Inequality and Aggregate Demand. USC/INET Conference on Inequality, Globalization, and Macroeconomics April 28, 2017

Transcription

1 Inequality and Aggregate Demand Adrien Auclert Stanford Matthew Rognlie Northwestern USC/INET Conference on Inequality, Globalization, and Macroeconomics April 28, 217

2 Inequality and macroeconomic performance Can rising income inequality cause poor macro performance? Two major arguments (Stiglitz, etc.): 1. MPCs are negatively correlated with income, so higher income inequality lowers aggregate consumption 2. More volatile and uncertain incomes raise precautionary savings Both supported by empirical evidence, both correct in partial eqbm

3 Inequality and macroeconomic performance Can rising income inequality cause poor macro performance? Two major arguments (Stiglitz, etc.): 1. MPCs are negatively correlated with income, so higher income inequality lowers aggregate consumption 2. More volatile and uncertain incomes raise precautionary savings Both supported by empirical evidence, both correct in partial eqbm Neither survives general eqbm in standard neoclassical models These forces lower real interest rates and raise investment

4 Inequality and macroeconomic performance Can rising income inequality cause poor macro performance? Two major arguments (Stiglitz, etc.): 1. MPCs are negatively correlated with income, so higher income inequality lowers aggregate consumption 2. More volatile and uncertain incomes raise precautionary savings Both supported by empirical evidence, both correct in partial eqbm Neither survives general eqbm in standard neoclassical models These forces lower real interest rates and raise investment We show that inequality lowers output at the zero lower bound Quantify the potential effect of 1 & 2 Investment usually falls ( paradox of thrift ) Depressed economy even in long run ( secular stagnation )

5 What we do Take canonical Huggett-Aiyagari model Add downward nominal wage ridigidites (DNWR) Parsimonious, allows focus on household demand Calibrate to 213 U.S. Binding zero lower bound (ZLB): r = π = i = % Mildly depressed employment: L < 1 Main questn: what happens if inequality unexpectedly rises further? Temporarily (income redistribution) Permanently (change in income process) under various assumptions about fiscal policy Key: binding ZLB + DNWR most of eqbm adjustment happens via unemployment In particular steady state r fixed, L adjusts to clear markets

6 Contributions Foundation for the transmission mechanism of inequality to output via an aggregate demand channel Key forces in general equilibrium: Inequality multiplier from endogenous inequality change Paradox of thrift due to effect of L on MPK Importance of government spending and public debt policy

7 Contributions Foundation for the transmission mechanism of inequality to output via an aggregate demand channel Key forces in general equilibrium: Inequality multiplier from endogenous inequality change Paradox of thrift due to effect of L on MPK Importance of government spending and public debt policy Novel two-step approach to quantifying magnitudes: Output effect = (GE multiplier) (PE sufficient statistic) Sufficient statistics are measurable: Short run: Cov ( ) MPC, dy Y Long run: elasticity of savings to idiosyncratic risk Multiplier characterizes the response to any aggregate demand shock Depends only on model parameters and policy

8 Related literature Incomplete markets, inequality, and aggregate savings Aiyagari (1994), Krusell-Smith (1998), Heathcote-Storesletten-Violante (21), Krueger-Mitman-Perri (215), Kuhmhof-Ranciere-Winant (215) Interaction with nominal rigidities Guerrieri-Lorenzoni (215), Oh-Reis (213), McKay-Reis (216) Gornemann, Kuester and Nakajima (214), Sheedy (214), McKay, Nakamura and Steinsson (215), Auclert (216), Werning (215), Kaplan, Moll and Violante (216), Bilbiie-Ragot (216) Ravn-Sterk (213), den Haan, Rendahl and Riegler (214), Bayer et al (214), Challe-Matheron-Ragot-Rubio (215), Heathcote-Perri (216) Secular stagnation Eggertsson-Mehrotra (214), Caballero-Farhi-Gourinchas (216), Benigno-Fornaro (216), Eggertsson, Mehrotra, Singh and Summers (216) Public debt, liquidity, and safe assets Woodford (199), Aiyagari-McGrattan (1998), Caballero-Farhi (215) Sufficient statistics approaches in macro Shimer-Werning (29), Auclert (216), Berger et al (215)

