Response of Inequality to a Growth Rate Slowdown in Japanese Economy during the Lost Decades

Response of Inequality to a Growth Rate Slowdown in Japanese Economy during the Lost Decades N. Sudo, M. Suzuki, T. Yamada May 27, 2014@CIGS Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 1 / 58

Table of Contents Introduction Time-series Analysis Model Calibration Results Discussion Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 2 / 58

Motivation Slowdown in aggregate growth after bubble burst in Japan (the Lost decades) Hayashi and Prescott (2002) Changes in income and consumption distribution across households during the same period Lise, Sudo, Suzuki, Yamada, and Yamada (2014,RED) Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 3 / 58

Time Path of Macroeconomic Variables 0.06 0.04 0.02 0 0.02 Real Consumption 0.04 1980 1990 2000 2010 0.1 0.05 0 Real GDP 0.05 1980 1990 2000 2010 0.06 0.04 0.02 0 0.02 Labor Compensation 0.04 1980 1990 2000 2010 0.1 0.05 0 TFP 0.05 1980 1990 2000 2010 Red line: the estimated mean of each variables with structural breaks Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 4 / 58

Variance of Log. Income and Consumption 0.38 Var. of Log Labor Income Var. of Log Non durable Consumption 0.3 0.36 Variance of Logarithm 0.34 0.32 0.3 0.28 Variance of Logarithm 0.25 0.2 0.26 0.24 1980 1985 1990 1995 2000 2005 2010 Year 0.15 1980 1985 1990 1995 2000 2005 2010 Year Full-time employed workers: 25 59 The lost decades are accompanied by the slowdown of inequality growth Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 5 / 58

Percentiles of the Earnings Distribution.5 Equivalized Household Earnings (log).4.3 p50 p25 p75 p95 p90.2.1 p10 p5 0 1980 1985 1990 1995 2000 2005 2010 Year Top income quantiles grow faster than bottom during 1980s Income growth rates decline in mid-1990s APPENDIX FIGURE Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 6 / 58

Questions 1. What are the driving forces of these changes in income and consumption distribution? (i) lower aggregate TFP growth, (ii) skill premium increases, or both? 2. Are these forces responsible for aggregate growth rate slowdown? 3. How do they affect the income and consumption distribution? Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 7 / 58

What We Do 1. Construct monthly time series of variance of log income, consumption, and correlation between the two variables Family Income and Expenditure Survey 2. Structural break tests on time series of cross-section moments 3. Examine link between aggregate slowdown and inequality in a dynamic general equilibrium model with heterogeneous households Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 8 / 58

Empirical Findings Macroeconomic changes during the lost decade? 1. Aggregate output growth rate slowdown 2. Income inequality growth rate slowdown 3. Consumption inequality growth rate slowdown 4. Falls in covariance/correlation between income and consumption Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 9 / 58

Theoretical Findings Slowdown of TFP and demand for skilled labor are both needed to account for the empirical findings TFP demand for skilled labor Slower aggregate output growth Yes Yes Slower income inequality growth No Yes Slower consumption inequality growth Yes Yes Lower Cov./Corr. between y & c Yes Yes/No Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 10 / 58

Literature Review TFP decline in Japan: Hayashi and Prescott (2002) Skill premium: Acemoglu (2002), Kawaguchi and Mori (2014), and so on Permanent/transitory shocks: Storesletten, et al. (2004), Blundell, et al. (2008), Guvenen, et al. (2013), and so on Consumption inequality: Meyer and Sullivan (2013) Overlapping-generations models: Heckman, et al. (1998), Kaplan and Violante (2009), Heathcote, et al. (2010), and so on Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 11 / 58

Data Family Income and Expenditure Survey (FIES) Monthly survey on household income and expenditures January 1981 December 2008 The number of observations: 8,000 Panel data: 6 months Focus on full-time employed workers: 25 59 Two-or-more household members Construct monthly series of variables on economic inequality Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 12 / 58

