WEALTH AND VOLATILITY

WEALTH AND VOLATILITY Jonathan Heathcote Minneapolis Fed Fabrizio Perri University of Minnesota and Minneapolis Fed EIEF, July 2011

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

1.1 1.05 1 0.95 0.9 0.85 0.8 0.75 0.7 Great Recession Great Recession Net Worth Price Durable Cons pc Unemp. Rate ( ve, right axis) 3 4 5 6 7 8 9 10 11

1.1 1 0.9 08 0.8 Asset Prices Asset Prices House Price Stock Price Unemp. Rate ( ve, right axis) 3 44 5 6 77 0.7 0.6 0.5 8 9 10 11

Theory Recession driven by self-fulfilling wave of pessimism (old idea, latest incarnations in Farmer 2010, Chamley 2011) 1. Rise in expected unemployment reduction in demand 2. Firms reduce hiring higher unemployment (Paradox of thrift)

Theory Recession driven by self-fulfilling wave of pessimism (old idea, latest incarnations in Farmer 2010, Chamley 2011) 1. Rise in expected unemployment reduction in demand 2. Firms reduce hiring higher unemployment (Paradox of thrift) Sensitivity of aggregate demand to shocks depends on wealth, due to precautionary reasons (Guerrieri and Lorenzoni 2009) Here level of wealth & cost of credit determines, through sensitivity of demand to expected unemployment, likelihood of self-fulfilling crises High wealth or cheap credit stable demand no sunspot-driven fluctuations Low wealth and costly credit demand more sensitive to expectations confidence-driven recessions possible

Empirical Motivation 1. Macro evidence on the importance of sunspot shocks when average wealth is high, aggregate volatility tends to be low 2. Micro evidence on the mechanism the wealth-poor reduced consumption more than the rich in the Great Recession

ealth & GDP Volatility: rolling window correlation Wealth & GDP Volatility: rolling window correlation Net worth to GDP ratio Volatility Correlation = -0.70 4.4 4.2 4.0 3.8 3.6 3.4 Wealth 3.2 3.0 55 60 65 70 75 80 85 90 95 00 05 10.016.014.012.010.008.006.004 Standard deviation of GDP growth 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

ealth & GDP Volatility: instantaneous correlation Wealth & GDP Volatility: instantaneous correlation Net worth to GDP ratio.020.016.012 Volatility.008 4.8 Correlation = -0.52.004 4.4 4.0 3.6 3.2 Wealth 2.8 55 60 65 70 75 80 85 90 95 00 05 10 Standard deviation of GDP growth Note: Standard deviation of quarterly GDP growth are computed using GARCH(1,1).

Wealth & GDP Growth Wealth & GDP Growth 4.4 Average GDP growth (per quarter).014.012.010.008.006.004 Correlation = -0.23 Growth Wealth.002 55 60 65 70 75 80 85 90 95 00 05 10 4.2 4.0 3.8 3.6 3.4 3.2 3.0 Net woth to GDP ratio 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

Few pictures CEX versus NIPA Consumption We start looking at a broad but comparable measure of consumption both in NIPA and CE.06.04.02 Growth in per capita total consumption expenditures (all households, excluding housing and health) Yearly growth.00 -.02 -.04 -.06 -.08 -.10 I II III IV I II III IV I 2008 2009 2010 CE Survey NIPA Note that the CEX fall much more than NIPA. Since the CEX does not include high wealth individ provides, very indirectly, some support for our story.

CEX Consumption Growth: Wealth Rich versus Poor.04 Consumption growth from CE, High and low w/y ratios Each growth rate is computed on the same group of houeseholds.02.00 -.02 -.04 -.06 -.08 -.10 I II III IV I II III IV I 2008 2009 2010 Wealth rich Wealth poor

CEX Income Growth: Wealth Rich versus Poor Total disposable income growth from CE, High and low w/y ratios Each growth rate is computed on the same group of houeseholds.12.10.08.06.04.02.00 -.02 -.04 IV I II III IV I II III IV I 2007 2008 2009 2010 Wealth rich Wealth poor

A Stylized Model 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. Household sends out workers with consumption order c t, assets p t h t, reservation wage w t 2. Firm randomly meets potential workers sequentially, decides whether to hire them 3. Firms pay wages w t = w t, workers pay for consumption - must borrow if unemployed and c t > p t h t d 4. Household regroups, net resources determine h t+1. Optimal firm strategy: hire worker iff aggregate order c t not yet filled and w t 1 Optimal household strategy: set w t = 1

