Day 5. Monetary Policy in Models with Heterogeneous Agents

Transcription

1 Day 5 Monetary Policy in Models with Heterogeneous Agents Gianluca Violante New York University Mini-Course on Policy in Models with Heterogeneous Agents Bank of Portugal, June 15-19, 215 p. 1 /16

2 Automatic fiscal stabilizers Fiscal stabilizers: rules in law that make fiscal revenues and outlays relative to total income change with the business cycle. Question: are the automatic stabilizers effective at reducing the volatility of macroeconomic fluctuations? Estimate how much higher the volatility of aggregate activity would be if some or all of the fiscal stabilizers were removed. Investigate the theoretical channels by which the stabilizers may attenuate the business cycle Investigate whether type of monetary policy matters for the results p. 2 /16

3 Automatic stabilizers in the US Revenues Outlays Progressive income taxes Transfers Personal Income Taxes 1.98% Unemployment benefits.33% Safety net programs 1.2% Proportional taxes Supplemental nutrition assistance.24% Corporate Income Taxes 2.57% Family assistance programs.24% Property Taxes 2.79% Security income to the disabled.36% Sales and excise taxes 3.85% Others.19% Budget deficits Budget deficits Public deficit 1.87% Government purchases 15.6% Net interest income 2.76% Figure 1: The personal income tax rate from TAXSIM.4.3 marginal tax rate.2.1 average statutory rate smoothed income normalized by mean household income p. 3 /16

4 Forces at work The literature suggests three main channels: Stabilization of average disposable income: makes aggregate demand more stable Social insurance: some of these policies reduce individual income fluctuations (eg, UI) Redistribution: from those with lower MPC to those with higher MPC stabilizes aggregate demand Model: Aiyagari meets Calvo-Woodford with 2 types (patient and impatient) p. 4 /16

5 Patient households Patient: measure 1 of hh with access to complete markets against idiosyncratic risk, thus RA with problem: max {c t,n t,b t+1 } E [ ] β t n 1+ϕ 2 t logc t ϕ 1 1+ϕ 2 t= s.t. (1+τ c t)p t c t +b t+1 b t = p t [x t τ x (x t )] x t = d t +(i t /p t )b t +w t εn t τ x (x t ) = xt τ x (z)dz Two assets: (i) trade bonds with the impatient households and the government, and (ii) invest capital in the production firms p. 5 /16

6 Impatient households There is a measure ν = 4 of impatient households indexed by i facing problem: max {c t,n t,b t+1 } E [ ] β t n 1+ϕ 2 it logc it ϕ 1 1+ϕ 2 t= s.t. (1+τ c t)p t c it +b i,t+1 b it = p t [x it τ x (x it )] b i,t+1 x it = (i t /p t )b it +w t ε it n t if e it = 2 (i t /p t )b it +Tit u if e it = 1 (i t /p t )b it +Tit s if e it = where Tit u is unemployment insurance and Ts it transfer, with Tit u > Ts it. is safety net p. 6 /16

7 Production sector Competitive final good sector combines intermediate goods: y t = ( 1 ) µt y t (j) 1/µ t dj where the subscript t on µ t allows for mark-up shocks A unit continuum of intermediate-goods monopolistic firms, each producing variety j using a production function: y t (j) = a t k t (j) α l 1 α t (j) Set prices subject to nominal rigidities a la Calvo (1983) Maximize profits with the patient household (owner) SDF λ t+1 Profits taxed at the flat corporate tax income rate τ corp p. 7 /16

8 Production sector Representative firm It owns the capital stock and solves v t (k t ) = max k t+1 (1 τ corp )[r t k t k t+1 g(k t, k t+1 )]+E t [λ t+1 v t+1 (k t+1 )] and pays off its after-tax profits as dividends to its owner, the patient RA Very crude asset ownership structure: stark assumptions p. 8 /16

