Inequality and Aggregate Demand. November PDF Free Download

Inequality and Aggregate Demand Adrien Auclert Stanford Matthew Rognlie Northwestern November 217

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. If inequality comes from more volatile and uncertain incomes, it could 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 if monetary policy is slow or unable to react to it (e.g. at the zero lower bound) Quantify the potential effect of 1 & 2 under various mp rules Investment usually falls ( paradox of thrift ) Depressed economy even in long run ( secular stagnation )

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 qstn: 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 equilibrium adjustment happens via unemployment In particular steady state r fixed, L adjusts to clear markets

Long-run adjustment in asset market 1 Asset Demand Real interest rate r (bps) 5 5 1 Asset Supply 3 3.5 4 4.5 5 5.5 6 Total assets B + K

Long-run adjustment in asset market 1 Real interest rate r (bps) 5 5 1 S 3 3.5 4 4.5 5 5.5 6 Total assets B + K

Contributions 1/2 Foundation for the transmission mechanism of inequality to output via an aggregate demand channel We find that the effects of increasing inequality: are small when inequality = temporary redistribution are small when inequality = permanent redistribution (fixed effects) are potentially large if inequality = increasing risk Always depend on the degree of endogenous inequality and the fiscal response (government spending and public debt)

Contributions 2/2 Our results rely on a new 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

Related literature Incomplete markets, inequality, and aggregate savings Aiyagari (1994), Krusell-Smith (1998), Heathcote, Storesletten, Violante (21), Krueger, Mitman and Perri (215), Athreya, Owens, Schwartzman (214)... 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) Ravn-Sterk (213), den Haan, Rendahl and Riegler (214), Bayer et al (214), Challe et al (215), Heathcote-Perri (216) Secular stagnation Eggertsson-Mehrotra (214), Caballero-Farhi-Gourinchas (216), Benigno-Fornaro (216), Eggertsson, Mehrotra, Singh and Summers (216) Sufficient statistics approaches in macro Shimer-Werning (29), Auclert (216), Berger et al (215)

Outline 1. Model and equilibrium definition 2. Calibration 3. Income inequality in the short run 4. Income inequality in the long run

Households Mass ρ(ω i ) of individuals of type ω i ex-ante identical within type, facing purely idiosyncratic risk idiosyncratic state σ it S, Markov process Λ (ω), at stat. distrib. combined state s it (ω i, σ it ) Separable preferences, constant EIS ν: u (c) = c1 ν 1 1 ν 1 Incomplete markets: bonds and shares + positive nw constraint max s.t. [ ] E β t u (c it ) t c it + b it + p t v it = y t (s it ) + (1 + r t 1 ) b it 1 + (p t + d t ) v i,t 1 b it + p t v it

Household labor income: pre-tax Pre-tax labor income: { Wt z t (s it ) = P 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 Wt P t real wage, e t (s it ) labor endowment, E I [e t (s it ) γ (s it, L t )] = 1 L t 1 fraction of aggregate endowment demanded by firms γ: incidence of employment L < 1 Equal incidence at L when γ (s, L) = 1 for all s Other cases: (in)equality multiplier e t main exogenous source of change in labor income inequality Proxy for many plausible underlying causes Can affect separately fixed effect, persistent, or transitory component

Household labor income: post-tax Post-tax labor income: y t (s it ) = T t + (1 τ t ) (1 τ r ) z t (s it ) Rate τ r earmarked for lump-sum rebate Tt = τ r (1 τ t ) E I [z it ] Govtt adjusts τt to satisfy its budget constraint

Household labor income: post-tax Post-tax labor income: y t (s it ) = (1 τ t ) (τ r E I [z it ] + (1 τ r ) z t (s it )) Rate τ r earmarked for lump-sum rebate Tt = τ r (1 τ t ) E I [z it ] Govtt adjusts τ t to satisfy its budget constraint (τ r t alternative exogenous source of change in income inequality)

Firms and factor markets Perfect competition, CRS production Y t = F (K t 1, L t ) No adjustment cost to labor: labor demand F L (K t 1, L t ) = W t P t Convex capital adjustment costs: investment demand ( ) 1 + ζ It δ = q t K t 1 with share price p t = q t K t. In steady state q = 1, F K (K, L) = r + δ. Dw wage rigidities: impose W t κw t 1, when binding L t < 1 Assume < κ 1: wages cannot fall too fast Why? NK sticky prices have counterfactual implications in HA models

Government policy and equilibrium Fiscal authority has budget constraint τ t W t P t L t + B t = G t + (1 + r t 1 ) B t 1 follows rules for spending and deficits G t Y ss = G ss Y ss ɛ GL (L t L ss ) B t B t 1 Y ss = ɛ DL (L t L ss ) ɛ DB B t 1 B ss Y ss Calibrate elasticities ɛ DL, ɛ DB, ɛ GL to historical U.S. experience cf fiscal rules literature (Leeper, Gali-Perotti, etc.)

