House Prices and Consumer Spending David Berger, Veronica Guerrieri, - - PowerPoint PPT Presentation

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

House Prices and Consumer Spending

David Berger, Veronica Guerrieri, Guido Lorenzoni, Joe Vavra BBLM, Departimento del Tesoro Giugno 2017

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Consumption Decline in Great Recession

5 10 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14

Total Consumption

1973-75 1980 1982-83 1990-91 2001 2007-09 5 10 0.95 1 1.05 1.1

Non-Durable Goods

5 10 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 Quarter Since Recession Start

Services

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Consumption Response to House Prices in the Data

• deep consumption decline in Great Recession
• growing literature points to large decline in housing wealth
• various measures of consumption respond strongly to

house price movements under various identifications:

• Campbell and Cocco (2007): UK non-durable exp (≈ 1.22)
• Case, Quigley and Shiller (2013): state-level data

(0.03−0.18)

• Mian, Rao, and Sufi (2013): county Mastercard spending +

autos spending (0.13−0.26)

• Stroebel and Vavra (2015): Nielsen homescan spending
• puzzle relative to standard PIH model (Sinai and Souleles)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Question

broad question: can consumption models rationalize this evidence? in particular:

• can a standard model with incomplete markets work?
• what are the channels?
• does the level/distribution of household debt matter?
• can we rationalize the recent boom-bust episode?

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Results

• wide class of Bewley-type of models ⇒ simple formula:

∆Cit

∆Pt Pt

= MPCit(1−δ)PtHit−1

• holds exactly with strong assumptions, but typically a

accurate approximation

• estimate our formula in the data using BPP approach

implies large elasticities consistent with:

• calibrated model
• other empirical estimates
• general equilibrium exercise: boom-bust episode
• main shock: expected housing appreciation shock
• consumption response dominated by partial equilibrium
• GE effect important for residential investment and for bust

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Set up

• households indexed by i live J = 60 periods
• work for Jy = 35 periods and retired for Jo = 25
• jit = age of household i at time t
• two assets: a risk-free asset (Ait) and housing (Hit)
• risk-free asset yields interest r
• housing stock yields housing services one for one
• depreciation rate δ and exogenous house prices Pt

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Preferences

• for household i at time t with jit < J:

U(Cit,Hit) = (Cα

it H1−α it

)1−σ 1−σ

• bequest motive for jit = J:

U(Cit,Hit)+β Ψ 1−σ Γi +(1−δ)Pt+1Hit +(1+r)Ait PXt+1 1−σ , Γi = human wealth of offspring PXt+1 = price index that converts nominal into real wealth

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Constraints

• budget constraint

Cit +PtHit +Ait = Yit +(1−δ)PtHit−1 +(1+r)Ait−1

• borrowing constraint

−(1+r)Ait ≤ (1−θ)(1−δ)Pt+1Hit

• income process when agent works:

Yit = exp{χ(jit)+zit} where χ(jit) age-dependent component and zit = ρzit−1 +ηit

• social security process as in Guvenen and Smith (2014)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Benchmark

• special case = permanent income:
• 1. no income uncertainty
• 2. no borrowing constraint
• 3. constant house prices
• assume

β (1+r) = 1 and Ψ = (1−β)−σ

• perfect consumption smoothing:

Ct = α (1−β)

• J

∑

j=0

(1+r)−jYt+j +(1−δ)PHt−1 +(1+r)At−1

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Benchmark: Some Numbers

• elasticity of consumption to house prices

dC C /dP P = (1−δ)PHt−1 ∑J

j=0(1+r)−jYt+j +(1−δ)PHt−1 +(1+r)At−1

• set r = 2.5%, then human wealth is ≈ Y/r = 40Y
• set (1−δ)PH = 2.15Y and A = −0.32Y (2001 SCF)

elasticity = 0.0514

• suppose household debt goes up by 0.5Y so that

A = −0.82Y elasticity = 0.0520

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Benchmark: Take Out

• implication 1:

aggregate elasticity is small relative to empirical literature

• implication 2:

aggregate elasticity minimally affected by household debt

• implication 3:

the old are the ones with higher elasticities

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

General Model: Simple Formula

• Proposition: individual consumption response to a

permanent change in house price: ∆Cit ∆Pt/Pt = MPCit(1−δ)PtHit−1

• 3 key assumptions:
• 1. liquid housing wealth
• 2. Cobb-Douglas/CRRA preferences
• formula can be extended for CES and θ = 0
• results robust numerically for CES with θ > 0
• 3. house prices follow a random walk (special case: constant)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Interpretation