Data (cont.) Definition of Variables Labor income y: Sum of monthly labor income of household members Household head + his/her spouse + other household members Equivalized by OECD equivalent scale Consumption c: Nondurable expenditures: housing, purchasing cars and durables such as furniture are excluded DETAILS Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 13 / 58

Time-series Analysis Structural Break Test: Bai and Perron (1998) ξ t = x t β + u t, for t = 1,..., T 1, ξ t = x t β + z 1 δ 1 + u t, for t = T 1 + 1,..., T 2,. ξ t = x t β + l j=1 z jδ j + u t, for t = T l + 1,..., T l+1. ξ t = x t β + m j=1 z jδ j + u t, for t = T m + 1,..., T. ξ t : each of the monthly time series T 1,..., T m : break dates, m: the number of breaks δ j : break size Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 14 / 58

Variance of Log. Income and Consumption Var. of Log Labor Income (L) Var. of Log Non durable Consumption (L) 0.3 0.35 0.25 0.3 0.2 0.25 0.04 0.02 0.02 0.04 1980 1990 2000 2010 0 Var. of Log Labor Income (YoY) 0.06 1980 1990 2000 2010 0.15 1980 1990 2000 2010 Var. of Log Non durable Consumption (YoY) 0.04 0.02 0 0.02 0.04 1980 1990 2000 2010 The lost decades are accompanied by the slowdown of inequality growth Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 15 / 58

Income Growth Rate with Different Income Quintiles 0.05 0 20% 0.05 20 40% 0 0 0.05 1980 1990 2000 2010 0.05 40 60% 0.05 1980 1990 2000 2010 0.05 60 80% 0 0 0.05 1980 1990 2000 2010 0.05 80 100% 0.05 1980 1990 2000 2010 0 0.05 1980 1990 2000 2010 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 16 / 58

Covariance and Correlation Covariance of Level 0.65 Correlation of Level 0.16 0.14 0.12 0.1 1980 1990 2000 2010 0.6 0.55 0.5 0.45 0.4 1980 1990 2000 2010 Covariance of Growth 0.5 Correlation of Growth 0.1 0.05 0 1980 1990 2000 2010 0.4 0.3 0.2 0.1 0 1980 1990 2000 2010 Transmission from income growth to consumption growth Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 17 / 58

Model An incomplete-market overlapping-generations model: transition between two steady states individuals face idiosyncratic income risks two types of individuals skilled and unskilled: e {s, u} age: j {1,..., j ret,..., J} population distribution: µ j+1 = s j+1 µ j Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 18 / 58

Labor Income Idiosyncratic Labor Income Risk: Labor income of individuals of age j at period t y e j,t = w e t κ e j η jε j, e {s, u} Persistent component of labor income ln η j+1 = λ ln η j + ω j, ω N (0, σω) 2 Transitory shock ln ε N ( σε 2 /2, σε 2 ), E t ε t+1 = 1 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 19 / 58

Household Problem Bellman Equation: Vj,t(a e j,t, η, ε) = max c1 γ j,t 1 γ + s j+1βe [ Vj+1,t+1(a e j+1,t+1, η, ε ) ] subject to c j,t + a j+1,t+1 = ỹ j,t + (1 + (1 τ k )r t )(a j,t + b t ) { (1 τ ỹ j,t = y τ ss )y j,t if j j ret ss t if j > j ret a j+1,t+1 0 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 20 / 58

Aggregation Labor supply by skill type: L e t = Aggregate labor: j ret µ j j=1 κ e j ηεdψe j,t(a, η, ε), e {s, u} L t = [(A s tl s t) ρ + (A u t L u t ) ρ ] 1 ρ, ρ 1 1 1 ρ : elasticity of substitution between skilled and unskilled Aggregate capital: K t = s,u J j=1 µ j adψ e j,t(a, η, ε) Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 21 / 58

Production A representative firm s production function: Factor prices: r t = αy t /K t δ, w e t = (1 α)a t ( Kt L t TFP factor growth rate: Y t = A t K α t L 1 α t A 1/(1 α) t+1 A 1/(1 α) t ) α L 1 ρ t (A e t ) ρ (L e t ) ρ 1, e {s, u} = 1 + g t+1 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 22 / 58

