Monetary Policy According to HANK

Monetary Policy According to HANK Greg Kaplan Princeton University Ben Moll Princeton University Gianluca Violante New York University Cornell March 17th, 216

HANK: Heterogeneous Agent New Keynesian models HANK = equilibrium framework for quantitative analysis of macroeconomic fluctuations, fiscal and monetary policy

HANK: Heterogeneous Agent New Keynesian models HANK = equilibrium framework for quantitative analysis of macroeconomic fluctuations, fiscal and monetary policy Two building blocks: (HA) Rich representation of hh portfolios and consumption behavior Bewley-Imrohoroglu-Huggett-Aiyagari-Krusell & Smith (NK) Nominal price rigidities Woodford s cashless limit

Monetary transmission in RANK and HANK C = direct response to r + indirect GE response due to labor Y

Monetary transmission in RANK and HANK C = direct response to r + indirect GE response due to labor Y RANK: >95% RANK: <5% HANK: <25% HANK: >75%

Monetary transmission in RANK and HANK C = direct response to r + indirect GE response due to labor Y RANK view: RANK: >95% RANK: <5% HANK: <25% HANK: >75% MPC out of r strong: intertemporal substitution MPC out of Y weak: the RA is a PIH consumer HANK view: MPC out of r weak: income effect of wealthy offsets int. subst. MPC out of Y strong: sizable share of hand-to-mouth agents

Why does this distinction matter? Suppose Fed wants to use i to stimulate C in the short run RANK view: sufficient to influence the path for the real rate {r t } household intertemporal substitution does the rest HANK view: must rely heavily on GE transmission to aggr. labor demand through fiscal policy reaction or an investment boom

RANK

Monetary transmission in RANK Preferences: CRRA with IES = 1 γ > and discount rate ρ > Technology: Y t = N t Prices perfectly rigid: p t = 1 Monetary authority sets time path: r t = ρ+e ηt (r ρ), η > Equilibrium: C t ({r s,y s } s t ) = Y t and lim t C t = C

Monetary transmission in RANK Decompose C response by totally differentiating C ({r t,y t } t ) dc = C dr t dt r }{{ t } direct response to r + C dy t dt Y }{{ t } indirect effects due to Y

Monetary transmission in RANK Decompose C response by totally differentiating C ({r t,y t } t ) dc = C dr t dt r }{{ t } direct response to r + C dy t dt Y }{{ t } indirect effects due to Y In our special case: dlogc = 1 [ η dr γη ρ+η }{{} direct response to r Plausible quarterly parameterization: ρ =.5 + ρ ] ρ+η }{{} indirect effects due to Y η =.5 (half-life 2 quarters) η ρ+η =.99

In RANK it s all about intertemporal substitution True also in medium-scale monetary DSGE (e.g., Smets-Wouters)

In RANK it s all about intertemporal substitution True also in medium-scale monetary DSGE (e.g., Smets-Wouters) What is wrong with this logic? Evidence Weak sensitivity of consumption to r failure of aggregate EE Strong sensitivity of consumption to y excess sensitivity MPCs vastly heterogeneous hh balance sheet effects

HANK

Building blocks Households Face uninsured idiosyncratic labor income risk Save in two assets (liquid and illiquid), consume and supply labor Firms Monopolistic competition for intermediate-good producers Quadratic price-adjustment costs à la Rotemberg (1982) Investment fund Intermediates illiquid assets/capital to producers Government Issues liquid debt, spends, taxes, and transfers lump-sum Monetary authority ( cashless limit ) Sets nominal rate on liquid assets based on a Taylor rule

Households max E e (ρ+λ)t u(c t,l t,h t )dt s.t. {c t,l t,d t } t ḃ t = r b t(b t )b t +w t z t l t T t (w t z t l t ) d t χ(d t,a t ) c t c h t ȧ t = r a t(1 ω)a t +d t h t = νωa t z t = some Markov process b t b, a t c t : non-durable consumption b t : liquid assets z t : individual productivity l t : hours worked T t : labor income tax/transfer d t : illiquid deposits χ: transaction cost function a t : illiquid assets h t : housing services

