The Distribution of Wealth and the Marginal Propensity to Consume

Transcription

1 The Distribution of Wealth and the Marginal Propensity to Consume Christopher Carroll 1 Jiri Slacalek 2 Kiichi Tokuoka 3 Matthew N. White 4 1 Johns Hopkins University and NBER ccarroll@jhu.edu 2 European Central Bank jiri.slacalek@ecb.int 3 Ministry of Finance, Japan kiichi.tokuoka@mof.go.jp 4 University of Delaware mnwecon@udel.edu

2 The MPC Theory and Evidence Friedman (1957) Our Claim: Heterogeneity Is Key To Modeling the MPC The Question: How Large Is the MPC ( κ)? If households receive a surprise extra 1 unit of income, how much will be in aggregate spent over the next year? Elements that interact with each other to produce the result: Households are heterogeneous Wealth is unevenly distributed c function is highly concave Distributional issues matter for aggregate C Giving 1 to the poor giving 1 to the rich

3 The MPC Theory and Evidence Friedman (1957) Consumption Concavity and Wealth Heterogeneity Consumption quarterly perm income ratio left scale Rep agent's ratio of M to quarterly perm income Histogram: empirical SCF2004 density of m t right scale m

4 The MPC Theory and Evidence Friedman (1957) Why Worry About the MPC ( κ)? Nobody trying to make a forecast in would ask: Big stimulus tax cuts Keynesian multipliers should be big in liquidity trap Crude Keynesianism: Transitory tax cut multiplier is 1/(1 κ) 1 If κ = 0.75 then multiplier is 4 1 = 3 Some micro estimates of κ are this large If κ = 0.05 then multiplier is only 0.05 This is about the size of κ in Rep Agent and KS models

5 The MPC Theory and Evidence Friedman (1957) Why Worry About the MPC ( κ)? Nobody trying to make a forecast in would ask: Big stimulus tax cuts Keynesian multipliers should be big in liquidity trap Crude Keynesianism: Transitory tax cut multiplier is 1/(1 κ) 1 If κ = 0.75 then multiplier is 4 1 = 3 Some micro estimates of κ are this large If κ = 0.05 then multiplier is only 0.05 This is about the size of κ in Rep Agent and KS models

6 The MPC Theory and Evidence Friedman (1957) Why Worry About the MPC ( κ)? Nobody trying to make a forecast in would ask: Big stimulus tax cuts Keynesian multipliers should be big in liquidity trap Crude Keynesianism: Transitory tax cut multiplier is 1/(1 κ) 1 If κ = 0.75 then multiplier is 4 1 = 3 Some micro estimates of κ are this large If κ = 0.05 then multiplier is only 0.05 This is about the size of κ in Rep Agent and KS models

7 The MPC Theory and Evidence Friedman (1957) To-Do List 1 Calibrate realistic income process 2 Match empirical wealth distribution 3 Back out optimal C and MPC out of transitory income 4 Is MPC in line with empirical estimates? Our Question: Does a model that matches micro facts about income dynamics and wealth distribution give different (and more plausible) answers than KS to macroeconomic questions (say, about the response of consumption to fiscal stimulus )?

8 The MPC Theory and Evidence Friedman (1957) Friedman (1957): Permanent Income Hypothesis Y t = P t + T t C t = P t Progress since then Micro data: Friedman description of income shocks works well Math: Friedman s words well describe optimal solution to dynamic stochastic optimization problem of impatient consumers with geometric discounting under CRRA utility with uninsurable idiosyncratic risk calibrated using these micro income dynamics (!)

9 Our (Micro) Income Process Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Idiosyncratic (household) income process is logarithmic Friedman: p t = permanent income ξ t = transitory income ψ t+1 = permanent shock W = aggregate wage rate y t+1 = p t+1 ξ t+1 W p t+1 = p t ψ t+1

10 Further Details of Income Process Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Modifications from Carroll (1992) Transitory income ξ t incorporates unemployment insurance: ξ t = µ with probability u = (1 τ) lθ t with probability 1 u µ is UI when unemployed τ is the rate of tax collected for the unemployment benefits

11 Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Model Without Aggr Uncertainty: Decision Problem v(m t ) = max {c t} s.t. [ ] u + β DE t ψ 1 ρ t+1 v(m t+1) a t = m t c t a t 0 k t+1 = a t /( Dψ t+1 ) m t+1 = (ℸ + r)k t+1 + ξ t+1 r = αz(k/ ll) α 1 (State and control variables normalized by p t W)