9 Outline 1. Model overview and calibration 2. Temporary increase in income inequality 3. Permanent increase in income inequality

10 Outline 1. Model overview and calibration 2. Temporary increase in income inequality 3. Permanent increase in income inequality

11 Model overview: households Mass 1 of ex-ante identical households facing idiosyncratic risk Trade in bonds and shares with same real return r t must maintain positive net worth Household in state s it has earnings ability e t (s it ) Gross earnings depend on employment level Lt { Wt P z t (s it ) = t e t (s it ) L t = 1 W t P t L t e t (s it ) γ (s it, L t ) L t 1 γ: incidence of rationed employment L < 1 Inequality multiplier when γ 1 e t main exogenous source of change in labor income inequality Alternative: changing progressivity of the (affine) tax system

12 Firms and the labor and capital markets Firms produce a final good (price P t ) Production function F t (K t 1, L t ) (constant returns) Exogenous markup µt ( monopoly profits) Always on labor demand curve F Lt (K t 1, L t ) = µ t W t P t Capital investment determined by Q theory Dw. wage rigidities: impose W t W t 1, when binding L t < 1 Labor share changes (µ t, F t ) alternative source of inequality

13 Government policy and equilibrium Fiscal authority: has fiscal rules for G t and deficits, ensuring τ t W t P t L t + B t = G t + (1 + r t 1 ) B t 1 In benchmark: G t = G and B t = B at all t. Other rules Central bank sets nominal interest rate i t st ZLB & infl. target { ) } φ 1 + i t = max φ > 1 (Taylor principle); r n t Equilibrium definition standard go 1, (1 + r n t ) ( Pt P t 1 is real rate without nominal frictions uniqueness

14 Calibration: steady state Parameters Description Main calibration Target (e, S, Λ) Income process KMV (216) W2 moments γ Incidence function 1 Equal incidence ν EIS.5 Standard calibration β Discount factor.964 r = ɛ K L elasticity 1 Standard calibration δ Depreciation rate 4.4% NIPA 213 i Nominal interest rate % ZLB r Eqbm real rate % TIPS yields 213 L Employment gap.97 CBO output gap estimate 1+i ξ Wage deflation rate 1 1+r K Y Capital-output ratio 33% FoF hh. net worth 213 θ(a) Initial asset allocation SCF 213 µ Monopoly markup 1 B Y Govt debt 59.% Domestic holdings 213 G Y Govt spending rate 18.7% NIPA 213 τ r Tax redistribution 17.5 CBO (216)

15 Labor income inequality trends US income inequality and the real interest rate.92 Log points Year Standard dev. of log gross earnings Model calibration Source: Song, Price, Guvenen, Bloom and von Wachter (216)

16 Labor income inequality trends US income inequality and the real interest rate Log points Per cent Year Standard dev. of log gross earnings Laubach-Williams r Model calibration Model calibration Source: Song, Price, Guvenen, Bloom and von Wachter (216); Laubach and Williams (215)

17 Outline 1. Model overview and calibration 2. Temporary increase in income inequality 3. Permanent increase in income inequality

18 Per cent Output Consumption Investment Real rate (bps) Per cent.5.1 Labor Capital Real wage sd log earnings (level) ZLB

19 Per cent Output Consumption Investment Real rate (bps) Per cent.5.1 Labor Capital Real wage sd log earnings (level) ZLB No-ZLB

20 Per cent Output Consumption Investment Real rate (bps) Per cent Labor Capital Real wage sd log earnings (level) ZLB No-ZLB Constant r

21 Understanding and decomposing the effect Consider general perturbation to after-tax incomes dy i st E [dy i ] = In partial equilibrium (r t, L t fixed): change in C t path C t = Cov I (MPC it, dy i ) where MPC it = is i s spending at t of date- income One shock, one sufficient statistic