Households max E e (ρ+λ)t u(c t,l t,h t )dt s.t. {c t,l t,d t } t ḃ t = r b t(b t )b t +w t z t l t T t (w t z t l t ) d t χ(d t,a t ) c t c h t ȧ t = r a t(1 ω)a t +d t h t = c h t +ωa t z t = some Markov process b t b, a t, c h t c t : non-durable consumption d t : illiquid deposits ( ) b t : liquid assets χ: transaction cost function z t : individual productivity a t : illiquid assets l t : hours worked h t : housing services T t : labor income tax/transfer

Households max E e (ρ+λ)t u(c t,l t,h t )dt s.t. {c t,l t,d t } t ḃ t = r b t(b t )b t +w t z t l t T t (w t z t l t ) d t χ(d t,a t ) c t c h t ȧ t = r a t(1 ω)a t +d t h t = c h t +ωa t z t = some Markov process b t b, a t, c h t Adjustment cost function d χ(d,a) = χ d +χ 1 a χ2 a Linear component: inaction region Convex component: finite deposit rates

Households max E {c t,l t,d t } t e (ρ+λ)t u(c t,l t,h t )dt s.t. ḃ t = r b t(b t )b t +w t z t l t T t (w t z t l t ) d t χ(d t,a t ) c t ȧ t = r a t(1 ω)a t +d t h t = ωa t z t = some Markov process b t b, a t c t : non-durable consumption d t : illiquid deposits ( ) b t : liquid assets χ: transaction cost function z t : individual productivity a t : illiquid assets l t : hours worked h t : housing services T t : labor income tax/transfer

Households max E {c t,l t,d t } t e (ρ+λ)t u(c t,l t,h t )dt s.t. ḃ t = r b t(b t )b t +w t z t l t T t (w t z t l t ) d t χ(d t,a t ) c t ȧ t = r a t (1 ω)a t +d t h t = ωa t z t = some Markov process b t b, a t Households are price-takers wrt: {Ψ t } t = { w t,r a t,r b t,t t } The stationary recursive solution of hh problem: 1. decision rules: c(a,b,z;ψ),d(a,b,z;ψ),l(a,b,z;ψ) 2. stationary distribution: µ(da, db, dz; Ψ) t

Firms Representative competitive final goods producer: Y = ( 1 y ε 1 ε j ) ε ε 1 dj

Firms Representative competitive final goods producer: Y = ( 1 y ε 1 ε j ) ε ε 1 dj Monopolistically competitive intermediate goods producers: Technology: y j = Zk α j n1 α j m = 1 Z ( r k α ) α ( ) 1 α w 1 α Set prices subject to quadratic adjustment costs: (ṗ ) Θ p = θ 2 (ṗ ) 2 Y p

Competitive investment fund sector Own intermediate firms and issue one-period security w/ return r a Hh productive assets (1 ω)a are savings into this security Two sources of income into the fund: 1. Rent illiquid asset as productive capital ( r k δ ) K 2. Receive dividends proportional to the K owned D = [(1 m)y]/k Competition among funds implies illiquid asset return r a = ( r k δ ) +D

Monetary authority and government Taylor rule i = r b +φπ +ǫ, φ > 1 with r b i π (Fisher equation)

Monetary authority and government Taylor rule i = r b +φπ +ǫ, φ > 1 with r b i π (Fisher equation) Tax/transfer system: T (wzl) = τwzl T Government budget constraint (in steady-state) G+T +r b B g = τ wzl(a,b,z)dµ

PARAMETERIZATION

Some aspects of parameterization Preferences: GHH

Earnings dynamics Parameter Component j = 1 Component j = 2 Arrival rate λ j.8.7 Mean reversion β j.761.9 St. Deviation of innovations σ j 1.74 1.53 A career shock perturbed by periodic temporary shocks Density 2 4 6 8-4 -2 2 4 1 Year Log Earnings Changes Density.5 1 1.5 2-5 5 5 Year Log Earnings Changes

