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Heterogeneity and the Business Cycle

Advances in Macroeconomic Modelling Vincent SterkUCL,CfM,CEPR

Tinbergen Today: Challenges for Macroeconomic Modelling

DNB, November 2019

Heterogeneity & Business Cycle Models

Since 1980s: strong emphasis on optimizing behavior and expectations

◮ Lucas critique,“conquest of inflation”, etc.

development of (New-Keynesian) DSGE models Representative Agent assumption

◮ greatly simplifies computational complexity (distributions not a state) ⋆ estimation, forecasting, quantitative policy analysis, etc.

Heterogeneity & Business Cycle Models

Since 1980s: strong emphasis on optimizing behavior and expectations

◮ Lucas critique,“conquest of inflation”, etc.

development of (New-Keynesian) DSGE models Representative Agent assumption

◮ greatly simplifies computational complexity (distributions not a state) ⋆ estimation, forecasting, quantitative policy analysis, etc.

Heterogeneity & Business Cycle Models

Since 1980s: strong emphasis on optimizing behavior and expectations

◮ Lucas critique,“conquest of inflation”, etc.

development of (New-Keynesian) DSGE models Representative Agent assumption

◮ greatly simplifies computational complexity (distributions not a state) ⋆ estimation, forecasting, quantitative policy analysis, etc.

Heterogeneity & Business Cycle Models

Since 2000s: growing unease about Representative Agent: vast (and growing) heterogeneity in the micro data

◮ inequality in household income, wealth and consumption ◮ differences in firm size, productivity and markups, measures of “misallocation”

and “dynamism”

policy makers faced with growing demand to consider distributional consequences growing evidence on non-linearities at the micro level

◮ households: interest rate sensitivities, marginal propensities to consume,

labour supply elasticities, etc.

◮ firms: lumpy investment and hiring, etc.

growing evidence of heterogeneous responses to aggregate shocks

◮ by age, ownership status, balance sheet characteristics, etc.

Heterogeneity & Business Cycle Models

Since 2000s: growing unease about Representative Agent: vast (and growing) heterogeneity in the micro data

◮ inequality in household income, wealth and consumption ◮ differences in firm size, productivity and markups, measures of “misallocation”

and “dynamism”

policy makers faced with growing demand to consider distributional consequences growing evidence on non-linearities at the micro level

◮ households: interest rate sensitivities, marginal propensities to consume,

labour supply elasticities, etc.

◮ firms: lumpy investment and hiring, etc.

growing evidence of heterogeneous responses to aggregate shocks

◮ by age, ownership status, balance sheet characteristics, etc.

Heterogeneity & Business Cycle Models

Since 2000s: growing unease about Representative Agent: vast (and growing) heterogeneity in the micro data

◮ inequality in household income, wealth and consumption ◮ differences in firm size, productivity and markups, measures of “misallocation”

and “dynamism”

policy makers faced with growing demand to consider distributional consequences growing evidence on non-linearities at the micro level

◮ households: interest rate sensitivities, marginal propensities to consume,

labour supply elasticities, etc.

◮ firms: lumpy investment and hiring, etc.

growing evidence of heterogeneous responses to aggregate shocks

◮ by age, ownership status, balance sheet characteristics, etc.

Heterogeneity & Business Cycle Models

Since 2000s: growing unease about Representative Agent: vast (and growing) heterogeneity in the micro data

◮ inequality in household income, wealth and consumption ◮ differences in firm size, productivity and markups, measures of “misallocation”

and “dynamism”

policy makers faced with growing demand to consider distributional consequences growing evidence on non-linearities at the micro level

◮ households: interest rate sensitivities, marginal propensities to consume,

labour supply elasticities, etc.

◮ firms: lumpy investment and hiring, etc.

growing evidence of heterogeneous responses to aggregate shocks

◮ by age, ownership status, balance sheet characteristics, etc.

