Distribution of Wealth: Mechanisms

Transcription

1 Distribution of Wealth: Mechanisms Benhabib,J, Bisin, A., Luo, M. Jess Benhabib, Alberto Bisin, Mi Luo Benhabib,J, Bisin, A., Luo, M. () 1 / 45

2 The Question Which factors drive quantitatively the cross-sectional distribution of wealth in the U.S.? And also the social mobility of wealth in the U.S.? Which factors drive, most notably, its skewed, thick right tail? Skewed/persistent earnings, non-homogeneous bequests, savings rates increasing in wealth, stochastic length of life/dynasty, persistent capital income risk, stochastic discount rates,... Theoretical models will let us categorize, organize, select, and then to put to data and estimate. We will mainly focus on i) persistent stochastic earnings, ii) savings rate increasing in wealth,iii) persistent stochastic returns. Preview: All three above will play a role. However labor income inequality by itself is insuffi cient, theoretically and empirically, to account for wealth inequalty at the top. Benhabib,J, Bisin, A., Luo, M. () 2 / 45

3 Linear Economy, to set ideas To set ideas: Let us start with a linear economy (For a possible micro-foundation in a T -period OLG model, see Benhabib-Bisin-Zhu (2011)). The wealth accumulation equation is: a t+1 = r t+1 a t + y t+1 c t+1 If the consumption function is linear, c t = ψa t + χ t, χ t 0 The wealth accumulation equation now is: a t+1 = (r t+1 ψ) a t + (y t+1 χ t ) (1) Benhabib,J, Bisin, A., Luo, M. () 3 / 45

4 A Tale of Two Tails: Income and Wealth Assume a t+1 = (r t+1 ψ) a t + (y t+1 χ t ) (2) {rt+1 ψ} is iid with E (r t+1 ψ) < 1, {yt χ t } is i.i.d. with ( right-tail index α E ((r ψ) α ) < 1, E (r ψ) β) < for β > α. Then equation 2 induces an ergodic stationary distribution for wealth a with right-tail α. [Grey (1994), extending Kesten, 1973]. ( If instead there exists 0 < α < α and E (r t ψ) α ) = 1, then the right-tail index of the stationary distribution of wealth is α, even if distributions {r t }, {y t } have finite support. (Kesten(1973)). Generalizations allow persistent (finite Markov chain) {r t+1 ψ} and {y t+1 χ t } as well as correlations between them, various coninuous time extensions with Brownian motion.. Benhabib,J, Bisin, A., Luo, M. () 4 / 45

5 Theorem In English: the tail of the wealth distribution is determined EITHER by the tail of the earning distribution OR by the stochastic properties of returns - NOT BOTH; if it is the tail of the earning distribution which determines the tail of the wealth distribution, the two distributions have the SAME tail. if it is stochastic properties of returns which determines the tail of the wealth distribution, then (roughly) the thickness of the tail depends on the distribution of returns (see Benhabib-Bisin-Zhu (2011) for richer and more precise characterization results). NOTE: to generate a thick wealth tail, returns do not have to have a thick tail, they could even be a two state Markov process. This is sometimes called: Thin Tails in, Thick Tails Out. Benhabib,J, Bisin, A., Luo, M. () 5 / 45

6 Basic Aiyagari Models Do the implications of the linear model above carry over to simple Aiyagari Models? Basic Aiyagari Models with homothetic preferences are not linear but asymptotically linear because precautionary motive for savings vanishes at high wealth levels. So Grey s result for the tail carries over, unless additional features, e. g. stochastic idiosyncratic returns, are introduced. "However, under some regularity conditions, the unique stationary distribution for wealth in the Aiyagari-Bewley model augmented with stochastic heterogeneous returns is unbounded above, and has a fat tail." (Benhabib, Bisin and Zhu (2016)). This analysis provides a suggestive theoretical result, BUT, whether it is empirically relevant (how far out is the tail) has to be addressed. Benhabib,J, Bisin, A., Luo, M. () 6 / 45

