation for consumption rates one group at a time, regressing the natural log of consumption rates on cohort dummies, an age profile, cohort-age interaction and household's characteristics, and it also implies that the estimated coefficients on the cohort dummies should be explained by the ratios of net pension to human wealth (%ia)- Our strategy is hence the following: • estimate (one group at a time) the regression where consumption rates are a function of household's characteristics, age, cohort dummies and age-cohort interaction in order to obtain group-specific cohort profiles for the estimated coefficients on the cohort dummies1; • test the hypothesis that the (across cohort/group) variation in those coeffi-cients can be explained by the across cohort/group variation in the values for the pension to human wealth ratio (% )^-To make the values of fully comparable across sectors and cohorts we con-struct a normalized retirement age, which we fix at age 60 for males and 55 for females. Then we create a variable called " Old age Net Wealth", which is equal to the sum of net pension wealth and the part of net human wealth received after normalized retirement. This is based on the assumption that what matters in the determination of consumption and saving rates is the ratio of Old age Net Wealth to Young age Net Wealth (the latter is defined as net human wealth up to nor-malized retirement age), and not the form in which old age income is received. This is indeed a strong assumption because it imposes the condition that future wages and future pensions are substitutable forms of wealth. The alternative (which we have JNotice that by estimating the previous equation one group at a time we lose one source of variation but we gain in simplicity because the differences across cohorts are explained only by differences in the ratio f^**. 47 tried) would be to treat the two variables separately. But then a serious problem of multicoilinearity emerges. We are not able to estimate the individual contributions of pension and human wealth to consumption rates. If we define Ri as our normalized retirement age and R2c,9 as the true retirement age for cohort c belonging to group g (notice that for the oldest cohorts of private sector workers R\ = R2c,g), we can write O t ) 9n{at) 9n(at) * (1 ~ rc<g) * VCt9 6c,g *(D- R2c,g) * 99g{Rlc,g) ) (4.1) Pc,g 9n(at_ (Gg + BiCi9 + B2c,g) where k=Ri Gg = £ (*) k=Q represents the age profile for net human wealth up to normalized retirement age R\ (which we have defined as "Young age Net Wealth"). G9 is the same within a group but changes across groups, while R\ is common across cohorts and groups since it represents normalized retirement age. Bic,9= £ gng{k) is the age profile for human wealth from normalized retirement age up to the actual (as forecasted) retirement age (which is potentially cohort and group dependent) and B2c,g = ( 1 " T ; - g ) * Uc'9 * 6C,9 * (D - R2c,9) * g$(R2c,9) is the age-cohort profile for net pension wealth (again cohort and group dependent). Old Age Net Wealth for cohort c and group g is defined as B\Ct9 + B2Cy9. It is worthwhile to remember that we are able to write our estimation equation in such a form because we have assumed that the age-cohort interaction terms in the wage equation are not very significant. This means that, for each group, more recent cohorts enter the labor market with higher wages but have analogous age profiles, and hence that the source of the across-cohort variation in consumption rates cannot be found in the labor market. In the following paragraph we explore in more details the behavior of the various components of Old to Young Age Net Wealth Ratio for the various groups. 48 4.2 The Components of Old to Young Age Net Wealth Ratio In this paragraph we characterize the behavior of the cohort profiles for Old to Young age Net Wealth ratios under the assumption of Perfect Foresight. This assumption implies that the older cohorts forecast to retire under the Pre-Amato regime while the others believe that the Amato reform will apply to them. Given that the two sectors are affected differently by the Amato reform we treat them separately2. 4.2.1 Public Sector In the public sector the value of R2C,G — R\ does not change across cohorts of the same group, because retirement age is constant (R2C,G = Rt)- This implies that the value for (the ratio between the present value of labor income received past age 60 and the present value of labor income received before age 60) is constant across cohorts that belong to the public sector (Fig.28), and that the only within-group across-cohort variation in the ratio B ^ , s for this sector (see Fig.29) are due to: (i) changes in the ratio (1~Tciff)*l/<iis, which captures how income taxation is distributed over the life-cycle and (ii) changes in the parameter <5CiS, which we interpret as the measure of the generosity of the Italian Social Security system, conditional on a given wage profile. In Fig.30 we report the cohort profiles for ^1~Tc<a)*Vc^ relative to the various groups. For all groups this ratio is rising. This is due to the fact that the tax regime that we have applied to pension benefits paid after 1995 is the same for all cohorts3 while in the past tax rates have risen. In Fig.31 we show the profiles for 8Ct9 * (D — R2) * g^(R2). Notice that, for each group within the public sector, the only across cohort variation for this variable is due to changes in the generosity of the Social Security System (represented by 6c,g), conditional on the actual wage path experienced by the cohort. For a given retirement age, such a generosity is a function of three factors: (i) the length of the period considered to compute the average of past wages, (ii) the coefficients used to capitalize past wages in order to compute the average and (iii) the indexation mechanism. By moving from the Pre-Amato to the Amato regime each of these 2Within the same sector but across groups the value of ratio of Old to Young Age Net Wealth differs also because Gg differs. 3We have assumed that agents forecast pension benefits to be received after 1995 using the tax rates in place in 1995. 49 factors4 was affected, because the Amato reform increased the number of years used to compute the average of past wages (such an increase is larger for younger cohorts), it increased the values of the coefficients used to capitalize past wages (such a change is larger for younger cohorts) and it abandoned indexation to prices and wage growth in the manufacturing sector in favor of indexation to prices. The first effect would tend to decrease the value of the Retribuzione Pensionabile, and hence of the first pension benefit, for groups characterized by monotonically rising wage profiles. The second effect tends to increase the value of the first pension benefit, while the latter tends to decrease the value of Pension Wealth. From the picture we can see that, for all the education groups, we have declining cohort profiles for 6Ctg * (D — R2) * g^(R2) (apart from the last cohort). For all the groups we also notice that the last cohort has a value of Sc<g * (D — R2) * pf (-R2) slightly above the one of the immediately preceding cohort. This is due to the fact that the (positive) effect coming from the increase in the value of the coefficients used to compute the Retribuzione Pensionabile is stronger for younger cohorts. The combination of all the previous effects can be appreciated in Fig.32, where we show the cohort profiles for Old to Young Age Net Wealth ratios (OTYAWR)5. We have regressed the values for OTYAWR on a cohort index and we have found that the effect coming from ^1~T^a)*v<',9 cancels the one arising from 5c,g*(D—R2)*g^(R2) for the group of College and Junior High School Graduates (we cannot reject the hypothesis that the profiles are flat), while the positive effect coming from the life-cycle distribution of tax rates dominates over the negative effect coming from the generosity of the Social Security system for the group of High School Graduates (so that the profile for OTYAWR is positively sloped). 4.2.2 Private Sector In the private sector, within the same group, cohorts differ because the Amato reform affected both the generosity of the Social Security system and the mandatory retirement age. Hence we focus on each of these components separately. When we look at the cohort profiles for (Fig.28), the retirement age effect is very clear. Cohort 2 retires at 60 while cohort 4 retires at 65. Cohort 3 retires at an intermediate age (63). Past cohort 4 the profiles are flat. 4The effects of the reform on these three factors are then translated into the shape of the cohort profiles for the Old to Young Age Wealth ratios. Notice that the cohorts retiring under the Pre-Amato regime are cohort 1 and 2. 5The cohort profiles for B l | g * ^ 2 c ' g are parallel to the cohort profiles for Old to Young Age Net Wealth Ratio, given that -q3- is constant across cohorts within the same group. 50 When we get to the profile for ^=r^ (the Social Security to human wealth ratio, see Fig.29), we observe an initial declining portion (referring to the oldest cohorts) followed by a natter one thereafter. The decline is due to the retirement age ef-fect, and it is the mirror image of what we observed for the ratio ^ q^3-- By raising retirement age, the Amato reform decreased the value of pension wealth (keeping generosity constant). But the reform affected also the generosity of Social Secu-rity. Moreover, the shape of the cohort profiles for depends on the behavior of (1 -T C , 3 )«1/ C , 3 >*c,g Focusing on ( 1~ T'' g )* t / c'» (see Fig.30), we observe rising cohort profiles, similar to the ones observed for the public sector. In order to disentangle the generosity from the retirement age effect in the de-termination of we construct a new variable (~%^Ji equal to the ratio of Pension Wealth to Young Age Wealth, obtained applying all the changes introduced by the Amato reform but excluding the retirement age effect6. The figures for 6Ct9 * (D — Ri) * g^(Ri) (see Fig.31) show declining cohort profiles for College and High School Graduates, while for the remaining group we have an initial declining portion which is then followed by a rising one7. Summarizing the forces affecting B ^ ' 3 , we have a positive effect coming from (1 Tc<a)*v^,a} a negative effect coming from the raise in retirement age and a negative effect (a part from the younger cohorts of Junior High School Graduates, for which the effect is positive) coming from the changes in the factors affecting the generosity of the pension system8. R R Summing and -g^4 to get the profiles for the Old to Young Net Wealth ratio, we observe overall rising profiles for all groups (Fig.32). Regressing ( B l c >a+ B ^,a ^ o n a cohort index we have positive and significant coefficients for Junior High and High School Graduates, while for the remaining group we get a positive coefficient that is significant at the 85% confidence level9. 6We have assumed that males retire at 60 and females at 55 (as under the Pre-Amato regime). 7 The forces at play are the same as those for the public sector. 8The different behavior for Junior High School Graduates is due to the fact that this group shows an age profile for wages that is negatively sloped towards the end of their working life. 9This result is due to the fact that the cohort profile for College Graduates is concave in the cohort index. 51 4.3 Estimation Our estimation strategy is the following: first we estimate the equation for cohort consumption rates using all the years to which the identification hypothesis applies and then we take the estimated cohort effects and we regress them on the ratio of Old to Young Age Net Wealth, at different levels of aggregation (within each sector-education group separately, within each sector separately and pooling all the groups together)10. As for the construction of the dependent variable l^n ^ng(°|])) we use different values according to the sample object of our study11. When focusing on the full sam-ple (male head of households, whatever their marital status) we construct Equivalent Scale consumption, given by the value of household's consumption divided by the square root of the number of household's members, and then we divide it by the net labor income of the head. For the smaller sample (households where the head is married) we use household's consumption and w*g(at) refers to total net labor income of the household. We then compute the natural log of these variables and thereafter the group average. We estimate the following equation: (<!K)) = + X ' C ' 9 ' a t *f39+^'*^ + ^ * * ^ + C ^ (4-2) where: mg(at) is a cubic in age (specific for group g), which captures the relationship between consumption rates and age coming from: (i) In (i+jj)] at (the age profile for consumption) and (ii) g^(at) (the age profile for net wages); Xc,g,at represents household/worker characteristics, which, in the structural ( ry (at)\ 7 ° l g ^ J . The control variables are: the proportion of managers (for the group with College education) and the fraction of blue collar workers (for the other two groups), the number of income recipients in the household, the number of dependent children, and the proportion of households where the head is married; 1 0This is analogous to treating the cohort effects as fixed effects estimated with a measurement error. u We have conducted the estimation using two different samples. The first one is composed of male head of households between the age of 20 (25 if College Graduate) and 60. The second one includes only households of married couples (for the same age intervals defined for the head). 52 • $ is a vector of cohort dummies, which captures both a common intercept (corresponding to the variable previously named Gg) and the differences in cohort values for B^s+B^,s • • fic * at represents cohort-age interaction, to control for factors such as age related household's characteristics which could be changing across cohorts. Clc is an index that identifies the various cohorts. Estimation is then conducted separately for each sector-education group. For each group we obtain a vector of estimated fixed effects which represents the cohort effects that should be entirely explained by the ratios of Old to Young Age Net Wealth. In a second stage we regress the estimated fixed effects on the explanatory variable (<Blc'a(tgB2c'a>j . When we pool the estimated cohort effects for all the groups and regress them on Bl^+B^9, we have to allow for differences in levels and slopes (related both to the sector to which the cohorts belong and to the education that they have achieved). We also conduct the estimation at two lower levels of aggregation: (1) for each sector-education group12; (2) for each sector, pooling all the education groups together. For each education group we drop from the estimation the most recent and the oldest cohorts, due to the small number of observations that characterizes them. Hence we will focus on cohorts 2 to 8 for College Graduates and 2 to 9 for Junior High and High School Graduates. 4.4 Estimating the cohort fixed effects-Males Heads of Households We estimate the fixed effects using two different definitions of consumption rates: (l) equivalent scale consumption divided by individual net labor income; (2) household's consumption divided by household's net labor income. The results are similar in the two cases. We present the results relative to equivalent scale consumption rates given that we focus on the individual as our unit of analysis (and we let Equivalent Scales take care of household's changes). 4.4.1 Public Sector Workers-Males Heads of Households See Table 5. 1 2We want to verify whether the results that we obtain for the larger sample are confirmed at the lowest level of aggregation. 53 For College Graduates we do not find evidence of significant cohort effects, but for the most recent cohort (and only when we do not consider age-cohort interaction). As for the group of High School Graduates, we find evidence of significant cohort effects when we do not control for age-cohort interaction (and particularly for the most recent cohorts). When we control for the latter variable, the significance on the individual coefficients drops but the explanatory power of the whole regression rises. Given that the cohort profiles have an analogous shape in both cases, we feel quite confident in using the profiles obtained under the specification that uses age-cohort interaction (so as to have full comparability with the other cases). For the group of Junior High School Graduates we get evidence of significantly rising cohort profiles when we do not control for household's characteristics, while their significance is reduced when we control for them13. The shape of the estimated cohort profiles is very similar in the two cases. 