Heterogeneity & Business Cycle Models

Since 2000s: growing unease about Representative Agent: vast (and growing) heterogeneity in the micro data

◮ inequality in household income, wealth and consumption ◮ differences in firm size, productivity and markups, measures of “misallocation”

and “dynamism”

policy makers faced with growing demand to consider distributional consequences growing evidence on non-linearities at the micro level

◮ households: interest rate sensitivities, marginal propensities to consume,

labour supply elasticities, etc.

◮ firms: lumpy investment and hiring, etc.

growing evidence of heterogeneous responses to aggregate shocks

◮ by age, ownership status, balance sheet characteristics, etc.

Heterogeneity & Business Cycle Models

Recent years: New generation of Heterogeneous-Agents DSGE models

◮ typically calibrated towards cross-sectional distributions

Challenging to solve: need to keep track of time-varying distributions Some popular computational approaches:

◮ Approximate aggregation: assume agents keep track only of certain moments

(Krusell and Smith,1998)

◮ Reiter (2009) method: solve model using perturbation, approximate

distribution with a histogram

◮ “MIT” shocks: one-time unanticipated shock, solve by computing perfect

foresight transition

Heterogeneity & Business Cycle Models

Recent years: New generation of Heterogeneous-Agents DSGE models

◮ typically calibrated towards cross-sectional distributions

Challenging to solve: need to keep track of time-varying distributions Some popular computational approaches:

◮ Approximate aggregation: assume agents keep track only of certain moments

(Krusell and Smith,1998)

◮ Reiter (2009) method: solve model using perturbation, approximate

distribution with a histogram

◮ “MIT” shocks: one-time unanticipated shock, solve by computing perfect

foresight transition

Heterogeneity & Business Cycle Models

Recent years: New generation of Heterogeneous-Agents DSGE models

◮ typically calibrated towards cross-sectional distributions

Challenging to solve: need to keep track of time-varying distributions Some popular computational approaches:

◮ Approximate aggregation: assume agents keep track only of certain moments

(Krusell and Smith,1998)

◮ Reiter (2009) method: solve model using perturbation, approximate

distribution with a histogram

◮ “MIT” shocks: one-time unanticipated shock, solve by computing perfect

foresight transition

Some challenges

Cannot possibly include all forms of heterogeneity. How to choose?

◮ Which cross-sectional patterns to match?

Large-scale heterogeneous-agents model often quite difficult to understand

◮ potentially complex equilibrium feedbacks

Monetary and fiscal policy intertwined

◮ breakdown of Ricardian equivalence ◮ seemingly innocuous assumptions on the distribution of factor payments may

be very important

Some challenges

Cannot possibly include all forms of heterogeneity. How to choose?

◮ Which cross-sectional patterns to match?

Large-scale heterogeneous-agents model often quite difficult to understand

◮ potentially complex equilibrium feedbacks

Monetary and fiscal policy intertwined

◮ breakdown of Ricardian equivalence ◮ seemingly innocuous assumptions on the distribution of factor payments may

be very important

Some challenges

Cannot possibly include all forms of heterogeneity. How to choose?

◮ Which cross-sectional patterns to match?

Large-scale heterogeneous-agents model often quite difficult to understand

◮ potentially complex equilibrium feedbacks

Monetary and fiscal policy intertwined

◮ breakdown of Ricardian equivalence ◮ seemingly innocuous assumptions on the distribution of factor payments may

be very important

Road map

Goal: highlight some lessons that have been learned on heterogeneity may affect the aggregate business cycle. Set up basic HANK (Heterogeneous Agents New Keynesian) model

◮ idiosyncratic income risk + incomplete insurance ⇒ heterogeneity

Compare two extreme, but tractable special cases:

Road map

Goal: highlight some lessons that have been learned on heterogeneity may affect the aggregate business cycle. Set up basic HANK (Heterogeneous Agents New Keynesian) model