7 Basic Aiyagari Models, Cont d Stochastic earnings alone are not enough A common approach used to match the right tail of the wealth distribution with the Aiyagari model is to add extraordinary (awesome) earnings (Markov) states to augment the right tail earnings data. For example, Castaneda, Diaz-Giminez and Rios Rull (JPE., 2003) use an earnings process where 0.04% of top wage earners make 1000 times that of the bottom 61%. In the World Top Income Database of Piketty and Saez, even the ratio of 0.01% of average top labor incomes ($9M) to the bottom 60% (Census Bureau, $32K) is about 280. In examples of other calibrations (e.g Diaz, Pijoan-Mas, Rios-Rull JME 2003), ratios of average earnings of top shares to bottom tend to be 2 to 3 times higher than average earnings of bottom shares in data. The added exceptional earnings states at the upper tail then affect the whole distribution and are critical for generating the match to the empirical skew in the wealth distribution. Benhabib,J, Bisin, A., Luo, M. () 7 / 45

8 Models with Lifespan Heterogeneity via Perpetual Youth The very rich are very old. Birth and death processes Variable life-spans can also produce differential sojourn times in the highest earnings states leading to variation in wealth across agents and dynasties. For example Kaymak and Poschke (2015) and others calibrate expected working lives to 45 years, with a constant exponential decay rate into retirement of µ = = 1/45. This however implies that at the stationary distribution 11% of the working population has been working for at least 100 years. A subset of those will spend long years in the extraordinary state, build large wealth, and populate the tail of the wealth distribution. See Kaymak and Poschke (2015, p. 37) and also Kaplan, Violante and Moll (2015). With stochastic death rates in an accumulation model calibrated to data, but stipulating death for certain at age 86 for example, De Nardi, Fella, and Pardo (2016) cannot match the wealth tail. Benhabib,J, Bisin, A., Luo, M. () 8 / 45

9 But, without augmenting earnings data with extraordinary states: De Nardi, Fella, and Pardo (2016) : Earnings processes derived from data (Guvenen, Karahan, Ozkan, and Song (2015)) "when introduced in a standard quantitative model of consumption and savings over the life cycle, generate a much better fit of the wealth holdings of the bottom 60% of people, but vastly underestimate the level of wealth concentration at the top of the wealth distribution". Carroll, Slacalek, and Tokuoka, ECB wp 1655, 2014 : "...for example the Gini coffi cient for permanent income measured in the Survey of Consumer Finances (2004) of roughly 0.5 is similar to that for wealth generated in the (Aiyagari) model. Since the empirical distribution of wealth, which has the Gini coeffi cient of around 0.8, is considerably more unequal than the distribution of income (or permanent income), the setup only captures part of the wealth heterogeneity in the data, especially at the top." Benhabib,J, Bisin, A., Luo, M. () 9 / 45

10 ... without augmenting earnings data with extraordinary states: Hubmer, Krusell, and Smith (2016): "the wealth distribution inherits not only the Pareto tail of the earnings distribution but also its Pareto coeffi cient. Because earnings are considerably less concentrated than wealth, the resulting tail in wealth is too thin to match the data". Guvenen, Karahan, Ozkan and Song, 2016: "...the improvement is not nearly large enough to generate the massive concentration of wealth at the very top observed in the U.S. data, where the top 1% holds 37% of aggregate wealth...thus, although the benchmark model provides a step in the right direction, we conclude that empirically measured income risk even with negatively skewed and leptokurtic income changes cannot generate the thick right tail of the U.S. wealth distribution." Benhabib,J, Bisin, A., Luo, M. () 10 / 45

11 Earnings vs Wealth Ginis: Uncorrelated Benhabib,J, Bisin, A., Luo, M. () 11 / 45

12 Theoretical models > Explanatory factors What does it take to fit the distribution of wealth (that is, to obtain Pareto tails) in a standard macro model (that is, micro-founded)? Factor 1: Skewed/ distribution of stochastic earnings- Diaz-Gimenez, Pijoan-Mas, and Rios Rull (2003); Castaneda, Diaz-Gimenez, Rios-Rull (2003; Kindermann and Krueger (2014); Factor 2: Differential saving rates across wealth levels - Atkinson (1973); Non-homogeneous bequests - Cagetti and DeNardi (2006), Piketty (2014); Factor 3: Capital income risk - Stochastic returns: Entrepreneurship - Quadrini (2000), Cagetti and DeNardi (2003); Benhabib, Bisin, Zhu (2011, 2016); Stochastic discount - Krusell and Smith (1988). Factor 4: Possibly, returns increasing in wealth, with effects similar to Factor 2. (Piketty (2014), Fagereng, Guiso, Malacrino and Pistaferri (2016)). Benhabib,J, Bisin, A., Luo, M. () 12 / 45