4.4.2 Private Sector Workers-Males Heads of Households See Table 6. For College and High School Graduates we find consistent and significant ev-idence of positive and rising cohort effects. The evidence for the group of Junior High School Graduates is less clear-cut. When we do not control for age-cohort interaction we obtain very strong and significant cohort fixed effects. Instead, when we control for this interaction, we get a higher Adjusted R2 but all the coefficients on the cohort dummies and the one on age-cohort interaction become not significant, due to some collinearity between the variables. When we compare the fixed effects obtained including age-cohort interaction with those obtained when this variable is excluded, we observe rising cohort profiles that have a very similar shape. This makes us quite confident in using the fixed effects obtained when we use age-cohort interaction. Notice that the coefficient on age-cohort interaction, when significant, is negative, indicating that the age profiles of younger cohorts are flatter. 4.5 Explaining Fixed effects-Perfect Foresight-Males Heads of Households In this section we present and discuss the results obtained from regressing the esti-mated cohort fixed effects on the cohort profiles for Old to Young Age Net Wealth 1 3The fact that the significany of the estimated cohort effects drops when we introduce additional household's characteristics depends on some collinearity between the two sets of variables. 54 ratios. The first issue concerns the significance of the estimated fixed effects. The general pattern that emerges is one of rising cohort effects (see Fig.33). But we do not find results with the identical level of significance for all the groups, either in terms of individual coefficients or in terms of overall significance. For this reason at the second stage, when we regress the estimated cohort effects on the explanatory variables, we use White (1980) consistent estimator. The second issue concerns the relationship between the fixed effects and the ex-planatory variable. The theoretical model implies that human and pension wealth affect consumption rates in a very particular way, because, as discussed in the pre-vious paragraph, after controlling for household's characteristics and age, log con-sumption rates are just a function of the ratio between Old and Young Age wealth. In other words, our model implies that consumption rates at normalized age-zero differ across cohorts of the same group if the values for the ratios of Old to Young Age wealth differ. Cohorts that expect higher values for Blc<a+B2c,a choose higher entry consumption rates. As for the functional form, the theoretical model implies that the estimated fixed effects are a function of the log of 1 + Blc<a+B^,a Besides this specification we have tried one where the cohort effects are a linear function of Old to Young Age wealth ratios, and the results are almost identical. In Fig.34 we report the values for OTYAWR under the perfect foresight hypoth-esis for the two sector separately. From a plot of the estimated fixed effects and the values for OTYAWR we observe a positive relationship between the estimated fixed effects and the values for OTYAWR for the groups of Junior High and High School Graduates in the private sector (group 1 and 2) and for High School graduates in the public sector -group 5- (relationship that is confirmed by a positive and significant coefficient obtained regressing the fixed effects on OTYAWR). As for the group of College Graduates in the private sector (group 3) the relationship between the two variables is less obvious (we have rising profiles for the fixed effects but a slightly concave profile for OTYAWR), but the regression still picks up a positive and sig-nificant correlation between the two variables. For the groups of College and Junior High School Graduates in the public sector, the coefficient obtained regressing the fixed effects on the explanatory variable is not significant (it is positive and almost significant for the first group and negative for the second one). Given the across-group variation, we have also estimated the relationship be-tween the estimated cohort effects and OTYAWR at the education-sector and sector levels of aggregation. Since the standard errors of the estimated cohort dummies 55 show across-cohort variation (due to the facts that the size of the cells varies and that we do not observe the cohorts for the same periods) we run the regression using White (1980) consistent estimator as well. In the private sector (Table 8), the fixed effects are positively and significantly correlated with OTYAWR (the coefficient on the interaction term between education and the explanatory variable is not significant)14. When we restrict our attention to the public sector we do not get such a strong result (Table 8). The fixed effects and OTYAWR are positively correlated but the coefficient is significant only at the 90% level of confidence. This result is due to the fact that the cohort profiles for the explanatory variable are quite flat (only for High School Graduates we have statistical evidence of rising profiles). Finally, when we pool all the groups (see Table 7), controlling for differences in the intercept and slope, we find a positive and significant relationship between the fixed effects and OTYAWR (with some evidence of a larger coefficient for the public sector)15. Notice that lower education groups have lower entry consumption rates16. 4.6 Conclusions The main point of our theoretical model is to clarify in a very precise way the relationship between the cohort fixed effects and their relationship with the ratio of Old to Young Age Wealth. The latter is a normalized variable that allows us to summarize in a very simple and effective way the distribution of wealth over the life cycle. Consumption rates depend on the latter variable. The more a (representative) individual gets wealth towards the end of the life-cycle relative to the initial part and the higher is his consumption rate during the working years. A corollary of this result, which holds under the assumption of perfect capital markets and no uncertainty, is that the form in which wealth is received does not matter. Wages or pensions are interchangeable from the standpoint of age zero (and up to normalized retirement age). When we get to the specific components of the Old to Young Age Wealth ratio, we assume that the relevant variables are net human and pension wealth. The main difficulty at this stage is to identify the marginal effect of each of those two components. The solution of such a problem depends on the assumption about 14When we use the fixed effects divided by their standard errors we obtain a positive but not significant coefficient. 1 5The result is analogous when we use the fixed effects divided by their standard errors. 1 6If consumption is a function of Permanent Income and we are comparing at age zero, we expect College Graduates to consume more of their entry wage since they expect a steeper wage profile. 56 forecasting. In this Part we have assumed that agents are able to forecast perfectly their actual (according to the Amato reform17) human and pension wealth profiles. We show how the Amato reform affects the shape of the cohort profiles for OTYAWR and we describe the different forces at hand. We conclude that those profiles are positively sloped for the three groups in the private sector (but there is evidence of concavity for College Graduates) and for High School Graduates in the public sector. The forces pushing towards rising cohort profiles are: (i) rising profiles for (1-T;.<)W^, which means that, relative to older cohorts, younger generations are facing higher tax rates at the beginning of their life-cycle compared to what they expect at the end18; (ii) an increase in retirement age which forces younger cohorts to works more years, hence substituting human wealth for pension wealth. Given that pension benefits are only a fraction of the last wage and that for most groups wages are rising with age, we get that Old Age Wealth is increased by the raise in retirement age. Notice that the first force works in the public sector as well, while the second one is specific to the private sector. On the other side we have the change in the "generosity" of the Social Security system, and the general effect of the Amato reform is one of reducing it. In our empirical exercise we show that the profiles for OTYAWR can explain the rising fixed effects in consumption rates only for the private sector. Instead, when we focus only on the public sector we do not find the positive correlation that theory would suggest. This result is due to the fact that in this sector more recent cohorts are not facing a more " generous" system. When we pool the two sectors we obtain that the positive effects from the private sector dominate over the one coming from the public sector. The evidence shows the relevance of the profiles for OTYAWR computed under the Perfect Foresight assumption in explaining the rising consumption rates fixed effects for the private sector, in which the positive slope of the profiles for OTYAWR is mostly the result of the retirement age effect. However, for the public sector we do not have evidence of enough across-cohort variation in the ratio of Old to Young Age Wealth to explain the observed across-cohort variation in age-zero consumption 1 7 As previously explained, the Amato reform of 1992 has different effects on private and public sector workers. Summarizing, for private sector workers the reform gradually raised retirement age of younger cohorts, while reducing the generosity of the system. For public sector workers the reform kept retirement age constant but reduced the generosity of the system and this was more so for younger cohorts. 1 8This result derives from the assumption that we apply the same tax regime to all the individuals retiring after 1995. 57 rates19. For this reason we believe that there might be other (common) long term forces that drive the behavior of younger cohorts in both sectors. This line of research is taken in Chapter 5. 19When we pool all the groups we obtain that the positive effects from the private sector dominate over the one coming from the public sector. 58 Part II Complete Surprise 59 4.7 Explaining Fixed effects-Complete Surprise The logic behind the complete surprise assumption is the following. Agents (indi-viduals or households) did not expect the reforms of the pension system that took place in 1992. Hence, for the years prior to 1992, they formed expectations regarding pension and human wealth profiles according to the rules prevailing under the Pre-Amato regime20. In this section we explore the performance of our model when we follow this assumption. This implies that we can look at the relationship between consumption rates and OTYAWR for both the period 1984-1991 and the period 1991-1993. With reference to the first one (1984-1991), we assume that agents fore-casted pension and human wealth according to the Pre-Amato regime. Considering the period 1991-1993 we test if the changes in OTYAWR (coming from the Amato reform) have statistically significant effects on consumption rates (after controlling for other co-variates). When we compare the profiles for Old to Young Age Net Wealth ratios obtained under the two alternative hypotheses (each group at a time) we find that, in the public sector (see Fig.34), the profiles obtained under the Complete Surprise hy-pothesis (olrahdps) lie above the ones obtained under the assumption of Perfect Foresight (olrahdpf), due to the decrease in benefits introduced by the Amato re-form (for a constant retirement age). Moreover, under the assumption of Complete Surprise, the profiles for olrahdps exhibit a (small21) positive slope, which is due to the across-cohort rise in the ratio of ^ 1~T C | g^* t / C | g (and not to changes in the generosity of the Social Security system). As for the private sector (Fig.34), the relationship between the profiles obtained under the two hypotheses is more complex, because of the interplay of the two conflicting forces previously mentioned. The result is that (for the chosen discount rate) the profiles obtained under the assumption of Perfect Foresight lie above those obtained under the assumption of Complete Surprise (with the exception of the older cohorts of Junior High School Graduates) because the increase in net human wealth due to a higher retirement age more than compensates the decrease in pension benefits. We also find evidence that the cohort profiles for olrahdps have a negative slope for all the groups in the private sector. Given that we are assuming that there are no changes in the legislation, the negative slope is due to the rule that sets an upper limit to the Retribuzione Pensionabile (the average of past wages) that can 2 0This is the approach followed by most of the literature on the Italian case (see Brugiavini (1987), Rossi and Visco (1994, 1995), Jappelli (1995)). 2 1 Regressing the profile for olrahdps on a cohort index we find a positive coefficient for all groups in the public sector, but only for High School and College Graduates such a coefficient is significant. 60 be used to compute the first pension. This limit affects young more than old cohorts because the real value of the upper limit is almost constant, while younger cohorts have life-cycle real wage profiles that dominate those of the previous cohorts. It is evident that we are going to have a hard time trying to explain rising cohort effects in consumption rates with declining profiles for Old to Young Age Net Wealth ratios22. We proceed in much the same way as we have done in the previous sections. We estimate the fixed effects and then we regress them on the ratio of Old to Young Age wealth, controlling for variation in the intercept and in the slope. In this case we work under the hypothesis that agents have not changed expectations between 1984 and 1991 and hence that we can estimate the relationship between the fixed effects and Old to Young Age wealth ratio for this period23. Then we verify if there is any evidence that agents reacted to the change in the environment (or simply have changed expectation at all). The theoretical model developed in Chapter 3, under the assumption of Complete Surprise, implies that, for the same age-sector-education groups working both in 1991 and 1993, the change in consumption rates between the two years can be expressed by the following equation in (9M^±A) _ l n (^MM) = ^ - l n U > t + 2 ) _ 7 c UT)\+U_ l n (±±L) *(at+2 - at)+ln 1 + + B 2c,g G„ -ln 1 + Blc,g + B2c,g - ( l n 5 f f > t + 2 ) - l n « £ ( a t ) ) (4.3) where Blc>9+B^,9 represents the value for the Old to Young Age Wealth ratio as seen after the Amato reform, from the standpoint of normalized age zero, and 7 c,g(.at+l) — lc,g(at) represents the change in other control variables (including age squared). If agents update their information set they will have non zero values for ln 1 + In 1 + If we could estimate a cohort-sector dummy for each group, we would regress it on the differences in the explanatory variables, as seen after and before the Amato reform. Unfortunately we cannot estimate all the fixed effects because we have more coefficient to estimate than observations. Hence we try different exercises to capture the significance of the changes in the explanatory variables. 22Notice also that, under the Complete Surprise hypothesis, we can have cohort profiles for olrahdps that have different slopes across the public and private sector because, under the Pre Amato regime, the rules governing pension benefits in the two sectors were different. 23Notice that, according to the assumptions about expectations, we estimate fixed effects using only the data from 1984 to 1991. 61 At this stage we stress a final important point. The assumption of Complete Surprise implies two separate hypothesis that we test. The first one, based on the fact that the environment was stable, says that the cohort fixed effects for the period 1984-1991 should be well explained by the cohort profiles for OTYAWR computed under the hypothesis of Complete Surprise. The second one says that the changes in consumption rates between 1991 and 1993, after controlling for the other co-variates, should be positively correlated with the changes in OTYAWR. If we do not find evidence for the second hypothesis, for instance because agents are slow to react to the change in legislation, we should not conclude that the whole hypothesis is to reject, because we might still find evidence that our model describes well the period 1984-1991. If instead we find that the model does not perform well relatively to both aspects, then we are left with the following alternative: either we abandon the Complete Surprise assumption or we look somewhere else for the explanation of rising consumption rates. 