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