- 2. For each iθ where i = 1,2,…,m, use the 1998 data on stockholders to estimate the Quantile Regression coefficient, 98 ( )ib θ , from the model: 98 98 98 98 [ | ] ( )i iQ y X Xθ β θ= 3. Make m random draws of characteristics and corresponding weights with replacement from the 1989 stockholder pool. Denote the outcomes of these draws by *89 ix for i = 1,2,….,m. 4. Generate counterfactual values (a random sample of size m from the desired distribution): * *89 98 ( )i i iy x b θ= , for i = 1,2,….,m. Use these values to generate * 89 98 ( ; )f y X b .
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- A similar argument was made by Jenkins (1995) in favor of using HSCV for analysis of income inequality. 7 The result mainly comes from the increasing factor correlation, implying a stronger association between housing value and total net wealth over time, which outweighs the decreasing factor shares. Factor shares decrease presumably due to movements in housing prices, since ownership rates move in the opposite direction. 8 The higher risky shares result from increasing ownership rates and sizeable stock gains in a decade marked by a spread of equity culture and a stock market boom. 9
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Albrecht, James, Anders Björklund, and Susan Vroman (2003). “Is There a Glass Ceiling in Sweden?â€, Journal of Labor Economics, 21, 145-77.
- Allen, Franklin and Douglas Gale (1994). “Limited Market Participation and Volatility of Assets Pricesâ€, The American Economic Review, 84, 933-55.
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- Appendix A: The Machado-Mata Algorithm The algorithm for constructing counterfactual densities is a variant of Machado and Mata (2003), recently used by Albrecht et al. (2003) and Nguyen et al. (2003): 1. Draw m random numbers from a uniform distribution on (0, 1): 1 2, ,...... mθ θ θ ; here we set m=1000.
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- Arrow, Kenneth (1987). â€The Demand for Information and the Distribution of Incomeâ€, Probability in the Engineering and the Informational Sciences 1, 3-13.
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- As Atkinson (1983) points out, “[inequality indices] embody implicit judgments about the weight to be attached to the inequality at different points in the […] scaleâ€. 6
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- Atkinson, Anthony (1983). The Economics of Inequality, Clarendon Press, Oxford.
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Bertaut, Carol C. and Martha Starr-McCluer (2001). “Household Portfolios in the United Statesâ€, in L. Guiso, M. Haliassos, and T. Jappelli (Eds.), Household Portfolios, Cambridge, MA: MIT Press.
- Bilias, Yannis and Michael Haliassos (2004). “The Distribution of Gains from Access to Stocksâ€, mimeo, University of Cyprus.
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Calvet, Laurent, Martin Gonzalez-Eiras, and Paolo Sodini (2001). “Financial Innovation, Market Participation and Asset Pricesâ€, Harvard Institute of Economic Research Discussion Paper No. 1928.
Campbell, John and Luis Viceira (2002). Strategic Asset Allocation: Portfolio Choice for Longterm Investors, Oxford: Oxford University Press.
- Carroll, Christopher D. (2001). “Portfolios of the Rich†in L. Guiso et al. (Eds.), Household Portfolios, Cambridge, MA: MIT Press.
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- Carroll, Christopher D. (2002). Lecture Notes on Solution Methods for Microeconomic Dynamic Stochastic Optimization Problems, mimeo, Johns Hopkins University.
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Carroll, Christopher D., and Andrew A. Samwick (1997). The Nature of Precautionary Wealth, Journal of Monetary Economics, 40, 41-71.
- Cocco, J., F. Gomes, and P.J. Maenhout (1997). “Consumption and Portfolio Choice over the Life Cycle,†Working Paper, Harvard University.
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- Cowell, Frank (1977). Measuring Inequality, Philip Allan, Oxford.
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- Fields, Gary S. (2002). “Accounting for Income Inequality and Its Change: A New Method, with Application to the Distribution of Earnings in the United Statesâ€, forthcoming in Research in Labor Economics.
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- Fields, Gary S. (2003). “Regression-Based Decompositions: A New Tool for Personnel Economics and Human Resource Managementâ€, mimeo, Cornell University.
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- Figure 1: Directly and Indirectly Equity Wealth densities for 1998 and 1989 0.05.1.15.2 density1989/density1998/density2001 0 5 10 15 20 log Equity density 1989 density 1998 density 2001 Kernel density estimates of log Equity Note: The estimation procedure is a kernel-density smoother on weighted data with a Gaussian kernel and an optimal bandwidth provided by STATA algorithm.