4.7.1 Estimated Fixed Effects-Males Heads of Households As for Perfect Foresight, we use both definitions of consumption rates - the one that uses household's consumption divided by household's labor income and the one that uses equivalent scale consumption divided by the value of individual labor income24. We present the results that refer to the latter. We find that the reduction in the number of observations (years 1993 and 1995 are not considered) makes a bit more problematic the estimation of the cohort fixed effects if we want to control for both age-cohort interaction and the same household's controls that we have introduced when we considered the Perfect Foresight case, particularly for the group of Junior High School Graduates in the public sector. We choose to control for age-cohort interaction and to include only the household's controls25 that appear to be more significant (when considered one at a time). Notice that what matter are not the levels but the shapes of the fixed effects cohort profiles and those are very similar under the various specifications that we have tried. • Public Sector (Table 9) For College Graduates we do not find evidence of significant fixed effects. More-over, the significancy of the evidence decreases when we control for age-cohort in-2 4The results show that when we use the second one we tend to get higher Adjusted R2. 25Those are the number of income recipients and the percentage of households (within the cell) whose head is a manager or a bluecollar worker. Notice that we already take into account the changes in the composition of the household by considering Equivalent Scale consumption rates. 62 teraction. As for the group of High School Graduates, we find evidence of "almost" significant cohort effects (p-values are 0.6) when we control only for age-cohort inter-action, but the significancy of the individual coefficients is reduced when we control also for household's characteristics. In both cases we get rising cohort profiles. As far as the group of Junior High School Graduates is concerned, we get evidence of significant (and rising) fixed effects when we do not control for household's charac-teristics, but this evidence is reduced when we control for them. We also find that age-cohort interaction, when significant, enters with a negative coefficient. • Private Sector (Table 10) As for the case of Perfect Foresight, for the groups composed of College and High School Graduates in the private sector we find consistent evidence of rising cohort profiles. For both groups the evidence is robust to the introduction of con-trols on the household's composition. The evidence for the group of Junior High School Graduates in the private sector is less robust when we use Equivalent Scale consumption rates because, when we do not control for age-cohort interaction, we obtain very strong and significant cohort fixed effects, while, when we control for this interaction, we get a higher Adjusted R2 but all the coefficients on the cohort dummies and the one on the age-cohort interaction become not significant. At the same time we feel quite confident in the fact that the profile are significantly pos-itively sloped because this result is very robust to the various specifications when we use household's consumption rates. We also notice that, when significant, age-cohort interaction has a negative coefficient, which means that the age profiles for consumption rates tend to be flatter for more recent cohorts. As a general comment, comparing these results with those obtained under the hypothesis of Perfect Foresight, we can conclude that the evidence points towards rising cohort profiles (a part for the case of College Graduates in the public sector, for which, though, the fixed effects are not significant under none of our specifications) and towards negative age-cohort interaction (when significant). The interesting point is to verify whether the behavior of the cohort fixed effects can be explained by the cohort profiles of the explanatory variables obtained under the hypothesis of complete surprise. 4.7.2 Fixed Effects on the explanatory variables-Males Head of Households The estimated fixed effects from the sample that uses Males Heads of Households are reported in Fig.35. As for the Perfect Foresight case we use White (1980) robust 63 estimator. When we pool the observations from both sectors and allow for variation in the slope between sectors (a part from variation in the intercept among education groups) we find that the correlation between the estimated fixed effects and the log of 1 plus OTYAWR is negative26 (see Table 11). When we restrict our attention to the private sector (and controlling for ed-ucation) we find a negative relationship (see Table 12) between the fixed effects and Old to Young Age Wealth Ratio. This result, which is robust to various spec-ifications, is not consistent with the theory underlying our model, which instead predicts a positive relationship between the two variables. When we use the fixed effects corrected by their standard errors the relationship remains negative but the coefficient is no longer significant. Notice that the result for the private sector is quite strong27 because for this sector the evidence of rising cohort fixed effects is stronger. Those rising profiles do not appear to be explainable in terms of the be-havior of OTYAWR computed under the assumption of Complete Surprise28.This result is also important because goes contrary to previous evidence that based the explanation for the decline in Saving Rates on Social Security. If we retain the as-sumption of Complete Surprise and focus on the years to which that assumption should logically apply (1984-1991) we do not find evidence that the rising profiles for consumption rates of private dependent workers are explained by the profiles for the log of 1 plus OTYAWR. When we look only at the public sector we find a positive and significant relationship between the fixed effects and the explanatory variable for the two groups that exhibit rising profiles and this result is confirmed when we pool the observations from the three groups (Table 12). Notice though that this result is not very robust. While in the private sector the introduction of the household's controls does not affect much the significancy and the estimated values for the cohort fixed effects (the profiles are always positive), the same is not true for the group of Junior High School Graduates in the public sector. We have verified that by introducing as controls the number of dependent children and the percentage of households (in the sex-age-sector-education cell) in which the head is married, the estimated cohort fixed effects 2 6The explanatory variable is always one plus OTYAWR, but it is now computed under the complete surprise assumption. 2 7The negative correlation between the fixed effects and the OTYAWR profiles is confirmed at the group level of aggregation. 28Regressing the values for OTYAWR on a cohort index, each group at a time, we find a negative coefficient for the private sector. This imply overall declining cohort profiles for the proposed explanatory variable. 64 cease to be significant (the cohort profile is actually flat) and the regression of the fixed effects on the log of 1 plus OTYAWR produces a non significant coefficient, both at the group and sector level of aggregation. 4.7.3 Conclus ions The evidence that we have obtained on the first part of the hypothesis based on the assumption of complete surprise is pointing towards a mixed result. When we focus on the private sector alone we find negative correlation between the estimated fixed effects and the profiles for OTYAWR, reflecting the fact that the generations considered in our exercise do no appear to be benefiting from a par-ticularly generous Social Security system, when compared to previous generations. When we consider the public sector we find evidence of positive correlation be-tween the cohort fixed effects and OTYAWR but the significancy of the coefficient is not robust to the various specification that we have tried. Overall, this might look like a result symmetric to that found under the Perfect Foresight hypothesis, but it is not so for three reasons. First, the fixed effects are stronger in the private sector (under both assumptions about forecasting), and for this sector, the first part of the Complete Surprise hypothesis is rejected. Second, under the Perfect Foresight hypothesis, regressing the estimated cohort fixed effects on the log of 1^ + BlciS^ie<a j for the public sector, we obtain an almost significant positive coefficient (p-value of 0.071). This is not the same as rejecting the hypothesis of a positive coefficient. Third, under the Complete Surprise hypothesis, the evidence of a positive statistical relationship between the estimated fixed effects and the log of | l + J J l c ' g g g P 2 c , g j for the public sector is not robust with respect to the different specifications adopted. The first result is hence pointing against the relevance of our model under the Complete Surprise hypothesis. In the next paragraph we test the second hypothesis deriving from the assump-tion of Complete Surprise, in order to strengthen our previous conclusion. 4.8 A control experiment A second (possible) implication of the assumption of myopic forecasting is that agents (households or individuals) where completely surprised by the Amato reform that took place in 1992. Notice that the effects of the reform are the following: (1) it increases the present value of net wages (human wealth) in the private sector, due 65 to the retirement age effect and (2) it decreases the present value of net pension benefits (pension wealth) in both the private and public sector. Agents recognizing the effects of the reform (and assuming that they are not limited in their choices by some sort of long term commitment or credit market constraint) should react optimally according to the theory presented in Chapter 3. One of the implications of that model is that, for a representative individual of cohort c and group g, we can describe the changes in (log) consumption rates between 1993 and 1991 (assuming that the structural parameters do not change) by 4.3 (which we report here for simplicity) K ^ ) - t a ( ^ ) - i ^ h ^ ) - T - w H T ^ , n ( ^ ) ] * (a t + 2 — at)+ln 1 + B\c,g + B; 2c,g -In 1 + Blc,g + B2c,g G0 - ( l n # ( a t + 2 ) - l n < £ ( a t ) ) where g l e , g c l g B 2 < : ' g represents the value for the Old to Young Age Wealth ratio as seen after the Amato reform, from the standpoint of an agent at normalized age zero, and 7C)9(at+2) — lc,g(at) represents the change in other control variables. The same logic behind our previous exercise leads us estimate the following reduced form equation In CCjg(at+2)\ wlg(at+2)) In Cc,g(at) ^ = mg(at+2) - mg(at) + ( X ^ , a t + 2 - X'^J * Pg+ * Vg + fic * (a t + 2 - at) *<pg + eCtgit (4.4) where mg(at) is a cubic in age (potentially group specific), which captures the relationship between consumption rates and age coming from: (1) (the age profile for consumption) and (2) gg(at) (the age profile for net wages); Xc,g,at represents household or workers characteristics, which corresponds to l 8 (°) / ' ^ e c o n t r o ^ variables are: the proportion of managers (for the group with College education) and the fraction of blue collar workers (for the other two groups), the number of income recipients in the household, the number of dependent children, and the proportion of households where the head is married; $ is a vector of cohort dummies; 6 6 • Qc * (at+2 — at) represents cohort-age difference interaction. Qc is an index that identifies the various cohorts. This formulation, apparently easily estimable, hides some relevant problems. The first concerns the theoretical interpretation of the cohort fixed effects (as-suming that we can actually estimate them). Given that between 1993 and 1991 the age difference is two years no matter what the normalized age is, we cannot interpret the cohort fixed effects only as a function of lifetime resources as seen from age-zero. The estimated fixed effects (the difference of the fixed effects in levels) should be actually interpreted as a difference in the levels of Old to Young Age Wealth ratios as seen from the standpoint of age s, where s could be any age, between age zero and the actual age. This would affect the value of the coefficients obtained from regressing the estimated fixed effects in the difference equation on the explanatory variables (in term of age zero values) while the sign would not be affected. The second problem concerns identification: we cannot estimate the cohort-sector dummies $ for each education-sector group (a fixed effect as a difference of fixed effects) because the number of observations is less than the number of the parameters to estimate. To verify the existence of some common behavior for the different cohorts across the three education groups, we have regressed, for each sector separately but including all the education groups, the difference in the log of consumption on a constant equal to two (the difference in age)29, on cohort dummies, education dummies and on other explanatory variables (changes in the number of household's components and number of income recipients). By doing so we have imposed the condition that, irrespective to their educational attainment, the representative (individuals) should react in the same ways to changes in the explanatory variables. The cohort dummies should tell us if, after having controlled for age, education level and other explanatory variables, there is still some evidence of across-cohort variation for the differences in consumption rate levels. For the public sector (see Table 13) we find some evidence of declining cohort fixed effects between 1993 and 1991, particularly for cohorts 6 and 7. We expect this result because for this group the Amato Reform has decreased the value of the ratio of Old to Young Age Wealth and this effect has been stronger for younger cohorts. Still we have to notice that: (1) such an effect is not very strong because the cohort dummies are not significant at the customary level, and (2) when we regress the estimated cohort fixed effects on the difference in Old to Young Age Wealth Ratio The estimated constant is a reduced form estimate for t^— In 1 —at 67 we find that the correlation coefficient and the overall regression are not significant. A possible interpretation of this result is that the overall surprise effect is quite small because agents anticipated the reform. As for the private sector (see Table 13), the retirement age and the pension benefit effects go in opposite directions and we do not expect a particular sign on the cohort dummies. The results show that the coefficients on the cohort dummies are not significant and when we regress them on the changes in OTYAWR we get results analogous to the one for the public sector. When we use the sample of married couples we confirm the previous result. Finally, to test the significance of the Complete Surprise hypothesis and given the identification problem previously described, we also directly relate the changes in log consumption rates with the changes in the explanatory variables, according to3 0 - i n ( t f e ! ) - • * < * « > - • " • < « > + - • ? ° + +(OTYAWRCt9(0) - OTYAWRCig(0)) * l g + ec<g>t (4.5) where OTYAWRCt9(0) - OTYAWRCi9(0) =B^+B^9 _ B^n+B^« represent the difference in Old to Young Age Wealth ratios, as computed after and before the Amato reform. If agents react optimally to the new information set, the coefficient *yg measuring the reaction of the changes in log consumption rates to the changes in expected Old to Young Age Wealth ratios, after we have controlled for all the other factor affecting consumption rates, should be significantly different from zero and positive. With this approach we allow cohort effects to enter only through the changes in Old to Young Age Wealth ratios, given that we control for the changes in age and the changes in the XC ) f f ) a t's. If we have a decline in the difference of Old to Young Age wealth ratio cohort profile (which means that recent generations have been affected more by the reform), this should be inducing downward sloping cohort profiles for the changes in log consumption rates, after controlling for age and the other explanatory variables. Hence we expect ln (^n g(°'^j) — In (^n'g[°,)) to be positively correlated with OTYAWRCi9(0) - OTYAWRc,g(0). We estimate the regressions both pooling the sectors and for each sector sepa-rately. 3 0 A n analogous equation holds for Saving Rates. 