◮ idiosyncratic income risk + incomplete insurance ⇒ heterogeneity

Compare two extreme, but tractable special cases:

Road map

Goal: highlight some lessons that have been learned on heterogeneity may affect the aggregate business cycle. Set up basic HANK (Heterogeneous Agents New Keynesian) model

◮ idiosyncratic income risk + incomplete insurance ⇒ heterogeneity

Compare two extreme, but tractable special cases:

Model overview

Households

◮ face idiosyncratic unemployment risk ⋆ employed: choose labour supply, lose their job with probability peu ⋆ unemployed: receive benefit ϑ, find job with probability pue ◮ save in nominal bonds subject to no-borrowing limit: Bt(i) ≥ 0,

Firms

◮ produce, set prices subject to adjustment cost

Monetary authority

◮ set nominal interest rate according to rule

Fiscal authority

Model overview

Households

◮ face idiosyncratic unemployment risk ⋆ employed: choose labour supply, lose their job with probability peu ⋆ unemployed: receive benefit ϑ, find job with probability pue ◮ save in nominal bonds subject to no-borrowing limit: Bt(i) ≥ 0,

Firms

◮ produce, set prices subject to adjustment cost

Monetary authority

◮ set nominal interest rate according to rule

Fiscal authority

Model overview

Households

◮ face idiosyncratic unemployment risk ⋆ employed: choose labour supply, lose their job with probability peu ⋆ unemployed: receive benefit ϑ, find job with probability pue ◮ save in nominal bonds subject to no-borrowing limit: Bt(i) ≥ 0,

Firms

◮ produce, set prices subject to adjustment cost

Monetary authority

◮ set nominal interest rate according to rule

Fiscal authority

Model overview

Households

◮ face idiosyncratic unemployment risk ⋆ employed: choose labour supply, lose their job with probability peu ⋆ unemployed: receive benefit ϑ, find job with probability pue ◮ save in nominal bonds subject to no-borrowing limit: Bt(i) ≥ 0,

Firms

◮ produce, set prices subject to adjustment cost

Monetary authority

◮ set nominal interest rate according to rule

Fiscal authority

Two special cases

1) Set peu = 0: no unemployment

◮ Representative Agent (RANK) version

2) Set B = 0 : zero liquidity Heterogeneous Agent (HANK) version

◮ “extreme market incompleteness” ◮ all agents hold zero wealth in equilibrium ◮ unemployed are “hand to mouth”, employed are on Euler equation, but

consider the possibility of future job loss

◮ analytically tractable (Ravn & Sterk, 2016)

Two special cases

1) Set peu = 0: no unemployment

◮ Representative Agent (RANK) version

2) Set B = 0 : zero liquidity Heterogeneous Agent (HANK) version

◮ “extreme market incompleteness” ◮ all agents hold zero wealth in equilibrium ◮ unemployed are “hand to mouth”, employed are on Euler equation, but

consider the possibility of future job loss

◮ analytically tractable (Ravn & Sterk, 2016)

Two special cases

1) Set peu = 0: no unemployment

◮ Representative Agent (RANK) version

2) Set B = 0 : zero liquidity Heterogeneous Agent (HANK) version

◮ “extreme market incompleteness” ◮ all agents hold zero wealth in equilibrium ◮ unemployed are “hand to mouth”, employed are on Euler equation, but

consider the possibility of future job loss

◮ analytically tractable (Ravn & Sterk, 2016)

Two special cases

1) Set peu = 0: no unemployment

◮ Representative Agent (RANK) version

2) Set B = 0 : zero liquidity Heterogeneous Agent (HANK) version

◮ “extreme market incompleteness” ◮ all agents hold zero wealth in equilibrium ◮ unemployed are “hand to mouth”, employed are on Euler equation, but

consider the possibility of future job loss

◮ analytically tractable (Ravn & Sterk, 2016)

