Balance Sheet Recessions Zhen Huo and Jos e-V ctor R os-Rull - - PowerPoint PPT Presentation

, Introduction Baseline Model Housing Model Appendix

Balance Sheet Recessions

Zhen Huo and Jos´ e-V´ ıctor R´ ıos-Rull

University of Minnesota, Federal Reserve Bank of Minneapolis, CAERP , CEPR, NBER

Conference on Money, Credit, and Financial Frictions

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Can households’ financial distress generate a recession?

In Standard Models it is Difficult The economy has a lot of wealth. Only the poor would be really affected: They want to work harder. An expansion. This project

1

We build a model with goods market frictions, where financial distress leads to a recession.

2

Crucially, the attempt to save reduces productivity due to real frictions.

3

We provide a theory of price dispersion during the onset of the recession.

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The logic

When hit by adverse financial shocks, agents tend to increase saving by cutting consumption expenditures. Goods market frictions translate lower consumption expenditures into

• utput loss, despite the decline of prices.

There is a realignment of consumption patterns: large drops of consumption for the poorest but modest increase of consumption for the richest. When we explicitly add housing that can be used as collateral, increased financial frictions greatly amplifies the magnitude of the recession.

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The ingredients

Heterogeneous agents model (How else can there be financial frictions?)

There are very rich, rich, poor, very poor, and borrowers; lucky and unlucky: a modern economy’s earnings and wealth distribution. Price dispersion: the rich are not into hassles (they pay higher prices).

Storage economy: fixed return to savings. In addition to goods (that can be saved) there are services (that cannot be saved). Goods (services, really) market frictions a la Bai, Rios-Rull and Storesletten

(2011) with a touch of Lagos and Wright (2005)

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The contribution

We show that

1

Financial distress can lead to a recession even when agents own a lot

• f wealth.

2

Goods market frictions are crucial in generating the recession.

3

No nominal rigidities are required.

4

Price dispersion is counter-cyclical.

5

With housing, the effects of financial distress are more pronounced.

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The Model

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Environment

Many agents that live forever and have idyosincratic shocks to

• endowments. Two goods per period:

Numeraire goods

Used for consumption and storage. As if traded in a centralized market.

Services

Used only for consumption. Traded in decentralized markets and subject to search frictions.

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Preference

Agents’ period utility function is u(c, s, d). Agents value numeraire goods consumption c and services s. To obtain services, agents have to exert search efforts d s = dΨb(q). Ψb(q): probability of a shopper finding services.

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Competitive search in services markets

Markets are indexed by price p and market tightness q = T

D.

In market (p, q)

Active markets, sellers have guaranteed revenue pΨs(q) ≥ ζ equilibrium determined object ζ. Buyers face a trade-off between p and Ψb(q) when choosing markets:

Rich agents go to high p, high q markets. Poor agents go to low p, low q markets.

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Endowments

An agent receives ys units of active locations capable of producing services.

When a location is found by a buyer, 1 unit of services is produced. When a location is not found by a buyer, nothing is produced.

An agent receives yc units of numeraire goods that can be consumed, sold, or stored/loaned. y = {yc, ys} follows a Markov process Πy,y′. Households’ asset position is a. There is an ad-hoc borrowing limit a.

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Agents’ recursive problem

V (y, a) = max

a′,c,s, d,p,q

u(c, s, d) + β

• y′

Πy,y′ V (y′, a′), subject to p s + c + a′ ≥ (1 + r) a + ζ ys + yc, s= d Ψb(q), ζ≤ p Ψs(q), a′ ≥ a. Note that agents choose consumption and savings as well as which market (p, q) to go to.

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Macroeconomic Aggregates (what NIPA measures)?

Aggregate active locations: Ts =

• ysdx(y, a)

Aggregate numeraire goods endowment: Yc =

• ycdx(y, a)

Aggregate savings: A =

• a dx(y, a)

Aggregate output (GDP): Y = rA + Yc + Ts pi Ψf(qi) di ≈ rA + Yc + p M(D, Ts) Total output is increasing in aggregate search effort D.

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Labor and Productivity

We impute labor to locations and then we can separate output changes due to labor and to productivity. Labor

To maintain a location, ǫ units of labor is required. When matched with a buyer , additional 1 − ǫ units of labor is required to produce services. Aggregate labor is N = ǫ Ts + (1 − ǫ) Ts Ψf(qi) di

Productivity A = Y N

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Analysis

We build an empirically informed quantitative economy. We report its properties in the steady state. and its properties in the aftermath of a financial shock.