9 Government Progressive income taxes, transfers, corporate income tax, sales taxes Government debt (the risk-free asset held by all households) and expenditures linked by a fiscal rule: log(g t ) = log(ḡ) γlog ( Bt /p t B γ measure the speed at which the deficits from recessions are paid back over time through a reduction in expenditures. Shocks: technology, markup, and monetary policy ) i t = ī+φ logp t +ε t all following independent AR(1) processes. p. 9 /16

10 IRFs to shocks 5 x 1 3 Output x 1 3 Consumption x 1 3 Hours 5 5 x 1 3 Inflation Quarter Quarter Technology Monetary Mark up In spite of all the heterogeneity, the aggregate responses to shocks are similar to those of the standard NK RA model p. 1 /16

11 Stationary equilibrium ˆβ 1 Interest Rate Impatient household savings β 1 Eq m capital stock Eq m impatient household savings Capital demand Assets p. 11 /16

12 Cyclicality of stabilizers in data and model Fiscal variable Data Model Tax revenues Sales tax.4.7 Property tax Personal income tax Corporate income tax Purchases UI payments Net government savings Quarterly data from 196:I- 211:IV and expressed relative to potential output (HP filter trend). Problem: cyclicality of corporate income tax due to countercyclical markups (and dividends) p. 12 /16

13 Main result Full model variance average output hours consumption Experiment: eliminate all stabilizers and move to a flat income tax Stabilizers have a small effect on the volatility of the U.S. business cycle for Y and H. Removing the stabilizers raises the variance of aggregate consumption because budget deficits (government purchases) would not be as countercyclical (pro-cyclical). By lowering marginal tax rates, it would be a significantly richer economy on average. p. 13 /16

14 Role of monetary policy Taylor rule Flexible prices Schmitt-Grohé Uribe Baseline Aggressive Accommodative output hours consumption inflation Reduction in volatility Standard Taylor rule not far from optimal policy With baseline/aggressive monetary policy, small additional room for fiscal policy to stabilize the economy With passive monetary policy, fiscal stabilizers important p. 14 /16

15 Welfare gain from stabilizers Recall experiment: eliminate all stabilizers and move to a flat income tax Patient CEV is +14% and Impatient CEV is -15% Do stabilizers reduce costs of recessions? Shock Table 14: Utilitarian cost of recessions. Cost with stabilizers Cost without stabilizers Difference TFP Mon. pol Markup ZLB Yes, but costs are small to begin with p. 15 /16

16 Monetary Policy According to HANK Greg Kaplan Ben Moll Gianluca Violante

17 HANK: Heterogeneous Agent New Keynesian models New framework for quantitative analysis of aggregate shocks and macroeconomic policy 1

18 HANK: Heterogeneous Agent New Keynesian models New framework for quantitative analysis of aggregate shocks and macroeconomic policy Three building blocks: 1. Uninsurable idiosyncratic income risk 2. Nominal rigidities 3. Assets with different degrees of liquidity Realistic MPC distributions 1

19 Questions for HANK 1. Aggregate and Distributional Effects of Shocks Supply shocks, demand shocks, idiosyncratic uncertainty shocks, liquidity shocks, redistributive shocks 2. Fiscal policy Government expenditure Transfers and fiscal stimulus payments 3. Monetary policy Conventional: nominal interest rate Quantitative easing: swap of illiquid assets for liquid assets Forward guidance: announcement of nominal interest rate 2

20 Questions for HANK 1. Aggregate and Distributional Effects of Shocks Supply shocks, demand shocks, idiosyncratic uncertainty shocks, liquidity shocks, redistributive shocks 2. Fiscal policy Government expenditure Transfers and fiscal stimulus payments 3. Monetary policy Conventional: nominal interest rate Quantitative easing: swap of illiquid assets for liquid assets Forward guidance: announcement of nominal interest rate 2

