WEALTH AND VOLATILITY

Jonathan Heathcote and Fabrizio PerriMinneapolis Fed

Aggregate Demand, the Labor Market and MacroeconomicPolicy

University of Cambridge, September 2014

Sources of Business Cycles

• Great Recession brought back old idea: business cyclesdriven by self-fulfilling waves of optimism/pessimism

• Problem: why now? why not after September 11?• Our idea: extent to which these waves can generate

fluctuations depends on the level of household wealth

• Decline in asset prices which occurred prior to the crisisleft many economies fragile and susceptible to aconfidence-driven recession

Sources of Business Cycles

• Great Recession brought back old idea: business cyclesdriven by self-fulfilling waves of optimism/pessimism

• Problem: why now? why not after September 11?

• Our idea: extent to which these waves can generatefluctuations depends on the level of household wealth

• Decline in asset prices which occurred prior to the crisisleft many economies fragile and susceptible to aconfidence-driven recession

Sources of Business Cycles

• Great Recession brought back old idea: business cyclesdriven by self-fulfilling waves of optimism/pessimism

• Problem: why now? why not after September 11?• Our idea: extent to which these waves can generate

fluctuations depends on the level of household wealth

• Decline in asset prices which occurred prior to the crisisleft many economies fragile and susceptible to aconfidence-driven recession

Sunspot-driven fluctuations

• Rise in expected unemployment→ consumers reduce demand→ firms reduce hiring→ higher unemployment

• For a wave of self-fulfilling pessimism to get started needhigh sensitivity of demand to expected unemployment

• High wealth:→ demand less sensitive to expectations→ no or small sunspot-driven fluctuations

• Low wealth:→ demand more sensitive to expectations→ sunspot-driven fluctuations

Outline

1. Some suggestive macro evidence2. A stylized model of confidence driven recessions3. Micro evidence on the mechanism4. Policy

Wealth & GDP Volatility

.004

.006

.008

.010

.012

.014

.016

-.08

-.04

.00

.04

.08

.12

60 65 70 75 80 85 90 95 00 05 10

Note: Standard deviation of GDP growth are computed over 40 quarters rolling windows.Observations for net worth are average over the same windows

Household N

et Worth (%

devs from trend)

Sta

ndar

d D

evia

tion

of G

DP

Gro

wth

Wealth

Volatility

A Stylized Model

• Related to Farmer 2010, Chamley 2011, Guerrieri andLorenzoni 2009

• Non-durable consumption good• Produced by competitive firms using labor

c + g = y = 1− u

where u is mass of workers unemployed• Durable housing h, in fixed supply with relative price p• Each representative household contains a continuum of

workers

A Stylized Model

• Related to Farmer 2010, Chamley 2011, Guerrieri andLorenzoni 2009

• Non-durable consumption good• Produced by competitive firms using labor

c + g = y = 1− u

where u is mass of workers unemployed• Durable housing h, in fixed supply with relative price p• Each representative household contains a continuum of

workers

Household Problem

maxcw

t ,cut

E∞∑

t=0

βt [(1− ut) log cwt + ut log cu

t + φht−1]

s.t.

cut ≤ ptht−1

cwt ≤ ptht−1 + wt

[1− ut] cwt + utcu

t + pt [ht − ht−1] ≤ [1− ut] [wt]

φ : Preference weight on housingut : Fraction of unemployedNote: no disutility from work, so unemployment inefficient

Timing and labor markets1. Households co-ordinate expectations on current

unemployment, distributions of future unemployment rates

2. Representative household sends out workers withcontingent consumption orders (cu

t , cwt ), assets ptht−1, and

reservation wage w∗t

3. Firms take orders as given and search for workers to fillthem in decentralized labor markets

4. Firms and workers meet randomly, firms decide whether ornot to hire at w∗t

5. Firms pay wages, all agents consume

6. Household regroups, net resources determine ht.

Wage Determination

Optimal firm strategy: hire worker iff aggregate orderct = (1− ut)cw

t + utcut not yet filled and w∗t ≤ 1

Optimal household strategy: set w∗t = 1

Frictions and Features

1. Labor market friction: No role for labor supply indetermining allocations⇒ equilibrium unemployment,multiplicity

• Workers cannot affect probability of meeting a firm byasking a lower wage, and when meet ask for reservationwage (alternatively downward wage rigidity)

2. Uninsurable unemployment risk: Can’t transfer resourcesfrom employed to unemployed⇒ precautionary motive,low consumption demand with low wealth

Frictions and Features

1. Labor market friction: No role for labor supply indetermining allocations⇒ equilibrium unemployment,multiplicity

• Workers cannot affect probability of meeting a firm byasking a lower wage, and when meet ask for reservationwage (alternatively downward wage rigidity)

2. Uninsurable unemployment risk: Can’t transfer resourcesfrom employed to unemployed⇒ precautionary motive,low consumption demand with low wealth