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- Figure 2A. Quantile Regression Decomposition 1998-1989: Coefficient and Covariate effects -2-1012 DifferenceinlogEquity 0 20 40 60 80 100 Percentile coefficient effects covariate effects actual difference Figure 2B. Quantile Regression Decomposition 1998-1989: Contributions of Fundamentals to Covariate effects -2-1012 DifferenceinlogEquity 0 20 40 60 80 100 Percentile fundamentals as in 1989 covariate effects
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- For effects of stock market participation on the equity premium, see for example Heaton and Lucas (1999), Peress (2001), Calvet et al. (2001). For effects regarding market volatility, see Pagano (1989), Allen and Gale (1994), and Herrera (2001). 3
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- For participation trends in the United States since the early 1980s, see Bertaut and Starr-McCluer (2001). International comparisons can be found in the volume edited by Guiso, Haliassos, and Jappelli (2001). 2
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- Gollier, Christian (2001). The Economics of Risk and Time, Cambridge, MA: MIT Press.
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- Gomes, Francisco and Alexander Michaelides (2004). “Optimal Life-Cycle Allocation: Understanding the Empirical Evidenceâ€, forthcoming, Journal of Finance.
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- Guiso, Luigi, Michael Haliassos, and Tullio Jappelli (Eds.) (2001). Household Portfolios, Cambridge, MA: MIT Press.
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Guvenen, Fatih (2002), “Reconciling Conflicting Evidence on the Elasticity of Intertemporal Substitution: a Macroeconomic Perspectiveâ€, mimeo, University of Rochester.
Haliassos, Michael and Carol C. Bertaut (1995).“Why Do So Few Hold Stocks?†The Economic Journal, 105, 1110-29.
- Heaton, John and Deborah Lucas (1999). “Stock Prices and Fundamentalsâ€, NBER Macroeconomics Annual, 213-42.
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Herrera, Helios (2001). “Participation Externalities and Stock Market Volatilityâ€, mimeo, New York University.
Hurst, Erik and Anna Maria Lusardi (2004). “Liquidity Constraints, Household Wealth and Entrepreneurshipâ€, Journal of Political Economy, 112, 319-47.
- In order to construct the counterfactual ** f we first divide each of the samples of equity owners in 1989 and 1998 into 8 cells representing all the possible combinations of the three attitudes. We follow steps 1 and 2 from above while in step 3 we make m random draws with replacement from 1998 sample, generating the 1998 equity wealth distribution implied by the model. Then we consider the subset of households in cell 1.
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Jenkins, Stephen (1995). “Accounting for inequality trends: decomposition analysis for the UK, 1971-1986â€, Economica, 62, 29-63.
- Kennickell, Arthur (2001). “An Examination of Changes in the Distribution of Wealth from 1989 to 1998: Evidence from the Survey of Consumer Financesâ€, mimeo.
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King, Mervyn and Jonathan Leape (1984). “Wealth and Portfolio Composition: Theory and Evidenceâ€, NBER Working Paper No. 1468.
Laibson, David, Andrea Repetto, and Jeremy Tobacman (2000). A Debt Puzzle, NBER Working Paper No. 7879, forthcoming in Philippe Aghion, Roman Frydman, Joseph Stiglitz, and Michael Woodford (Eds), Knowledge, Information, and Expectations in Modern Economics: In Honor of Edmund S. Phelps.
Lerman, Robert and Shlomo Yitzhaki (1991). “Income Stratification and Income Inequalityâ€, Review of Income and Wealth, 37, 313-329.
- Limited stockholding participation in the early to mid 1980s was documented in US data by King and Leape (1984), Mankiw and Zeldes (1991), and Haliassos and Bertaut (1995). A number of authors have recently explored determinants of participation in stockholding. See, for example, Haliassos and Bertaut (1995), Cocco, Gomes and Maenhout (1997), Heaton and Lucas (2000), Gollier (2001), Campbell and Viceira (2002), Haliassos and Michaelides (2003), and Gomes and Michaelides (2004). 4
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- Machado, Jose, and Jose Mata. (2003). “Counterfactual Decomposition of Changes in Wage Distributions using Quantile Regressionâ€, Mimeo, Universidad Nova de Lisboa.
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Mankiw, N. Gregory and Stephen Zeldes (1991). “The Consumption of Stockholders and NonStockholders â€, Journal of Financial Economics, 29, 97-112.
Morduch, Jonathan and Terry Sicular (2002). “Rethinking Inequality Decomposition, with Evidence from Rural Chinaâ€, The Economic Journal, 112, 93-106.