68 4.8.1 Males Head of Households • Both Sectors Controlling for education, household's characteristics, sector and the change in age, we find that there is some evidence of a negative but not significant correlation between the change in log consumption rates and the change in Old to Young Age Wealth ratios. When we allow for interaction between education and Old to Young Age Wealth ratio, we get that the coefficient on OTYAVVRCtg(0) - OTYAWRcig(0) becomes positive but remains not significant (see Table 14). • Public Sector Controlling for the age difference, for the change in the number of household's components and income recipients, and for education (both interaction and slope) we get (see Table 14) a positive correlation coefficient between the changes in the log for consumption rates and OTYAWRCt9(0) — OTYAWRc,g(0) but such a coefficient is (highly) not significant • Private Sector For all specifications (controlling for interaction at the intercept and at the slope) the coefficient on OTYAWRCtg(0) - OTYAWRc,g(0) is positive but (highly) not significant (see Table 14). 4.8.2 Households where the Head is married We find some evidence of positive correlation between the changes in the log of consumption rates and OTYAWRCt9(0) — OTYAWRCjg(0), however the coefficient is not significant. 4.8.3 Conclusions From our previous exercises we have obtained evidence that points towards the rejection of the Complete Surprise assumption. First, when we concentrate on the period 1984-1991 and regress the cohort fixed effects on the cohort profiles for OTYAWR we cannot explain the rising fixed effects cohort profiles observed in the private sector. Second, after having controlled for the changes in other potentially relevant fac-tors, we do not find consistently significant evidence that the 1993-1991 changes in 69 OTYAWR have induced changes in log consumption rate differences of the same sign31. These results induce us to conclude that our model, under the Complete Surprise hypothesis, fails to explain the observed rising cohort profiles for "Entry" consump-tion rates. Notice that our results differ from those obtained by Attanasio and Brugiavini (1999). This could be due to many factors among which: a) the different specification of the model; b) the different way in which we have computed Pension and Human Wealth; c) the different ways in which we have identified cohorts. 70 Chapter 5 What have we learned about saving rates? In the previous chapters we have documented the evidence that (i) under the Com-plete Surprise hypothesis our model cannot explain the rise in consumption rates cohort fixed effects and (ii) under the Perfect Foresight hypothesis our model works quite well for the private sector but not for the public one. Hence we concluded saying that, while we cannot exclude the relevance of the across-cohort variation in the profiles for Old to Young Age Net Wealth ratio (particularly for the private sector), we should also investigate the importance of other (common) forces driving the behavior of younger cohorts in both sectors. 5.1 The Role of Assets The model developed in Chapter 3 can include assets at age zero among the variables that affect consumption choices. In fact we expressed consumption rates as and ACt9(0) represents the (real) value of assets at age zero. This latter variable should be interpreted as "normalized bequests", in a model in which the parents die at the beginning of the period in which their sons and daughters enter the labor market. Introducing assets in our equation for total age-zero wealth we obtain ln a t + l n ¥ C | S ( 0 ) + l n wc,9(Q) wlg{at) where Wc,g(0) = Ac,g(0) + NPWCt9(0) + HWCt9(0) 71 Wc>g(0) Ac,g(0) + + (1 ~ Tc,g) * V, »c,g Jc,g * (D - R2c,g) * g%(R2c,g) 9% (<*t) Ac,9(0) , (Gg + Blc,g+B2c,g) (5.1) »c<g*9gl(at) <#(<**) Hence we rewrite the structural equation for consumption as In a t + ln*Ci9(0) +lnG 9+ Notice how consumption rates, among other things, are now a function of ^C|gffl which is the bequests to normalized net human wealth ratio. Cohorts that experience higher values for this ratio tend to have higher consumption rates. We do not have data on bequests received by all cohorts, but the SHIW dataset contains data on real and financial wealth that are comparable1 across the 1987, 1989, 1991, 1993 and 1995 surveys. In the Bank of Italy definition, real wealth refers to every form of wealth (house, paintings, etc.) that is not held in a financial instrument, while financial wealth refers to wealth held in the form of Treasury Bonds, other types of debt instruments, stocks, funds, etc. We consider the values of net of debt real and financial wealth. The available data allow us to sum real and financial nominal wealth, divide it by the CPI and create sex-age-sector-education cell averages2 (using the years from 1987 to 1995), similarly to what we do for consumption rates and wages. This creates a quasi-panel and allows us to follow the average wealth of a given cohort through his life. 1In May 2000 the Bank of Italy has released data on financial wealth for the interviewed house-holds, specifying that the definitions for real and financial wealth are comparable only after the survey of 1987. 2We do that using both household's total assets and equivalent scale assets, obtained dividing the first by the square root of the number of household's members. 72 To obtain normalized bequests we regress the log of cohort average wealth3 on cohort dummies, age, age square, age cube and the deviation of the unemployment rate from its trend. As for the case of saving rates, the inclusion of such a time dependent variable is just meant to control for cyclical factors. We choose to use log assets because of the high non linearity observed for the levels, which would imply a negative estimated constant (while all cell averages show positive values). We interpret the (exponential of the) estimated cohort dummies for total assets as "normalized bequests". For all groups we find evidence of significantly rising cohort profiles for age-zero assets, with the exception of College Graduates in the public sector, for which the evidence is less significant (see Tablel5 and 16). In Fig.36 we report the cohort profiles for ^C,9^ Q obtained dividing estimated age-zero assets by the values for normalized net human wealth. For all groups we get rising cohort profiles. To test whether the profiles for ^C,9}Q3 can explain the profiles for age zero consumption rates, we regress the estimated fixed effects from consumption rates on ^C,A^ Q j one group at a time, and we obtain positive and highly significant coefficients for all groups, with the exception of College Graduates in the public sector4. When we pool all the groups, controlling for between-sector and across-education variation in the intercept and the slopes, we obtain an Adj — R2 of 0.57 and a positive and significant coefficient on ^c'gffi . ^ Hc,g*Gg The previous results demonstrate the relevance of considering the entry assets to normalized net human wealth ratio among the variables that can explain the decline in cohort saving rates. Finally5, we test the relationship between the fixed effects from consumption rates on one side and both /^'ffi a n d the log of [l + B l c' g+ g 2 e- g 16 on the other one7, M c . s * ^ L ^9 J the latter computed under the hypothesis of Perfect Foresight8. When we consider 3While at the individual level we have some households with negative wealth, after the averaging all the cohorts show positive values for total wealth. By taking the logs after the averaging we did not have to exclude households with negative values. 4But notice that for this group the fixed effects from consumption rates are not significant and the same holds for the coefficient on the cohort dummies for log assets. 5The previous results demonstrate the relevance of considering the entry assets to normalized net human wealth ratio among the variables that can explain the decline in cohort saving rates. 6We have tried regressing the fixed effects on Ac<a^} and OTYAWR and the results were almost identical. 7We use White (1980) robust estimator. 8Remember that under the Complete Surprise hypothesis our model could not explain the ob-served behavior. 73 the two sectors separately (see Table 17) for both of them we get a (positive and) significant coefficient on both A c ' g W a n d the log of the observations from the two sectors, both explanatory variables enter with positive and significant coefficients and the regression has a high R2 of 0.8 (Table 17). Given that we do not have a structural model in which bequests arise endoge-nously it is difficult to interpret unambiguously our results. On the one hand they point towards the importance of studying how wealth is distributed within the house-hold, where the latter should be interpreted in an extended sense. On the other one, they direct our attention on institutional changes that might affect such a process. It is possible that what we are observing now is actually the result of the increased generosity of Social Security observed during the 1960's and the 1970's, partially transferred to the younger generations through higher bequests. Our future work will explore this research path. 5.2 Implications for Aggregate Saving Rates The main conclusions from the previous chapters are the following: (1) the ratio of Old to Young Age Net Wealth is significant in explaining the rising cohort effects in consumption rates, but only when we focus on the private sector and only under the Perfect Foresight hypothesis. Under such an assumption the rising profiles for OTYAWR are not due to an increase in the generosity of Social Security, but to an across-cohort increase in tax rates at the age of entry in the labor market (compared to taxation during retirement) and to the raise in retirement age introduced by the Amato reform; (2) the ratio of age-zero assets to normalized net human wealth is significantly and positively correlated with the cohort fixed effects from consumption rates for all the sectors in which the latter show positively sloped profiles. Keeping those results in mind we can now address the following two policy ques-tions. The first one is concerned with what would have been the observed aggregate saving rate in the absence of the Amato reform, while the second one investigates the quantitative relevance of the distribution of taxes over the life-cycle. In our model we have assumed that the only way in which the Government affects individual consumption rates is through taxes and pensions. We do not consider the case in which individuals forecast the general equilibrium effects (such as changes in wages and interest rates) of the Social Security 1992 reform. The only policy change that agents consider is the fact that the Amato reform affects individual pension benefits and retirement age. Under this assumption we obtain an estimate of the 1 + Bic,9+B2, When we pool 74 relationship between OTYAWR and consumption rates9. One of the implications of the previous conclusion is that we can take the esti-mate for the coefficients on OTYAWR (obtained under the assumption of Perfect Foresight), and use them on alternative values of OTYAWR, as long as we maintain the hypothesis that agents perfectly forecasted the implications of the alternative regime. To obtain the coefficients under the hypothesis of Perfect Foresight we pool the observations relative to all groups, for all years in which we observe them, and we regress the log of consumption rates on age, age square and age cube, household's characteristics10, group specific cohort-age interaction terms, group specific cohort profiles for the log of 1 + g l c ' g G f l B 2 c ' g ] , the ratio of age-zero assets to normalized net human wealth, allowing for sector specific profiles for the square of the log of 1 + g l C | g g g 2 c ' g j . The results that we obtain confirm our previous findings (see Table : i ) n . The ratio of age-zero assets to normalized net human wealth is positively and significantly affecting consumption rates, after having controlled for age, cohort-age interaction, OTYAWR and household's characteristics. We find evidence of a positive and significant relationship between consumption rates and the log of _j_ Bic,g+B2c,a o m y £ Q r three groups in the private sector. In the public sector we have evidence of a positive relationship for the two groups with lower education (for the group of Junior High School Graduates the coefficient is significant at the usual level of confidence, while for the group of High School Graduates it is significant only at the 90% level of confidence). The significance of the coefficients for those two groups is not very robust with respect to the introduction of extra variables, while the one for the private sector is. Notice also that for the private sector we find evidence of a significant second order effect for the log of 1 + gle'gj"B2c.g while this L 9 J is not the case for the public sector. 5.2.1 The role of Social Security Reform In Figs.37 to 39 we compare the estimated aggregate saving rate (resulting from considering both sectors) with the ones that would prevail under various alternative 9We cannot assume that the relationship between consumption rates and OTYAWR would not change were agents completely surprised by an unexpected change in Social Security. 10These are the same characteristics that we used when estimating the cohort fixed effects for consumption rates. 11Note that we do not include group dummies. Those group dummies should reflect the across group variation in the present value of the age profile for net wages. We have verified that once we control for group-specific cohort-age interaction terms, the group dummies cease to be significant. 75 scenarios12. The changes that we consider have two effects, because they affect both the level and the slope of the saving rate function. This is a result common to all the cases and it poses the delicate question on how to compare things across years and regimes. The comparison of the saving rates along the same line (hence keeping the scenario fixed) gives us information on the percentage drop that would prevail under a given regime, and is independent from everything that affects the intercept. On the other hand, comparing the saving rate across scenarios for the same year (we focus on 1984 and 1995) is a bit less "safe", in the sense that all the factors affecting the intercept get reflected in the outcome. For instance, our counterfactual exercises are based on the assumption that age-zero assets are not affected by the changes in regime. If this were not the case they would change as well and this would give rise to effects that would show up at the intercept level of the cohort consumption rate function and hence would affect the intercept of the aggregate saving rate as well. With this caveat we present our results. In the upper-left picture of Fig.37 we compare the estimated profile (under Per-fect Foresight, estsr) with the one that would be observed if the Social Security regime corresponded to the Pre-Amato era (predicl). Under the Pre-Amato regime the intercept of the aggregate saving rate would be higher (from 0.111 to 0.114 in 1984 and from -0.0022 to -0.00033 in 1995) but the percentage change would be very similar. The estimated saving rate drops by 102%, while, under the Pre-Amato scenario it would drop by 100%. The force at play are the following. On one side we have the reduction in benefit brought by the Amato reform, and on the other one we have the increase in retirement age that applies only to the private sector. While the first one would tend to lower the aggregate saving rate under the Pre-Amato reform, the second has the opposite effect. In the upper right picture in Fig.37 we report the aggregate effects of the retire-ment age effect. By fixing the generosity of the Social Security system (comparing the estimated series with the one that would prevail if we just had the benefit part of the Amato reform, predict) we can observe the aggregate effects of the increase in retirement age for the private sector. We can see that this change has the effect of lowering the saving rate, since, under the no-retirement-age-change scenario the whole series would be above the estimated one (it raises it to 0.13379 in 1984 and 1 2We present the results for the aggregate saving rate defined in terms of labor income because this is the appropriate series, given that we assume that wages are exogenously determined and hence are not affected by Social Security regime changes. On the contrary, total income is not independent from the variation in regimes because assets would change according to the variation in consumption. 