WEALTH AND VOLATILITY
Jonathan Heathcote
Minneapolis Fed
Fabrizio Perri
University of Minnesota and Minneapolis Fed

Canon Institute for Global Studies, May 2012

Sources of Business Cycles• Many feature of Great Recession (Little productivity

change, international dimension) brought back old idea:
business cycles can be driven by self-fulfilling waves ofoptimism or pessimism

Sources of Business Cycles• Many feature of Great Recession (Little productivity

change, international dimension) brought back old idea:
business cycles can be driven by self-fulfilling waves ofoptimism or pessimism• Problem: why now? why not 20 years ago?

Sources of Business Cycles• Many feature of Great Recession (Little productivity

change, international dimension) brought back old idea:
business cycles can be driven by self-fulfilling waves ofoptimism or pessimism• Problem: why now? why not 20 years ago?
• Our idea: extent to which these waves can generate

fluctuations depends on the level of household wealthand/or financial frictions• We will argue that decline in asset prices/increase infinancial frictions left US economy fragile and susceptible
to a confidence-driven recession

Sunspot-driven fluctuations• Rise in expected unemployment→ consumers reduce demand→ firms reduce hiring→ higher unemployment• For a wave of pessimism to be self-fulfilling need highsensitivity of demand to expected unemployment• Sensitivity of demand depends inversely on level ofhousehold wealth• High wealth or cheap credit→ demand less sensitive to expectations→ no sunspot-driven fluctuations• Low wealth and costly credit→ demand more sensitive to expectations→ confidence-driven recessions possible

Outline

1. Some suggestive evidence on the relation between wealthand fluctuations
2. A stylized model of confidence driven recessions
3. Micro evidence on the mechanism
4. Policy: Govt spending and unemployment insurance. The
role of wealth is important in shaping policy.

Household net worth in the long run
131211.4
10.3.29.1.0-.1-.2
1920

1930

1940

1950

1960

Log of Real Household Net Worth1970

1980

Trend (3.2%)

1990

2000

2010

Deviations from Trend

Household net worth in the long run
131211.4
10.3.29.1.0-.1-.2
1920

19301940

1950

1960

Log of Real Household Net Worth1970

1980

Trend (3.2%)

1990

2000

2010

Deviations from Trend• Mian, Rao and Sufi (2012): similar evidence for county

cross section

Wealth & GDP Volatility.08
WealthStandard Deviation of GDP Growth.04
.00
.016
-.04

.014

-.08

.012.010

Volatility

.008
.006
.004
60

65

70

75

80

85

90

9500

05

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

10Household Net Worth (% devs from trend).12Stylized Model (related to Farmer 2010, Chamley
2011, Guerrieri and Lorenzoni 2009)• Non-durable consumption good
• Used for consumption or government spending• Produced by competitive firms using labor with a linear

technologyc+g=y=nwhere n is mass of workers employed• Durable housing h, in fixed supply with relative price p• Each representative household contains continuum ofpotential workers

Timing
1. Households co-ordinate expectations on current
unemployment, distributions of future unemployment rates
2. Representative household sends out workers with
consumption order ct , assets pt ht , reservation wage w∗t
3. Representative firm randomly meets potential workers
sequentially, decides whether to hire them
4. Firms pay wages wt = w∗t , workers pay for consumption must borrow if unemployed and ct > pt ht − d
5. Household regroups, net resources determine ht+1 .
Optimal firm strategy: hire worker iff aggregate order ct not yet
filled and w∗t ≤ 1
Optimal household strategy: set w∗t = 1

Household Problemmax E{ct ,ht+1 }∞X

β t (log ct + φht )t=0s.t.
ct + pt (ht+1 − ht ) = (1 − ut )wt −ψut min {(pt ht − d − ct ) , 0}2 + Tt
2

φ : preference weight on housingψ : cost of creditd : part of home value that cannot be used as collateralut : fraction of household workers unemployed
Tt : lump-sum rebate of credit costs

Frictions
1. Labor market friction: No role for labor supply indetermining allocations ⇒ output demand-driven,
equilibrium unemployment• Workers cannot affect the probability of meeting a firm byasking a lower wage, and when they meet they ask for thereservation wage.

Frictions
1. Labor market friction: No role for labor supply indetermining allocations ⇒ output demand-driven,
equilibrium unemployment• Workers cannot affect the probability of meeting a firm byasking a lower wage, and when they meet they ask for thereservation wage.