Two special cases

1) Set peu = 0: no unemployment

◮ Representative Agent (RANK) version

2) Set B = 0 : zero liquidity Heterogeneous Agent (HANK) version

◮ “extreme market incompleteness” ◮ all agents hold zero wealth in equilibrium ◮ unemployed are “hand to mouth”, employed are on Euler equation, but

consider the possibility of future job loss

◮ analytically tractable (Ravn & Sterk, 2016)

HANK versus RANK

C

−σ

t

= βEt R Πt+1

• peuϑ−σ+(1 − peu)C −σ

t+1

• (EE)

C

ϕ+σ ϕ

t

= At(1 − u) wt κ 1

ϕ

1 − φ (Πt − 1)2 (LS) 1 − ε + εwt At = φ (Πt − 1) Πt − φEtβ (Πt+1 − 1) Πt+1 (PC) Rt = ztR (Πt)ξ (TR) Red terms present only in HA version. Modified Euler equation.

• therwise the HANK and the RANK model are equivalent.

HANK versus RANK

C

−σ

t

= βEt R Πt+1

• peuϑ−σ+(1 − peu)C −σ

t+1

• (EE)

C

ϕ+σ ϕ

t

= At(1 − u) wt κ 1

ϕ

1 − φ (Πt − 1)2 (LS) 1 − ε + εwt At = φ (Πt − 1) Πt − φEtβ (Πt+1 − 1) Πt+1 (PC) Rt = ztR (Πt)ξ (TR) Red terms present only in HA version. Modified Euler equation.

• therwise the HANK and the RANK model are equivalent.

HANK versus RANK

C

−σ

t

= βEt R Πt+1

• peuϑ−σ+(1 − peu)C −σ

t+1

• (EE)

C

ϕ+σ ϕ

t

= At(1 − u) wt κ 1

ϕ

1 − φ (Πt − 1)2 (LS) 1 − ε + εwt At = φ (Πt − 1) Πt − φEtβ (Πt+1 − 1) Πt+1 (PC) Rt = ztR (Πt)ξ (TR) Red terms present only in HA version. Modified Euler equation.

• therwise the HANK and the RANK model are equivalent.

HANK versus RANK

Long Run (steady state)

Real interest: lowered by precautionary saving motive R Π = 1 β (peu ϑ Ce −σ +(1 − peu))−1 ≤ 1 β

HANK versus RANK

Business Cycle

Log-linearized Euler Equation: −σ Ct + σβR(1 − peu)Et Ct+1 = Rt − Et Πt+1 Iterate forward:

• Ct = − 1

σ

∞

• k=0

(βR(1 − peu))k( Rt+k − Et Πt+k+1) Reduced sensitivity of consumption to (future) interest rates ⇒ dampening

◮ alleviates the “Forward Guidance Puzzle” (McKay, Nakamura, Steinsson,

2016)

HANK versus RANK

Business Cycle

Log-linearized Euler Equation: −σ Ct + σβR(1 − peu)Et Ct+1 = Rt − Et Πt+1 Iterate forward:

• Ct = − 1

σ

∞

• k=0

(βR(1 − peu))k( Rt+k − Et Πt+k+1) Reduced sensitivity of consumption to (future) interest rates ⇒ dampening

◮ alleviates the “Forward Guidance Puzzle” (McKay, Nakamura, Steinsson,

2016)

HANK versus RANK

Business Cycle

Log-linearized Euler Equation: −σ Ct + σβR(1 − peu)Et Ct+1 = Rt − Et Πt+1 Iterate forward:

• Ct = − 1

σ

∞

• k=0

(βR(1 − peu))k( Rt+k − Et Πt+k+1) Reduced sensitivity of consumption to (future) interest rates ⇒ dampening

◮ alleviates the “Forward Guidance Puzzle” (McKay, Nakamura, Steinsson,

2016)

HA versus RA revisited

Above analysis suggests that incorporating household heterogeneity can importantly change the predictions of the model. Heterogeneity matters! Werning (2016) however argues that this conclusion would be misleading.