76 to 0.0351 in 1995). We also note that the rate of decline would be reduced (75% instead of 102%). In the lower-left picture of Fig.37 we consider the aggregate effects of the re-duction in benefits brought by the Amato reform, keeping constant the retirement age at the value that prevailed under the Pre-Amato regime. We can see that the effect of the benefit reduction changes both the level and the slope of the aggregate saving rate function. Under the Pre-Amato regime the series would be below that one corresponding to the Amato reform without the retirement age change because the generosity of the Social Security system would be higher. The drop would be reduced as well (75% instead of 100%). Given that the underlying changes in the private and public sector have opposite signs it is worth looking at them separately. In Fig.38 we report the results for the private sector. The picture in the upper-left corner shows that the private sector is the one driving the aggregate results. Under the Pre-Amato regime the saving rate for the private sector (prsrprt) would have been higher in every year (from 0.099 to .1319 in 1984 and from 0.00886 to 0.0967 in 1995) and the drop would have been less dramatic (26.6% instead of 91.05%). Focusing on the latter, we can see that, at least for the private sector, Social Security variation can explain about 70% of the observed decline. When we look separately at the benefit and retirement age effects13 we note that the second largely dominates over the first one. At constant benefit (upper-right corner), the increase in retirement age lowers the saving rate and it also increases the rate of decline (in the absence of the retirement age provision saving rates would fall by 31%). On the other hand, at constant retirement age (lower-left corner), the drop in benefits induced by the Amato reform increases the saving rate (the whole series would be above the one computed under the Pre-Amato regime), but does not affect significantly the percentage drop (31% versus 26.6%). The public sector is considered in Fig.39. We know that for this group the Amato reform had only the effect of reducing benefits, which is translated into lower saving rates under the Pre-Amato scenario14. The effect is quite large, in terms of both the levels (from 0.128 to 0.091 in 1984 and from -0.0106 to -0.0695 in 1995) and the slope (108% under the estimated series and 178% under the predicted one). 13Estprt refers to the estimates series for the private sector, while nrsrprt refers to the series that would prevail with the changes in benefits introduced by the Amato reform, excluding the change in retirement age. ^Estput refers to the estimates series for the private sector, while prsrput refers to the series that would prevail with the changes in benefits introduced by the Amato reform. 77 Comparing the sector specific saving rates with the aggregate ones, we conclude that the opposite effects from the two sectors tend to offset each other. While in the private sector the retirement age effect is quite strong and hence can explain much of the decline in the saving rate for that sector, for the public sector the effects of the Amato reform go in the opposite direction, given that the reform reduced benefits relatively more for public sector workers. The aggregate result is that, in the absence of the Amato reform neither the shape nor the percentage drop would be significantly different from the observed one. We conclude that Social Security, including retirement age provision, does not appear to able to explain the observed drop in saving rates for the years 1984-1995. These results confirm our initial intuition from a quantitative point of view. 5.2.2 The role of taxes We have previously shown that part of the rise in the cohort profiles for OTYAWR is due to rising cohort profiles for ^~Tc^)*Vc<am Given fj.cg = (1 — tCi9) * vCf9 (where tc<9 represents the average income tax on the first wage), we write the previous ratio as ^~^C|g^, which expresses in one number how taxation affects cohort at the beginning relative to the end of their life-cycle. Given that we have assumed that after 1995 all cohorts pay taxes according to the legislation in place in 1995 and given that income tax rates have been rising with time, we observe positively sloped cohort profiles for ^~ T^ l g | . To explore the quantitative relevance of the distribution of taxes over the life-cycle we verify what the aggregate series for saving rates would look like if the cohort profiles for ^~^c,g^ were flat within each group. Hence we compare the estimated aggregate saving rates profiles with those that would be obtained if all the cohorts faced, at the entry in the labor market, the tax rates in place in 1995. This amounts to raising the profiles for ^~^c,gj experienced by the older cohorts. Given that those cohorts, after such a change, experience higher counterfactual values for OTYAWR, we expect them to exhibit higher consumption rates. Our results (lower-right corner of Figs. 37 and 38 and right picture in Fig.39, see also Table 20) show that the effect of the changes in tax rates is only marginal. Under the considered alternative scenarios we obtain that, for the aggregate economy and for both sectors separately, saving rates would be lower, and this effect would be larger in 1984 (because the alternative profiles for ^Z^'9) affect mostly the older cohorts which are not observed in 1995). In 1995 the effects are minor and they go in the opposite direction for the private sector, due to the second order term in the regression. However, when we focus on the rates of change we find that, for all cases, 78 they would resemble very closely the ones obtained using the estimated values. 79 Chapter 6 Conclusions In our thesis we study the relationship between saving rates and Social Security using Italian micro-data, Unking the empirical findings of relevant cohort effects in saving and consumption rates to a theoretical model able to interpret those effects in terms of across cohort (and group) variation in Social Security wealth. This objective is obtained under the simplification offered by the possibility of separating age and cohort effects for wages, which implies that we should not look at the labor market as the source of the variation in cohort saving rates. We document the existing literature on the explanation for the fall in aggregate saving rates, focusing mainly on the one that relates to Italy. This literature, in its macro and micro approaches, finds evidence that a relevant role in the decline of aggregate (and individual, when relevant) saving rates is played by the increasing generosity of Social Security. In a cohort framework this implies that if we observe rising cohort effects in consumption rates they should be explained by rising cohort profiles for Social Security wealth to Permanent Income ratios (named Old to Young Age Wealth ratios -OTYAWR- in our work). Our starting point is that the latter could have been a valid stylized fact for the past but it does not appear to be appropriate when we think of recent generations of Italian workers. To verify our intuition we develop a theoretical model that allows us to think of across-cohort differences in consumption rates in terms of across-cohort variation in the ratio of Old to Young Age Wealth. This is the ratio of net pension and human wealth that is received after normalized age (60 for males and 55 for females) to the value of human wealth prior to that age, and it captures the distribution of wealth over the life cycle, allowing us to estimate the model in a simpler way, given the collinearity that exists between human wealth and pension wealth (i.e. between pension benefits and wages). We shown that such a ratio can be simplified if, in the 80 wage equation, we can separate out an age and a cohort profile (for each group), and we verify that this is the case for most groups. Using the Bank of Italy SHIW dataset we construct a quasi-panel dataset that allows us to follow cohort consumption and saving behavior through time. We use such a quasi-panel dataset to test our model under the assumptions of Perfect Fore-sight and Complete Surprise. In each case we estimate the consumption equation (each group at a time) imposing that log consumption rates are a function of a polynomial in age, household's characteristics, cohort dummies and age-cohort in-teraction. According to the prediction of our model, we verify whether the estimated cohort effect profiles can be explained by the cohort profiles for the log of 1 plus OTYAWR. When we perform the exercise under the hypothesis of Complete Surprise, we find that the cohort effects for all the groups in the private sector are negatively correlated with the profiles for the log of 1 plus OTYAWR, while, for the public sector, we find evidence of a positive and significant coefficient for two of the three groups, but such evidence is not very robust to the various specifications. We also verify whether agents responded to the changes in pension and human wealth introduced by the Amato reform and we do not find evidence to support such hypothesis. This, together with the previous result, allows us to conclude that, if we accept the hypothesis that individuals did not expect a change in the Social Security regime, then we are not able to explain the drops in cohort saving rates using the proposed explanatory variable (OTYAWR). Under the Perfect Foresight hypothesis the correlation between the cohort effects and OTYAWR is positive and highly significant only for the cohorts belonging to the private sector and for High School Graduates in the public sector. This means that the values for OTYAWR constructed under the Perfect Foresight hypothesis can explain the rise in " Entry Consumption Rates" for one sector only, because only for this sector we have the "right" positive slope for the cohort profiles for OTYAWR. Moreover, we show that the positive slope for the those cohort profiles is due to both the retirement age effect and the across-cohort variation in tax rates over the life-cycle, and not to an increase in the generosity of the public pension system. When we verify the aggregate relevance of Social Security, we find that the between-groups and across-cohort variation in Social Security wealth cannot explain the drop in the observed aggregate saving rates. As an alternative scenario we consider the series that would be observed under the Pre-Amato regime. We find that, under such a regime, the private sector would have experienced higher saving rates while the opposite holds for the public sector. The two effects offset each 81 other so that the aggregate effects on the percentage drop in aggregate saving rates between 1984 and 1995 (computed using labor income) is almost identical under the two scenarios (100% instead of 102%). These results induce us to investigate whether there are other forces, common across sectors, that are able to explain the observed rising consumption rates. One of the implications of our model is that consumption rates are positively correlated with the ratio of age-zero assets to normalized human wealth. When we test this hypothesis we find that the rising "Entry Consumption Rates" cohort profiles are positively correlated with the ratio of age-zero assets to normalized human wealth in all the groups for which we have significantly rising profiles. This result is quite interesting because it shifts the focus from Social Security to the distribution of wealth within the household, to be interpreted in a dynastic sense. Future research should investigate this issue and develop and test a model that can explain why the ratio of age-zero assets to human wealth is rising across cohorts. 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Econometrica, 48, 817-838. 87 Appendix A Pension Legislation in Italy A . l Private Sector Employees A . 1.1 The Pre Amato Regime • Retirement Age: 60 for men, 55 for women. • Minimum Number of years of contribution to the system: 15 • Rule to determine the first pension: Pi = RP * (3 * N where RP (the Re-tribuzione pensionabile) is an function (average) of wages , 3 is a coefficient that is a function of the value of RP and N is the number of years that the person has contributed to the system. • Rule to determine RP: under the Pre-Amato regime RP is an average of the wages received in the last five years preceding retirement, after having multiplied those wages for given coefficients that are meant to correct for inflation. • Rule to determine 3: for the part of RP below or equal to a given value (say 137), 3 is equal to 0.02. For the part of RP between w and t*7(l + 1/3), 3 is equal to 0.015, for the part of RP between w(l + 1/3) and zo(l + 2/3) 3 is equal to 0.0125 and for the remaining part 3 is equal to 0.01. has a value of approximately 45.000.000 of 1990 equivalent Liras. • Maximum value for N: 40 years. • There is a minimum pension rule that integrates the pensions that are below the minimum value (approximately 6.700.000 in 1990 equivalent Liras). The 88 rule governing the integration is quite complex and relates the possibility of obtaining the integration and its amount to the income of the recipient. • Pensions are indexed to the growth rate of wages in the manufacturing sector (hence approximately to the growth rate of prices plus the growth rate of productivity in this sector). Indexation though is a function of the value of the pension itself: 100% for the part that is below twice the minimum, 90% for the part of the pension that is between 2 and 3 times the minimum and 75% for the remaining part. A . 1.2 Amato Reform • Retirement Age: to be extended to 65 for men and 60 for women (one year every two calendar years until 2001). • Minimum Number of years of contribution to the system: to be extended to 20 (one year every two calendar years until 2001). • Different treatment according to the number of years of working experience (more or less than 15) as of 31/12/1992. • Rule to determine the first pension: the first pension is now a sum of two parts (Qiand Q2) each of them computed according to the following formula Qi = RPi * Pi* Ni , i = 1,2. The second part varies according to the total working experience of the retiree. • For those who have more than 15 years of working experience as of 31/12/1992: RP\ is an average of the wages received in the last five years previous to retirement, after multiplying those wages by some coefficients (Coeff.A) meant to take into account the increase in prices, 81 is the same as in the Pre-Amato and N i is the number of years that the person has contributed to the system prior to 1993. RP2 is an average of the wages received over the last 6 years, where 6 is equal to 5 in 1993 and reaches a maximum value of 10 for those retiring in 2001. Note that the values of the coefficients by which the past wages have to be multiplied (Coeff.B) are 1% higher (per year) then the values used to compute RP\ in the first part. For the part of RP2 below or equal to vj, /32 is equal to 0.02. For the part of RP2 between w and zv(l + 1/3), 82 is equal to 0.016,for the part of RP2 between zu(l + 1/3) and w(l + 2/3) f32 is equal to 0.0135, for the part of RP2 between xu(l + 2/3) and zu(l +0.9) 82 is equal to 0.011 and for the remaining 89 part 82 is equal to 0.009. N2 is given by the number of years worked after 1993 until retirement. • For those who have less than 15 years of working experience as of 31/12/1992: the first part is the same as the one for those who have working experience greater than 15 years, and so are B2 and N2, while RP2 is an average of the wages received over the last i? years, where z? is equal to [5+(Retirement Year- 1993)]. Note that the values of the coefficients by which the past wages have to be multiplied (Coeff.B) are 1% higher (per year) then the values used to compute RP\ in the first part. • Maximum value for N\ + N2'\s : 40 years. • There is a minimum pension rule that integrates the pensions that are below the minimum value (approximately 6.700.000 in 1990 equivalent Liras). The rule governing the integration elates the possibility of obtaining the integration and its amount to the income of the recipient and of his/her spouse. • Pensions are indexed to the growth rate of prices. Indexation though is a function of the value of the pension itself: 100% for the part that is below twice the minimum, 90% for the part of the pension that is between 2 and 3 times the minimum and 75% for the remaining part. A.2 Public Sector Employees As already mentioned, public sector employees are managed by two different funds and are governed by slightly different rules, depending on their status as State or Local employees. Since from our dataset it is not possible to know to which group every worker belongs we had to make a choice. We assumed that every public sector employee belongs to the State and its pension is hence managed by the Treasury. We only focus on Old Age Pension (Pensione di Vecchiaia). A.2.1 Pre Amato Regime • Retirement Age: 65 for men and women. • Minimum Number of years of contribution