2. Credit friction: Unemployed with low wealth must use
expensive credit ⇒ precautionary motive
3. Consumption commitment friction: Consumption chosen
before unemployment status known ⇒ precautionary
motive sensitive to expected unemployment

Equilibrium Conditions• wt = w∗t = 1• ht = 1• Tt = ψut min {(pt − d − ct ) , 0}2• ct = nt = 1 − utEquilibrium Conditions• wt = w∗t = 1• ht = 1• Tt = ψut min {(pt − d − ct ) , 0}2• ct = nt = 1 − ut
•



1
1
pt+1
pt ×= βEt φ +ct(1 − ψut min {(pt ht − d − ct ) , 0})
ct+1

Agenda for Theory• Characterize paths for unemployment that satisfy theinter-temporal FOC and the condition ct = 1 − ut• Especially interested in expectations-driven multiplicity• Multiple Steady States• Multiple Paths leading to Steady State• Sunspots

Role of Asset Prices• Introduce “marginal investor” with same preferences thatfaces no risk (c = c̄ = 1) and is measure zero
• In equilibrium no housing trade between the two types• Marginal investor establishes a floor p for house prices:pt ≥ p =βφc̄
1−β• Will see that marginal investor rules out equilibria with veryhigh unemployment

Strong Housing demand ⇒ full employmentIfφ ≥ φ̄ = (1 + d)1−ββthen the only steady state is p = p and u = 0Logic: φ ≥ φ̄ ⇒ p − d ≥ cmax = 1... so even the unemployed never needs credit
Absent credit constraints,
p=β(1 − u)
βφ≤p=
φ
1−β
1−β

But marginal investor implies p ≥ p, so p = p, u = 0High wealth ⇒ High consumption demand ⇒ Full Employment

Steady state: high prices
ppuWeak housing demand ⇒ positive unemployment
If φ < φ̄ andψ ≥ ψ̄ =(1 − β)2(1 − β)(1 + d) − βφthen
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• Intuition: p = p & u > 0 ⇒ asset has liquidity value ⇒c>p−d

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

Low housing prices: Multiple steady state u, given pppp0u

Low housing prices: Multiple steady state pppp0u

Constraints and multiplicity• When credit constraint not binding:

p1chpi= β φ+cβ(1 − u)φ = pf (u),p =1−βp0f (u) < 0Constraints and multiplicity• When credit constraint not binding:

p1chpi= β φ+cβ(1 − u)φ = pf (u),p =1−βp0f (u) < 0• When credit constraint binding:ph11pi=β φ+c [1 + ψu (c − (p − d))]c|{z}Liquidity discountp = pf (u)1−β= pf (u)Ψ(u)1/ [1 + ψu (c − (p − d))] − β• Ψ(u) is the liquidity premium• Key to multiple u, given p, p0f (u) < 0, Ψ0 (u) > 0.

Multiplicity 2: many paths to a steady state pair (p, u)• Suppose pt = p > p ⇒ constraint always binding• Difference equation defining equilibrium isp1
1×= βφ+βpEt(1 − ut ) (1 − ψut [p − d − (1 − ut )])1 − ut+1• Assume no uncertainty / sunspots / expectational errors:


1
1= Et
1 − ut+1
1 − ut+1

A numerical example

ψ = 1 β = 0.96 φ = 0.05 d = 0.75
1. ψ > ψ̄ = 0.7 (credit expensive)
2. φ < φ̄ = 0.12 (housing demand weak)
3. Chosen to match observed net worth to income ratio,
unemployment ranges

Unemployment Dynamics

u(t+1)-u(t) 0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000







0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
-0.001uLuHu(t)Intuition for Differential Local Dynamics• Consider a hypothetical rise in unemployment starting fromsteady state• Low unemployment stable steady state• Each unemployed worker borrows a lot ⇒ high marginal

credit cost ⇒ optimal to cut consumption sharply eventhough recovery expected• Expected consumption growth during recovery offsets
stronger precautionary motive ⇒ stable demand for savings• High unemployment unstable steady state• Each unemployed worker borrows little ⇒ low marginal

credit cost from rise in unemployment ⇒ a sharp cut in
consumption not consistent with expected recovery

Multiplicity 3: Sunspot• Low unemployment steady state is dynamically stable ⇒possibility of “sunspots”• Define sunspot shock vt+1

1
1vt+1 =− Et
1 − ut+1
1 − ut+1
where vt+1 is iid over time with mean zero and a support
that ensures we stay in the stable region

Range of equilibrium u decreasing in pp
High pLow p

Unemployment ranges

Unemployment

Review: Asset Prices and Macro Volatility• High asset prices ⇒ credit constraint does not bind ⇒unique full employment equilibrium• Lower asset prices ⇒ constraint binds ⇒ range ofequilibrium unemployment rates larger the lower is theasset priceUsing the model to capture The Great Recession

1. Fall in demand for housing (fall in φ) reduces p so thateconomy becomes fragile
2. Sunspot (Lehman Brothers?) triggers jump in
unemployment
3. Slow recovery to low unemployment steady stateGraphicallypHigh p1Low p2

34

Unemployment

Model Can Produce A Great Recession
Great recession and slow recovery
1.2
Unemployment

1

Stock Prices

House Prices

0.8
0.6
0.4
0.2
0
‐9‐7‐5‐3‐1

1

3579

11 13 15 17 19 21 23 25 27 29

Preference Shock at t=‐6, Sunspot Shock at t=0

Why is the recovery slow?