13 Synthetic savings rates Using data, Saez and Zuchman (2014) found that synthetic savings rates are indeed increasing with wealth levels. The three lines represent retirement savings profiles for the 25%, median and 75%. Benhabib,J, Bisin, A., Luo, M. () 13 / 45

14 Our Estimation Construct a finite life model with bequests nesting stochastic earnings, stochastic returns, wealth possibly increasing in wealth. To estimate parameters target the distribution of wealth as well as wealth mobility. The model is a generalization of Atkinson (1971) to incorporate the features above. Benhabib,J, Bisin, A., Luo, M. () 14 / 45

15 Model Each agent s life is finite and deterministic: T years. Consumer of dynasty j chooses consumption {c j,t } and savings each period, subject to a no-borrowing constraint. Consumers also choose a bequest e n j,t. We abstract from precautionary savings, so wage profiles and rates of return are drawn from distributions at the beginning of working-life. We also abstract from inter-vivos transfers that serve to smooth life-cycle income profiles. Benhabib,J, Bisin, A., Luo, M. () 15 / 45

16 Model, Cont d Assumption: Consumer of dynasty j, generation n, draw a lifetime { } T return rj n, a deterministic earnings profile yj,t n parameterized by 0, and maximizes utility (single heir, no estate tax for simplicity): y n j,0 V n j ( a n j,0 ) = Max{c n j,t} T t=0 ( ) 1 σ cj,t n 1 σ + A ( ) 1 µ ej,t n 1 µ for t [0, T ] s.t. aj,t+1 n = (1 + rj n )(aj,t n cj,t) n + yj,t n 0 cj,t n aj,t n If µ < σ, savings rates increase in wealth. (Atkinson, 1971). Connecting generations: e n j,t = an+1 j,0. Benhabib,J, Bisin, A., Luo, M. () 16 / 45

17 Earnings and Returns The process for { the rate } of return of wealth and earnings processes over generation n, rj n, y j,0 n is a finite irreducible Markov Chain with transition ( ) P rj n, y j,0 n r n 1 j, y n 1 j,0 such that (abusing notation): ( ) ( ) P rj n r n 1, y n 1 j,0 = P rj n r n 1 j, ( ) ( ) P yj,0 n r n 1, y n 1 j,0 = P yj,0 n y n 1 j,0 The life-cycle structure of the model implies that the initial wealth of the n th generation coincides with the final wealth of the n 1 th generation: a n = a n 0 = a n 1 T. Benhabib,J, Bisin, A., Luo, M. () 17 / 45

18 Quantitative exercise: Method of Simulated Moments We start with the assumption that the wealth and social mobility data observed in the U.S. are generated by a stationary distribution. Later we re-estimate dropping this assumption. In detail, our quantitative exercise is an application of the Simulated Method of Moments, where we fix several parameters of the model (externally calibrated), select some relevant moments, and estimate the remaining parameters by matching the moments generated by the model and those in the data. Benhabib,J, Bisin, A., Luo, M. () 18 / 45

19 Quantitative exercise Specifically, we fix σ = 2, T = 36, β = 0.97 per annum, the stochastic process for individual income and its transition across generations, following Chetty et al. (2014). We select the following wealth percentiles: bottom 20%, 20 40%, 40 60%, 60 80%, 90 95%, 95 99%, and top 1%, and the diagonal of the social mobility matrix, as the moments to match. We estimate µ, A, a 5-state Markov Chain grid for r n, and a restricted form of the social mobility matrix consisting in leaving diagonal elements free and imposing equal probabilities off the diagonal (or decreasing geometric weights for off diagonals). We take wealth distribution data from the SCF, Benhabib,J, Bisin, A., Luo, M. () 19 / 45

20 Labor Income We use ten deterministic life-cycle household-level income profiles at different quantiles, estimated from the PSID. Labor income: individual income profiles (PSID data from Heathcote, Perri, and Violante, 2010) and its transition across generations ( U.S. birth cohort and their parental income, Chetty et al., 2014) Originally a 100-state Markov chain: each percentile of income distribution Reduce that to a 10-state Markov chain: each decile is a state for y n 0. Benhabib,J, Bisin, A., Luo, M. () 20 / 45