to the system: 15 • Rule to determine the first pension: Pi = RP * (3a * N a + (3b * iVj,),where RP is the last wage increased by 18 % , Qa is equal to 0.0233, iVa represents 90 the first 15 years of contribution to the pension system, 8b is equal to 0.018 and iVftis equal to the Number of years of contribution minus 15, where the maximum number of working years valid to compute the pension is 40. • There is a minimum pension rule that integrates the pensions that are below the minimum value. • Pensions are indexed to the growth rate of wages in the manufacturing sector (hence approximately to the growth rate of prices plus the growth rate of productivity in this sector). Indexation though is a function of the value of the pension itself: 100% for the part that is below twice the minimum, 90% for the part of the pension that is between 2 and 3 times the minimum and 75% for the remaining part. .2.2 Amato Reform • Retirement Age: remains the same. • Minimum Number of years of contribution to the system: to be extended to 20 (one year every two calendar years until 2001). • Different treatment according to the number of years of working experience (more or less than 15) as of 31/12/1992. • Rule to determine the first pension: the first pension is now a sum of two parts (Q\ and Q2) each of them computed according to the formula presented below. The second part varies according to the total working experience of the retiree, while Qi is computed in the same way for both type of workers. • For those who have more than 15 years of working experience as of 31/12/1992: Q\ is computed in the same way as the first pension according to the Pre Amato regime, which the caveat that now N\ amounts to the total number of years of contribution as of 31/12/1992. Q2 is computed in the same way as for private sector workers. • For those who have less than 15 years of working experience as of 31/12/1992: Q\ is the same as the one for those public sector workers who have working experience greater than 15 years, while Q2 is computed according to the formula Q2 = RP2 * 02 * N2, where RP2 is an average of the wages received over the last ip years, where ip is equal to [l+(Retirement 91 Year- 1993)], while 82 and N2 are identical to those defined for private sector workers. Maximum value for N\ + N2 is : 40 years. There is a minimum pension rule that integrates the pensions that are below the minimum value. Pensions are indexed to the growth rate of prices. Indexation though is a function of the value of the pension itself: 100% for the part that is below twice the minimum, 90% for the part of the pension that is between 2 and 3 times the minimum and 75% for the remaining part. 92 Appendix B Wage estimation: Age and Cohort Effects Our discussion has been based largely on the possibility of separating age and cohort effects in the wage equation1. We have tested this hypothesis using two data sets. The first one collects in-dividual observations. The second one is obtained from the first one by averaging wages for the various sex-age-sector-education cells. In both cases we control for cohort-age interaction. When we have individual data we can take into account cer-tain characteristics over which we could not condition when creating representative individuals (due to an insufficient number of observations) like the area where the household resides (North West, North East, Center, South and Islands ) and the type of job (white collar, blue collar, manager). The results that we obtain when using group-cohort averages show signs of sig-nificant age-cohort interaction for males Junior High and High School Graduates in the public sector, for males Junior High Graduates in the private sector and for females Junior High and High School Graduates in the private sector. When we use individual data we find significant evidence of age-cohort interac-tion only for males College Graduates in the public sector, for most cohorts of males Junior High School Graduates in the private sector, for very few cohorts of females Junior High and High School graduates in the private sector and for most cohorts of females College graduates in the private sector. The coefficient on age-cohort interaction is negative in all cases but for females College Graduates in the private 1 Notice that we do not claim of separately identifying cohort, age and time. Our point is just to show that the age profiles within the various groups are not cohort specific. 93 sector, whose sign is positive2. We have also verified that when we drop the interaction term, the explanatory power of the regressions is affected in only a minor way. Given the previous conclusions we feel quite confident in concluding that, par-ticularly when using individual data, there is not much evidence of cohort specific age profiles . The following represents the wage equation that we have estimated when we used individual data (including age-cohort interaction) \nwjt = 6O+DJ*<5I+OJ*<52-MJ*<53+^^ where Dj is a vector of cohort dummies, Oj is a dummy that has a value 1 for blue-collar workers (or managers if the sample is constrained to include only College workers), Aj is a vector of area dummies, a,jt is age of individual j at time t and ut is a common time effect that captures cyclical effects. The coefficient on the squared or cubic term for age is not significant for all groups and when this is the case we drop it. One important point concerns sample selection. We had do choose the age interval outside which we should drop observations. Given that we wanted to restrict the sample to individuals attached to the labor market in stable way we chose to restrict the sample to those who, in each year, are above 20 if Junior High or High School graduates and 25 if College graduates. This values are slightly higher than the average starting age computed obtained from the sample but we wanted to avoid including individuals that are only temporarily attached to the labor market. Analogously, we had to choose the upper limit of the interval. We conducted various experiments. First we excluded individuals older than 60 if males and 55 if females (those were the two mandatory retirement ages for Old Age Pensions in the private sector). Then we excluded individuals older than 60 if males and 55 if females if they work in the public sector and individuals older than 55 (males) and 50 (females) in the private sector, hence dropping those who were closer than five years to the mandatory retirement age. By comparing the results obtained in the two cases using individual data we found that for High School graduates in the private sector (males and females) the age profile estimated using the first sample points towards a steep increase in the wage in the years immediately prior to retirement. When we applied the estimated coefficients (on age) on the individual observation in order to construct the full fife-cycle profile, we found values for real wages that were growing 2 A negative coefficient means that for more recent cohorts an extra year of experience increases labor income by less. 94 "too fast", particularly when we considered the profiles for private sector workers after the pension reform (which raised the retirement age in the private sector). We might have a selection bias according to which, in the presence of early retirement option, those who keep working until mandatory retirement age are also those who have higher wages. When we exclude from the sample those who are closer than five years to the mandatory retirement age (in both sectors) we obtain results (after the averaging) that are more convincing. The results for log net wage estimation at the individual level are reported (only for males) in Tables 3 and 4 for net wages (see Figs.22 to 25). In the following paragraph we focus separately on the age and cohort profiles obtained for net wages, pointing out the differences that exist between the dataset that uses individual observations and the one that uses cohort averages. When looking at the graph we should keep in mind that not all the coefficients on the cohort dummies or on the age-dependent variables are significant. B . l Age profiles (Net Wages) In this paragraph we briefly analyze the age profiles obtained for the various groups using both individual observations and cohort averages. We just want to bring to attention the fact that when we compare the results obtained with the two datasets what matters is she shape of the age profile and not the intercept, because the starting salary, for each dataset, has been constructed in a different way. • Males-College Graduates-Public Sector. The results obtained with indi-vidual and cohort data are very similar. The log of wage can be well approxi-mated by a linear function of age (the coefficient is 0.019). Higher order terms are not significant. • Males High School Graduates-Public Sector. In both cases the log of wage equation is well described by a quadratic function of age. The values of the coefficients are not identical but the overall shape of the age profile is similar. When we use individual data we find that the age profile is slightly more concave than when we use cohort data. • Males Junior High School Graduates-Public Sector. The two estima-tions point towards a log wage profile that is quadratic in age. The profile is steeper at the beginning and then more concave according to cohort data. The overall shapes differ in terms of implication for wage growth close to retirement 95 age. Note that tinder both scenarios we do not have drops in real wages at the end of the carrier. We conclude that public sector workers are quite protected, even at the lowest educational level. Males-College Graduates-Private Sector. For this group the estimation from both samples points towards a log wage profile that is quadratic in age. The profile is steeper at the beginning and then more concave according to cohort data. The overall shapes differ in terms of implication for wage growth close to retirement age. According to cohort data, in the latest years real net wages drop. We do not have this result when we use individual data. Males High School Graduates-Private Sector. For this group the results obtained with the two types of data differ substantially. When we use individ-ual data we find strong evidence that the age profile for log wages can be well described by a cubic function. Net wages growth substantially from the age of 20 to the age of 35, then they almost stop growing and finally start rising again after 48. When we use cohort averages, we do not find evidence of sig-nificancy of the cubic term. Instead we find that log wages are well described by a quadratic in age. Notice that even in this case we do not have drops in real net wages at the end of the working life. Males Junior High School Graduates-Private Sector. In both cases the log of wages is strongly concave (the coefficients are almost identical) and we have actual drops in real net wages at the end of the working period. This appears to be the group that faces the "worst" age profile (among males). Females College Graduates-Public Sector. With both individual and cohort data the log wage does not vary much with age. Coefficients on the quadratic and cubic term are not significant. We find that the significance of the coefficients on the linear term is higher with individual data . The value of the coefficient is still quite low (0.00795), which gives rise to a quite flat age profile. Females High School Graduates-Public Sector. In both cases the cu-bic term is not significant, and the combined effect of the coefficients on the quadratic and linear terms imply an almost linear age profile (the profile is slightly steeper with individual data). In fact, the effect of age on wage growth decreases only in the working years prior to retirement, but such an effect does not induce a decline in real net wages. 96 • Females Junior High School Graduate-Public Sector. With both dataset we find concave age profiles with almost identical values for the coefficients (the cubic term is not significant) with a decline in real net wages in the years prior to retirement. • Females College Graduates-Private Sector. In both cases we find that log wages are linear in age (the coefficients on the square and cubic terms are not significant) with a coefficient approximately equal to 0.04. • Females High School Graduates-Private Sector. For this group we find that the coefficient on the cubic term is significant when we use individual data while, with cohort averages, it is significant at a lower confidence level. Even if the significance level is lower than the usual one, we have kept this coefficient because when we drop it the significance of the other age variables and the overall significance of the regression drop. As for males with a High School Diploma, we can see that wages first increase then, at around thirty, remain almost stable and then rise again prior to retirement. • Females Junior High Graduates-Private Sector. For this group the age profile is very flat, according to the estimation obtained using both dataset. The coefficients on the squared and cubic term are not significant and the linear hypothesis is accepted at the normal level of significance only for individual data. For cohort data we get that we cannot reject the hypothesis that the log of real net wages does not grow with age. Having described the relationship between age and net wages we notice that, using both dataset, males have a steeper age profile than females but more so in the private sector3. Moreover only in the private sector and for High School Graduates (males and females) we find that the cubic term on age is significantly altering the shape of the age profile. In the public sector, as expected, wage profiles are more similar (comparing between sex and educational attainment). B.2 Cohort Profiles (Net Wages) Given the way we have structured our estimation, cohort effects can be interpreted as "Entry Wage" effects, because we allow for differences between cohorts that operate at the intercept level, which is the wage received at zero experience (or normalized 3See Figs. 25 and 27. 97 age zero). In terms of biological age, the zero experience age corresponds to 20 years for Junior High and High School Graduates and 25 for College Graduates. Notice also that human wealth profiles, defined as the present value of net wages from the standpoint of normalized age, depends on the entry wage, on the age profile and on retirement age. For instance, for the same retirement age and for identical entry wages, a cohort that has a steeper age profile will also have a higher present value of net wages. But, if we keep constant only the retirement age, it could be that a certain cohort experiences a low entry wage but a steep age profile, so that at the end the present value of net wages for that cohort is higher than the one experienced by another cohort that has higher entry wages but flatter age profiles. It is also important to notice that, at the individual level, we have more obser-vations for the two groups with the lowest education and for the middle cohorts. This implies that our estimates of the entry wages (cohort effects) for the most re-cent generations of College Graduates could be biased. For this reason, when we estimate the relationship between fixed effects in consumption and pension wealth (and human wealth) we drop the most recent cohorts. In the remaining part of the paragraph when we talk about cohort effects we refer to differences in "Entry Wages". For each group, the oldest cohort is our reference point. Notice that with individual data we cut the sample at different retirement ages: 60 for males in the public sector, 55 for males in the private sector, 55 for females in the public sector and 50 for females in the private sector. This means that the oldest cohort used as a reference changes according to sex, education and sector4. • Males-College Graduates-Public Sector. Using both types of data we find that there are no significant cohort effects. • Males High School Graduates-Public Sector. When we use cohort data, we find that there are significant cohort effects (with respect to the oldest cohort) for cohort 7, 8 and 9. For the remaining ones the effects are quite strong but they are not significant at the 95% confidence level. All cohorts exhibit entry wages higher than the reference one, and all cohorts but cohort 9, which enters the labor market in 1987, show entry wages that are higher than the one characterizing the immediately preceding cohort. When we use individual data we find that there are no significant cohort effects but that the 4See Tables 3 and 4 and Figs. 26 and 28. 