21 Literature and contribution Combine two workhorses of modern macroeconomics: 1. New Keynesian models with limited heterogeneity Campell-Mankiw, Gali-Lopez Salido-Valles, Iacioviello, Challe-Matherau-Ragot-Rubion Ramirez Micro-foundation of spender-saver behavior 2. Aiyagari models with sticky prices Oh-Reis (212), Guerrieri-Lorenzoni (213), Ravn-Sterk (213), Gornemann et al. (214), Den Haan-Rendal-Riegler (214), Bayer et al. (214), McKay-Reis (214), McKay-Nakamura- Steinsson (215), Huo-Rios Rull (214) Assets with different liquidity Kaplan-Violante (213) New view of individual earnings risk Guvenen-Karahan-Ozkar-Song (214) Continuous time approach Achdou-Lasry-Lions-Moll (214) Literature on inventory management and asset illiquidity Baumol, Tobin, Romer, Alvarez-Lippi, Alvarez-Guiso-Lippi and many others 3

22 Model elements Households face uninsured idiosyncratic labor income risk hold two assets: liquid and illiquid consume and supply labor Firms monopolistic competition quadratic price adjustment costs à la Rotemberg (1982) Assets liquid assets: return determined by monetary policy rule illiquid assets: return determined by profitability of capital ``MIT shocks" 4

23 Households max {c t,c h t,l t,d t } t E e (ρ+λ)t u(c t, l t, h t )dt s.t. ḃ t = r b (b t )b t + (1 ξ)wz t l t d t χ(d t, a t ) c t c h t ȧ t = r a (1 ω)a t +ξwz t l t +d t h t = c h t + r h ωa t z t = some Markov process b t b, a t, c h t c t : non-durable consumption b t : liquid assets z t : individual productivity a t : illiquid assets d t : illiquid deposits χ: transaction cost function ct h : housing services expend h t : total housing services l t : hours worked 5

24 Households max {c t,c h t,l t,d t } t E e (ρ+λ)t u(c t, l t, h t )dt s.t. ḃ t = r b (b t )b t + (1 ξ)wz t l t d t χ(d t, a t ) c t c h t ȧ t = r a (1 ω)a t +ξwz t l t +d t h t = c h t + r h ωa t z t = some Markov process b t b, a t, c h t c t : non-durable consumption b t : liquid assets z t : individual productivity a t : illiquid assets d t : illiquid deposits χ: transaction cost function ct h : housing services expend h t : total housing services l t : hours worked 5

25 Households max {c t,c h t,l t,d t } t E e (ρ+λ)t u(c t, l t, h t )dt s.t. ḃ t = r b (b t )b t + (1 ξ)wz t l t d t χ(d t, a t ) c t c h t ȧ t = r a (1 ω)a t +ξwz t l t +d t h t = c h t + r h ωa t z t = some Markov process b t b, a t, c h t c t : non-durable consumption b t : liquid assets z t : individual productivity a t : illiquid assets d t : illiquid deposits χ: transaction cost function ct h : housing services expend h t : total housing services l t : hours worked 5

26 Households max {c t,c h t,l t,d t } t E e (ρ+λ)t u(c t, l t, h t )dt s.t. ḃ t = r b (b t )b t + (1 ξ) wz t l t d t χ(d t, a t ) c t c h t ȧ t = r a (1 ω) a t + ξwz t l t + d t h t = c h t + r h ωa t z t = some Markov process b t b, a t, c h t c t : non-durable consumption b t : liquid assets z t : individual productivity a t : illiquid assets d t : illiquid deposits χ: transaction cost function ct h : housing services expend h t : total housing services l t : hours worked 5

27 Households Adjustment cost function: d χ(d, a) = χ 1 {d } + χ 1 a χ 2 a Fixed component implies inaction Convex component implies finite deposit rates Recursive solution consists of: joint distribution of households µ(da, db, dz; t) consumption policy function c(a, b, z; t) deposit policy function d(a, b, z; t) labor supply policy function l(a, b, z; t) 6

28 Typical policy functions Deposit Policy Function Consumption Policy Function Illiquid Wealth Lliquid Wealth Illiquid Wealth 1 2 Lliquid Weal 7