21 Benhabib,J, Bisin, A., Luo, M. () 21 / 45

22 Transition matrix for labor decile y0 n, from Chetty et al. T gen = Benhabib,J, Bisin, A., Luo, M. () 22 / 45

23 Wealth shares Cross-sectional wealth distribution: shares in bottom 20%, 20-40%, 40-60%, 60-80%, 80-90%, 90-95%, 95-99%, and top 1% of net worth holdings in the 2007 SCF. Benhabib,J, Bisin, A., Luo, M. () 23 / 45

24 Wealth transition Social mobility. We estimate an intergenerational mobility matrix from the SCF 2-year panel as follows. We first construct age-dependent 2-year transition matrices for age groups running from to We then multiply these age-dependent 2-year transition matrices for all age groups, to construct the intergenerational social mobility matrix. T ,avg = It displays substantial social mobility: the Shorrocks mobility index is 0.98.Formally, for a square mobility transition matrix A of dimension m, the Shorrocks index given by s(a) = m j a jj m 1 with 0 indicating complete immobility. Benhabib,J, Bisin, A., Luo, M. () 24 / 45

25 Mobility Matrix, cont d Kennickell and Starr-McCluer (1997) s estimates for SCF data over , raised to power 6 is similar i) the matrix obtained by Klevmarken et al. (2003) with the PSID data is qualitatively similar; ii) the matrix estimated by Charles and Hurst (2003) capture the inter-generational transmission in wealth exploiting information contained in the PSID about parent-child pairs (both child and one parent are alive ), adjusted for age.their data is more recent and spans 15 years, but end of life bequests are left out as matched parent child pairs have to be living throughout. In the estimation we are only matching the diagonal of the above matrix. This assumption brings down the number of parameters we need to estimate. Benhabib,J, Bisin, A., Luo, M. () 25 / 45

26 Capital income risk - what is it? In the 1989 SCF studied by Moskowitz and Vissing-Jorgensen (2002) and Bitler, Moskowitz and Vissing-Jorgensen (2005) both capital gains and earnings on private business equity (entrpreneurship), which is highly concentrated, exhibit very substantial variation, even conditional on survival. Private business equity is highly concentrated: 75% owned by households for which it constitutes at least 50% of their total net worth. Case and Shiller (1989) documented a 15% standard deviation of yearly capital gains or losses on owner-occupied housing; Flavin and Yamashita (2002) find a 14% standard deviation on the return on housing, at the level of individual houses, from the waves of the PSID. Fagereng, Guiso, Malacrino and Pistaferri (2016) find (in Norwegian data) that returns to portfolio wealth exhibit substantial heterogeneity. Their cross-sectional heterogeneity (STD) of returns on total wealth is 5% in 2013, and if within-lifetime variations are excluded, it is 3%. Benhabib,J, Bisin, A., Luo, M. () 26 / 45

27 Benhabib,J, Bisin, A., Luo, M. () 27 / 45

28 Standard errors in (); fixed parameters in []. Benhabib,J, Bisin, A., Luo, M. () 28 / 45 Parameter Estimates-Baseline The estimated state space and diagonal of the transition matrix of the 5-state Markov process for r we postulate. It also reports, to ease the interpretation of the estimates, the implied mean and standard deviation of the on simulated data from the estimated process. Preferences σ µ A β T [2] [0.97] [36] (0.0010) (0.0011) Rate of return process state space (0.0019) (0.0022) (0.0027) (0.0077) (0.0091) transition diagonal (0.1015) (0.1270) (0.1112) (0.1775) (0.1781) statistics E(r) σ(r) ρ(r) 2.76% 2.54% (0.80%) (0.87%) (0.063) Notes:

29 Estimated shares and mobility Wealth distribution moments Data Model Social mobility moments Data Model We match for the baseline life-cycle model the top 1% share, yet we understimate the 90-99%. We will see that allowing the return process r to depend on wealth substantially improves our fit. Differential savings rates are also important to account for observed wealth dynamics. Our estimate of µ is 1:0108, significantly lower than 2, the value of σ we fixed. Thus savings out of wealth increase with wealth: the rich save proportionally more than the poor. Benhabib,J, Bisin, A., Luo, M. () 29 / 45