98 ones that almost reach the usual level of significancy refer to the cohorts that show significantly higher entry wages according to the other dataset. Males Junior High School Graduates-Public Sector. According to the estimation that uses cohort data we find that there are significant Entry Wage effects for cohorts 7, 8, 9, 10, while they seem very unlikely for cohorts 2, 3 and 4. Each cohort has been experiencing cohort effects that are positive when compared both to the reference cohort and to the previous cohort, a part for cohort 10, the most recent one, for which we have a cohort effect that is slightly lower than the one for cohort 9. Analogous results are obtained when we use individual data, with the difference that in this case the coefficient for cohort 10 is no longer significant, while the one for cohort 6 becomes significant. The picture that emerges in both cases is of a cohort profile that is initially quite flat (for the oldest cohorts) and then rises, but for the last cohort, for which the "Entry Wage" drops. Males-College Graduates-Private Sector. With the quasi-panel dataset we do not find significant cohort effects. With individual data we find signifi-cant cohort effects for cohort 5, 6, 7, 8 and 9. They are all positive and for all cohorts but the last one (that enters in 1993) each younger cohort experiences entry wages higher than the one experienced by the immediately preceding cohort. Males High School Graduates-Private Sector. For this group we find less evidence of significant cohort effects. With the quasi-panel dataset none of the cohort dummies is significant at the 95% confidence level, even tough there is evidence that the data suggest positive cohort effects for all but the most recent cohort. With individual wages we find significant and positive cohort effects for cohorts 4 and 9. What is interesting is that from 4 to 7 each cohort experience entry wages that are lower than those of the immediately preceding cohort. Those effects are not statistically significant at the ordinary level but the data still point towards declining cohort effects. Males Junior High School Graduates-Private Sector. With cohort data we have no evidence of significant cohort effects. Instead, with individual data we find strong evidence of "Entry Wage" effects for all cohorts but 3. They are all positive and they imply a smoothly raising "Entry Wages" profile, but for cohorts 7 and 10, who experience cohort effects that are lower than those of the immediately preceding ones. 99 Females College Graduates-Public Sector. Using cohort data we do not find evidence of significant cohort effects. An analogous result is reached when we use individual data. Females High School Graduates-Public Sector. From the quasi-panel that uses cohort averages we find evidence of cohort effects. For cohort 6 and 9 they are significant at the 95% confidence level, while for the other cohorts they are significant at a level of confidence higher that 90%. They are all positive and imply that each following cohort experiences higher entry wages than the preceding ones, but for the cohorts immediately following cohort 6 and 9 (the two that show significant fixed effects). The results obtained using individual data points towards even stronger cohort effects. They are all significant and positive. Only for cohort 7 the estimated cohort effect implies a lower "Entry Wage" than the previous cohort. Females Junior High School Graduate-Public Sector. Using the quasi-panel we do not find evidence of significant cohort effects. The same is true for the other dataset. Females College Graduates-Private Sector. For this group the quasi-panel dataset signals strong cohort effects. They are all positive and they all imply a raising "Entry Wages" profile. Using individual data we find that significant cohort effects are present only for cohorts 6, 7 and 8. The picture that emerges is one of rising cohort profiles. Females High School Graduates-Private Sector. Cohort data show sig-nificant cohort effects for cohorts 4, 5 and 6. For those three cohorts the ef-fects are positive but they also imply that each cohort has been facing "Entry Wages" that are lower than the one experienced by the immediately preceding one. With individual data we do not find significant cohort effects. Females Junior High Graduates-Private Sector. When we use the quasi-panel we find significant (and positive) cohort effects for cohort 4, 5 and 6, for which the estimated coefficients imply a negative "Entry Wage" profile. When we use individual data we do not find evidence of significant cohort effects. 100 Appendix C Perfect Foresight-Households where the Head is Married For this sample we adopt a different definition for consumption, which is now total household consumption. Human and pension wealth are also different because they are the sum of the values for the husband and the wife. The underlying hypothesis is that the household optimizes as a unique entity and that the relevant explana-tory variables are just the sum of the two individual variables. Notice also that we attribute households to a particular group according to the characteristics of the Head of the households. Given our approach we can have the following types of households, as far as sectors are concerned: 1) both the husband and the wife work in the private sector; 2) they both work in the public sector; 3) they work in two different sectors. Given the reduced number of observations we could not create a representative household for each type and we conditioned only on the basis of the sector and education relevant for the husband. In the estimation process we keep the distinction between sectors but the results should now interpreted carefully, given that we do not specify anything regarding the wife. Given that we have households composed of members from different sectors and with different educational attain-ments, the distinction between groups and sectors are less meaningful than for the previous paragraphs. C . l Estimation of the Fixed effects-Perfect Foresight-Households where the Head is married We find evidence of age-cohort interaction only for the group of High School Gradu-ates working in the private sector. We have verified that for this group the exclusion 101 of the term that captures age-cohort interaction does not affect either the signifi-cance of the coefficients (they are significant in both cases) or the slope of the fixed effects cohort profiles. To get consistency across groups, we present the fixed effects estimated when we do not control for age-cohort interaction. C . l . l Private Sector We do not find significant evidence of rising cohort effects profiles for College Grad-uates, while we do find them for High School and Junior High School graduates. Moreover, we find evidence of age-cohort interaction only for the group of High School graduates. When significant, the fixed effects show rising cohort profiles. Notice that when we use the larger sample that gathers males heads of house-holds, the group of College Graduates in the private sector shows significant age-cohort interaction. In the previous paragraphs we focused on Equivalent Scale con-sumption rates while here we look at total household consumption rates. We created Equivalent Scale consumption dividing household's consumption by the square root of the number of components, which is a variable strongly correlated with age (it is actually concave in age). By controlling for the number of components and hence in part for age we would expect for Equivalence Scale consumption less interaction between cohort dummies and age. Instead we find the opposite result. A possible interpretation of this result is based on sample selection. If people choose to get married only when they can provide a sufficiently high income and hence sufficiently high consumption levels to the household, by restricting the sample to married cou-ples we take away cohort variation in the age at which people get married and hence observe less age-cohort interaction. C.1.2 Public Sector For College Graduates we find some evidence of significant cohort fixed effects that imply rising (but not for all cohorts) profiles. We do not find evidence of age-cohort interaction. For the group of High School Graduates we find evidence of significant fixed effects (almost for all cohorts) implying rising cohort profiles. We do not have evidence of significant age-cohort interaction. For the group of Junior High School Graduates the evidence points towards not significant cohort fixed effects (only for the middle cohorts we have some evidence of significantly rising "Entry consumption rates") and no age-cohort interaction. 102 C.2 Explaining the Fixed Effects-Perfect Foresight-Households where the Head is married Given that we assign households to one sector or to the other depending on the characteristics of the Head of the household, the across-sector comparison is less meaningful than it was for the sample of Male Head of Households. Still we attain results that are very close to those got for the larger sample. When we pool all the data and regress the fixed effects (eventually corrected for their standard errors) on ln [l + B ic+ B 2c j ? including sector and education dummies (interacted among themselves) and interaction between OTYAWR and the educa-tion and sector dummies, the regression obtains a very high Adj-i?2 (0.94) and the explanatory variable (OTYAWR) is significant and affects positively entry consump-tion rates. The coefficient on the interaction between OTYAWR and the dummy for the public sector is negative but not significant. When we analyze the two sectors separately the results obtained for the larger sample are confirmed (but only when we use the original fixed effects, when we use the corrected fixed effects OTYAWR ceases to be statistically significant in both sectors). We get a positive and significant coefficient on OTYAWR in the private sector and a positive but not significant coefficient for the public sector. C .3 Conclusions We can conclude that the results obtained for the larger sample are confirmed when we focus on married couples. For most groups we have estimated statistically significant and rising cohort fixed effects and only for one group we have found evidence of significant age-cohort interaction. The implied rising entry consumption rate cohort profiles are positively correlated with the ratios of Old to Young Age wealth. 103 Appendix D Complete Surprise-Households where the Head is Married Using this restricted sample we confirm and strengthen the results obtained for the larger sample under the hypothesis of Complete Surprise. The same results for age-cohort interaction that we discussed for the case of Perfect Foresight apply to Complete Surprise as well. D . l Estimation of the Fixed effects-Complete Surprise-Households where the Head is married D . l . l Private Sector For College Graduates we find evidence of significant (but for cohort 4) cohort effects, while we do not find evidence of significant negative age-cohort interaction. The cohort profiles for consumption rates are positively sloped. For the group of High School Graduates we find significant (and rising) cohort effects and significant age-cohort interaction. For the group of Junior High School Graduates we have evidence of significant and rising cohort effects, but no evidence of age-cohort interaction. D.1.2 Public Sector For College Graduates we do not find evidence neither of significant cohort effects, nor of significant age-cohort interaction. For the group of High School Graduates we find some evidence of rising cohort effects but this evidence is not significant at the customary level of confidence, while 104 we do not find evidence of age-cohort interaction. Even less evidence of significant cohort effects we have for the group of Junior High School Graduates. D.2 Explaining the Fixed Effects-Complete Surprise-Households where the Head is married The results show that when we pool the observations for the two sectors, including sector and education dummies (interacted among themselves) and interaction be-tween OTYAWR and the education and sector dummies, the coefficient on OTYAWR is negative and significant. The coefficient on the interaction between OTYAWR and the public sector is positive but eve for this sector, the overall effect of OTYAWR remains negative. Analogous results are found when we look at the two sectors separately. D.3 Conclusions The previous results confirm and strengthen the results obtained for the larger sam-ple under the same assumptions regarding the agents' information set. When we work under the hypothesis of Complete Surprise the relationship that we attain the result that, under the proposed model, the rising consumption rates cohort profiles cannot be explained by the profiles for the Old to Young Age Wealth ratio. 105 Table 1: Males Public Sector-Saving Rates College High School Junior High School Graduates Graduates Graduates Age -.016855 .0064563 .0387736 (.0401485) (.0242149) (.0199238) Age Square .0004716 -.0009574 -.0017989 (.0024614) (.0013101) (.001121) Age Cube -5.43e-06 .0000148 .0000183 (.000044) (.0000206) (.0000181) Cohort3 -.1028095 -.0884633 .0729315 (.0987873) (.0714232) (.0691963) Cohort4 -.0493048 -.2576866 -.0671068 (.1198336) (.0865554) (.0838508) Cohort5 -.0641521 -.2804531 -.1606418 (.1434428) (.1022818) (.099001) Cohort6 .0198227 -.3152613 -.2619685 (.168036) (.1189687) (.114877) Cohort7 -.1543298 -.3081918 -.2837126 (.1873116) (.1348407) (.1303987) Cohort8 -.3769796 -.4130473 -.2286282 (.204716) (.1472314) (.1424933) Cohort 9 n.a. -.449918 -.2951421 (.1588751) (.1538569) Unemp.rate -.0183412 -.1417412 -.0022934 deviation (0.527943) (.0353265) (.033847) Intercept 1.407606 1.579383 1.11494 (.2598238) (.1912375) (.1725366) Adj-R2 0.098 0.3483 0.2178 Number of Obs. 43 50 51 Dependent Saving rate Saving rate Saving rate Variable Note: Standard Errors are in parenthesis. 106 Table 2: Males Private Sector-Saving Rates College High School Junior High School Graduates Graduates Graduates Age .0125321 .0222383 -.0111934 (.032276) (.0167272) (.0103773) Age Square -.0011884 -.0018225 .0004378 (.00207) (.0009411) (.0005839) Age Cube .0000213 .0000273 -9.32e-06 (.0000381) (.0000152) (9.41e-06) Cohort3 .1183549 -.087025 -.0866492 (.0965175) (.0580944) (.0360409) Cohort4 .0619545 -.1354546 -.1561929 (.1170725) (.0703978) (.0436737) Cohort5 .1425127 -.2165198 -.2351573 (.1397272) (.0831173) (.0515647) Cohort6 .082121 -.2973639 -.2529834 (.1636175) (.0964468) (.0598341) Cohort7 .0431078 -.3101313 -.2747509 (.182939) (.1094776) (.0679182) Cohort8 .0025584 -.3624817 -.3319552 (.1998202) (.1196317) (.0742177) Cohort 9 n.a. -.527473 -.4035976 (.1291721) (.0801364) Unemp.rate -.10506 -.044379 -.0314608 deviation (.0509347) (.0284166) (.0176292) Intercept 1.115322 1.472744 1.458928 (.2302557) (.1448549) (.0898658) Adj-R2 0.0922 0.3054 0.4475 Number of Obs. 44 51 51 Dependent Saving Rate Saving Rate Saving Rate Variable Note: Standard Errors are in parenthesis. 107 Table 3; Males Public Sector-Log of Net Wages College High School Junior High School Graduates Graduates Graduates Age .0192163 .0381413 .0350246 (.0035619) (.0094727) (.0069282) Age Square n.a. -.0005177 -.0004682 (.0001977) (.0001338) Age Cube n.a. n.a. n.a. Area2 -.0414541 -.0473714 -.0020835 (.0523965) (.030259) (.0270569) Area3 -.0327131 -.0296818 -.0188404 (.0552004) (.0320878) (.0278986) Area4 -.1143948 -.1225811 -.0817291 (.0515868) (.0306461) (.0280146) Area5 -.0979358 -.1379989 -.1156504 (.0567903) (.0352548) (.0347057) Manager .4101354 n.a. n.a. (.048886) Blue Collar n.a. -.1169717 -.1931744 (.037672) (.0175172) Cohort 2 -.0193609 .0392605 -.047521 (.1051049) (.0801883) (.0659337) Cohort 3 -.0276743 .0800477 -.0062095 (.1065959) (.0799971) (.0566664) Cohort 4 .0973573 .1044831 .0363369 (.1121068) (.0900114) (.0589897) Cohort 5 .1469033 .0699301 .1163352 (.1258947) (.0945699) (.0638088) Cohort 6 .1867857 .1094805 .1657013 (.1290033) (.0973197) (.06746) Cohort 7 .1640385 .1908446 .2311799 (.1406776) (.1009273) (.0717285) Cohort 8 .1064572 .1981194 .2915384 (.1501808) (.1104519) (.0810963) Cohort 9 -.1489575 .1538456 .3078689 (.2511085) (.1151937) (.0963593) Cohort 10 n.a. .1279997 .2326103 (.1533168) (.1537603) Urate .0705033 -.0155403 -.0275824 (.041878) (.0235684) (.0180156) Intercept 9.658632 9.341286 9.322329 (.1716403) (.1357741) (.1078318) Adj-R2 0.30 0.1573 0.1574 Number of Obs. 1063 2271 2405 Dependent Log of Real Net Log of Real Net Log of Real Net Variable (Annual) Wage (Annual) Wage (Annual) Wage Note: Standard Errors are in parenthesis. Table 4: Males Private Sector-Log of Net Wages College High School Junior High School Graduates Graduates Graduates Age .0698378 .1273706 .0437679 (.0143096) (.016626) (.0051614) Age Square -.0009615 -.005386 -.0007767 (.0004107) (.0009499) (.0001115) Age Cube n.a. .000081 n.a. (.0000162) Area2 -.1529305 -.1049044 -.0772598 (.046439) (.0211169) (.013293) Area3 -.0485079 -.0907516 -.0812546 (.0465332) (.0186196) (.0136341) Area4 -.2055662 -.2247091 -.2626822 (.0526701) (.0209553) (.0153364) Area5 -.1677483 -.1990446 -.2877594 (.0543115) (.0303049) (.0378549) Manager .3393984 n.a. n.a. (.0401782) Blue Collar n.a. -.2315021 -.2521247 (.0208529) (.0119992) Cohort 3 .0812977 .1172824 .0586685 (.091329) (.0735897) (.0353676) Cohort 4 .0394465 .168034 .0823853 (.099985) (.073306) (.0354324) Cohort 5 .2220611 .1484543 .1082699 (.1175306) (.081954) (.0391641) Cohort 6 .2961728 .1337141 .1205971 (.1318556) (.0849453) (.0445875) Cohort 7 .4663878 .1288794 .1200127 (.1515685) (.0873331) (.0454348) Cohort 8 .4878311 .1587496 .1323545 (.1563043) (.0903066) (.0497624) Cohort 9 .3742283 .2032076 .1649659 (.1750775) (.0940309) (.0631724) Cohort 10 n.a. .1525304 .1530174 (.1054093) (.0625451) U.rate .0781055 .0334454 .0011863 (.0292808) (.0137141) (.0102913) Intercept 9.198364 9.015619 9.434808 (.1841171) (.1288134) (.0711671) Adj-R2 0.34 0.35 0.214 Number of Obs. 1256 5978 10782 Dependent Log of Real Net Log of Real Net Log of Real Net Variable (Annual) Wage (Annual) Wage (Annual) Wage Note: for the Private Sector we cut the sample at the age of 55 and hence cohort 2 is the oldest one. Note: Standard Errors are in parenthesis. 