Household Problem s.t. max E β t (log c t + φh t ) {c t,h t+1 } t=0 c t + p t (h t+1 h t ) = (1 u t )w t ψ 2 u t min {(p t h t d c t ), 0} 2 + T t φ : preference weight on housing ψ : cost of credit d : part of home value that cannot be used as collateral u t : fraction of household workers unemployed T t : lump-sum rebate of credit costs

Equilibrium Conditions 1. 2. 3. 4. 5. w t = w t = 1 h t = 1 T t = ψu t min {(p t d c t ), 0} 2 c t = n t = 1 u t [ 1 1 p t c t (1 ψu t min {(p t h t d c t ), 0}) = βe t φ + p ] t+1 c t+1

Key Frictions Decentralized labor market: unemployed cannot work for lower wage demand can drive output Pre-committed consumption + costly credit: unemployed must pay credit cost when wealth is low demand is sensitive to expected unemployment

Key Frictions Decentralized labor market: unemployed cannot work for lower wage demand can drive output Pre-committed consumption + costly credit: unemployed must pay credit cost when wealth is low demand is sensitive to expected unemployment Potential for expectations-driven multiplicity: 1. Low wealth plus high expected unemployment 2. high effective tax on current consumption 3. low demand 4. high unemployment Note: wages not too high relative to full employment equilibrium.

Role of Wealth Level of wealth key to what can happen in model 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: p t p = β 1 β φ Fundamental house value p depends on pref. weight φ

If Strong housing demand full employment φ φ = (1 + d) 1 β β then the only steady state is p = p and u = 0 Logic: φ φ p d c Even when demand is high and agents lose their job they do not need to use credit. FOC are: p = β(1 u) 1 β φ p = β 1 β φ p = p, u = 0 Asset price are high enough so that demand is high enough to guarantee full employment (Farmer 2010)

Weak housing demand positive unemployment If φ < φ and ψ ψ > 0. then 1. There is (still) a steady state with p = p and u = 0 2. There are additional steady states with p p and u > 0. In these steady states c > p d Intuition: p p & u > 0 asset has liquidity value c > p d Liquidity value must be large to support p p : ψ ψ = (1 β) 2 (1 β)(1 + d) βφ

Example Steady state demand c d and supply c s defined by FOC and resource constraint ] = β [φ + pcd p c d 1 [1 ψu (p d c d )] c s = 1 u Example: ψ = 1 β = 0.9 φ = 0.05 d = 0.1 p = 0.6 : 1. ψ > ψ = 0.15 (credit not cheap) 2. φ < φ = 0.12 (housing demand weak) 3. p > p = 0.45 (price above full employment fundamental)

Multiplicity 1: Two steady state u s for a given p Multiplicity 1: Two steady state u s for a given p

Multiplicity 2: Multiple steady states p s Multiplicity 2: Multiple steady states p s

Multiplicity 3: Multiple paths to a steady state pair (p, u) Suppose p t = p > p constraint always binding Difference equation defining equilibrium is [ ] p (1 u t ) 1 (1 ψu t [p d (1 u t )]) = βφ+βpe 1 t 1 u t+1 Assume no uncertainty / sunspots / expectational errors: [ ] 1 1 = E t 1 u t+1 1 u t+1 Many solutions to difference equation corresponding to different initial unemployment rates

Unemployment Dynamics

Multiplicity 4: Sunspots generate fluctuations in u t Low unemployment steady state is dynamically stable possibility of sunspots Define sunspot shock v t+1 [ ] 1 1 v t+1 = E t 1 u t+1 1 u t+1 where v t+1 is iid over time with mean zero and a support that ensures we stay in the stable region

Wealth and volatility p High p Low p Unemployment ranges Unemployment

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 1 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 5 3 1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Preference Shock at t= 3, Sunspot Shock at t=0

Conclusions Developed loss of confidence theory for Great Recession Decline in home values + costly credit left economy vulnerable to wave of pessimism Provided macro evidence of a link between level of wealth and aggregate volatility Provided micro evidence that low wealth households reduced consumption sharply Model stylized but suggests role for policy