Government Budget Government budget: G t = τ y j ret µ j s,u j=1 +τ k s,u Social security system: j ret µ j s,u j=1 s,u J j=j ret +1 J j=1 µ j w e t κ e j ηεdψe j,t(a, η, ε) r t adψ e j,t(a, η, ε). τ ss w e t κ e j ηεdψe j,t(a, η, ε) = µ j ϕw e t L e t dψ e j,t(a, η, ε) Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 23 / 58

Parameters TFP factor growth rates: Muto, et al. (2013) 1.84%: initial steady state 0.16%: final steady state Preference parameters: β = 0.98, γ = 2 Production parameters: İmrohoroğlu and Sudo (2011) α = 0.377, δ = 0.08 Persistent shock parameters: Lise, et al. (2014) λ = 0.97, σω 2 = 0.01 Transitory shock parameter: Lise, et al. (2014) σε 2 = 0.03 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 24 / 58

Calibration j ret = 45 and J = 81 Individuals enter at age 20, retire at 65, and live at most 100 {s j } J j=1 : Survival probabilities National Institute of Population and Social Security Research Tax rates: τ y =10%, τ k =39.8%, τ ss : 13.58% Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 25 / 58

Calibration Factor-augmenting skill terms (Acemoglu, 2002): A s A u = S ζ/(ζ 1) H L s /L u, S H = w s L s w u L u use Basic Survey on Wage Structure s: college graduates, u: high school graduates ζ 1 1 ρ = 1.4: Heathcote, et al. (2010,JPE) w s /w u = 1.26 in 1980s w s /w u = 1.35 in 2000s {κj e}jret j=1 : age-efficiency profile Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 26 / 58

Age-Efficiency Profile 2 Skilled Unskilled Age Efficiency Profiles 1.5 1 0.5 20 30 40 50 60 Age Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 27 / 58

TFP Factor Growth Rate Shock TFP factor growth rate declines at period 1 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 28 / 58

TFP Factor Growth Rate and Skill Premium 1.025 1.4 TFP Factor Growth Rate 1.02 1.015 1.01 1.005 Skill Premium: w s /w u 1.35 1.3 1.25 1-10 0 10 20 30 40 50 60 Period 1.2-10 0 10 20 30 40 50 60 Period Left: TFP factor growth rate, Right: skill premium Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 29 / 58

Output Growth Rate and Var. Log. y 1.025 0.25 Output Growth Rate 1.02 1.015 1.01 1.005 Variance of Logarithm 0.24 0.23 0.22 0.21 1-10 0 10 20 30 40 50 60 Period 0.2-10 0 10 20 30 40 50 60 Period Left: output growth rate, Right: variance of logarithm of earnings Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 30 / 58

Interest Rate and Wage 7.5 3.4 7 3.2 Interest Rate (%) 6.5 6 5.5 5 Wage 3 2.8 2.6 2.4 Skilled Unskilled 4.5 2.2 4-10 0 10 20 30 40 50 60 Period 2-10 0 10 20 30 40 50 60 Period Left: after-tax rate of return, Right: wages of skilled and unskilled workers Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 31 / 58

Variance of Log. y and c 0.24 0.22 Variance of Logarithm 0.2 0.18 0.16 0.14 Earnings Consumption 0.12 0.1-10 0 10 20 30 40 50 60 Period # simulated households=60,000, aged 25 59 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 32 / 58

Covariance and Correlation: y and c 0.162 0.94 Covariance between y and c 0.16 0.158 0.156 0.154 0.152 0.15 0.148 Correlation between y and c 0.935 0.93 0.925 0.92 0.915 0.91 0.146-10 0 10 20 30 40 50 60 Period 0.905-10 0 10 20 30 40 50 60 Period Left: covariance, Right: correlation Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 33 / 58