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

consumption demand• Large fall in consumption demand only happens if

persistent fall in income is expected (PIH logic)• Large fall <-> Slow recovery• Consistent with data from Michigan Consumers

Expectation

Micro Evidence for the Mechanism• Key mechanism: Elasticity of demand wrt unemployment

risk is larger when wealth is low• Natural test: Did wealth-poor households reduce

consumption more than rich households as unemployment
rose during the Great Recession?

Differential Sensitivity in the Model
1.2
1.1
10.9
0.8
0.7

u = 5%
u = 15%

0.6
0.5
0.4
0123
Housing456Consumer Expenditure Survey• Households aged 25-60 with 4 quarters of consumption

data• Sort households by wealth (net financial wealth plus homeequity) relative to consumption• Compare consumption growth of top and bottom halves ofwealth distribution

0.93

0.91

0.89

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‐III2010‐IV
2011‐I

2005q1=1

CE Survey versus NIPA

Aggregate real consumption expenditures per capita

1.05

1.03

1.01

0.99

0.97

0.95

NIPACE

0.87

0.85

Characteristics of Rich versus Poor

Sample size
Average age of head
Heads with college
Average household size
Net wealth p.c. (2005$)
MeanMedian
Mean after-tax income p.c. (2005$)
Mean consumption p.c. (2005$)

Wealth Group
0-50
50-100
8,864
8,873
41.4
46.9
25.7%
40.5%
2.9
2.8
1,498
238

119,796
63,162

22,117
9,353

32,811
11,252

‐0.1

‐0.2
2005
5q4
2006
6q1
2006
6q2
2006
6q3
2006
6q4
2007
7q1
2007
7q2
2007
7q3
2007
7q4
2008
8q1
2008
8q2
2008
8q3
20088q4
2009
9q1
2009
9q2
2009
9q3
2009
9q4
2010
0q1
2010
0q2
2010
0q3
2010
0q4
2011
1q1

Growth in consumpttion expen
Gnditures (aannual ratee)

Consumption Growth: Rich versus Poor

0.1

0.05

0‐0.05
Wealth poor

Wealth rich

‐0.15

Consumption vs. Income Growth

Mean growth income p.c.
Mean growth cons. p.c.

Wealth Group0-50 50-100
-0.3%
-1.0%
-5.6%
-3.1%

0 04
‐0.04

‐0.06
2005q4
2006q1
2006q2
2006q3
2006q4
2007q1
2007q2
2007q3
2007q4
2008q1
2008q2
2008q3
2008q42009q1
2009q2
2009q3
2009q4
2010q1
2010q2
2010q3
2010q4
2011q1

Change inn consumpption rate

Consumption Rates: Rich versus Poor

0.02

0.01

0‐0.01

‐0.02

‐0.03
Wealth poor

Wealth rich

‐0.05

Micro Evidence: summary• Low wealth households reduce consumption much moreduring recession, despite facing similar increase in
unemployment/income risk

Policy 1: Tax and Spend

p1.6
1.5

equilibria G=01.4

pbar G=0 1.3
1.2

equilibria G=0.3

1.1
1.0

pbar G=0.3 0.9
-0.1

0.0

0.1

0.2

0.3

0.4

0.5u

Policy 1: Review• Reduces elasticity of aggregate demand to expectations• Also reduces asset values (credit constraint more binding)• 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
p1.6

1.5

equilibria b=0
1.4

1.3

pbar b=0.3

1.2

equilibria b=0.3

1.1
0.0

0.1

0.2

0.3

0.4

0.5

uPolicy 2: Review• Policy reduces need for costly credit ⇒ shrinks range ofpossible unemployment rates• Unique full employment equilibrium ifb≥βψ (d + 1) + (β−1)φ + (β − 1)
(β − 1) + ψ• ... which implies b ≥ 0.61 in our numerical example

Conclusions• Model in which macroeconomic stability threatened by low

asset values or tight credit markets• Great Recession: Decline in home values + costly credit

left economy vulnerable 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