Monetary policy Central bank sets nominal interest rate i t, follows either 1. Neoclassical rule: set i t to achieve L t = 1. Obtain real rate rt n. 2. ZLB rule: { ) } φ 1 + i t = max 1, (1 + r n t ) ( Pt P t 1 with φ > 1 (Taylor principle) 3. Constant-r rule 4. Simple Taylor rule in inflation and/or unemployment Equilibrium definition standard

Outline 1. Model and equilibrium definition 2. Calibration 3. Income inequality in the short run 4. Income inequality in the long run

Benchmark calibration Gross income process from Kaplan, Moll, Violante 216. Has form log e it = ξ it + χ it with ξ it persistent, χ it transitory. Matches: Earnings dynamics from W2 data (Guvenen, Ozkhan, Song 214) Cross-sectional earnings distribution without fixed effects τ r = 17.5% from Congressional Budget Office (26) Details Incidence rule γ(s, L) matches W2 worker betas from Guvenen, Schulhofer-Wohl, Song and Yogo (217) [GSSY] Alternative: equal incidence (γ = 1) Asset allocation θ (a) imported parametrically from 213 SCF Details

Calibrated γ function Elasticity of gross earnings to employment 4 3 2 1 GSSY Equal incidence (γ = 1).2.4.6.8 1 Earnings percentile

Parameters Description Main calibration Target ν EIS.5 Standard calibration β Discount factor.962 r = ɛ K L elasticity 1 Standard calibration α Labor share 87.2% α = 1 (r + δ) K Y δ Depreciation rate 4.% NIPA 213 K Y Capital-output ratio 321% FoF hh. net worth 213 I Y Investment rate 12.8% δ K Y ɛ I Elasticity of I to q 1 Macro invtt literature i Nominal interest rate % ZLB r Eqbm real rate % TIPS yields 213 L Employment gap.975 CBO output gap estimate 1+i κ Wage deflation rate 1 1+r B ss Y Govtt debt 55.4% Domestic holdings 213 G ss Y Govtt spending 18.7% NIPA 213 ɛ GL Response of spending to L.1 Estimated fiscal rule ɛ DL Response of deficits to L.75 Estimated fiscal rule ɛ DB Response of deficits to debt.7 Estimated fiscal rule

Increasing labor income inequality (1/2) Recall income process: Our experiments change this to: log e it = ξ it + χ it log e it = ω i + A t ξ it + B t χ it C t for various paths (ω i, A t, B t ) that achieve target path for sd (log e it ) Ct ensures E [e it ] = 1 Main case: ω i =, A t = B t cf. Gottschalk Moffitt (1994), Kopczuk Saez (24) Alternatives: increase entirely due to ω i, A t, or B t

Increasing labor income inequality (2/2).96 US labor income inequality.92 Log points.88.84.8 198 199 2 21 22 23 24 25 Year sd log earnings Calibration Short-run experiment Source for historical data: Song, Price, Guvenen, Bloom and von Wachter (216)

Increasing labor income inequality (2/2).96 US labor income inequality.92 Log points.88.84.8 198 199 2 21 22 23 24 25 Year sd log earnings Calibration Short-run experiment Long-run experiment Source for historical data: Song, Price, Guvenen, Bloom and von Wachter (216)

Outline 1. Model and equilibrium definition 2. Calibration 3. Income inequality in the short run 4. Income inequality in the long run

Partial eqbm effect Consider first partial equilibrium effect, holding (r t, L t ) fixed Consumption Assets sd log earnings.6.96 Percent of s.s. output.5.1.15.2 1 2 3 4 5 Percent of s.s. output.4.2 1 2 3 4 5 Level.95.94.93.92 1 2 3 4 5 Result 1: For any change in after-tax incomes dy i st E [dy i ] =, the partial equilibrium change in the path for C t is given by C t = Cov I (MPC it, dy i ) where MPC it = is i s spending at date t of date income. In particular, NPV ( C) =.