Nguyen, Binh, James Albrecht, Susan Vroman, and M.Daniel Westbrook (2003). “A Quantile Regression Decomposition of Urban-Rural Inequality in Vietnamâ€, mimeo, Georgetown University.
Oaxaca, R. (1973). “Male-Female Wage Differentials in Urban Labor Marketsâ€, International Economic Review, 14, 693-709.
Pagano, Marco (1989). “Endogenous Market Thinness and Stock Price Volatilityâ€, The Review of Economic Studies, 56, 269-87.
Peress, Joel (2002) “Wealth, Information Acquisition, and Portfolio Shares,†mimeo, INSEAD.
Shorrocks, Anthony (1982). “Inequality Decomposition by Factor Componentsâ€, Econometrica, 50, 193-212.
- Table 1: Net Wealth Inequality Indices Generalized Entropy Class Year GE(0) MLD GE(1) Theil GE(2) HSCV Gini 1989 1.9961 1.5035 13.316 0.7668 1998 1.8391 1.6338 18.176 0.7741 2001 1.9438 1.6114 12.405 0.7874 Note:WeighteddatafromSurveysofConsumerFinances.Thesampleexcludeshouseholdswithnegativenet worth.
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- Table 10: Characteristics of Direct and Indirect Stockholders (%) 1998 2001 Education Less than high school education 5.51 4.95 High school graduates 48.04 45.94 College degree or more 46.45 49.11 Use of professional advice 58.7 56.8 Investment decisions influenced by social interactions 53.2 50.0 Mean income 75,766 84,585
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- Table 11: Incidence of Cumulative Gains or Losses in Stock Value since Purchased, by Education Group (%) Direct Stockholding Holders by Educational Attainment 1998 All Holders Less than High School Education High School Graduates College Degree or More Cumulative Gains 79.7 73.19 78.67 80.92 No Gains or Losses 8.46 15.38 9.68 7.04 Cumulative Losses 11.86 11.43 11.66 12.05 2001 Cumulative Gains 52.7 41.24 48.66 55.66 No Gains or Losses 12.03 15.92 13.41 11.39 Cumulative Losses 35.3 42.83 37.93 32.94
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- Table 12: Incidence of Cumulative Gains or Losses in Mutual Fund Value since Purchased, by education group (%) Mutual Funds By Educational Attainment 1998 All Holders Less than High School Education High School Graduates College Degree or More Cumulative Gains 87.2 69.08 84.64 88.65 No Gains or Losses 6.7 17.38 7.29 7.21 Cumulative Losses 6.0 13.54 8.07 4.14 2001 Cumulative Gains 54.1 27.8 49.98 56.12 No Gains or Losses 10.9 20.07 13.96 9.32 Cumulative Losses 35.1 52.11 36.06 34.57
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- Table 5: Probit Regressions for Ownership of Equity Holdings 1989 1998 2001 PseudoR2 : 0.26 Obs: 3,143 PseudoR2 : 0.30 Obs:4,305 PseudoR2 : 0.31 Obs:4,442 Log-likelihood: -1599.99 Log-likelihood: -2030.45 Log-likelihood: -2018.36 Marginal Effect (z-value) Marginal Effect (z-value) Marginal Effect (z-value) Age .0303 (7.98) *** .0298 (9.08) *** .0170 (5.28) *** Age squared -.0002 (-6.58) *** -.0002 (-7.77) *** -.0001 (-4.51) *** Male .0179 (.5) .0204 (.67) .0561 (1.9) *
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- Table 6: Equity Holdings: OLS Regression Results 1989 1998 2001 log (equity) log (equity) log (equity) R2 : 0.42 Obs: 1,481 R2 : 0.49 Obs:2,601 R2 : 0.54 Obs:2,822 Estimated Coefficient (standard error) Estimated Coefficient (standard error) Estimated Coefficient (standard error) Age .1439 (.0256) *** .1521 (.0189) *** .1506 (.0164) *** Age squared -.00084 (.0002) *** -.00086 (.00018) *** -.00082 (.0002) *** Male .5029 (.2349) ** .2009 (.1508) .4913 (.1537) *** High school Graduate .7852 (.2219) *** .7544 (.2227) *** .9853 (.2099) *** College graduate 1.8507 (.2246) *** 1.7721 (.2221) *** 2.1423 (.2089) *** Married .3278 (.1935) * .4412 (.1260) *** .3796 (.1324) *** Kids -.0824 (.1212) -.1549 (.0887) * .1372 (.0827) *
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- Table 8: Contribution of Variation in Educational Attainment to Inequality All households with positive equity (1998) Risky wealth (actual) Risky Wealth after removing the estimated effect of educational attainment* HSCV 23.84 8.44 Gini .83 .79 Theil 1.92 1.51 Less than High School Education (householdswithpositiveequity,1998) HSCV 51.53 9.32 Gini .70 .71 Theil 1.26 1.03 High School Graduates (households with positive equity, 1998) HSCV 23.44 9.80 Gini .80 .79 Theil 1.80 1.57 College Graduates (households with positive equity, 1998) HSCV 17.95 7.02 Gini .81 .79 Theil 1.77 1.51 * estimated coefficients derived from the quantile regression that produced the closest fitted value to the observed wealth level for each household.