12 What Happens After Death? Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume You are replaced by a new agent whose permanent income is equal to the population mean Prevents the population distribution of permanent income from spreading out

13 What Happens After Death? Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume You are replaced by a new agent whose permanent income is equal to the population mean Prevents the population distribution of permanent income from spreading out

14 Ergodic Distribution of Permanent Income Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Exists, if death eliminates permanent shocks: DE[ψ 2 ] < 1. Holds. Population mean of p 2 : M[p 2 ] = D 1 DE[ψ 2 ]

15 Parameter Values Motivation Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume β, ρ, α, δ, l, µ, and u taken from JEDC special volume Key new parameter values: Description Param Value Source Prob of Death per Quarter D Life span of 40 years Variance of Log ψ t σ 2 ψ 0.016/4 Carroll (1992); SCF DeBacker et al. (2013) Variance of Log θ t σ 2 θ Carroll (1992)

16 Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Annual Income, Earnings, or Wage Variances σψ 2 σξ 2 Our parameters Carroll (1992) Storesletten, Telmer, and Yaron (2004) Meghir and Pistaferri (2004) Low, Meghir, and Pistaferri (2010) Blundell, Pistaferri, and Preston (2008) DeBacker, Heim, Panousi, Ramnath, and Vidangos (2013) Implied by KS-JEDC Implied by Castaneda et al. (2003) Meghir and Pistaferri (2004) and Blundell, Pistaferri, and Preston (2008) assume that the transitory component is serially correlated (an MA process), and report the variance of a subelement of the transitory component. σ 2 ξ for these articles are calculated using their MA estimates.

17 Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Typology of Our Models Four Dimensions 1 Discount Factor β β-point model: Single discount factor β-dist model: Uniformly distributed discount factor 2 Aggregate Shocks (No) Krusell Smith Friedman/Buffer Stock 3 Empirical Wealth Variable to Match 4 Life Cycle Net Worth Liquid Financial Assets Perpetual Youth (a la Blanchard) Overlapping Generations

18 Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Dimension 1: Estimation of β-point and β-dist β-point model Estimate single `β by matching the capital output ratio β-dist model Heterogenous Impatience Assume uniformly distributed β across households Estimate the band [ `β, `β + ] by minimizing distance between model (w) and data (ω) net worth held by the top 20, 40, 60, 80% min (w i ω i ) 2, { `β, } i=20,40,60,80 s.t. aggregate net worth output ratio matches the steady-state value from the perfect foresight model

19 Results: Wealth Distribution Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume KS JEDC Β Point Β Dist US data SCF KS Hetero Percentile

20 Results: Wealth Distribution Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Micro Income Process Friedman/Buffer Stock KS-JEDC KS-Orig Point Uniformly Our solution Hetero Discount Distributed Factor Discount Factors U.S. β-point β-dist Data Top 1% Top 20% Top 40% Top 60% Top 80% Notes: : `β = Carroll, Slacalek, : ( `β, ) Tokuoka = (0.9867, and ). White Bold Wealth pointsand arempc targeted. K t /Y t = 10.3.

21 Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Marginal Propensity to Consume & Net Worth c t Most Impatient left scale Identical Patience left scale f Most Patient left scale Rep agent's ratio of M to quarterly perm income 0.2 Histogram: empirical density of net worth right scale m t

22 Results: MPC (in Annual Terms) Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Micro Income Process Friedman/Buffer Stock KS-JEDC β-point β-dist Our solution Overall average By wealth/permanent income ratio Top 1% Top 20% Top 40% Top 60% Bottom 1/ By employment status Employed Unemployed Notes: Annual MPC is calculated by 1 (1 quarterly MPC) 4.

23 Estimates of MPC in the Data: Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Consumption Measure Authors Nondurables Durables Total PCE Horizon Event/Sample Blundell et al. (2008b) 0.05 Estimation Sample: Coronado et al. (2005) Year 2003 Tax Cut Hausman (2012) Year 1936 Veterans Bonus Johnson et al. (2009) Months 2003 Child Tax Credit Lusardi (1996) Estimation Sample: Parker (1999) Months Estimation Sample: Parker et al. (2011) Months 2008 Economic Stimulus Sahm et al. (2009) 1/3 1 Year 2008 Economic Stimulus Shapiro and Slemrod (2009) 1/3 1 Year 2008 Economic Stimulus Souleles (1999) Months Estimation Sample: Souleles (2002) Year The Reagan Tax Cuts of the Early 1980s Notes: : elasticity.