Evaluating C = Cov I (MPC i, dy i ) Quality of approximation within model? Date consumption effect dc, % Y.4.2.2.4.6.1.5.5.1 Change in sd log earnings dσ Fit to data on joint distribution of (MPC i, y i )? (Use Italian SHIW 21) Sufficient ( statistic ) Value, Data Value, Model Cov MPC i, dy i 1 Y dσ.49.45

General eqbm effect under alternative monetary policies Percent of s.s. output Output.1.2 1 2 3 4 5.1.2 Consumption Investment Government Spending.1.1.2.2 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Percent of s.s. output.4.3.2.1 Government Bonds 1 2 3 4 5.4.3.2 Capital.5.1 Employment vs s.s..1.15.2 1 2 3 4 5 1 2 3 4 5 ZLB 5 1 15 2 25 Real Interest Rate (bps) 1 2 3 4 5

Relating partial and general equilibrium effect (1/2) Result 2: the general equilibrium path of aggregate output Y t is dy = G Y C where G Y is the GE matrix, independent of the source of shock Reflects many equilibrium forces In a benchmark case with no investment, no endogenous spending, and constant r monetary policy: G Y = k= M k where M t,s is incidence-weighted matrix of MPCs Intertemporal Keynesian Cross (Auclert, Rognlie and Straub 217) Here, for ZLB and constant-r, we have G Y I, so GE PE.

Relating partial and general equilibrium effect (2/2) dy Y = G Y C Y Percent of s.s. output.5.1.15 PE consumption C/Y.2 1 2 3 4 5 Level.8.6.4.2 GE multipliers for dyt t = t = 5 t = 1 t = 15 t = 2 t = 25 1 2 3 4 5 Percent of s.s. output.5.1.15 GE output dy /Y Actual path dy/y Approximation GY C/Y.2 1 2 3 4 5

Paradox of Thrift Why does investment fall? Q-theory given a change in {r t, L t }, net investment responds by d (I t δk t 1 ) = ɛ I I s= ( ) 1 s+1 {dmpk t+s+1 dr t+s} 1 + r where MPK t F K (K t 1, L t ) Race between cost of capital effect ( ) and MPK effect ( ) Under constant-r policy, latter always dominates Typically also at ZLB, due to limited r response Consistency with market clearing? Savings = Investment Redistribution rise in desired household savings But in equilibrium, L aggregate savings, consistent with investment

Outline 1. Model and equilibrium definition 2. Calibration 3. Income inequality in the short run 4. Income inequality in the long run

Partial equilibrium effect Consider again partial equilibrium effect, holding (r t, L t ) fixed Consumption Assets sd log earnings Percent of s.s. output.5 1 1.5 2 4 6 8 1 Percent of s.s. output 4 3 2 1 2 4 6 8 1 Benchmark Only transitory Only persistent Only fixed effects Level.96.95.94.93.92 2 4 6 8 1 Convergence to higher SS asset level if inequality implies risk Are these magnitudes plausible? Compare to micro literature on savings effect of earnings risk Large literature, large range of estimates (Browning Lusardi 1996)

Empirical evaluation Carroll-Samwick (1997) run in PSID: log a i = α ξ s 2 iξ + α χs 2 iχ + βz i + u i with siξ 2 variance of innovations to permanent component of earnings, siχ 2 variance of transitory Compute equivalent semielasticity in the model Value, Data Value, Model α ξ 12.9 12.87 α χ 7.11.5 Semielasticities in line with empirical estimates

General eqbm effect under alternative monetary policies Percent of s.s. output Percent of s.s. output Output Consumption Investment Government Spending 1 1 1 1 1 1 1 1 2 2 2 2 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 Government Bonds Capital 1 Employment vs s.s. Real Interest Rate (bps) 1 2 2 1 1 1 1 2 2 1 2 4 6 1 8 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 ZLB

General eqbm effect under alternative monetary policies Percent of s.s. output Percent of s.s. output Output Consumption Investment Government Spending 1 1 1 1 1 1 1 1 2 2 2 2 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 Government Bonds Capital Employment vs s.s. Real Interest Rate (bps) 1 1 2 2 1 1 1 1 2 2 1 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 ZLB Neoclassical

General eqbm effect under alternative monetary policies Percent of s.s. output Percent of s.s. output Output Consumption Investment Government Spending 1 1 1 1 1 1 1 1 2 2 2 2 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 Government Bonds Capital Employment vs s.s. Real Interest Rate (bps) 1 1 2 2 1 1 1 1 2 2 1 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 2 4 6 8 1 ZLB Neoclassical constant-r