First Order Conditions

pt

cwt

= βE

[pt+1

cwt+1

(1 + ut+1

max{

cwt+1 − cu

t+1, 0}

cut+1

)]+ βφ

cut = ptht−1

• Unemployment risk ' tax on consumption, which dependson expected unemployment

• Basis for self-fulfilling crisis: high expected unemployment→ high tax→ low consumption→ high realizedunemployment

• If low pt -> low cut , strong sensitivity of consumption (and

thus u) to expected unemployment

Asset Prices

• Measure zero “marginal investor” same preferences asRA, faces no unemployment risk (c = c̄ = 1)

• In equilibrium no housing trade between the two types

• Marginal investor establishes a floor p for house prices:

pt ≥ p =β

1− βφ

• Price never go below p

Characterizing Equilibria

• Characterize paths for unemployment that satisfy theinter-temporal FOC and the condition ct = 1− ut

• Unique Steady State• Multiple Steady States• Equilibria with unemployment dynamics• Sunspots

Steady state asset price decomposition

u

pFundamental part φβ

1−β (1− u)

Equilibrium p

Liquidity part ' cw − cu

p

Unique full employment steady state

If φ ≥ φ̄ = f (β) then:

Only steady state is p = p and u = 0

Logic:• when φ high, p high (because of marginal investor)⇒ cu

high⇒ small liquidity component of p,• Suppose consumers expect high u• Since cu high, no much increase in saving, rather sell

house -> Inconsistent with pt ≥ p• Unique equilibrium• Pinning down p pins down u

Unique full employment equilibrium

u

pFundamental p = φβ

1−β c = φβ1−β (1− u)

FOC p

p

Multiple Steady States

If φ < φ̄ then

1. There is (still) a steady state with p = p and u = 0

2. There is another steady state with p = p and u > 0

3. There are additional steady states with p > p and u > 0.

Multiple Steady States

u

pFundamental p φβ

1−β (1− u)

FOC p

p

Multiple Steady States

Logic:• When φ low, p low⇒ cu low, high liquidity value of housing

if u > 0• Equilibrium 1: (u = 0): price = fundamental, no liquidity

value of housing• Equilibrium 2: (u > 0): same price with lower fundamental,

but higher liquidity

Unemployment dynamics with fixed prices

ut

ut − ut−1

Time

ut

Intuition for Dynamics

• Consider the high unemployment phase• Incentive to accumulate (because wealth helps reduce

unemployment risk): low consumption/output• Incentive to consume (because expected recovery): high

consumption/output• Two incentives balance out as unemployment declines⇒

stable demand for savings⇒ stable prices

The Great Recession?

0

2

4

6

8

10

12

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

House Price (left axis)

Unemployment Rate (right axis)

4

5

6

7

8

9

10

0.0

0.2

0.4

0.6

0.8

1.0

House Price (left axis, real minus 2% trend)

Unemployment Rate (right axis)

Model Data

Sunspots

• Characterize Markov equilibria switching from high to lowunemployment, with a fixed probability 1− λ and a fixedprice.

• Results:• For these equilibria to exist λ has to be large enough• Equilibria with higher prices are characterized by low

volatility

Sunspot recessions and persistence

0

0.05

0.1

0.15

0.2

0.25

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Unem

ploym

ent R

ate in R

ecessio

n State

λ

Understanding Persistence

• It is only because agents expect high ut+1 that they cut ct

• Logic extends forwards: only expect high ut+1 (low ct+1) ifalso high expected ut+2

• Permanent income intuition: Only persistently highexpected unemployment consistent with low optimalcurrent consumption

• The longer things are expected to stay bad, the sharper isthe fall in demand and the larger the recession on impact

• Consistent with data from Michigan Survey of Consumers

More Wealth⇒ Less Volatility

‐0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85

Une

mploymen

t Rates

Asset Price

Recession State (Red)Solid line: λ=0.99Dashed line: λ=0.98

Boom State (Blue)

Review: Asset Prices and Macro Volatility

• High asset prices⇒ weak precautionary motive⇒ uniquefull employment equilibrium

• Lower asset prices⇒ strong precautionary motive⇒range of equilibrium unemployment rates larger the loweris the asset price

• Volatility of unemployment is larger for low asset pricesbecause low asset prices make consumption demandmore sensitive to expectation

Why is the recovery slow?

• Large demand driven recession is driven by a large fall inconsumption demand

• Large fall in consumption demand only happens ifpersistent fall in income is expected (PIH logic)

• Large fall <-> Slow recovery• Consistent with data from Michigan Consumers

Expectation, showing slow expected recovery in 2008

Micro Evidence for the Mechanism

• Key mechanism: Elasticity of demand wrt unemploymentrisk is larger when wealth is low

• Natural test: Did wealth-poor households reduceconsumption more than rich households as unemploymentrose during the Great Recession?