29 Firms Representative final goods producer: ( 1 ) ε Y = y ε 1 ε 1 ε j dj y j = ( pj ) ε Y P 8

30 Firms Representative final goods producer: ( 1 ) ε Y = y ε 1 ε 1 ε j dj y j = ( pj ) ε Y P Monopolistically competitive intermediate goods producers: Technology: y j = Zk α j n 1 α j Marginal costs: m = 1 Z ( r α ) ( α w ) 1 α 1 α Set prices subject to quadratic adjustment costs: (ṗ ) Θ = θ (ṗ ) 2 Y p 2 p. Intermediate good firm pricing problem 8

31 New Keynesian Phillips Curve Lemma Inflation rate implied by firms' optimal price-setting satisfies ( r b Ẏ ) π = ε 1 ( ) ε Y θ ε 1 m 1 + π 9

32 New Keynesian Phillips Curve Lemma Inflation rate implied by firms' optimal price-setting satisfies ( r b Ẏ ) π = ε 1 ( ) ε Y θ ε 1 m 1 + π In present value form π t = ε 1 θ t e r b (s t) Y ( ) s ε Y t ε 1 m s 1 ds Logic: increase prices when markup < flex price optimum ε ε 1 m s 1 = M M s M s, M = ε ε 1 Exact NK Phillips curve: no log-linearization 9

33 Investment fund sector Investment funds receive illiquid assets from households: A p = (1 ω) adµ Investment funds have three sources of income: 1. Rent out illiquid asset as capital to intermediate producers (r δ)k 1

34 Investment fund sector Investment funds receive illiquid assets from households: A p = (1 ω) adµ Investment funds have three sources of income: 1. Rent out illiquid asset as capital to intermediate producers (r δ)k 2. Dividends from ownership of intermediate producers qk Steady state: q = (1 m)y Outside steady state: No dividend smoothing: q = (1 m)y θ 2 π2 Y Dividend smoothing: q = ρ q (q q) 1

35 Investment fund sector Investment funds receive illiquid assets from households: A p = (1 ω) adµ Investment funds have three sources of income: 1. Rent out illiquid asset as capital to intermediate producers (r δ)k 2. Dividends from ownership of intermediate producers qk 3. Liquidity transformation: issue liquid assets, reinvest as capital K = A p + ( B f ) 1

36 Illiquid asset return Investment fund can issue deposits up to fraction of its assets B f ζk K 1 1 ζ Ap Interpret ζ as leverage of financial sector Investment fund optimization implies illiquid asset return r a = 1 ( r δ + q ζr b ) 1 ζ. Fund optimization detail 11

37 Illiquid asset return Investment fund can issue deposits up to fraction of its assets B f ζk K 1 1 ζ Ap Interpret ζ as leverage of financial sector Investment fund optimization implies illiquid asset return r a = 1 ( r δ + q ζr b ) 1 ζ. Fund optimization detail 11

38 Illiquid asset return Investment fund can issue deposits up to fraction of its assets B f ζk K 1 1 ζ Ap Interpret ζ as leverage of financial sector Investment fund optimization implies illiquid asset return r a = 1 ( r δ+q ζr b ) 1 ζ. Fund optimization detail 11

39 Illiquid asset return Investment fund can issue deposits up to fraction of its assets B f ζk K 1 1 ζ Ap Interpret ζ as leverage of financial sector Investment fund optimization implies illiquid asset return r a = 1 ( r δ+q ζr b ) 1 ζ. Fund optimization detail 11

40 Monetary authority and liquid assets Taylor rule i = max{ r b + ϕπ, }, ϕ > 1 Fisher equation r b = i π Four participants in bond market: Households: Investment fund: Government: Foreign sector: B h = bdµ B f = ζk B g = ḡy B w Bond market clearing: B h + B f + B g + B w = 12

41 World bond demand World has exogenous demand function for domestic liquid assets: Ḃ w = ϕ[η(r b r b ) (B w B w )] Special cases η = or ϕ = : bonds in fixed supply η = : small open economy with r b = r b Three reasons 1. Realism 2. Symmetry with illiquid assets 3. Makes computations easier 13