109 Table 5; Males Public Sector- Estimation of Cohort Effects-Perfect Foresight College High School Junior High School Graduates Graduates Graduates Age -.025133 .242618 -.043993 (.120818) (.138114) (.172611) Age Square .000654 -.003217 .002635 (.002157) (.002085) (.002044) Age Cube -6.92e-06 .000015 -.00004 (.00003) (.00002) (.000016) Number of Income -.040550 .190545 .191350 Recipients (.094636) (.108686) (.152497) Manager -.377283 -.446839 5.50131 (.142854) (.393188) (4.4687) Blue Collar n.a. .220016 -.203736 (.209365) (.101161) Number of -.086477 -.169422 -.146837 Dependent Children (.064905) (.079092) (.075192) Wife .287755 .086508 -.063421 (.142825) (.145249) (.195413) Cohort3 -.09901 .889657 -.064011 (.429712) (.488056) (.631929) Cohort4 -.195416 1.66962 .023189 (.785141) (.901736) (1.19336) Cohort5 -.211592 2.2599 .109588 (1.06638) (1.24948) (1.65857) Cohort6 -.259779 2.72244 .159815 (1.28518) (1.52732) (2.0414) Cohort7 -.198293 3.07655 .199681 (1.43136) (1.75072) (2.3371) Cohort8 .025164 3.41468 .142491 (1.51063) (1.90050) (2.54037) Cohort 9 n.a. 3.60026 .253890 (1.9940) (2.65018) Age*Cohort Index .004153 -.021858 -.000363 (.013479) (.013359) (.017761) Intercept -.127476 -4.25269 -.361886 (.013479) (2.02769) (2.76487) Adj-R2 0.5097 0.3699 0.5249 Number of Obs. 43 50 51 Dependent Variable Log of Equivalent Scale Log of Equivalent Scale Log of Equivalent Scale Consumption Rate Consumption Rate Consumption Rate Note: Standard Errors are in parenthesis. 110 Table 6; Males Private Sector-Estimation of Cohort Effects-Perfect Foresight College Graduates High School Graduates Junior High School Graduates Age .376369 .433822 .086612 (.156935) (.117565) (.07350) Age Square -.003763 -.004007 -.001156 (.002582) (.001605) (.309653) Age Cube -5.26e-06 -1.64e-06 6.02e-06 (.000034) (.000014) (.0.00012) Number of Income .202774 -.155137 .338435 Recipients (.167947) (.113800) (.137666) Manager -.140658 .105062 10.0395 (.161107) (.307332) (5.29601) Blue Collar n.a. .139731 .290467 (.150505) (.183738) Number of -.117415 -.201452 -.141958 Dependent Children (.088124) (.055012) (.074224) Wife -.173698 .574515 -.340548 (.178020) (.159275) (.233344) Cohort3 1.43165 1.71506 .282188 (.538444) (.415702) (.282787 Cohort4 2.62517 3.17420 .589444 (.990439) (.782537) (.525687) Cohort5 3.63409 4.40818 .875075 (1.36148) (1.0860) (.722368) Cohort6 4.39714 5.40330 1.06626 (1.63995) (1.32392) (.88505) Cohort7 4.92870 6.13480 1.29361 (1.83279) (1.50396) (1.00595) Cohort8 5.27682 6.67294 1.44515 (1.93917) (1.62927) (1.08804) Cohort 9 n.a. 7.12640 1.55069 (1.69795) (1.12631) Age*Cohort Index -.044097 -.045004 -.006807 (.017250) (.011599) (.007805) Intercept -5.59467 -7.19166 -2.43409 (1.94530) (1.73053) (1.193638) Adj-R2 0.4085 0.8125 0.8315 Number of Obs. 44 51 51 Dependent Variable Log of Equivalent Scale Log of Equivalent Scale Log of Equivalent Scale Consumption Rate Consumption Rate Consumption Rate Note: Standard Errors are in parenthesis. I l l Table 7: Males All Groups Cohort Effects on Explanatory Variables Perfect Foresight Both Sectors Log OTYAWR 307.077 (37.722) Log OTYAWR*Public 469.601 Sector (408.21) Public Sector -9.88340 (9.006) High School Graduates -6.89817 (.6229) College Graduates -7.39752 (.7705) Public Sector*High 5.18182 School Graduates (.7477) Public Sector* College -5.74114 Graduates (6.9283) Intercept -7.5666 (.7507) R2 0.733 Number of Obs. 46 Dependent Variable Cohort Fixed Effects (Robust Estimation) Note: Robust Standard Errors are in parenthesis. 112 Table 8: Males Private and Public Sector-Cohort Effects on Explanatory Variables Perfect Foresight Private Sector Public Sector Log OTYAWR 307.077 (37.722) 776.678 (406.46) High School Graduates -6.89817 (.6229) -1.71634 (.4135) College Graduates -7.39752 (.7705) -13.1386 (6.888) Intercept -7.56662 (.7507) -17.4500 (8.975) Adj-R2 0.686 0.65 Number of Obs. 23 23 Dependent Variable Cohort Fixed Effects (Robust Estimation) Cohort Fixed Effects (Robust Estimation) Note: Robust Standard Errors are in parenthesis. 113 Table 9: Males Public Sector-Estimation of Cohort Effects-Complete Surprise College High School Junior High School Graduates Graduates Graduates Age -.496787 .375369 .259819 (.371059) (.375788) (.395396) Age Square .009855 -.003081 -.000085 (.005828) (.004644) (.004796) Age Cube -.000083 -6.55e-06 -.000047 (.00007) (.000056) (.000036) Number of Income .023589 .317101 .381932 Recipients (.120875) (.116964) (.160997) Manager -.504861 -1.08052 8.22972 (.293183) (.861392) (7.32769) Blue Collar n.a. -.042596 -.181232 (.270771) (.130144) Cohort4 -1.21293 1.41537 1.16005 (1.06642) (1.18468) (1.23377) Cohort5 -2.07762 2.54902 2.05008 (1.90466) (2.16149) (2.24905) Cohort6 -2.70541 3.49242 2.82990 (2.52043) (2.95127) (3.07177) Cohort7 -3.13169 4.11247 3.42991 (2.92031) (3.52638) (3.66975) Cohort8 -3.12562 4.67675 3.67026 (3.09927) (3.89663) (4.08263) Cohort 9 n.a. 4.82784 4.064118 (4.04917) (4.28093) Age*Cohort Index .053508 -.042551 -.035895 (.043954) (.041014) (.041595) Intercept 3.22682 -5.44126 -4.32275 (3.11496) (3.99768) (4.37569) Adj-R2 0.1895 0.3732 0.5711 Number of Obs. 27 32 33 Dependent Log of Equivalent Scale Log of Equivalent Scale Log of Equivalent Scale Variable Consumption Rate Consumption Rate Consumption Rate Note: Standard Errors are in parenthesis. 114 Table 10; Males Private Sector- Estimation of Cohort Effects-Complete Surprise College Graduates High School Graduates Junior High School Graduates Age .174201 .553015 .211898 (.311937) (.208927) (.175372) Age Square .003678 -.006272 -.001157 (.004825) (.002802) (.002138) Age Cube -.000119 9.90e-06 -.00001 (.000052) (.000024) (.00001) Number of Income .213835 .427787 .419513 Recipients (.136815) (.112726) (.099009) Manager -.384397 -.030864 4.10751 (.141660) (.488901) (5.88999) Blue Collar n.a. .454429 .281704 (.218035) (.210466) Cohort4 .872380 1.64710 .899871 (.89006) (.660365) (.549224) Cohort5 1.67823 3.17068 1.63424 (1.58452) (1.19666) (.99623) Cohort6 2.30461 4.36605 2.23392 (2.09910) (1.61273) (1.35282) Cohort7 2.77382 5.28607 2.76111 (2.43259) (1.91942) (1.61440) Cohort8 2.92462 5.94944 3.01808 (2.59151) (2.11883) (1.78597) Cohort 9 n.a. 6.59821 3.11157 (2.21476) (1.86052) Age*Cohort Index -.029980 -.055565 -.025979 (.036509) (.021817) (.018590) Intercept -3.19473 -7.44485 -4.15341 (2.60251) (2.22640) (1.94131) Adj-R2 0.6754 0.8687 0.8393 Number of Obs. 28 33 33 Dependent Log of Equivalent Scale Log of Equivalent Scale Log of Equivalent Scale Variable Consumption Rate Consumption Rate Consumption Rate Note: Standard Errors are in parenthesis. 115 Table 11: Males All Groups Cohort Effects on Explanatory Variables Complete Surprise Both Sectors Log OTYAWR -655.483 (177.77) Log OTYAWR*Public 1611.27 Sector (1162.43) Public Sector -35.3694 (29.057) High School Graduates -1.25613 (.6865) College Graduates 6.29330 (1.6908) Public Sector*High .064229 School Graduates (1.2979) Public Sector* College -27.1932 Graduates (29.029) Intercept 9.52447 (3.144) Adj-R2 0.6477 Number of Obs. 40 Dependent Variable Cohort Fixed Effects (Robust Estimation) Note: Robust Standard Errors are in parenthesis. 116 Table 12: Males Private and Public Sector-Cohort Effects on Explanatory Variables Complete Surprise Private Sector Public Sector Log OTYAWR -854.270 4755.34 (355.197) (1649.55) High School Graduates 13.3277 14.1735 (6.3166) (41.564) College Graduates -4.77805 220.040 (6.2579) (47.0937) Log OTYAWR* High -804.336 -693.537 School Grad. (370.19) (1658.292) Log OTYAWR*College 484.292 -6703.3 Grad. (360.28) (1710.144) Intercept 13.0807 -121.173 (6.066) (41.333) Adj-R2 0.885 0.933 Number of Obs. 20 20 Dependent Variable Cohort Fixed Effects Cohort Fixed Effects (Robust Estimation) (Robust Estimation) Note: Robust Standard Errors are in parenthesis. 117 Table 13: Males-Differences in Log Consumption Rates (1993-1991)-CompIete Surprise Private Sector Public Sector Cohort4 -.077407 -.186156 (.099687) (.119729) Cohort5 .066647 -.111080 (.078285) (.129254) Cohort6 -.051003 .229961 (.087124) (.157058) Cohort7 -.142017 -.319976 (.086447) (.170071) Cohort8 .007565 -.096003 (.107236) (.158258) Cohort 9 -.00975 -.129737 (.096231) (.178317) High School Graduate -.087596 .073712 (.065760) (.087494) College Graduate -.132114 -.050585 (.058220) (.083853) Age Difference .021534 .049084 (.038190) (.056664) Number of Income -.108829 .136012 Recipients Difference (.160051) (.267550) Number of Components -.079268 -.003847 Difference (.169569) (.143295) Adj-R2 0.4943 0.1451 Number of Obs. 20 20 Dependent Variable Log of Equivalent Scale Log of Equivalent Scale Consumption Rate Differences Consumption Rate Differences Note: Standard Errors are in parenthesis. 118 Table 14; Males- Differences in Log Consumption Rate (1993-1991)-Complete Surprise Both Sectors Private Sector Public Sector OTYAWR Difference 28.1735 15.9920 12.0844 (19.9899) (24.2187) (49.0984) Age Difference -.034825 -.013116 .00016 (.031554) (.037220) (.064266) High School Graduate .001032 -.210033 .603227 (.069115) (.314205) (261482) College Graduate -.1111318 -.121396 .013838 (.050571) (.149866) (.279549) Public Sector .107249 n.a. n.a. (.108342) OTYAWR Difference* -28.3990 -9.33799 161.220 High School Graduate (17.0984) (26.8283) (84.5506) OTYAWR Difference* -25.5820 -15.5518 -1.99393 College Graduate (17.4418) (25.3482) (51.7887) Number of Income .093370 .038325 .129363 Recipients Difference (110142) (.140411) (.211422) Number of Components -.146496 -.088692 -.240514 Difference (.068528) (.148404) (.089137) Adj-R2 0.2743 0.3225 0.3070 Number of Obs. 40 20 20 Dependent Variable Log of Equivalent Scale Log of Equivalent Scale Log of Equivalent Scale Consumption Rate Consumption Rate Consumption Rate Differences Differences Differences Note: Standard Errors are in parenthesis 119 Table 15: Males Public Sector- Estimation of Cohort Effects in Real Assets College High School Junior High School Graduates Graduates Graduates Age .2872425 .031800 -.091630 (.156373) (.093785) (.092815) Age Square -.00773 .003138 .009433 (.00933) (.004956) (.004905) Age Cube .000069 -.00003 -.000134 (.000016) (.000076) (.000075) Cohort3 .569736 .787948 .429628 (.365254) (.258317) (.255645) Cohort4 .427206 1.06489 1.16454 (.46848) (.33150) (.328071) Cohorti .864269 1.62093 1.66151 (.565127) (.397481) (.393370) Cohort6 .951445 2.1606 2.07105 (.666628) (.462556) (.457772) Cohort7 1.13329 2.56830 2.63047 (.754111) (.528632) (.523164) Cohort8 2.00973 2.89608 2.42052 (.825760) (.582078) (.576058) Cohort 9 n.a. 3.41079 2.70699 (.629682) (.623169) Unemp.rate deviation -.0307446 .020752 -.12857 (.154373) (.101136) (.100009) Intercept 8.02054 7.45822 7.95727 (1.08381) (.783362) (.77526) Adj-R2 0.4059 0.6369 0.629 Number of Obs. 31 36 36 Dependent Variable Log of Equivalent Log of Equivalent Scale Log of Equivalent Scale Scale Real Assets Real Assets Real Assets Note: Standard Errors are in parenthesis. 120 Table 16: Males Private Sector- Estimation of Cohort Effects in Real Assets College Graduates High School Graduates Junior High School Graduates Age .104016 .400179 -.036313 (.11005) (.067851) (.049607) Age Square .00048 -.0144275 .009273 (.007168)) (.00387) (.002829) Age Cube -.000019 .0002126 -.000156 (.000132) (.000062) (.000045) Cohort3 .361246 .690330 .333828 (.361721) (.251554) (.183915) Cohort4 .963221 1.25354 .590191 (.463972) (.322733) (.235955) Cohort5 1.31576 1.43709 1.01463 (.557016) (.386621) (.282665) Cohort6 1.69795 1.83647 1.54358 (.653393) (.44713) (.326904) Cohort7 1.83023 1.99701 2.04034 (.74519) (.510704) (.373383) Cohort8 1.96164 2.62028 2.26192 (.817658) (.56655) (.414216) Cohort 9 n.a. 3.1071 2.77989 (.612985) (.448163) Unemp.rate deviation .09910 -.134294 -.076785 (.152285) (.098155) (.071762) Intercept 8.659169 5.784463 7.46999 (.938524) (.689564) (.504151) Adj-R2 0.4746 0.8314 0.8109 Number of Obs. 32 37 37 Dependent Variable Log of Equivalent Scale Log of Equivalent Scale Log of Equivalent Scale Real Assets Real Assets Real Assets Note: Standard Errors are in parenthesis. 121 Table 17: Males-Fixed Effects on Explanatory Variables Both Sectors Private Sector Public Sector Log O T Y A W R 264.604 (41.439) 264.604 (41.439) 580.7403 (229.321) Log O T Y A W R * P u b l i c Sector 316.135 (233.035) n.a. n.a. Age-Zero Assets to Normalized Net Human Wealth Ratio 14.5329 (6.739) 14.5329 (6.7395) 6.87147 (2.009) Age-Zero Assets to Normalized Net Human Wealth Ratio* Public Sector -7.66148 (7.032) n.a. n.a. Public Sector -6.34225 (5.2048) n.a. n.a. High School Graduate -5.46852 (.8228) -5.46852 (.8228) -1.54272 (.2892) College Graduate -6.83298 (.7925) -6.83298 (.7925) -9.27671 (3.8316) Public Sector*High School Graduates 3.92579 (.8722) n.a. n.a. Public Sector*College Graduates -2.443728 (3.9127) n.a. n.a. Intercept -7.563621 (.7047) -7.56362 (.7047) -13.90587 (5.1568) Adj-R2 0.8 0.744 0.798 Number of Obs. 46 23 23 Dependent Variable Cohort Fixed Effects (Robust Estimation) Cohort Fixed Effects (Robust Estimation) Cohort Fixed Effects (Robust Estimation) Note: Robust Standard Errors are in parenthesis. 122 Table 18: Males- Log Consumption Rate- All Groups-Perfect Foresight All Groups Age -.035466 (.007339) Age Square .0014802 (.000304) Age Cube -.000016 (4.54e-06) Number of Income Recipients .060611 (.033899) Manager -.315661 (.065892) Number of Dependent Children -.154925 (.020056) Wife .207818 (.052446) Groupl*(Age*Cohort Index) .001903 (.000363) Group2*(Age*Cohort Index) .000837 (.000560) Group3*(Age*Cohort Index) .002176 (.000721) Group4*(Age*Cohort Index) .000959 (.000477) Group5*(Age*Cohort Index) .002391 (.000528) Group6*(Age*Cohort Index) .002580 (.000719) Groupl *Log OTYAWR 55.6673 (19.5400) Group2*Log OTYAWR 51.7169 (17.6235) Group3*Log OTYAWR 51.04573 (17.7539) Group4*Log OTYAWR 60.2765 (30.8171) Group5*Log OTYAWR 56.5492 (30.7865) Group6*Log OTYAWR 60.8675 (42.2245) Square Log OTYAWR*Private Sector -721.825 (252.848) Square Log OTYAWR*Public Sector -992.465 (961.409) Age-Zero Assets to Normalized Net Human Wealth Ratio .535824 (.226256) Intercept -1.15760 (.322136) Log likelihood 319.207 Number of Obs. 290 Dependent Variable Log of (Equivalent Scale) Consumption Rate Note: Standard Errors are in parenthesis 123 Table 19 Counterfactual Aggregate Saving Rates- Contributions by Sectors The Effect of Socia Security Conterfactual Scenario Percentage Change Aggregate Saving Rates 1984-1995 Estimated Aggregate Saving Rates Both Sectors -102% Aggregate Saving Rates under Pre-Amato Regime Both Sectors Changing -100% Aggregate Saving Rates under Amato Reform No Retirement Age Change for the Private Sector -75% Estimated Saving Rates Private Sector -91.05% Saving Rates under Pre-Amato Regime Private Sector -26.6% Saving Rates under Amato Reform No Retirement Age Change for the Private Sector -31% Estimated Saving Rates Public Sector -108% Saving Rates under Pre-Amato Regime Public Sector -176% 124 Table 20 Counterfactual Aggregate Saving Rates- Contributions by Sectors The Effect of Tax Rates Conterfactual Scenario Percentage Change Aggregate Saving Rates 1984-1995 Estimated Aggregate Saving Rates Both Sectors -102% Aggregate Saving Rates when the Income Tax Schedule for 1995 Applies to all Cohorts Both Sectors Changing -103% Saving Rates when the Income Tax Schedule for 1995 Applies to all Cohorts Private Sector -88% Saving Rates when the Income Tax Schedule for 1995 Applies to all Cohorts Public Sector -112.5% 125 d Q 0 o & CD 0) c •> to c 0 (0 c m o o in o n r i r U) N in r CO 126 127 i f l N m r m o i n r m N i n n .— CM T - o q r ^ ,• c\i i- L L I' r i 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 8 8 o 8 8 3 8 8 S ° a 3 a. 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