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Functional forms: So consumption and productivity move together

Preferences u(c, s, d) = 1 1 − σ

• cA − ξd

d1+γ 1 + γ 1−σ cA =

• (1 − ω)c

η−1 η

+ ωs

η−1 η

• η

η−1

Matching M(D, T) = DT (Dµ + T µ)

1 µ

Ψd(q) = (1 + q−µ)− 1

µ

Ψf(q) = (1 + qµ)− 1

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Wealth Lorenz curve

Parameter

Four types of agents: poor, normal, rich and super rich.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Model Data Huo & R´ ıos-Rull Balance Sheet Recessions 16/34

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Steady state properties

Rich agents go to expensive markets with short waiting lines. Poor agents go to cheap markets with long waiting lines.

Price Prob of finding services

2 4 6 8 10 12 14 16 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 2 4 6 8 10 12 14 16 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54

Wealth Wealth

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A Shock to the Borrowing Constraint

The borrowing constraint is tightened unexpectedly but gradually. Agents cannot borrow any more in the new steady state.

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Transition

The borrowing constraint changes gradually.

1 2 3 4 5 6 7 8 9 10 −0.18 −0.16 −0.14 −0.12 −0.1 −0.08 −0.06 −0.04 −0.02

Borrowing limit, a

Otherwise, some agents may have to default on their debts.

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The Economy After the Shock

We now look at the evolution of aggregate variables after the financial shock. It requires to solve for the equilibrium values of ζt along the transition.

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Transition: aggregate

5 10 15 20 25 30 35 40 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.1 5 10 15 20 25 30 35 40 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.1

Output Services

5 10 15 20 25 30 35 40 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0.05 5 10 15 20 25 30 35 40 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0.05 0.1

Labor Productivity

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Transition: aggregate

5 10 15 20 25 30 35 40 −5 −4.5 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 5 10 15 20 25 30 35 40 −0.5 0.5 1 1.5 2 2.5 3 3.5 4

Average price Price dispersion

5 10 15 20 25 30 35 40 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 5 10 15 20 25 30 35 40 −2.5 −2 −1.5 −1 −0.5

Wealth Numeraire consumption

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Transition: cross-section

5 10 15 20 25 30 −12 −10 −8 −6 −4 −2 2 Type 1 Type 2 Type 3 Type 4 5 10 15 20 25 30 −14 −12 −10 −8 −6 −4 −2 2 Type 1 Type 2 Type 3 Type 4

Goods finding probability Search efforts

5 10 15 20 25 30 −10 −8 −6 −4 −2 2 Type 1 Type 2 Type 3 Type 4 5 10 15 20 25 30 −8 −7 −6 −5 −4 −3 −2 −1 Type 1 Type 2 Type 3 Type 4

Services Numeraire consumption

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Properties of the Recession

Total Services decline. Aggregate savings increases. Realignment of consumption

Poor agents reduce both both types of consumption and switch to worse markets (with longer lines). But the richest agents increase consumption of services and switch to better markets (with shorter lines).

Average price of services declines, but price dispersion increases.

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Why the Recession is small

Insufficient people in real trouble (borrowers). Those in trouble do not matter much (they are poor). A Larger recession requires more people in trouble and the trouble to be larger: Housing

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An Economy with housing

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Housing sector

Decreasing returns to scale in housing construction. A reduction in demand for housing cuts construction Reduces the price of existing houses: Capital loses.

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Agents’ problem

Utility function

V (y, a) = max

a′,c,s,d, h,p,q,b

u(c, s, d, h) + β

• s′

Πs,s′ V (y′, a′), subject to p s + c + ph h + b ≥ a + ζys + yc + π, s = d Ψb(q), ζ ≤ p Ψs(q), a′= p′

h h (1 − δh) + (1 + r)b,

b≥ −λ ph h.

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A Shock to the Collateral Constraint

The collateral constraint is tightened unexpectedly and gradually. The size of the shock in the housing economy has to be comparable with the shock to the baseline economy:

Same consumption reduction of poorest quintile.

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Transition: aggregate

5 10 15 20 25 30 35 40 −1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0.2 0.4 Baseline model Housing model 5 10 15 20 25 30 35 40 −3 −2.5 −2 −1.5 −1 −0.5 0.5 1 Baseline model Housing model

Output Wealth

5 10 15 20 25 30 35 40 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.1 Baseline model Housing model 5 10 15 20 25 30 35 40 −0.8 −0.6 −0.4 −0.2 0.2 0.4 0.6 Baseline model Housing model

Labor Productivity

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Transition: aggregate

5 10 15 20 25 30 35 40 −12 −10 −8 −6 −4 −2 2 Baseline model Housing model 5 10 15 20 25 30 35 40 −1 1 2 3 4 5 6 Baseline model Housing model

Average price Price dispersion

5 10 15 20 25 30 35 40 −2 −1.5 −1 −0.5 0.5 Baseline model Housing model 5 10 15 20 25 30 35 40 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 Baseline model Housing model

Service Numeraire consumption

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Transition: aggregate

Cross Section

5 10 15 20 25 30 35 40 −8 −7 −6 −5 −4 −3 −2 −1 5 10 15 20 25 30 35 40 −18 −16 −14 −12 −10 −8 −6 −4 −2

Housing price Housing investment

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Properties of the Recession

The magnitude of the recession is much larger. Aggregate wealth declines initially: capital loss. Larger fraction of agents are affected: more agents are leveraged.