• important implication: larger consumption response the

larger correlation of MPC and housing values

• house price increases affect C in 4 ways:
• 1. endowment effect: existing house worth more (C ↑)
• 2. income effect: housing more expensive (C ↓)
• 3. substitution effect: housing relatively more exp. (C ↑)
• 4. collateral effect: relaxed borrowing constraint (C ↑)
• our formula: consumption response represented as pure

endowment effect! ⇒ effects 2-4 cancel out

• however all effects are large in isolation (more later ...)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Calibration

• annual model → interest rate r = 2.4%
• intertemporal elasticity σ = 2
• housing depreciation rate δ = 2.2% (BEA data)
• collateral constraint θ = 0.25 (minimum down payment)
• income process using PSID data:
• life-cycle component to fit regression of earnings on age (as

Kaplan and Violante 2010)

• temporary component: ρ = 0.91, σ = 0.21 (as Floden and

Linde 2001)

• remaining parameters target life-cycle profiles of housing

and liquid wealth in 2001 SCF data (9 age bins)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Model Fit

25 30 35 40 45 50 55 60 65 70 1 1.5 2 2.5 3 3.5

Housing wealth

Age 25 30 35 40 45 50 55 60 65 70 −1 1 2

Liquid wealth net of debt

Age Model SCF 2001

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Elasticities over the Life Cycle

30 35 40 45 50 55 0.35 0.4 0.45 0.5 0.55

Age

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Understanding the Life Cycle

25 30 35 40 45 50 55 1 1.5 2 2.5 3 3.5

Housing over the lifecycle

Age

25 30 35 40 45 50 55 0.05 0.1 0.15 0.2 0.25 0.3 MPC over the lifecycle

Age

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Decomposition

Age 30 35 40 45 50 55

• 0.2
• 0.1

0.1 0.2 0.3

Substitution effect Income effect Collateral effect Endowment effect

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

More on Decomposition

• substitution, collateral, and "net-wealth" effect of similar

size

• "net-wealth" effect = endowment + income effect
• borrowing constraints in our model ⇒ net-wealth effect > 0

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

More on Decomposition

• substitution, collateral, and "net-wealth" effect of similar

size

• "net-wealth" effect = endowment + income effect
• borrowing constraints in our model ⇒ net-wealth effect > 0
• Comparison to existing "small wealth effects" models:
• 1. PIH:
• Collateral effect = 0
• Net-wealth effect ≃ 0
• 2. Sinai and Souleles (2005):
• Collateral effect = 0
• Net-wealth effect = 0
• Substitution effect = 0

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Some Implications

• 1. all 4 effects are large in isolation

consistent with DeFusco (2015): large collateral channel

• 2. larger consumption responses when both MPC and PH

are large consistent with Mian, Rao, Sufi (2013): biggest effects for most levered

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Baseline: Take Out

• implication 1:

aggregate elasticity over working life is large = 0.47

• implication 2:

aggregate elasticity affected by household debt distribution

• implication 3:

the young are the ones with higher elasticities because are more levered (Attanasio et al. 2009)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Adjustment Costs

• with liquid housing wealth housing adjusts too much
• ⇒ introduce adjustment costs
• fixed cost of trading housing proportional to house value

κit = F ·PtHit−11Hit=Hit−1

• adjustment cost F = .05

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Elasticities over the Life Cycle

25 30 35 40 45 50 55 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Age Aggregate C Elasticity Approximation

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Rental Option

• so far everybody is homeowner...
• while US homeownership rate is roughly 2/3
• → introduce the option to rent
• flow cost of renting to match the homeownership rate
• rent/price ratio is constant trade-off:
• advantage: keep savings in liquid assets
• disadvantage: renting is more costly and rental house

cannot be used as collateral

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Calibration

Shock size matters since MPC non-linear:

25 30 35 40 45 50 55 60 65 70

Age

2 4

Housing Wealth

25 30 35 40 45 50 55 60 65 70

Age

• 2

2

Liquid wealth net of debt

25 30 35 40 45 50 55 60 65 70

Age

0.5 1

Homeownership Rate

Model SCF 2001

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Elasticities over the Life Cycle

25 30 35 40 45 50 55 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

age

Elasticity

rental option approx no rental option approx

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Understanding the Life Cycle

25 30 35 40 45 50 55 60 0.5 1 1.5 2 2.5 3

Housing over the lifecycle

age

25 30 35 40 45 50 55 60 0.2 0.4 0.6 0.8 MPC over the lifecycle

age

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

More Dimensions of Heterogeneity

10 20

Income Bin

0.2 0.4 0.6

Elasticity Approximation

10 20

Housing Bin

0.2 0.4 0.6

Elasticity Approximation

10 20

Voluntary Equity Bin

0.5 1

Elasticity Approximation

30 40 50

Age

0.1 0.2 0.3 0.4 0.5

Elasticity Approximation

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Accuracy

• 0.5

0.5 1 1.5 2 Elasticity Approximation

• 0.5

0.5 1 1.5 2 Elasticity

R2 for a simple linear regression is 0.95.

