The historical evolution of the wealth distribution: A quantitative-theoretic investigation Joachim Hubmer, Per Krusell, and Tony Smith Yale, IIES, and Yale March 2016
Evolution of top wealth inequality (Kopczuk 2015) Wealth Share in % 55 50 45 40 35 30 25 20 Capitalization, Top 1% Capitalization, Top 0.1% SCF, Top 1% SCF, Top 0.1% Estate tax multiplier, Top 1% Estate tax multiplier, Top 0.1% 15 10 5 1920 1930 1940 1950 1960
Overview: objective calibrate a quantitative macro model that accounts for the full US wealth distribution, including the Pareto tail study the transition path: starting in the 1960s, feeding in observed changes in earnings inequality and tax rates can the standard macro-inequality framework explain movements in the wealth distribution?
Overview: findings model is partially successful in explaining the evolution of the wealth distribution magnitude of increase in inequality explained for bulk of distribution misses speed of changes at the very top and short-run dynamics active channels: decreasing tax progressivity has a dramatic effect on the wealth distribution increase in idiosyncratic labor income risk has in general a dampening effect on wealth inequality via the precautionary savings channel (vanishes at the top) changes in r g not important, partly working in the opposite direction cautious prediction for 21st century: long-term effects of decreasing tax progressivity on wealth inequality
Trends in wealth inequality: recent literature Data: Saez and Zucman (2015); Kopczuk; Bricker, Henriques, Krimmel, and Sabelhaus (2016). Models of Pareto tails: Piketty and Zucman (2015); Benhabib, Bisin, and Luo (2015); Nirei and Aoki (2015). Models of transitions: Kaymak and Poschke (2016); Gabaix, Lasry, Lions, and Moll (2016).
Quantitative model Aiyagari 94 framework: log labor income as sum of persistent and transitory component; adjusted at the top to match the observed Pareto tail in labor income stochastic discount factor follows AR1 process (Krusell-Smith 98 extended) stochastic i.i.d. return on capital progressive taxation: use data on federal effective tax rates for 11 income brackets (Piketty & Saez 2007) parsimonious modeling of social safety net: 60% of tax revenues rebated as lump-sum transfers time-varying tax system and labor income process
The consumer s problem V t (x t, p t, β t ) = max a t+1 a {u(x t a t+1 ) + β t E [V t+1 (x t+1, p t+1, β t+1 ) p t, β t ]} subject to x t+1 =a t+1 + y t+1 τ t+1 (y t+1 ) + T t+1 (2) y t+1 =r t+1 η t+1 a t+1 + w t+1 l t+1 (p t+1, ν t+1 ) (3) (1) x t cash on hand p t persistent component of earnings process l t+1 (, ) efficiency units of labor, moves over time ν t+1 transitory earnings shock η t+1 return to capital shock τ t (y t ) tax function based on gross income, moves over time T t lump-sum transfer
Main qualitative mechanism stochastic-β alone generates a Pareto tail in the wealth distribution add stochastic return to capital and Pareto tail in labor income to improve quantitative properties of the model Pareto tail in labor income alone would be inherited by wealth distribution, but tail coefficient would be too high (top inequality inequality too low) follows from random growth theory (Kesten 1973, see also Gabaix 2009) mechanism has been employed by Benhabib, Bisin and Zhu (2011), Nirei & Aoki (2015), Piketty & Zucman (2015) main alternative calibration (Castañeda, Días-Giménez, Ríos-Rull 2003) cannot deliver this Pareto tail
Stochastic-β yields stochastic, linear savings decisions marginal propensity to save 1 0.95 0.9 0.85 high beta, high earnings high beta, low earnings low beta, high earnings low beta, low earnings 2 4 6 8 10 12 14 16 log(k)