24 Income Process Decision Problem There Is an Ergodic Distribution of Permanent Income Parameter Values Annual Income Variances Our Strategy Results: Marginal Propensity to Consume Typology of Our Models Four Dimensions 1 Discount Factor β β-point model: Single discount factor β-dist model: Uniformly distributed discount factor 2 Aggregate Shocks (No) Krusell Smith Friedman/Buffer Stock 3 Empirical Wealth Variable to Match 4 Life Cycle Net Worth Liquid Financial Assets Perpetual Youth (a la Blanchard) Overlapping Generations

25 Krusell Smith Permanent/Transitory Aggregate Shocks Dimension 2.a: Adding KS Aggregate Shocks Model with KS Aggregate Shocks: Assumptions Only two aggregate states (good or bad) Aggregate productivity Z t = 1 ± Z Unemployment rate u depends on the state (u g or u b ) Parameter values for aggregate shocks from Krusell and Smith (1998) Parameter Value Z 0.01 u g 0.04 u b 0.10 Agg transition probability 0.125

26 Krusell Smith Permanent/Transitory Aggregate Shocks Dimension 2.b: Adding FBS Aggregate Shocks Friedman/Buffer Stock Shocks Motivation: More plausible and tractable aggregate process, also simpler Eliminates good and bad aggregate state Aggregate production function: K α t (Lt)1 α L t = P tξ t P t is aggregate permanent productivity P t+1 = P tψ t+1 Ξ t is the aggregate transitory shock. Parameter values estimated from U.S. data: Description Parameter Value Variance of Log Ψ t σ 2 Ψ Variance of Log Ξ t σ 2 Ξ

27 Krusell Smith Permanent/Transitory Aggregate Shocks Dimension 2.b: Adding FBS Aggregate Shocks Friedman/Buffer Stock Shocks Motivation: More plausible and tractable aggregate process, also simpler Eliminates good and bad aggregate state Aggregate production function: K α t (Lt)1 α L t = P tξ t P t is aggregate permanent productivity P t+1 = P tψ t+1 Ξ t is the aggregate transitory shock. Parameter values estimated from U.S. data: Description Parameter Value Variance of Log Ψ t σ 2 Ψ Variance of Log Ξ t σ 2 Ξ

28 Krusell Smith Permanent/Transitory Aggregate Shocks Results Our/FBS model A few times faster than solving KS model The results are similar to those under KS aggregate shocks

29 Krusell Smith Permanent/Transitory Aggregate Shocks Results: MPC Over the Business Cycle Model: β-dist Krusell Smith (KS) Friedman/Buffer Stock (FBS) Scenario Large Bad Large Bad Base Recssn Expnsn Base Perm Shock Trans Shock Overall average By wealth/permanent income ratio Top 1% Top 10% Top 20% Top 40% Top 50% Top 60% Bottom 50% By employment status Employed Unemployed

30 Krusell Smith Permanent/Transitory Aggregate Shocks Results: MPC Over the Business Cycle Krusell Smith Aggregate and idiosyncratic shocks positively correlated Higher MPC during recessions, especially for the unemployed Friedman/Buffer Stock Shocks uncorrelated MPC essentially doesn t vary over BC

31 Krusell Smith Permanent/Transitory Aggregate Shocks Typology of Our Models Four Dimensions 1 Discount Factor β β-point model: Single discount factor β-dist model: Uniformly distributed discount factor 2 Aggregate Shocks (No) Krusell Smith Friedman/Buffer Stock 3 Empirical Wealth Variable to Match 4 Life Cycle Net Worth Liquid Financial Assets Perpetual Youth (a la Blanchard) Overlapping Generations

32 Net Worth vs Liquid Assets Dimension 3: Matching Net Worth vs. Liquid Financial (and Retirement) Assets c t f Most impatient left scale Most patient left scale 0.3 Histogram: empirical density of 0.5 liquid financial asset retirement assets right scale 0.2 Histogram: empirical density of net worth right scale m t

33 Net Worth vs Liquid Assets Match Net Worth vs. Liquid Financial Assets Buffer stock saving driven by accumulation of liquidity May make more sense to match liquid (and retirement) assets (Hall (2011), Kaplan and Violante (2014)) Aggregate MPC Increases Substantially: Net Worth β-dist Liq Fin and Ret Assets Overall average By wealth/permanent income ratio Top 1% Top 20% Top 40% Top 60% Bottom 1/ Wealth 4 and MPC

34 Net Worth vs Liquid Assets Distribution of MPCs Wealth heterogeneity translates into heterogeneity in MPCs Percentile KS JEDC KS Hetero 25 Matching net worth Matching liquid financial retirement assets Annual MPC