30 Estimated shares and mobility These values are roughly consistent with the empirical values calculated by Saez and Zucman [2016] using data on wealth accumulation with the capitalized income tax method, though our model clearly over-estimates the savings rate in the 90-99% range. In particular, retirement savings in the data do not decline along the age path and, furthermore, this pattern is more accentuated for the 75% percentile, as our estimates also imply. (Hurd and Smith (2003)). Benhabib,J, Bisin, A., Luo, M. () 30 / 45

31 Returns Depend on Wealth? We extend our analysis to allow for the rate of return process r to depend on wealth, explicitly introducing a dependence of the stochastic rate of return r on wealth percentiles. The functional form we introduce allows for r to depend on wealth a as follows: r = r 0 + bp(a) where p(a) = 1; 2; :::; 8 numbers the wealth percentiles we identify as moments and r 0 is a 5-state Markov process along the lines what we assumed in the baseline model for r. Benhabib,J, Bisin, A., Luo, M. () 31 / 45

32 Returns Depend on Wealth? Preferences σ µ A β T [2] [0.97] [36] (0.0010) (0.0011) Rate of return process state space (0.0004) (0.0018) (0.0148) (0.0369) (0.0062) transition diagonal (0.2169) (0.1342) (0.2859) (0.1312) (0.2401) wealth dependence, b (0.0105) statistics E(r 0) σ(r 0) ρ(r 0) E(r) σ(r) 2.28% 2.16% % 2.37% (1.53%) (0.87%) (0.007) Note b is positive but insignificant. Benhabib,J, Bisin, A., Luo, M. () 32 / 45

33 Returns Depend on Wealth?, FGMP Statistics Mean Std β Our baseline 2.76% 2.54% FGMP (2016) 2.98% 2.82% Benhabib,J, Bisin, A., Luo, M. () 33 / 45

34 Estimate - Moments: r depends on wealth Wealth Shares Moments Share of wealth 0-20% 20-40% 40-60% 60-80% 80-90% 90-95% 95-99% % Data (SCF 2007) Simulation (1) r depends on wealth Transition Diagonal Moments Share of wealth 0-20% 20-40% 40-60% 60-80% 80-90% 90-95% 95-99% % Data Simulation (1) r depends on wealth Benhabib,J, Bisin, A., Luo, M. () 34 / 45

35 Counterfactual re-estimation Wealth distribution Data Model (1) Baseline (2) Constant r (3) Constant w (4) µ = Social mobility Data Model (1) Baseline (2) Constant r (3) Constant w (4) µ = Top 5% shares missed in all cases. Upward Mobility fails for constant w.the wealth-poor get trapped Benhabib,J, Bisin, A., Luo, M. () 35 / 45

36 Counterfactual estimation Preferences σ µ A β T baseline [2] [0.97] [36] (0.0010) (0.0011) constant r [2] [0.97] [36] (0.0145) (0.0498) constant w [2] [0.97] [36] (0.0042) (0.0014) µ = 2 [2] [0.97] [36] - (0.0147) Rate of return process E(r ) σ(r ) ρ(r ) baseline 2.76% 2.54% (0.80%) (0.87%) (0.063) constant r 2.99% (1.70%) constant w 3.13% 2.34% (1.65%) (1.48%) (0.008) µ = % 2.97% (2.10%) (1.76%) (0.006) Benhabib,J, Bisin, A., Luo, M. () 36 / 45

37 Estimation without Stationarity Assumption Without requiring that the wealth distribution in 2007 be stationary - or requiring that a stationary distribution exist... We re-estimate our model: feeding the observed SCF wealth distribution as an initial condition; iterating two generations ( 72 periods in the model); matching the SCF 2007 wealth distribution and social mobility. Note: the exercise has to be taken as a robustness check to gauge at speed of transitional dynamics; e.g., we do not feed in any shock, like tax reforms and the like. Benhabib,J, Bisin, A., Luo, M. () 37 / 45