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- Table 9: Simulated Inequality in Stock Holdings, by Education Category and Age Age Mean HSCV Mean HSCV Mean HSCV 25 31778 0.02874 17643 0.02615 733 0.34827 35 71858 0.00811 64175 0.02353 5715 0.05691 45 75391 0.00701 83395 0.01204 22944 0.04725 55 64854 0.00725 75542 0.01407 56868 0.05972 65 46004 0.00925 56703 0.01844 47909 0.07666 75 22153 0.01129 24041 0.05999 17163 0.19092 85 7988 0.01353 2887 0.24062 2969 0.15131 High School Education College Degree or MoreLess-than-high-school Education
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- The growth factors of the permanent component of income are based on regressions using data from PSID 1983-1990 and are taken from Laibson et al. (2000, Tables 3 and 4). The retirement age for high-school dropouts is set to 61, for high-school graduates to 63, and for college graduates to 65, based on mean ages observed in the data. Estimated age income profiles are hump-shaped during working age for all education categories.
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- The model is solved using a MATLAB algorithm recently developed by Haliassos and Mavridis, which incorporates some of the computational shortcuts proposed in Carroll (2002).
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- The Survey excludes only households that belong to the Forbes 400. See also Kennickell (2001). 5
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- Then, for each of the three sequences of variables (log equity holdings in 1989 and 1998 and counterfactual values), we calculate percentiles using population weights. The difference between percentiles of the distributions of the endogenous variable in 1998 and 1989 can be decomposed into: 98 89 98 * 89 98 * 89 98 89 ( ) ( ) { ( ) ( ; )} { ( ; ) ( )}f y f y f y f y X b f y X b f y− = − + − The term in the first curly brackets represents the contribution of the covariates to the overall difference between the 1998 and 1989 densities. The term in the second curly brackets shows the contribution of the QR coefficients. The method is a generalization of Oaxaca (1973) to the whole distribution.
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- We calibrate variances for income shocks, (σu, σn), for the three education categories during working life using estimates of Carroll and Samwick (1997). For highschool dropouts, we use the Carroll-Samwick estimates for those who had completed between 9 and 12 grades: (0.0658, 0.0214); for high-school graduates, we use (0.0431, 0.0277); and for college graduates (0.0385, 0.0146).
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- We follow Laibson et al. (2000) in calibrating shocks to retirement income. They estimate variances of transitory shocks for high-school dropouts, high-school graduates, and college graduates at 0.077, 0.051, 0.042, respectively.
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- We randomly draw with replacement observations from this subset to generate a relative sample size equal to the fraction of households in cell 1 in 1989. We repeat the last two steps for cells 2 to 8. A similar approach is followed for the period 1998-2001. Appendix B: The Portfolio Model This Appendix describes the main features of the model and calibration settings.
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- We use conditional probabilities of survival from the 1998 United States Life Tables (National Vital Statistics Report, 2001). We set the rate of time preference equal to 0.05. The expected rate of return on equity, μr, is set to 0.06 and the constant real interest rate, r, to 0.01. Understating the historical equity premium is an often used shortcut to introducing proportional transactions costs. The standard deviation of the equity premium is at its historical value of 18 percent. The benchmark value for risk aversion is Ï=2. Perceived access costs are unobservable. We use a real amount of 250 dollars, close to empirical estimates of implied participation costs. Assuming the same real cost of participation regardless of education is a useful benchmark, but also consistent with our purpose of focusing on the implications of income processes as distinct from any differences in the ability to process financial information across education groups.
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Wolff, Edward (1998). “Recent Trends in the Size Distribution of Household Wealthâ€, The Journal of Economic Perspectives, 12, 131-150.