Steady state long-run effect: a special case Consider first the following special case: Constant income incidence (γ = 1) No endogenous fiscal policy (ɛ GL = ɛ BL = ɛ BG = ) Monetary policy: either ZLB or constant-r Experiment: increase index of inequality σ Asset market clearing (from homotheticity): (1 τ) W P Lâ (r, σ) = B + K â (r, σ) partial eqbm savings schedule at r (income=1)

Steady state long-run effect: a special case Consider first the following special case: Constant income incidence (γ = 1) No endogenous fiscal policy (ɛ GL = ɛ BL = ɛ BG = ) Monetary policy: either ZLB or constant-r Experiment: increase index of inequality σ Asset market clearing: ( W P L ( G + rb ) ) â (r, σ) = B + K â (r, σ) partial eqbm savings schedule at r (income=1) Government budget constraint: τ W P L = G + rb

Steady state long-run effect: a special case Consider first the following special case: Constant income incidence (γ = 1) No endogenous fiscal policy (ɛ GL = ɛ BL = ɛ BG = ) Monetary policy: either ZLB or constant-r Experiment: increase index of inequality σ Asset market clearing: ( w (r) L ( G + rb )) â (r, σ) = B + κ (r) L â (r, σ) partial eqbm savings schedule at r (income=1) Government budget constraint: τ W P L = G + rb Factor demand conditions: K L κ (r), W P w (r)

Equilibrium: (A, L) space ( w (r) L ( G + rb )) â (r, σ) = B + κ (r) L 1.8 Asset Demand Employment L.6.4.2 Asset Supply.5 1 1.5 2 2.5 3 3.5 4 Total assets B + K

Equilibrium: (A, L) space ( w (r) L ( G + rb )) â (r, σ) = B + κ (r) L 1.8 Asset Demand S Employment L.6.4.2 Asset Supply.5 1 1.5 2 2.5 3 3.5 4 Total assets B + K

Role of incidence and fiscal response 1.95 Employment L.9.85.8 S.75 2 2.5 3 3.5 4 4.5 5 Total assets B + K

Role of incidence and fiscal response 1 w. benchmark fiscal policy.95 S Employment L.9.85.8.75 2 2.5 3 3.5 4 4.5 5 Total assets B + K

Role of incidence and fiscal response 1 + GSSY income incidence.95 S Employment L.9.85.8.75 2 2.5 3 3.5 4 4.5 5 Total assets B + K

Sufficient statistic formula for dy Y Differentiating SS asset market clearing and using dl L = dy Y A/A σ dy Y = 1 B B+K + τ 1 τ + η A/A F + η I σ dσ }{{}}{{} PE suff. stat. GE multiplier average semielasticity of individual savings to σ η F mitigation from fiscal response, η I effect of income incidence In special case: η F = η I =, Multiplier = 2.31 In main calibration: η F, η I >, Multiplier =.3

Extensions 1. Inequality and the r decline 2. Change in capital-labor distribution: Decline in labor share due to changing technology or relative price of investment (Piketty/Karabarbounis-Neiman) Monopoly profits (Summers/Krugman) 3. Alternative policy at the zero lower bound 4. Taylor-rule monetary policy

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 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)

Thank you!

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 ] =.143 +.666 z it E[z it ] with R2 =.9988 Implying τ r =.143.143+.666 Back

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 Fraction of shares in net worth θ(a).8.6.4.2 8 6 4 2 2 4 Log (net worth/average net worth) SCF 213: broad capital Fitted curve θ b (a) SCF 213: narrow capital Fitted curve θ n (a) Back

Distribution summary statistics Model Data (SCF 213) Percentage of total 1.8.6.4.2 Consumption Post-tax labor income Pre-tax labor income Wealth Percentage of total 1.8.6.4.2 Consumption Pre-tax labor income Wealth.2.4.6.8 1 Percentage of population.2.4.6.8 1 Percentage of population Back

Inequality and the r decline 4 Real rate.95 sd log earnings 38.9 Basis points 36 34 Level.85 32 198 199 2 21 22 23 24 Year.8 198 199 2 21 22 23 24 Year

Policy solutions at the ZLB Wage deflation Effective lower bound Inflation target Steady-state employment.9.8.7 3 2.5 2 1.5 1.5 Steady state wage inflation κ 1 (%) Steady-state employment 1.99.98.97.96.95 1.8.6.4.2 Nominal rate lower bound i (%) Steady-state employment 1.99.98.97.96 Full employment equilibrium.95.5 1 1.5 2 Inflation target π (%)

Inequality and Aggregate Demand. November 2017