Differential Sensitivity in the Model

0.7

0.8

0.9

1

1.1

1.2

u = 5%

0.4

0.5

0.6

0 1 2 3 4 5 6Housing

u = 15%

Consumer Expenditure Survey

• Households aged 25-60 with 4 quarters of consumptiondata

• Sort households by wealth (net financial wealth plus homeequity) relative to consumption

• Compare consumption growth of top and bottom halves ofwealth distribution

CE Survey versus NIPA

0.85

0.87

0.89

0.91

0.93

0.95

0.97

0.99

1.01

1.03

1.05

 2005‐I

 2005‐II

 2005‐III

 2005‐IV

 2006‐I

 2006‐II

 2006‐III

 2006‐IV

 2007‐I

 2007‐II

 2007‐III

 2007‐IV

 2008‐I

 2008‐II

 2008‐III

 2008‐IV

 2009‐I

 2009‐II

 2009‐III

 2009‐IV

 2010‐I

 2010‐II

 2010‐III

 2010‐IV

 2011‐I

2005q1=1

Aggregate real consumption expenditures per capita

NIPA

CE

Characteristics of Rich versus Poor

Wealth Group0-50 50-100

Sample size 8,864 8,873Average age of head 41.4 46.9Heads with college 25.7% 40.5%Average household size 2.9 2.8Net wealth p.c. (2005$)

Mean 1,498 119,796Median 238 63,162

Mean after-tax income p.c. (2005$) 22,117 32,811Mean consumption p.c. (2005$) 9,353 11,252

Consumption Growth: Rich versus Poor

0.1

e)

0.05

annu

al ra

te

0

nditu

res (a

‐0.05

tion expe

n

Wealth poor

‐0.1

consum

pt Wealth poor

Wealth rich 

‐0.15

5q4

6q1

6q2

6q3

6q4

7q1

7q2

7q3

7q4

8q1

8q2

8q3

8q4

9q1

9q2

9q3

9q4

0q1

0q2

0q3

0q4

1q1

Growth in

 

‐0.2

2005

2006

2006

2006

2006

2007

2007

2007

2007

2008

2008

2008

2008

2009

2009

2009

2009

2010

2010

2010

2010

2011

G

Consumption vs. Income Growth

Wealth Group0-50 50-100

Mean growth income p.c. -0.3% -1.0%Mean growth cons. p.c. -5.6% -3.1%

Consumption Rates: Rich versus Poor

0.02

0

0.01

‐0.01

ption rate

‐0.02

n consum

p

0 04

‐0.03

Change in

Wealth poor

‐0.05

‐0.04Wealth rich 

‐0.06 2005

q420

06q1

2006

q220

06q3

2006

q420

07q1

2007

q220

07q3

2007

q420

08q1

2008

q220

08q3

2008

q420

09q1

2009

q220

09q3

2009

q420

10q1

2010

q220

10q3

2010

q420

11q1

Evidence from PSID

Low Wealth High Wealth2006 2006-2008 2006 2006-2008

Disposable Income 36600 +15% 73600 +6%Consumption 24800 -13% 33600 -2%Consumption Ratio 68% -16% 46% -3%

2008 2008-2010 2008 2008-2010Disposable Income 41200 +2% 77800 -2%Consumption 22600 +3% 31600 +10%Consumption Ratio 55% +1% 41% +5%

Micro Evidence: summary

• Low wealth households reduce consumption more duringrecession, despite facing similar increase inunemployment/income risk

Policy 1: Tax and Spend

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24

0.66

0.68

0.70

0.72

0.74

0.76

0.78

0.80

0.82

0.84

u

p

G=0

G=0.1

Figure 1:

1

Policy 1: Review

• Reduces elasticity of aggregate demand to expectations

• Also reduces asset values (induces more precautionarysaving)

• Can narrow/expand range of equilibrium unemployment

• Welfare implications depend on utility from G• Not necessarily effective!

Policy 2: Unemployment benefit b financed byproportional tax τ on earnings

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24

0.66

0.68

0.70

0.72

0.74

0.76

0.78

0.80

0.82

0.84

u

p

b=0

b=0.1

Figure 1:

1

Policy 2: Review

• Policy reduces precautionary motive⇒ shrinks range ofpossible unemployment rates

• Policy reduces asset prices but..• Unique full employment equilibrium if b sufficiently large

Conclusions

• Model in which macroeconomic stability threatened by(exogenously) low asset values

• Great Recession: Decline in home values left economyvulnerable to wave of pessimism

• Macro evidence of a link between level of wealth andaggregate volatility

• Micro evidence that low wealth households reducedconsumption most sharply

• Can evaluate effectiveness of policies geared towardstabilization of these fluctuations

Household net worth in the long run

-.2

-.1

.0

.1

.2

.3

.4

9

10

11

12

13

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Log of Real Household Net Worth Trend (3.2%) Deviations from Trend