House Price Movements Jos´e-V´ıctor R´ıos-Rull

Virginia S´anchez-Marcos

Penn, CAERP, Universidad de Cantabria

Preliminary NBER 2005, July 21, 2005

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Introduction

• Two intriguing properties of houses.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Introduction

• Two intriguing properties of houses.

1

Houses prices are much more volatile than GDP in Canada and in the U.S.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Introduction

• Two intriguing properties of houses.

1

Houses prices are much more volatile than GDP in Canada and in the U.S.

2

Units sold fluctuate together with house prices but with larger volatility in Canada and in the U.S.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Canada. Percent deviations from trend using HP filter,Q 0.1 GDP House Price Index 0.08

0.06

0.04

0.02

0

−0.02

−0.04

−0.06

−0.08

1982

1984

1986

1988

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

1990

1992

1994

1996

1998

2000

2002

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US.Percent deviations from trend using HP filter,A 0.1 Median Price Existing Houses Sold Median Price New Houses Sold GDP

0.08

0.06

0.04

0.02

0

−0.02

−0.04

−0.06

−0.08

−0.1 1970

1975

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

1980

1985

1990

1995

2000

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US.Percent deviations from trend using HP filter,Q 0.06 GDP House Price Index

0.04

0.02

0

−0.02

−0.04

−0.06 1975

1980

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

1985

1990

1995

2000

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Canada. Percent deviations from trend using HP filter,Q House Price Index Units Sold 0.1

0

−0.1

−0.2

−0.3

−0.4

−0.5

1990

1992

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

1994

1996

1998

2000

2002

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US.Percent deviations from trend using HP filter,A 0.3 Units Sold Median Price Existing Houses Sold Median Price New Houses Sold

0.2

0.1

0

−0.1

−0.2

−0.3

−0.4

−0.5

−0.6 1970

1975

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

1980

1985

1990

1995

2000

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Our Question

Can a model with suitable chosen frictions deliver some of these features?

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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What are Houses?

Big items that people like. They are costly to buy and sell. There is more than one size (costly to change size). There is a large advantage to own the house you live in. Households can borrow some to buy the house.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Our paper Pose a model of the Bewley-Imrohoroglu-Huggett-Aiyagari variety with the above notion of houses and with with aggregate fluctuations and study housing prices. Exponential population, so that there is a rationale for some buying and selling of houses. Uninsurable shocks to earnings. Borrowing constraints but houses serve as collateral, although borrowing commands a premium. Adjustments costs when buying or selling a house. Two types of property that we call dwellings : flats and houses. There is aggregate uncertainty: earnings, dividends and demographics together or alone. Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Housing Papers that we Like Ortalo-Magne and Rady (2003). We use some of their ideas (the capital gain associated to owning partial equity on the house and bearing all the price risk accounts for price volatility) in a quantitative model. Nakajima (2005) Asks whether the stock market and housing prices rise due to increase volatility in individual earnings. They do, although not dramatically (20%) (steady state comparison). Diaz and Luengo-Prado (2004) look at business cycle properties of housing construction. They care about quantities not prices. D´ıaz-Gim´enez and Puch (1998) document how the properties of model economies relate to the down payment requirements. Chambers, Garriga, and Schlagenhauf (2005) also.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Model economy 1: A stationary version • Exponential population with turnover rate π. • Shocks to earnings  drawn from F(, e) with e ∼ Γee0 . • Assets: a tree and dwellings d = {0, f, h}. Own at most 1 1 A Lucas tree in fixed supply of 1, with dividends z. (or storage technology with return z), and price p` , (or 1). 2 A flat, if held affects utility. ∃µf flats, with pf . 3 A house. Like a flat but better 0 < µf + µh < 1, with ph . • There are borrowing constrains and need of collateral (can borrow a fraction 1 − α of dwellings value). • Dwellings are traded with costs (on the buyer): φ(d, d0 ) = p0d (1 + δ) φ(d, d0 ) = p0d (1 + δ) − pd Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

if d = 0, if d 6= d0 . CAERP

Maximization problem:

We,d (a) =

Wde,d (a) = max ud (c) + E {Ve0 ,d (y)|e}

maxd 0



d0 We,d (a)

if not trading dwelling

y

Z c + p` y = a,

Ve,d (y) =

We,d (y + ε) F(dε, e) ε

0

Wde,d (a) = max ud0 (c) + E {Ve0 ,d0 (y)|e} y

c + p` y − φ(d, d0 ) = a,

if trading dwelling

Z Ve,d (y) =

We,d (y + ε) F(dε, e) ε

• Note that while We,d (a) is a non concave function of cash in hand, Ve,d (y) is a concave function of savings. Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Another detail to take care of

• People die with probability 1 − π. We build an annuity market so that no assets disappear. This means that in addition to the return z and to the utility from dwelling there is a bonus π1 of the value of the assets. No big deal.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Steady State Equilibrium It is a stationary distribution of agents x over dwellings, assets, and earnings shocks, and a set of prices {q, p} such that agents maximize, markets clear, Z