35 Net Worth vs Liquid Assets Typology of Our Models Four Dimensions 1 Discount Factor β β-point model: Single discount factor β-dist model: Uniformly distributed discount factor 2 Aggregate Shocks (No) Krusell Smith Friedman/Buffer Stock 3 Empirical Wealth Variable to Match 4 Life Cycle Net Worth Liquid Financial Assets Perpetual Youth (a la Blanchard) Overlapping Generations

36 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Dimension 4: Overlapping Generations Realistic Life-Cycle Model Three education levels: e {D, HS, C} Age/education-specific income profiles y t = ξ t p t = (1 τ)θ t p t, p t = ψ t ψ es p t 1 Age-specific variances of income shocks Transitory unemployment shock with prob u Household-specific mortality D es

37 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Household Decision Problem v es (m t ) = max u c t

38 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Macro Dynamics Population growth N, technological progress Γ Tax rate to finance social security and unemployment benefits: τ = τ SS + τ U [ e {D,HS,C} θ 384 ( ep e0 t=164 ((1+Γ)(1+N)) t ) ] t s=0 τ SS = (ψ es D es) ) ] τ U = uµ e {D,HS,C} [ θ ep e0 163 t=0 ( ((1+Γ)(1+N)) t t s=0 (ψ es D es)

39 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Calibration Description Parameter Value Coefficient of relative risk aversion ρ 1 Effective interest rate (r δ) 0.01 Population growth rate N Technological growth rate Γ Rate of high school dropouts θ D 0.11 Rate of high school graduates θ HS 0.55 Rate of college graduates θ C 0.34 Average initial permanent income, dropout p D Average initial permanent income, high school p HS Average initial permanent income, college p C Unemployment insurance payment µ 0.15 Unemployment rate u 0.07 Labor income tax rate τ

40 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Results: Wealth Distribution US data SCF KS JEDC Β Point Β Dist Percentile

41 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Results: MPC (in Annual Terms) Micro Income Process Life-Cycle Model KS-JEDC FBS Our solution β-dist β-point β-dist β-dist Wealth Measure NW NW NW NW Liquid Overall average By wealth/permanent income ratio Top 1% Top 20% Top 40% Top 60% Bottom 1/ By employment status Employed Unemployed Notes: Annual MPC is calculated by 1 (1 quarterly MPC) 4.

42 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Results: MPC by Age 1 Most impatient 0.5 Population average 0 Most patient Initial drop in MPC: Build-up of buffer stock Rise while rapid income growth, fall before retirement, then incrsing mortlty risk

43 Overlapping Generations Household Decision Problem Macro Dynamics Calibration Results Conclusions Definition of serious microfoundations: Model that matches Income Dynamics Wealth Distribution The model produces more plausible implications about: Aggregate MPC Distribution of MPC Across Households Version with more plausible aggregate specification is simpler, faster, better in every way!

44 I Motivation Blundell, Richard, Luigi Pistaferri, and Ian Preston (2008): Consumption Inequality and Partial Insurance, American Economic Review, 98(5), Carroll, Christopher D. (1992): The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence, Brookings Papers on Economic Activity, 1992(2), , Castaneda, Ana, Javier Diaz-Gimenez, and Jose-Victor Rios-Rull (2003): Accounting for the U.S. Earnings and Wealth Inequality, Journal of Political Economy, 111(4), DeBacker, Jason, Bradley Heim, Vasia Panousi, Shanthi Ramnath, and Ivan Vidangos (2013): Rising Inequality: Transitory or Persistent? New Evidence from a Panel of U.S. Tax Returns, Brookings Papers on Economic Activity, Spring, Friedman, Milton A. (1957): A Theory of the Consumption Function. Princeton University Press. Hall, Robert E. (2011): The Long Slump, AEA Presidential Address, ASSA Meetings, Denver. Kaplan, Greg, and Giovanni L. Violante (2014): A Model of the Consumption Response to Fiscal Stimulus Payments, Econometrica, 82(4), Krusell, Per, and Anthony A. Smith (1998): Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy, 106(5), Low, Hamish, Costas Meghir, and Luigi Pistaferri (2010): Wage Risk and Employment Over the Life Cycle, American Economic Review, 100(4), Meghir, Costas, and Luigi Pistaferri (2004): Income Variance Dynamics and Heterogeneity, Journal of Business and Economic Statistics, 72(1), Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2004): Cyclical Dynamics in Idiosyncratic Labor-Market Risk, Journal of Political Economy, 112(3),