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Comments

• sufficient statistic still works approximately pretty well
• aggregate elasticity drops to .24 (working life)
• why?
• mechanical effect because renters do not respond to

prices, but also selection!

• MPC tend to be bigger for the young
• the old have accumulated a lot of liquid wealth!
• BUT in a model with rental option the young tend to rent

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

More Realistic Mortgages

• we model mortgages as one-period loans subject to

collateral constraints

• two steps towards more realistic loans:
• 1. introduce costly equity extraction
• if households increase their debt level they need to pay a

fixed cost

• 2. introduce asymmetric adjustment to the borrowing limit
• when house price falls lenders cannot force households to

put up additional collateral

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Results for More Realistic Mortgages

25 30 35 40 45 50 55 60 0.1 0.2 0.3 0.4 0.5 Age

Costly Refinancing Model

Aggregate C Elasticity Approximation 25 30 35 40 45 50 55 60 0.1 0.2 0.3 0.4 0.5 Age

Asymmetric Mortgage Model

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Full Model: Take Out

• implication 1:

aggregate elasticity is sizeable = 0.24

• implication 2:

aggregate elasticity still affected by household debt level and distribution

• implication 3:
• ur simple formula still a good approximation
• implication 4:

rental option matters a lot, adjustment cost and mortgage simplifications not

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Estimation

• we estimate the sufficient-statistic formula with micro data

→ new measure independent of calibration

• we follow Blundell, Pistaferri and Preston (2008) to

estimate MPC to temporary shocks using PSID data

• BPP estimator: instrument for change in income with

change in future income

• do this separately for different housing bins to estimate

MPC ×H in data

• our estimation gives an average elasticity of 0.33 (similar to

Mian, Rao and Sufi (2013))

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Elasticity in the PSID

1 2 3 4 5

Income Bin

• 0.5

0.5 1 2 4

Housing Bin

0.5 1 2 4 6 8 10

Voluntary Equity Bin

0.5 1 30 40 50 60

Age

0.5 1

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Boom-Bust Experiment

• simple general equilibrium exercise to think about recent

house price boom-bust episode in the US

• partial equilibrium model has counterfactual implications

for housing demand and debt

• ⇒ new shock to expectations about future house price

appreciation Et

• Pt+j
• = Pt exp
• gt

1−λ j 1−λ

• for j = 1,2,...
• set λ = .5 and choose {gt} and housing supply to match

residential investment and housing market clearing at prices from Shiller (2015)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

With g shocks (blue) vs no g shocks (red)

2000 2005 2010 0.6 0.8 1 1.2 1.4 1.6 House price 2000 2005 2010 % 0.5 1 1.5 Expected price growth 2000 2005 2010 % deviation from steady state

• 5

5 Consumption baseline g=0 2000 2005 2010 % deviation from steady state

• 300
• 200
• 100

100 200 300 Residential investment

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Effects of Changing g

g (in %)

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2

• 4
• 2

2 4 Consumption (% change) g (in %)

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2

• 2000
• 1000

1000 2000 3000 Residential investment (% change)

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Endogenous Changes in Wealth Distribution

2006 2007 2008 2009 2010 2011 2012 2013 % deviation from steady state

• 16
• 14
• 12
• 10
• 8
• 6
• 4
• 2

Consumption

baseline starting at initial steady state distribution

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Final Remarks

• we explore models with incomplete markets to think about

the response of consumption to changes in house prices

• with liquid housing, this response = MPC ·(1−δ)H
• formula works approximately well also in more general

model

• model delivers large elasticities in line with empirical

literature

• estimate formula with macro data and find similar results
• GE exercise with shocks to price growth expectations to

match residential investment

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Proof: step 1

• state (W,s) where W ≡ total wealth and s ≡ (z,j)
• for all j < J:

Vt(W,s) = max

C,H,A,W ′ U(C,H)+βE[Vt+1(W ′,s′)|s]

subject to C +PtH +A = W +Y(s) W ′ = (1−δ)Pt+1H +(1+r)A (1−θ)(1−δ)Pt+1H +(1+r)A ≥ 0

• for j = J +1, bequest motive:

Vt(W,s) = Ψ 1−σ Γ(s)+W ˆ PXt 1−σ

Motivation Baseline Model Full Model Empirics Boom-Bust Conclusions Appendix

Proof: step 2

• let ˜

H = PH: V(W,s) = max

C,˜ H,A,W ′ P(σ−1)(1−α)U(C, ˜

H)+βE[V(W ′,s′)] subject to C + ˜ H +A = W +Y(s) W ′ = (1−δ) ˜ H +(1+r)A (1−θ)(1−δ) ˜ H +(1+r)A ≥ 0

• ⇒ consumption policy C(W,s) does not depend on P!
• ⇒ dC(W,s)/dP = dC(W,s)/dW ·dW/dP