Some aspects of parameterization Preferences: GHH Measurement and partition of asset categories into: liquid (cash, bank accounts + government/corporate bonds) illiquid productive (equity) + non-productive (housing) Continuous time household earnings dynamics Match variance and kurtosis of 1- and 5-yr earnings changes Adjustment cost function χ(d,a) and discount factor ρ Match mean/median liquid/illiquid wealth and fraction HtM

Kinked adjustment cost function χ(d, a) % of Stock 1.5 1.5 Adjustment Cost, % of Stock.5.45.4.35.3.25.2.15.1.5-5 5 Quarterly Deposit/Withdrawal, % of Stock Total transaction costs (financial services to households): 2% of GDP

Wealth distribution statistics.1.9.8.7.6.5.4.3.2.1 Pr(b = ) =.29 Liquid wealth distribution.1.9.8.7.6.5.4.3.2.1 Pr(a = ) =.25 Illiquid wealth distribution 2 4 6 8 1 $ Thousands 2 4 6 8 1 $ Millions Data Model Mean illiquid assets (rel. to GDP) 2.92 2.92 Mean liquid assets (rel. to GDP).26.26 Gini coefficient for liquid wealth.98.85 Gini coefficient for illiquid wealth.8.81 Poor hand-to-mouth (a = b = ) 1% 12% Wealthy hand-to-mouth (a >, b = ) 2% 17%

Some aspects of parameterization Preferences: GHH Measurement and partition of asset categories into: liquid (cash, bank accounts + government/corporate bonds) illiquid productive (equity) + non-productive (housing) Continuous time household earnings dynamics Nature of earnings risk affects household portfolio Adjustment cost function χ(d,a) and discount factor ρ Match mean/median liquid/illiquid wealth and fraction HtM Production side: standard calibration of NK models

MPC heterogeneity Quarterly MPC $5.4.3.2.1 4 3 2 1 Illiquid Wealth ($) 1-1 Liquid Wealth ($) 2 Quarterly (annual) MPC out of a $5 windfall: 17% (5%) MPC declining with the size of the transitory income change

RESULTS

Expansionary monetary policy shock Innovation ǫ < to the Taylor rule: i = r b +φπ +ǫ All experiments: ǫ =.25, i.e. 1% annualized

Expansionary monetary policy shock Innovation ǫ < to the Taylor rule: i = r b +φπ +ǫ All experiments: ǫ =.25, i.e. 1% annualized Deviation (pp annual).5 -.5-1 Taylor rule innovation: ǫ Liquid return: r b Inflation: π -1.5 5 1 15 2 Quarters Deviation (%).5.4.3.2.1 -.1 Total Consumption 5 1 15 2 Quarters

Transmission of monetary policy shock to C dc = C rt b drtdt b + }{{} direct [ C rt a drt a + C dw t + C ] dt t dt w t T t }{{} indirect

Transmission of monetary policy shock to C dc = C rt b drtdt b + }{{} direct [ C rt a drt a + C dw t + C ] dt t dt w t T t }{{} indirect 5 Deviation 4 3 2 1 Liquid return: r b (pp annual) Iliquid return: r a (pp annual) Real wage: w (%) Lump sum transfer: T (%) -1 5 1 15 2 Quarters

Transmission of monetary policy shock to C dc = C r b t dr b tdt+ [ C r a t drt a + C dw t + C ] dt t dt w t T t Intertemporal substitution and income effects from r b.5.4 Total Response Direct: r b Deviation (%).3.2.1 -.1 5 1 15 2 Quarters

Transmission of monetary policy shock to C dc = C r b t dr b tdt+ [ C r a t drt a + C dw t + C ] dt t dt w t T t Portfolio reallocation effect from r a r b Deviation (%).5.4.3.2.1 Total Response Direct: r b Indirect: r a -.1 5 1 15 2 Quarters

Transmission of monetary policy shock to C dc = C r b t dr b tdt+ [ C r a t drt a + C dw t + C ] dt t dt w t T t Labor demand channel from w Deviation (%).5.4.3.2.1 Total Response Direct: r b Indirect: r a Indirect: w -.1 5 1 15 2 Quarters