Gives rise to a Pareto tail in the wealth distribution 0-2 -4-6 log-log plot of countercumulative distribution function log(1-f(k)) Top 10% Top 1% Top 0.1% Top 0.01% log(1-f(k)) -8-10 -12-14 -16-18 -5 0 5 10 15 log(k)
Calibration strategy earnings process, tax rates, social safety net calibrated to observables randomness in discount factor and return to capital calibrated to replicate the wealth distribution in the initial steady state (1960s) focus on tail coefficient alone misleading: even if say the richest 10% can be described exactly by a Pareto distribution, the shape parameter only tells us how wealth is distributed within these 10%, not how much wealth the top 10% control as a fraction of total wealth
Calibration: stochastic-β and r Stochastic-β: follows AR(1) process µ = 0.92, ρ = 0.992, σ = 0.0019 i.e in cross-section, standard deviation = 0.0148 i.e. over 50 years, mean reversion is 1/3 Stochastic Return to Capital: pre-tax return (1 + r t η t ) η t i.i.d N(1, 0.725) i.e. in steady state, standard deviation of 0.048 or 90% have return (1 + r η t ) [0.9874, 1.1437] Fagereng, Guiso, Malacrino & Pistaferri (2016) find a standard deviation of 0.04 in Norwegian data
Matching the wealth distribution US Wealth distribution in 1967: Top 10% Share Top 1% Top 0.1% Top 0.01% Data* 70.8% 27.8% 9.4% 3.1% Model 70.6% 28.1% 9.5% 2.9% fraction w negative wealth Bottom 50% share Data* 8.0% 4.0 % Model 7.0% 3.1 % (* Top wealth shares (capitalization): Saez & Zucman, 2014; bottom 50% share (SCF): Kennickell, 2012) model matches wealth distribution well on its entire domain
Observed change 1: decrease in tax progressivity federal effective tax rates (Piketty & Saez 2007): income, payroll, corporate and estate taxes 0.8 0.7 0.6 top rate 5 * average income 3 * average income average income 0.5 0.4 0.3 0.2 0.1 1970 1975 1980 1985 1990 1995 2000
Observed change 2: increase in labor income risk estimates for variance of persistent and temporary components 1967-2000 (Heathcote, Storesletten & Violante 2010) 0.6 0.55 0.5 Cross-sectional Standard Deviations persistent component transitory component 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 1970 1975 1980 1985 1990 1995 2000 2005 2010
Observed change 3: increase in top labor income shares adjust standard AR1 in idiosyncratic productivity by imposing a Pareto tail for the top 10 % earners: calibrated tail coefficient decreases from 2.8 to 1.9 (Piketty & Saez, 2003 [updated series -2011]) 35 top 10% share 14 12 top 1% share 30 10 25 model data 8 6 top 0.1% share 5 4 3 2 1 top 0.01% share 2 1.5 1 0.5
Main result: evolution of top wealth shares 80 75 top 10% wealth share model data (SZ) data (SCF) 40 35 top 1% wealth share 70 30 65 25 top 0.1% wealth share 12 top 0.01% wealth share 20 10 15 8 6 10 4 2
Other statistics 6 5.5 capital - net output ratio model (capital) data (national wealth) data (private wealth) 4 3.5 bottom 50% share 5 3 4.5 2.5 4 2 3.5 1.5 model data (SCF) 3 1 captures dynamics of capital stock (but capital wealth) and share of wealth held by asset-poor
Summary of transitional dynamics model captures the salient features of the evolution of the US wealth distribution perfect foresight assumption does not seem to be critical ( myopic transition ) robust to CES production function with elasticity > 1 ( CES ) shortcomings: miss on short-run dynamics (heterogeneous portfolios and valuation effects?) explosion of wealth concentration at the very top (0.1 % and above) as measured by Saez & Zucman (2014) not explained well