22 Understanding and decomposing the effect Consider general perturbation to after-tax incomes dy i st E [dy i ] = In partial equilibrium (r t, L t fixed): change in C t path C t = Cov I (MPC it, dy i ) where MPC it = is i s spending at t of date- income One shock, one sufficient statistic In general equibrium dy = G C G is GE matrix, independent of source of demand shock C can be evaluated with micro data G easily solved for numerically in our calibration, loads on C and is close to 1 Show

23 PE consumption response C/Y GE multipliers for date output G.2 1 Benchmark Γ =.15 Per cent.4.6 Level GE output response dy /Y dy /Y with varying Γ Per cent Actual path dy /Y Predicted G C/Y Benchmark Γ =

24 Applying the methodology In model and data: C Y = Cov I ( MPC i, dy ) i Y Comparison (data from Italy 21 SHIW survey) ) Value, Data Value, Model Cov I (MPC i, dy i Y.9%.9% MPC Suggests correct (small) magnitude for PE effect May understate GE effect a little, but overall still likely small

25 Outline 1. Model overview and calibration 2. Temporary increase in income inequality 3. Permanent increase in income inequality

26 Per cent Output Consumption Investment Real rate (bps) Labor Capital Real wage sd log earnings (level) Per cent ZLB

27 Per cent Output Consumption Investment Real rate (bps) Per cent Labor Capital Real wage sd log earnings (level) ZLB No-ZLB

28 Per cent Output Consumption Investment Real rate (bps) Per cent Labor Capital Real wage sd log earnings (level) ZLB No-ZLB Constant r

29 Per cent Per cent Per cent Labor Capital Real wage sd log earnings (level) Output Consumption Investment Real rate (bps) Govt spending Govt debt Tax rate Benchmark ZLB

30 Per cent Per cent Labor Capital Real wage sd log earnings (level) Per cent Output Consumption Investment Real rate (bps) Govt spending Govt debt Tax rate Benchmark ZLB Spending

31 Per cent Per cent Labor Capital Real wage sd log earnings (level) Per cent Output Consumption Investment Real rate (bps) Govt spending Govt debt Tax rate Benchmark ZLB Spending Deficits

32 Understanding the effect: steady state Assume Γ = (no ineq. multiplier) Experiment: steady-state comp statics wrt index of inequality σ Asset market clearing A (r, σ, τ, WP ), L = B + K Homotheticity + govt budget constraint + factor demands ( w (r) L ( G + rb )) â (r, σ) = B + κ (r) L

33 Equilibrium: (A, L) space ( w (r) L ( G + rb )) â (r, σ) = B + (κ (r) + π (r)) L L L Asset Demand G+rB w(r) Asset Supply B A = B + K

34 Equilibrium: (A, L) space ( w (r) L ( G + rb )) â (r, σ) = B + (κ (r) + π (r)) L L L G+rB w(r) B A = B + K Government multipliers Multiple SS with Γ <

35 Sufficient statistic formula for dy Y Differentiating the main equilibrium equation and using dl L dy Y = 1 B B+XK+Π + τ 1 τ } {{ } GE multiplier log â σ dσ }{{} PE suff. stat. = dy Y log â σ average semielasticity of individual savings to σ Large literature, large range of estimates [Browning Lusardi 1996] Ours are in line with Carroll-Samwick (1997) PSID numbers

36 Extensions 1. Change in capital-labor distribution: Decline in labor share from relative price of investment (Piketty/Karabarbounis-Neiman) Monopoly profits: µ t (Summers/Krugman) 2. Inequality and the r decline Go 3. Government spending and liquidity multipliers Go

37 Conclusion Canonical macro model of inequality + nominal wage rigidities Allows to study effect of aggregate demand shocks on output, including inequality Very tractable and flexible, codes online soon Theory highlights importance of empirical evidence on MPC heterogeneity [Cov (MPC, y)] (short-run) Effect of income uncertainty on savings [ log A σ ] (long-run) Distributional incidence of recessions [Γ] (both) Amplification role of private investment Stabilizing role of monetary (r) and fiscal policy (G and B)