Z y dx = 1

e,d,y

Z dx = µf ,

e,f,y

dx = µh . e,h,y

and the distribution is stationary which is the typical condition that updating the distribution just repeats itself.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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We calibrate this model meaning – Target population turnover features, 1.5% per year, 67 years. – Choose the process for earnings so that the earnings and the financial assets joint distribution match the data. Fine tune to get people buying dwellings with close to the down payment. – We target the value of financial versus housing wealth. Financial wealth is 2.8 times Disposable Income. Owner occupied housing wealth is 2.3 times Disposable Income. – Target share of the population living in each of the type of dwelling. We target 25% as flats and 40% as houses (later up to 89% total). – Costly turnover of houses: 10%, borrowing interest rate premium: 1%, minimum down payment of 20%.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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The Stochastic version has aggregate uncertainty on 1

Dividends, z ∼ Γz,z0 .

2

Earnings distribution, e ∼ Γe0 |e,z,z0 .

3

Population size which changes by having random increases in the number of entrants. Say π is the survival probability but π ˆ , the number of new entrants is random, π ˆ ∼ Γπˆ 0 |πˆ . Population size Π.

Of course, the problem is that now the state variables now include {x, z, π ˆ , Π}. In addition we have to calculate the pricing function p(x, z, π ˆ , Π). A daunting task. So we pull a relative of the bag of tricks of Krusell and Smith (1997). • Supercomputer territory (26 processor MPI cluster for days).

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Solving the Stochastic version

• The key question is what moments of the distribution to use to both COMPUTE and FORECAST prices.

• The simplest may be the price themselves so lets go for it.

• We need to pose a forecasting pricing function. Let p0 = Ψz,z0 (p) be such a forecasting function. Moreover, let Ψ be an afine function. Therefore it is characterized by 36 parameters (3 × 3 × 4).

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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The Stochastic Problemn without π ˆo. Wz,e,d (a, p) =

maxd0

0

Wdz,e,d (a, p)

Wdz,e,d (a, p) = max ud (a − p` y) + E {Vz,e0 ,d (y, p)|e} y

Vz,e,d (y, p) =

X

Z Γz,z0 ε

z0

Wz,e,d [(Ψ`z,z0 (p) + z0 )y + ε, Ψz,z0 (p)] F(dε, e)

0

Wdz,e,d (a, p) = max ud0 [a − p` y − φ(d, d0 )] + E{Vz,e0 ,d0 (y, p)|e} y

Vz,e,d (y, p) =

X z0

Z Γz,z0 ε

if d 6= d0

Wz,e,d [(Ψ`z,z0 (p) + z0 )y + ε, Ψz,z0 (p)] F(dε, e)

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

if d = d0

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Equilibrium with Limited Rationality • A set of decision rules that depend on the aggregate exogenous state, on prices and on individual states. A true pricing function p = ζ(z, x), and a forecasting function such that - Decision rules solve the hhold problem given forecasting function Ψ. - Pricing function ζ clears the market. - Forecasting function Ψ is a good one, i.e. is the best (log)linear predictor of prices given the aggregate shock and current prices and, moreover, lagged prices and aggregate statistics of the distribution (correlation of financial and housing wealth for instance) do not really help to forecast prices.

• Note that function ζ does not really have to be computed. Along the simulations we solve each period for the market clearing prices. Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Model at Work 1: Baseline Little motive for housing (65% ownership rate). Constant Financial Asset Prices.

• Experiment 1

Shocks to Mortage Premium 0% to 2%.

• Then we let the economy run. 50 periods with the first state 11 periods with the second state 20 more periods in the first state

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Time Series with Aggregate Mortgage Premium Shock 1.2

House Price Flat Price

Price

1.1 1 0.9 0.8 10

20

2

30 Period

40

50

60

40

50

60

Financial Wealth Dwelling Sales

1.5

1

0.5 10

20

30 Period

0% or 2% mortgage premium: +-1% Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Baseline 0% or 2% mortgage premium: +-1%

Nothing. People are too rich to be affected: Too little borrowing.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Model at Work 2: Large housing motive Large housing motive (89% ownership rate). Constant Financial Asset Prices.

• Experiments 1

Shocks to both Earnings and Dividends (+-5%): (Large TFP shock).

2

Shocks to Earnings (from -5% to plus 5%): +-3% of GDP.

3

Shocks to Dividends (from -5% to plus 5%): +-.7% of GDP.

4

Shocks to Mortage Premium 0% to 2%.