Main channels what fraction of the increase in the top wealth shares do the three channels account for? Earnings Risk Top Earnings Taxes Combined Top 10 % -0.78 0.22 1.89 1.32 Top 1 % -0.19 0.05 0.82 0.65 larger earnings risk induces higher precautionary savings (vanishes for the rich), depressing the interest rate and thus increasing the Pareto tail coefficient (i.e. decreasing top wealth inequality) in general equilibrium, the average tax level does not matter much for wealth inequality, but changing progressivity has a large effect
Only Changes in Earnings Risk I top 10% wealth share top 1% wealth share 75 70 model data (SZ) data (SCF) 40 35 30 65 25 top 0.1% wealth share 12 top 0.01% wealth share 20 15 10 10 8 6 4 2
Only Changes in Earnings Risk II 6 capital - net output ratio 4 bottom 50% share 5.5 5 model (capital) data (national wealth) data (private wealth) 3.5 3 4.5 2.5 4 3.5 2 1.5 model data (SCF) 3 1
Only Changes in Top Earnings Shares I top 10% wealth share top 1% wealth share 75 70 model data (SZ) data (SCF) 40 35 30 65 25 top 0.1% wealth share 12 top 0.01% wealth share 20 15 10 10 8 6 4 2
Only Changes in Top Earnings Shares II 6 capital - net output ratio 4 bottom 50% share 5.5 5 model (capital) data (national wealth) data (private wealth) 3.5 3 4.5 2.5 4 2 model data (SCF) 3.5 1.5 3 1
Only Changes in Taxes I top 10% wealth share top 1% wealth share 80 75 70 model data (SZ) data (SCF) 40 35 30 65 25 top 0.1% wealth share 12 top 0.01% wealth share 20 15 10 10 8 6 4 2
Only Changes in Taxes II 6 capital - net output ratio 4 bottom 50% share 5.5 model (capital) data (national wealth) data (private wealth) 3.5 5 3 4.5 2.5 4 2 3.5 1.5 model data (SCF) 3 1
Capital in the 21st century? 85 top 10% wealth share 50 top 1% wealth share 80 75 45 40 35 70 65 model data (SZ) 30 25 1980 2000 2020 2040 2060 2080 2100 1980 2000 2020 2040 2060 2080 2100 top 0.1% wealth share 12 top 0.01% wealth share 20 10 15 8 6 10 4 2 1980 2000 2020 2040 2060 2080 2100 1980 2000 2020 2040 2060 2080 2100 long-run effects of decrease in tax progressivity
Other channels: what about r g? increase in r g decreases wealth inequality in the medium run (a few decades) Pareto tail coefficient decreases (i.e., top wealth inequality increases), but very slowly r-g graphs more important in short-run: low-asset agents savings decisions more elastic w.r.t. the interest rate random growth models generally feature slow transitions, it takes long to fill a thick long tail (see Gabaix, Lasry, Lions, and Moll [2015])
Conclusion: where next? speed of changes at the very top hard to match asset price movements and portfolio choice? why are portfolios heterogeneous? why are asset prices moving that much? (outside the scope of our model - What would Shiller say? )
Price-earnings ratio (Shiller) return
Perfect foresight vs myopic transition I return 80 78 top 10% wealth share perfect foresight myopic 38 36 top 1% wealth share 76 34 74 32 72 70 top 0.1% wealth share 13 12 11 10 30 28 top 0.01% wealth share 4 3.5 3
Perfect foresight vs myopic transition II return capital - net output ratio 3.5 bottom 50% share 4.2 4.1 4 3.9 perfect foresight myopic 3 2.5 2 3.8 3.7 1.5 1
CES with elasticity of substitution > 1 σ = 1.25 (Karabarbounis and Neiman, 2014) return 4.3 4.2 4.1 4 3.9 3.8 38 36 34 32 30 capital - net output ratio Cobb-Douglas CES sigma=1.25 top 1% wealth share 0.065 0.06 0.055 0.5 0.45 interest rate (pre-tax) Gini gross income 28 0.4
r g? return model increase in r g as temporary 50% - increase in interest rate partial equilibrium, holding wage and transfers constant
r g experiment return 10 pre-tax interest rate 29 top 1% wealth share 9 28 % 8 % 27 7 26 6 0 20 40 60 80 100 year Gini Coefficient for Wealth 0.82 0.81 0.8 0.79 0.78 0 20 40 60 80 100 year 25 0 20 40 60 80 100 year Gini Coefficient for Income 0.5 0.45 0.4 0.35 pre-tax income post-tax income 0.3 0 20 40 60 80 100 year