38 Thank you!

39 Fiscal rule Fiscal rules are for government spending and target deficits G t = G (L t ) D t = D (L t ) Ensure debt sustainability by setting τ t such that W t τ t L t = ( G (L t ) + r t 1 B t 1 D (L t ) ) ( Bt 1 P t }{{} B ss Target taxes Implies elasticity of B to L of ɛ B,L = 1 1 ɛ τ,b G ss + rb ss e D,L = 1 1 ρ 1 B ss e D,L ) ɛτ,b where e D,L is semielasticity of D to L and ρ is persistence of deficits Calibration: ρ =.5 and Deficits : e D,L = 1, e G,L = Spending : e D,L =, e G,L = 1 Back

40 Steady-state with ZLB has constant r Proposition Assume a unique neoclassical steady state with r n <. Then, in any steady state of the model with rigidities & ZLB, i = and Pt P t 1 = ξ < 1 In particular, steady state r = 1 ξ 1 > > r n Proof: in steady-state Pt P t 1 = Wt W t 1 = Π If Π > ξ, by complementary slackness L = 1, so r = r n < Impossible by monetary policy rule: If ZLB does not bind, inflation target Π = 1, so ZLB does bind If ZLB binds, Π = 1 1+r n, so monetary policy raises i > Hence Π = ξ < 1, so (1 + r n ) (Π) φ < 1, so ZLB binds Corollary (Paradox of flexibility) Lower ξ higher r lower L (typically) Back

41 Equilibrium Given K 1, shocks {e t, τt r, X t, µ t, F t } and initial joint distribution Ψ (s, b, v), equilibrium is {C t, I t, Y t, K t 1, L t, d t, B t, τ t }, {r t, i t, P t, W t, q t }, {c t (s, b, v), b t (s, b, v), v t (s, b, v)} and Ψ t (s, b, v) such that: Households and firms optimize Government follows fiscal and monetary policy rules Goods, bonds and capital markets clear ( ) Kt K t 1 C t + X t I t + G t + X t ζ K t 1 = Y t = F (K t 1, L t ) K t 1 B t E [b it ] = B t V t E [v it ] = 1 L t 1 W t W t 1 (L t 1) (W t W t 1 ) = Distributions evolve consistently with policy functions Back

42 Calibrating the retention function Model relationship between net income y and gross z: ( ) y it z it = (1 τ) τ r + (1 τ r ) E [z it ] E [z it ] CBO data on avg transfers and taxes per nonelderly household by income in 26: overall AMI $95, and Quintiles of market income Q1 Q2 Q3 Q4 Q5 Average market income (AMI) z it 12,6 36,1 59,5 89,9 24,8 AMI + Transfers minus taxes y it 25,2 36,3 51,4 72,7 174,8 Yields y it E[z it ] = z it E[z it ] with R2 =.9988 Implying τ r = Back

43 Calibrating household portfolios Obtain θ (a) parametrically from SCF fraction invested in shares as function of total assets a = b + pv broad definition: all net worth except deposits and bonds narrow definition: only equity and shares 1 Micro-level distribution of capital holdings.9 Fraction of shares in net worth θ(a) SCF 213: broad capital ownership Fitted curve, θ b (a) SCF 213: directly held equity Fitted curve, θ eq (a) Log (net worth/average net worth) Back

44 Aggregating SCF and Flow of Funds SCF 213 FoF 213, Households Assets Liabilities and Net Worth Assets Liabilities and Net Worth Consumer credit $11.2trn Consumer credit $13.8trn Real estate $26.1trn Real estate $22.4trn Consumer durables $2.4trn Consumer durables $4.9trn Deposits&bonds $6trn Deposits&bonds $13.9trn Net worth $54.9trn Net worth $61.1trn Equities&pensions $31.6trn Equity&pensions $33.6trn