Covariance and Correlation: y and c 0.019 0.62 Covariance between y and c 0.018 0.017 0.016 0.015 0.014 0.013 Correlation between y and c 0.61 0.6 0.59 0.58 0.57 0.56 0.55 0.012-10 0 10 20 30 40 50 60 Period 0.54-10 0 10 20 30 40 50 60 Period Left: covariance of the first differences, Right: correlation of the first differences Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 34 / 58

Skill Premium Shock Skill premium increases gradually for 10 years Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 35 / 58

TFP Factor Growth Rate and Skill Premium 1.025 1.4 1.38 TFP Factor Growth Rate 1.02 1.015 1.01 1.005 Skill Premium: w s /w u 1.36 1.34 1.32 1.3 1.28 1.26 1.24 1.22 1 10 0 10 20 30 40 50 60 Period 1.2 10 0 10 20 30 40 50 60 Period Left: TFP factor growth rate, Right: skill premium Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 36 / 58

Output Growth Rate and Var. Log. y 1.025 0.25 0.245 Output Growth Rate 1.02 1.015 1.01 1.005 Variance of Logarithm 0.24 0.235 0.23 0.225 0.22 0.215 0.21 0.205 1 10 0 10 20 30 40 50 60 Period 0.2 10 0 10 20 30 40 50 60 Period Left: output growth rate, Right: variance of logarithm of earnings Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 37 / 58

Interest Rate and Wage 7.25 3 2.9 7.2 2.8 Interest Rate (%) 7.15 7.1 Wage 2.7 2.6 2.5 2.4 2.3 Skilled Unskilled 7.05 2.2 7 10 0 10 20 30 40 50 60 Period 2.1 2 10 0 10 20 30 40 50 60 Period Left: after-tax rate of return, Right: wages of skilled and unskilled workers Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 38 / 58

Variance of Log. y and c 0.26 0.24 Variance of Logarithm 0.22 0.2 0.18 0.16 0.14 Earnings Consumption 0.12 10 0 10 20 30 40 50 60 Period # simulated households=60,000, aged 25 59 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 39 / 58

Covariance and Correlation Covariance between y and c 0.174 0.172 0.17 0.168 0.166 0.164 0.162 0.16 0.158 0.156 10 0 10 20 30 40 50 60 Period Correlation between y and c 0.93 0.929 0.928 0.927 0.926 0.925 0.924 0.923 0.922 0.921 10 0 10 20 30 40 50 60 Period Left: covariance, Right: correlation Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 40 / 58

Covariance and Correlation: y and c 0.018 Covariance between y and c 0.0175 0.017 0.0165 0.016 0.0155 Correlation between y and c 0.605 0.6 0.595 0.59 0.585 0.58 0.575 0.015 10 0 10 20 30 40 50 60 Period 0.57 10 0 10 20 30 40 50 60 Period Left: covariance of the first differences, Right: correlation of the first differences Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 41 / 58

TFP Shock and Skill Premium Shock TFP shock and skill premium shock Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 42 / 58

TFP Factor Growth Rate and Skill Premium 1.025 1.4 TFP Factor Growth Rate 1.02 1.015 1.01 1.005 Skill Premium: w s /w u 1.35 1.3 1.25 1-10 0 10 20 30 40 50 60 Period 1.2-10 0 10 20 30 40 50 60 Period Left: TFP factor growth rate, Right: skill premium Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 43 / 58

Covariance and Correlation 0.164 0.935 Covariance between y and c 0.162 0.16 0.158 0.156 Correlation between y and c 0.93 0.925 0.92 0.915 0.154-10 0 10 20 30 40 50 60 Period 0.91-10 0 10 20 30 40 50 60 Period 0.02 0.62 Covariance between y and c 0.018 0.016 0.014 0.012 Correlation between y and c 0.6 0.58 0.56 0.54 0.52 0.01-10 0 10 20 30 40 50 60 Period -10 0 10 20 30 40 50 60 Period Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 44 / 58