HA versus RA revisited

Above analysis suggests that incorporating household heterogeneity can importantly change the predictions of the model. Heterogeneity matters! Werning (2016) however argues that this conclusion would be misleading.

HA versus RA revisited

To see Werning’s point, consider a slightly modified model, in which unemployment benefits are proportional to aggregate income: ϑt = ϑYt. The Euler equation can now be written as: C

−σ

t

= βEt Rt Πt+1 C −σ

t+1

where β = β

• peu (γ(1 − u))−σ + (1 − peu)
• is a modified discount factor.

Log-linearized Euler equation now given by: −σ Ct + σEt Ct+1 = Rt − Et Πt+1 Now observationally equivalent to the representative agent model at the macro level!

HA versus RA revisited

To see Werning’s point, consider a slightly modified model, in which unemployment benefits are proportional to aggregate income: ϑt = ϑYt. The Euler equation can now be written as: C

−σ

t

= βEt Rt Πt+1 C −σ

t+1

where β = β

• peu (γ(1 − u))−σ + (1 − peu)
• is a modified discount factor.

Log-linearized Euler equation now given by: −σ Ct + σEt Ct+1 = Rt − Et Πt+1 Now observationally equivalent to the representative agent model at the macro level!

HA versus RA revisited

To see Werning’s point, consider a slightly modified model, in which unemployment benefits are proportional to aggregate income: ϑt = ϑYt. The Euler equation can now be written as: C

−σ

t

= βEt Rt Πt+1 C −σ

t+1

where β = β

• peu (γ(1 − u))−σ + (1 − peu)
• is a modified discount factor.

Log-linearized Euler equation now given by: −σ Ct + σEt Ct+1 = Rt − Et Πt+1 Now observationally equivalent to the representative agent model at the macro level!

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

HA versus RA revisited

Compared two HANK models: Model 1: constant unemployment benefit

◮ Wages, are procyclical ◮ larger income fall upon job loss during a boom ◮ procyclical unemployment risk ◮ stronger precautionary saving motive during booms ⇒ lower aggregate demand ⋆ dampening relative to RANK

Model 2: pro-cyclical unemployment benefit

◮ Benefits move with wages ◮ time invariant income fall upon job loss during a boom ⇒ constant

unemployment risk

◮ time invariant precautionary saving motive ⋆ neither amplification nor dampening

Taking stock

Cyclicality of risk is key. Dampening when risk is procyclical (Model 1). Quantitative importance?

Taking stock

Cyclicality of risk is key. Dampening when risk is procyclical (Model 1). Quantitative importance?

Determinacy (Taylor Principle)

determinacy region

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Taylor rule coefficient ( )

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

EE discount

determinacy indeterminacy

Productivity shock

10 20 30

quarter

0.2 0.4 0.6 0.8 1

% Output (Y)

10 20 30

quarter

• 0.2
• 0.15
• 0.1
• 0.05

% Inflation (PI)

10 20 30

quarter

0.5 1 1.5

% TFP (A)

ZL-HANK RANK

Monetary policy shock (tightening)

10 20 30

quarter

• 1.5
• 1
• 0.5

% Output (Y)

10 20 30

quarter

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

% Inflation (PI)

10 20 30

quarter

0.5 1 1.5

% policy shock (zR)

ZL-HANK RANK

HA versus RA

So far found either no difference between RA and HA model, or some dampening. Three caveats:

1

both models abstract from redistributional effects

1

empirical evidence suggests that income risk is substantially counter-cyclical

1

both models have a trivial wealth distribution

HA versus RA

So far found either no difference between RA and HA model, or some dampening. Three caveats:

1

both models abstract from redistributional effects

1

empirical evidence suggests that income risk is substantially counter-cyclical

1

both models have a trivial wealth distribution

HA versus RA

So far found either no difference between RA and HA model, or some dampening. Three caveats:

1

both models abstract from redistributional effects

1

empirical evidence suggests that income risk is substantially counter-cyclical

1

both models have a trivial wealth distribution

HA versus RA

So far found either no difference between RA and HA model, or some dampening. Three caveats:

1

both models abstract from redistributional effects

1

empirical evidence suggests that income risk is substantially counter-cyclical

1

both models have a trivial wealth distribution

• 1. Redistribution experiment
• ne-time, unexpected tax on employed, equal to 10% of s.s. output

give all proceeds to unemployed

• 1. Redistribution experiment
• ne-time, unexpected tax on employed, equal to 10% of s.s. output

give all proceeds to unemployed

• 1. Redistribution experiment

10 20 30

quarter

0.05 0.1

% Output (Y)

10 20 30

quarter

0.05 0.1

% Inflation (PI)

10 20 30

quarter

0.05 0.1

% of s.s. output Tax on employed (T)

ZL-HANK RANK

Intuition: unemployed are borrowing constrained –> high Marginal Propensity to Consume (MPC) employed are unconstrained –> low MPC distribution towards unemployed increases aggregate demand

• 1. Redistribution experiment

10 20 30

quarter

0.05 0.1

% Output (Y)

10 20 30

quarter

0.05 0.1

% Inflation (PI)

10 20 30

quarter

0.05 0.1

% of s.s. output Tax on employed (T)

ZL-HANK RANK

Intuition: unemployed are borrowing constrained –> high Marginal Propensity to Consume (MPC) employed are unconstrained –> low MPC distribution towards unemployed increases aggregate demand

• 1. Redistribution experiment

10 20 30

quarter

0.05 0.1

% Output (Y)

10 20 30

quarter

0.05 0.1

% Inflation (PI)

10 20 30

quarter

0.05 0.1

% of s.s. output Tax on employed (T)

ZL-HANK RANK

Intuition: unemployed are borrowing constrained –> high Marginal Propensity to Consume (MPC) employed are unconstrained –> low MPC distribution towards unemployed increases aggregate demand

• 1. Redistribution experiment

10 20 30

quarter

0.05 0.1

% Output (Y)

10 20 30

quarter

0.05 0.1

% Inflation (PI)

10 20 30

quarter

0.05 0.1

% of s.s. output Tax on employed (T)

ZL-HANK RANK

Intuition: unemployed are borrowing constrained –> high Marginal Propensity to Consume (MPC) employed are unconstrained –> low MPC distribution towards unemployed increases aggregate demand

• 2. Endogenous countercyclical risk

So far, income risk was either constant or pro-cyclical. Empirical evidence strongly suggest that income risk is countercyclical. Ravn and Sterk (2016): integrate search and matching frictions in the labour market

• 2. Endogenous countercyclical risk

So far, income risk was either constant or pro-cyclical. Empirical evidence strongly suggest that income risk is countercyclical. Ravn and Sterk (2016): integrate search and matching frictions in the labour market

• 2. Endogenous countercyclical risk

So far, income risk was either constant or pro-cyclical. Empirical evidence strongly suggest that income risk is countercyclical. Ravn and Sterk (2016): integrate search and matching frictions in the labour market

• 2. Endogenous countercyclical risk

Modified Euler equation: −σ Ce,t + σβR(1 − ¯ peu)Et Ce,t+1 − βR ϑ C −σ − 1

• peu

peu

t

= Rt − Et Πt+1

• 2. Endogenous countercyclical risk

Amplification channel: productivity ⇑ aggregate output and income ⇓, inflation ⇓ job loss probability ⇓ precautionary saving motive ⇓ aggregate demand ⇑, inflation ⇑ aggregate output and income ⇑ job loss probability ⇓ etc.