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Conclusion

1

In standard models, financial distress generates an expansion.

2

We build a model with goods market frictions, where financial distress can generate a recession.

3

Our model provides a framework to understand price dispersion in business cycles.

4

When housing is added, the magnitude of the recession is much larger.

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Numerical example: parameter

Parameter Value Risk aversion, σ 2.0 Return to storage (anual), r 4% Elasticity of substitution between tradables and nontradables, η 0.83 Frisch Elasticity of Substitution of Search Effort 1/γ 0.60 Fixed labor to keep a location open, ǫ 0.59

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Numerical example: parameter

Parameter Value Target Value Model β 0.96 Wealth to output ratio 4.00 4.00 a 0.12 Fraction of negative wealth 0.15 0.15 µ 2.98 Services occupation ratio 0.81 0.81 ξd 0.04 St.d of price dispersion 0.10 0.09 ω 0.89 Services to output ratio 0.67 0.67 α 0.20 Numeraire endowments to output 0.15 0.16 ys,4 7.385 Wealth held by top 10% 0.70 0.70 ys,1 0.155 Total number of locations, Ts 1.00 1.00 Π1,4 0.001 Income Gini index 0.64 0.64 Π4,1 0.007 Wealth Gini index 0.82 0.82 Π1,1 0.965 Persistence, ρs 0.91 0.91 Π2,2 0.976 St.d of innovation, σs 0.20 0.20

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Numerical example: parameter

Return

Transition matrix ǫ1 ǫ2 ǫ3 ǫ4 ǫ1 0.965 0.033 0.000 0.001 ǫ2 0.018 0.976 0.018 0.001 ǫ3 0.000 0.033 0.965 0.001 ǫ4 0.007 0.007 0.007 0.979 Skill Value 0.155 0.388 0.872 7.385

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Utility function

Return

Separable between consumption and housing. As households become richer, they do not want to hold many houses. u(c, s, d, h) =

• 1

1−σ

• cA − ξd d1+γ

1+γ

1−σ +

ξh 1−σ1

h h1−σ1 h,

if h < h

1 1−σ

• cA − ξd d1+γ

1+γ

1−σ +

ξh 1−σ2

h (h + h)1−σ2 h ,

if h ≥ h

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Calibration

Parameter Value Risk aversion, σ 2.00 Curvature for Low Level of Housing, σ1

h

2.00 Curvature for High Level of Housing, σ2

h

10.00 Elasticity of substitution bw tradables and nontradables, η 0.83 Return to storage, r 4% Frisch Elasticity of Substitution of Search Effort 1/γ 0.60 Fixed labor to keep a location open, ǫ 0.59 Collateral requirement, λ 0.85 Elasticity of housing price w.r.t investment, ϕ 0.30

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Housing parameters:

Return

Parameter Value Target Value Model β 0.96 Wealth to output ratio 4.00 4.20 ξh 0.64 Housing value to output ratio 1.50 1.50 µ 2.98 Average occupation ratio 0.81 0.81 ξd 0.04 St.d of price dispersion 0.10 0.09 α 0.18 Numeraire endowments to output 0.15 0.14 ω 0.89 Services to output ratio 0.67 0.70

• h

1.85 Housing held by top 10% 0.25 0.24 h

• 0.71

uh is continuous at h — — δh 0.006 Investment to output ratio 0.04 0.04 zh 0.005 Housing stock 1.00 1.00

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Transition: cross-section

Return

5 10 15 20 25 30 −6 −5 −4 −3 −2 −1 1 Type 1 Type 2 Type 3 Type 4 5 10 15 20 25 30 −10 −8 −6 −4 −2 2 Type 1 Type 2 Type 3 Type 4

Goods finding probability Search efforts

5 10 15 20 25 30 −10 −8 −6 −4 −2 2 4 Type 1 Type 2 Type 3 Type 4 5 10 15 20 25 30 −16 −14 −12 −10 −8 −6 −4 −2 2 Type 1 Type 2 Type 3 Type 4

Services Numeraire goods

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Transition: cross-section

5 10 15 20 25 30 −15 −10 −5 5 10 15 20 Type 1 Type 2 Type 3 Type 4 5 10 15 20 25 30 −40 −30 −20 −10 10 20 30 40 Type 1 Type 2 Type 3 Type 4

Housing Debt

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