Download The views expressed herein are those of the authors and not

The views expressed herein are those of the authors and not
necessarily those of the Federal Reserve Bank of Minneapolis or the
Federal Reserve System
WEALTH AND VOLATILITY
Jonathan Heathcote
Minneapolis Fed
Fabrizio Perri
University of Minnesota and Minneapolis Fed
FRB St Louis, 2011 Economic Policy Conference
Source of Business Cycles
• Old idea: business cycles can be driven by self-fulfilling wave of
optimism or pessimism
• Our idea: extent to which non-fundamentals-driven changes in
expectations can generate fluctuations depends on the level of
household wealth
• We will argue that declines in US house prices left the 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 high sensitivity
of demand to expected unemployment
• Sensitivity of demand depends inversely on level of household
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. Micro evidence on the mechanism from the CEX
• Wealth-poor reduced consumption more than the rich as
unemployment surged during the Great Recession
2. Macro evidence on the importance of sunspot shocks
• Historically, US macroeconomic volatility tends to be high in
periods when US household wealth is low
3. Model
• Committed consumption ⇒ demand sensitive to
expectations when wealth is low
4. Great Recession as an equilibrium outcome
5. Policy: Govt spending and unemployment insurance
Micro Evidence from the CEX
• Households aged 25-60, who report consumption and income in
the 2nd and 5th quarterly interviews
⇒ can compute annual consumption and income growth for
the same households
• Split sample in two based on household net worth to income
ratio in the 5th interview
• Compare consumption and income growth for the wealth rich
versus the wealth poor during the Great Recession
Summary statistics (2007.1 -2010.1)
Sample
Age
Family size
% Male
% College
Income after tax
Consumption
Wealth
Wealth Rich
3,522
47
2.9
47
52
$79,659
$62,943
$280,414
Wealth Poor
3,527
41
2.9
48
38
$60,315
$47,394
$2,060
Log Changes in Ave. Total Consumption:
Wealth rich v/s wealth poor
6.0%
4.0%
Wealth rich (avg. growth =‐2.2%)
2.0%
0.0%
‐4.0%
‐6.0%
‐8.0%
‐10.0%
‐12.0%
Wealth poor (avg. growth = ‐4.0%)
2010Q1
2009Q4
2009Q3
2009Q2
2009Q1
2008Q4
2008Q3
2008Q2
2008Q1
2007Q4
‐2.0%
Log Changes in Ave. Disposable Income:
Wealth rich v/s wealth poor
10.0%
8.0%
6.0%
Wealth poor (avg. growth = 3.6%)
4.0%
2.0%
0.0%
2
2010Q1
Wealth rich (avg. growth = 0.0%)
2
2009Q4
2
2009Q3
2
2009Q2
2
2009Q1
2
2008Q4
2
2008Q3
‐8.0%
2
2008Q2
‐6.0%
2
2008Q1
‐4.0%
2
2007Q4
‐2.0%
‐0.02
‐0.04
Wealth poor
‐0.06
‐0.08
‐0.1
Wealth rich
2010q4
2010q3
2010q2
2010q1
2009q4
2009q3
2009q2
2009q1
2008q4
2008q3
2008q2
2008q1
2007q4
2007q3
2007q2
2007q1
2006q4
2006q3
2006q2
2006q1
2005q4
Log Changes in Ave. Consumption:
0.1
Extended sample period
0.08
0.06
0.04
0.02
0
Macro Evidence
• What is the relation between household-sector net worth and
GDP volatility?
• Measure volatility as (i) rolling-window standard deviation of
GDP growth, (ii) estimate of instantaneous volatility from a
Garch (1,1) model
• Also investigate relation between net worth and level of GDP
Wealth & GDP Volatility: rolling window correlation
.014
.012
.010
Volatility
.008
Net worth to GDP ratio
Correlation = -0.70
4.4
.006
4.2
.004
4.0
3.8
3.6
3.4
W ealth
3.2
3.0
55
60
65
70
75
80
85
90
95
00
05
10
Note: Standard deviation of quarterly GDP growth are computed over 10 years rolling windows.
Observations for net worth to GDP ratio are average over the same windows
Standard deviation of GDP growth
.016
Wealth & GDP Volatility: instantaneous correlation
.016
.012
Volatility
Net worth to GDP ratio
.008
4.8
.004
Correlation = -0.52
4.4
4.0
3.6
3.2
Wealth
2.8
55
60
65
70
75
80
85
90
95
00
05
Note: Standard deviation of quarterly GDP growth are computed using GARCH(1,1).
Standard deviation of GDP growth
.020
10
Wealth & GDP Growth
4.4
Average GDP growth (per quarter)
4.0
.014
3.8
Wealth
Correlation = -0.23
3.6
3.4
.012
3.2
.010
3.0
.008
.006
Growth
.004
.002
55
60
65
70
75
80
85
90
95
00
05
Note: Average quarterly GDP growth are computed over 10 years rolling windows.
Observations for net worth to GDP ratio are average over the same windows
Net woth to GDP ratio
4.2
10
Stylized Model (related to Farmer 2010, Chamley
2011, Guerrieri and Lorenzoni 2009)
• Non-durable consumption c, produced by competitive firms
using indivisible labor
• Durable housing h, in fixed supply with relative price p
• Each representative household contains continuum of potential
workers
• Each representative firm produces with linear technology:
y=n
where n is mass of workers employed
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 Problem
max E
{ct ,ht+1 }
∞
X
β t (log ct + φht )
t=0
s.t.
ct + pt (ht+1 − ht ) = (1 − ut )wt −
ψ
2
ut min {(pt ht − d − ct ) , 0} + Tt
2
φ : preference weight on housing
ψ : cost of credit
d : part of home value that cannot be used as collateral
ut : fraction of household workers unemployed
Tt : lump-sum rebate of credit costs
Frictions
1. Labor market friction: No role for labor supply in determining
allocations ⇒ output demand-driven
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
1.
wt = w∗t = 1
2.
ht = 1
3.