42 Government Progressive tax on labor income: T (wzl) = τ + τ 1 wzl Exogenous government spending G Issues debt. Steady state debt level is fraction ḡ of GDP: B g = ḡy Government budget constraint G r b B g = T (wzl (a, b, z)) dµ Out of steady state we will consider various alternatives 14

43 Summary of market clearing conditions Liquid asset market B h + B f + B g + B w = Illiquid asset market K = A p + ( B f ) Labor market N = zl(a, b, z)dµ Goods market: Walras Law 15

44 Calibration Three particularly important aspects, relatively unique to paper: 1. Continuous time household earnings dynamics 2. Definition and measurement of asset categories Liquid vs illiquid Productive vs non-productive 3. Adjustment cost function 16

45 Calibration Three particularly important aspects, relatively unique to paper: 1. Continuous time household earnings dynamics [no time today] 2. Definition and measurement of asset categories Liquid vs illiquid Productive vs non-productive 3. Adjustment cost function 16

46 5 shades of K Non-productive Productive Liquid Illiquid Total Household deposits Net of revolving debt Govt bonds B h =.22 Deposits at inv fund B f =.55 Net housing Net durables A d = 1.31 Indirectly held equity Directly held equity Noncorp bus equity A p = K Total B w + B g =.33 A = ζ = Bf K = =.255 ω = Ad A = =.449 ḡ =.25 B g =.25 B w =.33 B g =.58.6 of B g is from domestic households,.19 from foreign sector 17

47 Adjustment cost function calibration Three parameter function d χ(d) = χ 1 {d } + χ 1 a χ 2 a Choose χ, χ 1, χ 2 together with: discount rate ρ borrowing intermediation wedge: κ b = r bor r b + to match five features of the household wealth distribution 18

48 Adjustment cost function calibration Three parameter function d χ(d) = χ 1 {d } + χ 1 a χ 2 a Choose χ, χ 1, χ 2 together with: discount rate ρ borrowing intermediation wedge: κ b = r bor r b + to match five features of the household wealth distribution Moment Data Model Mean Illiquid assets (rel to GDP) Median Illiquid assets (rel to GDP) Mean Liquid assets (rel to GDP) Fraction with Liquid assets [, $1] Fraction with Liquid assets <

49 Adjustment cost function 2 Adjustment Cost: Median Illiquid Assets 2 Adjustment Cost: Mean Illiquid Assets $ s $ s Quarterly Deposit / Illiquid Assets Quarterly Deposit / Illiquid Assets 19

50 Description Value Target / Source Preferences λ Death rate 1/18 Av. lifespan 45 years γ Risk aversion 2 φ Frisch elasticity.5 ψ Disutility of labor 27 Av. hours worked equal to 1/3 Weight on housing.15 Production ε Demand elasticity 1 Profit share 1 % α Capital share.33 δ Depreciation rate (p.a.).9 θ Price adjustment cost 1 Bayer et. al. (214) Government τ Proportional labor tax.25 T Lump sum transfer (rel GDP).73 4% hh with net govt transfer ḡ Govt debt to annual GDP.25 Flow of Funds Monetary Policy ϕ Taylor rule coefficient 1.25 r b Steady state real liquid return (pa) 2% Housing ω Fraction of illiquid assets in housing.449 r h Net housing return (pa).25 Illiquid Assets ξ Fraction of labor income auto deposited.5 ζ Investment fund leverage.255 r a Illiquid asset return 11.4% Equm outcome 2

51 Wealth distributions.2 Liquid wealth distribution.18 Illiquid wealth distribution $ Thousands $ Millions 21

52 Marginal propensities to consume 1. Slope of consumption function MPC = c(a, b, z) b 2. Marginal propensity to consume over a period τ [ τ ] C τ (a, b, z) = E c(a t, b t, z t )dt a = a, b = b, z = z MPC τ = b C τ(a, b, z) 3. Consumption out of x dollars over period (empirical estimates) MPC τ,x = C τ(a, b + x, z) C τ (a, b, z) x 22