38 Estimation without Stationarity Assumption Preferences σ µ A β T [2] [0.97] [36] (0.0208) (0.0003) Rate of return process state space (0.0011) (0.0011) (0.0032) (0.0021) (0.0098) transitional diagonal (0.3672) (0.0539) (0.3805) (0.4357) (0.1892) statistics E(r) σ(r) ρ(r) 3.27% 3.03% (0.96%) (0.42%) (0.010) Benhabib,J, Bisin, A., Luo, M. () 38 / 45

39 Estimation without Stationarity Assumption Data: SCF Data: SCF Model Social mobility Data Model Benhabib,J, Bisin, A., Luo, M. () 39 / 45

40 Estimation without Stationarity Assumption Our parameter estimates overshoot the actual increase in the top shares of wealth relative to the data from 1962 to 2007 (two periods or generations in our model), in large part due to the volatility of the estimated rate of return that fattens and fills the tail. A small increase in the volatility of the rate of return, therefore not only helps generate a fat tail, but also speeds up the transition to the tail, as in Gabaix et al (2016). To the extent that we abstract from exogenous factors like tax changes that can account for the fatter tail of wealth, the estimated rate of return volatility may in fact be a bit upward biased, and explain the overshoot in the We note that along with increased estimated inequality, mobility also seems reduced relative to the data (higher diagonal elements of transition matrix. Benhabib,J, Bisin, A., Luo, M. () 40 / 45

41 Policy implications: Without stochastic idiosyncratic returns Can capital and estate taxes reduce inequality? Becker and Tomes (1979), JPE: They find that tax increases not only have a negligible influence on the stationary wealth distribution, but may in fact increase inequality even if the tax receipts were redistributed lump sum in an egalitarian fashion: "Consequently, our analysis offers no comfort to the prevailing view that redistribution within a progressive tax-subsidy system reduces (relative) inequality in disposable income. Indeed, two explicit definitions of taxable income suggest the opposite conclusion, namely, that the inequality in disposable income is widened." Benhabib,J, Bisin, A., Luo, M. () 41 / 45

42 Policy implications: Without stochastic idiosyncratic returns Can capital and estate taxes reduce inequality? Castaneda, Jimenez and Rios-Rull (2003), JPE: "Finally, as far as the policy experiment of abolishing estate taxation is concerned, we find that the steady-state implications of this policy change are to increase output by 0.35 percent and the stock of capital by 0.87 percent, and that its distributional implications are very small." "Estate Taxation, Entrpreuneurship and Taxes," Cagetti and DeNardi (2009), AER More generally, all of the policy experiments that we consider contradict the claim that most households would benefit from abolishing estate taxation...in none of the policy experiments do wealth and consumption inequality go up significantly as a result of the abolition of estate taxes. Benhabib,J, Bisin, A., Luo, M. () 42 / 45

43 Policy implications: With stochastic idiosyncratic returns Can capital and estate taxes reduce inequality? Benhabib, Bisin and Zhu, 2011, Econometrica: In our model fiscal policy is used for government consumption and does not have any direct redistributive and wealth equalizing effect. Nonetheless, both capital income and estate taxes dampen the effect of luck acting through the stochastic returns on capital. The effect of a streak of luck acting multiplicatively on wealth can be powerful, and in fact generates the skewness and fat tails of the wealth distribution. Any dampening either of returns to wealth through capital taxes or of the transmission of wealth through estate taxes will tend to flatten the heavy tails of the wealth distribution. Capital income risk, inducing a stochastic return on capital, therefore, is the main reason why our results on fiscal policies differ substantially from those of Becker and Tomes (1979). Benhabib,J, Bisin, A., Luo, M. () 43 / 45

44 Conclusion We estimated a macroeconomic model of the distribution of wealth in the U.S. While emphasize the tail of the distribution, the model performs well in hitting the whole distribution of wealth in the data. Importantly, the model is also successful in hitting the social mobility of wealth in the data. Capital income risk and differential savings are fundamental factors in explaining wealth distribution and social mobility (in the U.S.). Variable earnings are also essential but by themselves are not enough. Capital income risk estimates are roughly consistent with observations regarding return on real estate and private business equity. Ongoing work in estimating parameters to incorporate non-stationary changes in distribution induced by recent changes in taxes, regulations. Benhabib,J, Bisin, A., Luo, M. () 44 / 45

45 Conclusion Benhabib,J, Bisin, A., Luo, M. () 45 / 45