Tt = ψut min {(pt − d − ct ) , 0}
2
4.
ct = nt = 1 − ut
5.
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 the
inter-temporal FOC and the condition ct = 1 − ut
• Will mostly abstract from asset price dynamics, focus on how
dynamics for unemployment vary with (fixed) price level
• Especially interested in expectations-driven multiplicity
Role of Asset Prices
• Introduce “marginal investor” with same preferences that faces
no risk and is measure zero
• Assume no housing trade between the two types
• Marginal investor establishes a floor p for house prices:
pt ≥ p =
β
φ
1−β
• Will see that marginal investor rules out equilibria with very high
unemployment
Strong housing demand ⇒ full employment
If
φ ≥ φ̄ = (1 + d)
1−β
β
then the only steady state is p = p and u = 0
Logic: φ ≥ φ̄ ⇒ p − d ≥ c
... so even the unemployed do not need credit
Absent credit constraints,
p=
β(1 − u)
φ≤p
1−β
But marginal investor implies p ≥ p, so p = p, u = 0
High wealth ⇒ Strong Demand ⇒ Full Employment
Weak housing demand ⇒ positive unemployment
If φ < φ̄ and
2
ψ ≥ ψ̄ =
(1 − β)
(1 − β)(1 + d) − βφ
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
• Intuition: p = p & u > 0 ⇒ asset has liquidity value ⇒
c>p−d
3. There are additional steady states with p > p and u > 0.
Steady state demand and supply
• Demand cd and supply cs defined by FOC and resource
constraint:
1
p
×
cd
[1 − ψu (p − d − cd )]
cs
=
=
p
β φ+
cd
1−u
• Closed-form solution with φ = 0:
cd =
where ρ =
1−β
β
ρ
+p−d
ψu
is rate of time preference
• Consumption elasticity wrt unemployment decreasing in home
equity
More general example with φ > 0
Numerical example: ψ = 1 β = 0.9 φ = 0.05 d = 0.1
1. ψ > ψ̄ = 0.15 (credit expensive)
2. φ < φ̄ = 0.12 (housing demand weak)
Multiple steady states p’s
Multiple paths to a steady state pair (p, u)
• Suppose pt = p > p ⇒ constraint always binding
• Difference equation defining equilibrium is
p
1
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
Unemployment Dynamics, p = 0.6
Sunspots generate fluctuations in ut
• Low unemployment steady state is dynamically stable ⇒
possibility of “sunspots”
• Define sunspot shock vt+1
vt+1 =
1
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
Intuition for Differential Local Dynamics
• Consider a hypothetical rise in unemployment starting from
steady state
• Low unemployment stable steady state
• Each unemployed worker borrows a lot ⇒ high marginal
credit cost ⇒ optimal to cut consumption sharply even
though 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 ⇒ not optimal to cut
consumption sharply
Range of equilibrium u decreasing in p
p
High p
Low 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 of equilibrium
unemployment rates larger the lower is the asset price
Features of the Great Recession
1. Large fall in asset values
2. Sharp decline in consumer spending, especially durables
3. Sharp rise in unemployment, labor productivity strong
4. Slow recovery
Great Recession
1.1
1.05
1
Net Worth Price (real, rel. to trend)
Durable Cons (real, pc, rel to trend)
Unemp. Rate (‐ve, right axis)
‐3
‐4
‐5
0.95
0.9
0.85
0.8
‐6
‐7
‐8
0.75
‐9
0.7
0.65
0.6
‐10
‐11
Asset Prices
1.1
‐3
House Price (real, rel to 2.1% trend)
1
Stock Price (real, rel to 2.1% trend)
0.9
08
0.8
07
0.7
Unemp. Rate (‐ve, right axis)
‐4
4
‐5
‐6
‐7
7
‐8
‐9
0.6
0.5
‐10
‐11
Using the model to capture The Great Recession
1. Fall in demand for housing (fall in φ) reduces p so that economy
becomes fragile
2. Sunspot (Lehman Brothers?) triggers jump in unemployment
3. Slow recovery to low unemployment steady state
Graphically
p
High p
1
Low p
2
3
4
Unemployment
Model Can Produce A Great Recession
1.2
1
Unemployment
Stock Prices
House Prices
0.8
0.6
0.4
0.2
0
‐9 ‐7 ‐5 ‐3 ‐1
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29
Preference Shock at t=‐6, Sunspot Shock at t=0
Policy 1: Tax and Spend
p
0.7
equilibria G=0
0.6
0.5
pbar G=0
0.4
equilibria G=0.3
pbar G=0.3
0.3
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
u
Policy 1: Review
• Reduces elasticity of aggregate demand to expectations
• Also reduces asset values
• Narrows range of equilibrium unemployment, but need very high
G to rule out equilibria with unemployment
• Welfare implications will depend on utility from G
Policy 2: Unemployment benefit b financed by
proportional tax τ on earnings
p
0.7
equilibria b=0
0.6
0.5
equilibria b=0.3
0.4
pbar b=0.3
0.3
0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
u
Policy 2: Review
• Policy reduces need for costly credit ⇒ shrinks range of possible
unemployment rates
• Unique full employment equilibrium if
ψ (d + 1) +
b≥
β
(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 and aggregate
volatility
• Micro evidence that low wealth households reduced
consumption most sharply