45 Aggregating SCF and Flow of Funds, ctd FoF 213, Business (simplified) FoF 213, Government Assets Liabilities Assets Liabilities Deposits&Bonds $13.9trn Backing assets $9.2trn Govtt Bonds $9.2trn Business capital $24.5trn Consumer credit $13.8trn Equity&pensions $33.6trn Govtt Bonds $9.2trn Household assets Value of capital XK 2.29 Y Monopoly profits Π.82 Y Government bonds B.55 Y Back

46 Calibration: steady state, with eq premium Back Parameters Description Main calibration Target ν EIS.5 Standard calibration β Discount factor.972 r = ɛ K L elasticity 1 Standard calibration α Labor share 62.5% NIPA 213 δ Depreciation rate 5.6% NIPA 213 r Eqbm real rate % TIPS yields 213 µ Monopoly markup 1.67 Π Y = 1 µ 1 r+ϱ ϱ Equity premium 7.3% 1 µ α r+ϱ+δ = K Y XK Y Capital-output ratio 229% BEA Fixed Assets 213 Π Y Capitalized profits 82.% FoF hh. net worth 213 B Y Govt debt 55.% Domestic holdings 213 I Y Investment rate 13.5% δ K Y G Y Govt spending rate 18.7% NIPA 213 G+rB τ Headline tax rate 29.8% αy r Keynesian policy rate % Zero lower bound

47 Distribution summary statistics Consumption Pretax Income Wealth Back Percentage held by Bottom/Top sd. log Gini B 4% T 2% T 1% T 5% T 1% Model % 41% 26% 16% 5% Data % 4% 24% 14% 4% Model % 52% 31% 26% 5% Data % 55% 39% 28% 13% Model % 83% 66% 47% 17% Data % 84% 72% 6% 33%

48 Approximation to GE matrix G Obtain by assuming L t = 1 for t 1: employment changes only today From investment problem: q, I and p are constant Neoclassical theory determines changes in real wage and dividend as ( ) R d (d ) = d K 1 = 1 α ( ) W dy = d L ɛ P α labor share, ɛ elasticity of subst. bw capital and labor Individual i s consumption changes by dc i = MPC i { dyi + d ( y GE i y i ) + vi d (d ) } Direct effect of the redistribution + effects from changing post-tax incomes and dividends P

49 Approximation to GE matrix G, ctd Aggregate per capita consumption: Putting it all together: dy Y 1 1 cγ (MPC y MPC v ) 1 α ɛ 1 MPC }{{ y } Inequality multiplier dc = E [dc i ] = dy = W P dl y v MPC : income-weighted, ( MPC : share-weighted ( )) c = (1 τ)(1 τ r z )Cov MPC i, i E[z i ] log zi E[z i ] Captures all static GE effects ( 1 1 MPC y Cov MPC i, dy ) i Y }{{}}{{} Keynesian multiplier Redistributive impulse Misses dynamic feedbacks from future L to C and I Back

50 Effects of G and B ( w (r) L ( G + rb )) â (r, ϕ) = B + κ (r) L 1 L G +rb w(r) G+rB w(r) B A = B + K

51 Effects of G and B ( w (r) L ( G + rb )) â (r, ϕ) = B + κ (r) L 1 L G+rB w(r) B B A = B + K

52 Government multipliers and crowding-in Proposition While L < 1, steady-state output is given by Y = α G G + α B B where the government spending multiplier is α G = 1 ( ) > 1 K+Π α 1 (1 τ) B+K+Π and the government debt multiplier is Back α B = α G C A >

53 Inequality multiplier and multiple steady states 1.8 Employment L.6.4 Γ =.2 Γ =.15 Γ =.3 Γ = Total Assets B + K + Π Back

54 Per cent Output Consumption Investment Real rate (bps) Per cent Labor Capital Real wage sd log earnings (level) Keynesian regime

55 Per cent Output Consumption Investment Real rate (bps) Per cent Labor Capital Real wage sd log earnings (level) Keynesian regime + deficit-financed tax cuts

56 Inequality and the r decline Real interest rate (bps) sd log earnings Capital (per cent from SS) Level Per cent from steady state Output Consumption Investment Back