53 Marginal propensities to consume.5 Theoretical MPC distribution.5 Quarterly MPC distribution Annual MPC distribution Quarterly Responses to $5 Rebate

54 MPC heterogeneity Theoretical MPC Quarterly MPC $ Illiquid Wealth ($) Liquid Wealth ($) 15 1 Illiquid Wealth ($) Liquid Wealth ($) 24

55 Channels for monetary policy Innovation ϵ < to the Taylor rule: i = r b + ϕπ + ϵ 25

56 Channels for monetary policy Innovation ϵ < to the Taylor rule: i = r b + ϕπ + ϵ Direct effects from r b 1. Intertemporal substitution: C (households on EE) 2. Cash flow effect (or income, or URE): C (savers), C (borrowers) 25

57 Channels for monetary policy Innovation ϵ < to the Taylor rule: i = r b + ϕπ + ϵ Direct effects from r b 1. Intertemporal substitution: C (households on EE) 2. Cash flow effect (or income, or URE): C (savers), C (borrowers) Indirect effects 3. Aggregate demand effect C (high MPC households) Through labor market: C L d w 4. Asset returns effect C (households with high a) Through fund leverage r b r a 25

58 IRF: Monetary policy shock I Liquid return (r b ), % pa Consumption (C), % dev Output (Y ), % dev Real wage (w), % dev 3 Inflation (π), % pa 12.5 Illiquid return (r a ), % pa

59 IRF: Monetary policy shock II 8 6 Investment (I), % dev Hours (H), % dev Portfolio (A,B), % dev Liquid assets Illiquid assets Markup (µ), % 14.5 Rental rate (r), % pa 5 Nominal rate (i), % pa

60 Which channel of monetary policy? Consumption (C) Baseline Only r b Only r a Only w 8 6 Investment (I) Baseline Only r b Only r a Only w % deviation 1.5 % deviation Intertemporal substitution channel is tiny Financial intermediation channel is large Aggregate demand effect through labor demand is huge 28

61 Consumption responses by wealth 3 Consumption (C) % deviation Q1 net worth Q2 net worth Q3 net worth Q4 net worth Consumption response is twice as large for the bottom quartile of net worth distribution compare to the top quartile 29

62 MP channels across the wealth distribution 3 Consumption (C), only r b 3 Consumption (C), only w % deviation Q1 net worth Q2 net worth Q3 net worth Q4 net worth % deviation Q1 net worth Q2 net worth Q3 net worth Q4 net worth Even high net worth households have a small substitution channel Q4 households: mean $9k liquid wealth, $1m illiquid wealth 3

63 Final thoughts Heterogeneous Agent New Keynesian models: a new framework for quantitative analysis of monetary policy Consistency with income, wealth and MPC distributions allows: Analysis of broader set of channels for policy Distributional analysis of policies Policy implications: transmission of nominal rates to real rates is not enough for real effects, crucial that real rates affect labor demand. 31

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65 Intermediate good firm pricing problem max {p t } t e r b t { )} (ṗt Π t (p t ) Θ t dt p t s.t. ( p ) ( p ) ε Π(p) = P m Y P m = 1 ( r ) α ( w ) 1 α Z α 1 α Θ(π)= θ 2 π2 Y. Back to firms 33

66 Investment fund optimization problem Objective: Maximize PDV of dividends max e t Λ sds D t dt s.t. D + I + A + Ḃ = rk + qk + r a A + r b B K = I δk, B ζk q: dividend rate paid by intermediate firms ( no. of shares) Fund's problem (stationary version) ΛV (W ) = max D + V (W )Ẇ D,K,A,B Ẇ = (r + q δ)k + r a A + r b B D W = K + A + B, B ζk Fund balance sheet: assets K, liabilities A B, net worth W. back 34

67 THANK YOU FOR ATTENDING! p. 16 /16