• Again the economy runs 50-11-20 state-periods.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Time Series with Aggregate Earnings & Dividends Shock 1.25 1.2

House Price Flat Price

Price

1.15 1.1 1.05 1 0.95 0.9

10

20

30

40

50

60

40

50

60

Period

2

Financial Wealth Dwelling Sales

1.5

1

0.5 10

20

30 Period

+ − 5% of Earnings and Dividends, TFP shock Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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+ − 5% of Earnings and Dividends, TFP shock

Flat prices increase about 5%. House prices increase about 4%. Increase is not immediate but almost. Sales are not procyclical. Financial Wealth moves up and down.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Time Series with Aggregate Earnings Shock 1.25 1.2

House Price Flat Price

Price

1.15 1.1 1.05 1 0.95 0.9

2

10

20

30

40 Period

50

60

70

80

30

40 Period

50

60

70

80

Financial Wealth Dwelling Sales

1.5

1

0.5 10

20

+ − 5% of Earnings, 3.% of GDP Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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+ − 5% of Earnings, 3.% of GDP

Flat prices increase first 7% and creep up to 12%. House prices increase first 4% and creep up to 6%. Even after economy comes back down house prices adjust within two periods. Sales are not procyclical. Financial Wealth gets the slack.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

CAERP

Time Series with Aggregate Dividends Shock 1.25 1.2

House Price Flat Price

Price

1.15 1.1 1.05 1 0.95 0.9

2

10

20

30

40 Period

50

60

70

80

30

40 Period

50

60

70

80

Financial Wealth Dwelling Sales

1.5

1

0.5 10

20

+ − 5% of Dividends, (increase in interest rate) .7% of GDP Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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+ − 5% of Dividends, (increase in interest rate) .7% of GDP

A small increase in the interest rate. Financial Assets do not move. Flat prices drop 7% House prices drop 4% But they do so late (??) Sales are countercyclical.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

CAERP

Time Series with Aggregate Mortgage Premium Shock 1.25 1.2

House Price Flat Price

Price

1.15 1.1 1.05 1 0.95 0.9

2

10

20

30

40 Period

50

60

70

80

30

40 Period

50

60

70

80

Financial Wealth Dwelling Sales

1.5

1

0.5 10

20

0% or 2% mortgage premium: +-1% Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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0% or 2% mortgage premium: +-1%

Flat prices go up 24% (11%). Relatively slowly. House prices go up 10% (5%). Prices come down fast. Sales are strongly countercyclical. We do not see the effect of the multiplicaton of the capital gain.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Model at Work 3: Lucas Tree: 3 Endogenous prices

Large housing motive (89% ownership rate). Moving Financial Asset Prices.

• Experiments 1

Shocks to Mortage Premium 0% to 2%.

• Again the economy runs 50-10-20 state-periods.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

CAERP

Time Series with Aggregate Mortgage Shock House Flat Financial Asset

1.3

Prices

1.2 1.1 1 0.9 10

2

20

30 Period

40

50

60

20

30 Period

40

50

60

Dwelling Sales

1.5

1

0.5 10

0% or 2% mortgage premium: +-1% Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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0% or 2% mortgage premium: +-1%

All prices move together. They seem to move quite a bit. Direct premium on the price. Still too early to tell.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Temporary Conclusions

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Temporary Conclusions

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

........ Sort of

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Temporary Conclusions

........ Sort of

• Effects of +-5% changes

All Income Earnings Dividends Mrtg Prem(+r )

Flat Price 5.% 12.% -7.% 11.4%

House Price 4.% 7.% -4.% 5.%

• Prices change more but not a lot more than fundamentals. • Price movements do not seem to be amplified across dwelling types. • Mortgage premium movements matter most. • Promising Endogenous Stock Prices Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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References

and D. E. Schlagenhauf (2005): “Accounting for Changes in the Homeownership Rate,”

Chambers, M., C. Garriga, Mimeo, Florida State University.

and

Diaz, A., M.-J. Luengo-Prado (2004): “Precautionary Savings and Wealth Distribution with Durable Goods,” http://www.eco.uc3m.es/ andiaz/pdfs/research/durables.pdf.

and

D´ıaz-Gim´ enez, J., L. A. Puch (1998): “Borrowing Constraints in Economies with Indivisible Household Capital and Banking: an application to the Spanish Housing Market (1982-89),” ie, XXII(3), 469–499.

and

Krusell, P., A. Smith (1997): “Income and Wealth Heterogeneity, Portfolio Choice, and Equilibrium Asset Returns,” Macroeconomic Dynamics, 1(2), 387–422. Nakajima, M. (2005): “Rising Earnings Instability, Portfolio Choice, and Housing Prices,” Mimeo, University of Illinois.

and

Ortalo-Magne, F., S. Rady (2003): “Housing Market Dynamics: On the Contribution of Income Shocks and Credit Constraints,” http://research.bus.wisc.edu/fom/documents/hm-latest.pdf.

Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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Time Series with Aggregate Earnings Shock 1.25 1.2

House Price Flat Price

Price

1.15 1.1 1.05 1 0.95 0.9

2

10

20

30

40 Period

50

60

70

80

30

40 Period

50

60

70

80

Financial Wealth Dwelling Sales

1.5

1

0.5 10

20

+ − 5% of Earnings, 3.% of GDP Jos´ e-V´ıctor R´ıos-Rull,, Virginia S´ anchez-Marcos House Price Movements

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