• 2. Endogenous countercyclical risk

Amplification channel: productivity ⇑ aggregate output and income ⇓, inflation ⇓ job loss probability ⇓ precautionary saving motive ⇓ aggregate demand ⇑, inflation ⇑ aggregate output and income ⇑ job loss probability ⇓ etc.

• 2. Endogenous countercyclical risk

Amplification channel: productivity ⇑ aggregate output and income ⇓, inflation ⇓ job loss probability ⇓ precautionary saving motive ⇓ aggregate demand ⇑, inflation ⇑ aggregate output and income ⇑ job loss probability ⇓ etc.

• 2. Endogenous countercyclical risk

Amplification channel: productivity ⇑ aggregate output and income ⇓, inflation ⇓ job loss probability ⇓ precautionary saving motive ⇓ aggregate demand ⇑, inflation ⇑ aggregate output and income ⇑ job loss probability ⇓ etc.

• 2. Endogenous countercyclical risk

Amplification channel: productivity ⇑ aggregate output and income ⇓, inflation ⇓ job loss probability ⇓ precautionary saving motive ⇓ aggregate demand ⇑, inflation ⇑ aggregate output and income ⇑ job loss probability ⇓ etc.

• 2. Endogenous countercyclical risk

Amplification channel: productivity ⇑ aggregate output and income ⇓, inflation ⇓ job loss probability ⇓ precautionary saving motive ⇓ aggregate demand ⇑, inflation ⇑ aggregate output and income ⇑ job loss probability ⇓ etc.

• 2. Endogenous countercyclical risk

Consequences of amplification channel (Ravn & Sterk, 2016): breakdown Taylor Principle increased business cycle volatility long run “unemployment trap” “endogenous demand shock”, hitting the Zero Lower Bound

• 3. Distributional Dynamics

Finally, consider the baseline model but with B > 0: positive liquidity.

◮ re-calibrate to target the same steady-state interest rate

Wealth distribution now moves around over the business cycle. Does this matter quantitatively?

• 3. Distributional Dynamics

Finally, consider the baseline model but with B > 0: positive liquidity.

◮ re-calibrate to target the same steady-state interest rate

Wealth distribution now moves around over the business cycle. Does this matter quantitatively?

• 3. Distributional Dynamics

Finally, consider the baseline model but with B > 0: positive liquidity.

◮ re-calibrate to target the same steady-state interest rate

Wealth distribution now moves around over the business cycle. Does this matter quantitatively?

Productivity shock

5 10 15

quarter

0.2 0.4 0.6 0.8 1

% Output (Y)

5 10 15

quarter

• 0.2
• 0.15
• 0.1
• 0.05

% Inflation (PI)

5 10 15

quarter

0.5 1 1.5

% TFP (A)

B=0 B=0.02 B=0.04 B=0.06 B=0.08 B=0.10 B=0.12 B=0.14

Monetary Policy shock

5 10 15

quarter

• 1.5
• 1
• 0.5

% Output (Y)

5 10 15

quarter

• 0.4
• 0.3
• 0.2
• 0.1

% Inflation (PI)

5 10 15

quarter

0.5 1 1.5

% policy shock (zR)

B=0 B=0.02 B=0.04 B=0.06 B=0.08 B=0.10 B=0.12 B=0.14

Conclusion

Rapidly growing literature on incorporating heterogeneity in models of the business

• cycle. Still in exploratory phase as to which aspects of heterogeneity matter.

◮ firms, housing, mortgages, banks, etc..

Important channels not present in RA models:

◮ countercyclical idiosyncratic risk / precautionary saving ◮ redistributional effects

Conclusion

Rapidly growing literature on incorporating heterogeneity in models of the business

• cycle. Still in exploratory phase as to which aspects of heterogeneity matter.

◮ firms, housing, mortgages, banks, etc..

Important channels not present in RA models:

◮ countercyclical idiosyncratic risk / precautionary saving ◮ redistributional effects