Transmission of monetary policy shock to C dc = C r b t dr b tdt+ [ C r a t drt a + C dw t + C ] dt t dt w t T t Fiscal policy channel from T due to r b B Deviation (%).5.4.3.2.1 Total Response Direct: r b Indirect: r a Indirect: w Indirect: T -.1 5 1 15 2 Quarters

Transmission of monetary policy shock to C dc = C rt b drtdt b + }{{} 12% [ C rt a drt a + C dw t + C ] dt t dt w t T t }{{} 88% Deviation (%).5.4.3.2.1 Total Response Direct: r b Indirect: r a Indirect: w Indirect: T -.1 5 1 15 2 Quarters

The distribution of the monetary transmission 1.4 Direct Effects Indirect Effects 1.2 1.2.18.16.14 % Change.8.6.4.2 -.2 5 1 15 2 25 $ Thousands.12.1.8.6.4.2 Aggregate elasticity = c-weighted average of elasticity for given b

Transmission across the distribution: direct effects 1.4 Consumption Response (Direct) Deposit Response (Direct) 1.2 1.2.18.16.14 % Change.8.6.4.2 -.2 5 1 15 2 25 $ Thousands.12.1.8.6.4.2 Intertemporal substitution: (+) for non-htm Income effect: (-) for rich savers and (+) for borrowers Portfolio reallocation: (-) for those with b low but positive

Transmission across the distribution: indirect effects 1.4 Indirect Effect: r a 1.2 1 Indirect Effect: T Indirect Effect: w.2.18.16.14 % Change.8.6.4.2 -.2 5 1 15 2 25 $ Thousands.12.1.8.6.4.2 c response to (w,t) income: (+) and strong for HtM c l complementarity: (+) for non-htm

Role of fiscal response in monetary transmission

Role of fiscal response in monetary transmission T adjusts G adjusts B g adjusts (1) (2) (3) Change in C (%).47%.63%.9% Elasticity of C to r b -2.1-3.1 -.36 Direct effect: r b 12% 9% 37% G adjusts: G translates 1-1 into aggregate demand B g adjusts: no direct stimulus to aggr. demand from fiscal side

Monetary policy transmission in HANK RANK Main findings Intertemporal subst. weak, indirect GE channels strong Both HtM and wealthy households are important Fiscal response to monetary policy shock is key Implications for conduct of monetary policy Fed must rely heavily on GE feedbacks that boost labor Y

THANKS!

Summary of market clearing conditions Liquid asset market B h = B g Illiquid asset/capital market r a K = (1 ω)a Labor market w N = zl(a, b, z)dµ Goods market π Y = C +H +I +G+χ+borrowing costs+θ

Fifty shades of K Liquid Illiquid Total Non-productive Household deposits net of revolving debt Corp & Govt bonds B h =.26.6 net housing.6 net durables ωa =.79 1.5 Indirectly held equity Productive Deposits at inv fund B f =.48 Directly held equity Noncorp bus equity.4 housing, durables 2.13 K (1 ω)a = 2.13 Total B g =.26 A = 2.92 3.18 Quantities are multiples of annual GDP Sources: Flow of Funds and SCF 24

Description Value Target / Source Preferences λ Death rate 1/18 Av. lifespan 45 years γ Risk aversion 1 ϕ Frisch elasticity (GHH).5 ψ Disutility of labor 27 Av. hours worked equal to 1/3 ζ Weight on housing.15 ρ Discount rate (pa) 4.7% Internally calibrated Production ε Demand elasticity 1 Profit share 1 % α Capital share.33 δ Depreciation rate (p.a.) 1% θ Price adjustment cost 1 Slope of Phillips curve, ε/θ =.1 Government τ Proportional labor tax.25 T Lump sum transfer (rel GDP).75 4% hh with net govt transfer ḡ Govt debt to annual GDP.26 government budget constraint Monetary Policy φ Taylor rule coefficient 1.25 Kaplan-Moll-Violante, r b Monetary Policy According to HANK Steady state real liquid return (pa) 2%