Data Again Covariance of Level 0.65 Correlation of Level 0.16 0.14 0.12 0.1 1980 1990 2000 2010 0.6 0.55 0.5 0.45 0.4 1980 1990 2000 2010 Covariance of Growth 0.5 Correlation of Growth 0.1 0.05 0 1980 1990 2000 2010 0.4 0.3 0.2 0.1 0 1980 1990 2000 2010 Transmission from income growth to consumption growth Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 45 / 58

Discussion: Other Important Mechanisms? 1. Labor supply decisions 2. Borrowing limit due to the bubble burst 3. Demographic change 4. Tax reforms and transfers 5. Changes in permanent/transitory shocks Precautionary savings Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 46 / 58

Conclusion 1. The lost decades has come together with permanent slowdown of income and consumption inequality growth and weakening of income and consumption correlation 2. Declining the macroeconomic growth rate can be a possible explanation for the weakening of income and consumption correlation Future works: expected/unexpected shocks, demography, mpc, borrowing limit, tax code etc. Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 47 / 58

Appendix Figures Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 48 / 58

Percentiles of the Earnings Distribution.5 Equivalized Disposable Income (log).4.3 p50 p75 p95 p90.2 p25.1 p10 p5 0 1980 1985 1990 1995 2000 2005 2010 Year Top income quantiles grow faster than bottom during 1980s Income growth rates decline in mid-1990s RETURN Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 49 / 58

Earnings Distribution in the U.S. Fig.9, Heathcote, Perri, and Violante (2010) Log (normalized to 0 in 1967).3.2.1 0.1.2.3.4.5.6 p5 p10 p25 p95 p50 p90 p75 1967 1972 1977 1982 1987 1992 1997 2002 2007 Year Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 50 / 58

Data Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 51 / 58

Data (cont.) Definition of Variables Labor income y: sum of monthly labor income of household members, which include household head, his/her spouse and other household members Nondurable expenditure c: food; repair and maintenance of houses; fuel, light and water charges; domestic utensils, non-durable goods, and services; clothing and footwear; medical care; transportation and communication, excluding purchase of vehicles and bicycles; education; culture and recreation, excluding recreational durable goods; and other consumption expenditure, excluding remittance RETURN Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 52 / 58

Two Period Model Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 53 / 58

Two Period Model Why declines in economic growth rate affect second moments (consumption inequality)? max c 1,c 2,a 2 u(c 1 ) + βu(c 2 ), subject to c 1 + a 2 = y 1 + a 1, c 2 = y 2 + (1 + r)a 2, a 2 0, y 2 = αy 1, a 1 given, c 1, c 2 > 0. u(c) = c1 γ 1 γ α: income growth rate Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 54 / 58

Two Period Model Analytical solution: non-binding case 1 a 2 = 1 + r + Γ (Γx 1 y 2 ) ( 1 + r )( c 1 = x 1 + 1 ) 1 + r + Γ 1 + r y 2 {( 1 + r )( c 2 = Γ x 1 + 1 )} 1 + r + Γ 1 + r y 2 = Γc 1 x 1 y 1 + a 1 : cash on hand Γ [β(1 + r)] 1 γ : consumption growth rate Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 55 / 58

Numerical Examples Discount factor: β = 0.96 IES: γ = 1 Interest rate: r = 1/β 1 Γ = 1 Labor income at period 1: y 1 {0.8, 1, 1.2} Growth rate: α {1, 1.5} Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 56 / 58

Growth Rate Decline and Borrowing Limit 2.2 2 α=1.0 α=1.5 45-Degree 1.8 1.6 c 1 1.4 1.2 1 0.8 a L a H 0.6 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 x 1 Consumption function: y 1 = 1, a L = 0.4, a H = 0.6 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 57 / 58

Growth Rate Decline and Borrowing Limit Low Growth High Growth α = 1 α = 1.5 c 1 : a H 1.3061 1.5510 c 1 : a L 1.2041 1.4000 c 2 : a H 1.3061 1.5510 c 2 : a L 1.2041 1.5000 Var. Log. c 1 0.0033 0.0052 Response of Inequality to a Growth Rate Slowdown N. Sudo, M. Suzuki, T. Yamada 58 / 58