Does money illusion explain house price

movements?

Doctoral School of Finance DOFIN

MSc Student: Secuesu AndreiSupervisor: Professor Dr. MOISA ALTAR

Definition of money illusion

Money illusion refers to the tendency of people to think of currency in nominal, rather than real, terms. In other words, people mistake nominal variables for real variables. The term was coined by John Maynard Keynes in the early twentieth century, and Irving Fisher wrote an important book on the subject, Money Illusion, in 1929. The existence of money illusion is disputed by monetary economists who contend that people act rationally (ie think in real prices) with regard to their wealth.

Shafir, Diamond and Tversky (1997) have provided compelling empirical evidence for the existence of the effect and it has been shown to affect behaviour in a variety of experimental and real world situations.

Nominal prices provide a convenient rule of thumb for determining value and real prices are only calculated if they seem highly salient (eg. in periods of hyperinflation or in long term contracts).

BUT

future mortgage payments are larger in real terms

(mortgage is not inflated away.)

Decision: Monthly rent versus monthly mortgage payments

•Example of money/inflation illusion decline in inflation decline in nominal interest rate i monthly payments decline larger mortgage higher house prices

Money illusion - Related literature

U.K. evidence Real versus nominal - A first-cut

Decomposing inflation effects

Empirical evidence

Canada evidence

“An economic theorist can, of course, commit no greater crime than to assume money illusion.” Tobin (1972)

Money Illusion: Patinkin (1965), Leontief (1936), Fisher (1928) “That shirt I sold you will cost me just as much to replace as I am charging you [...] But I have made a profit on that shirt because I bought it for less.” Recent survey evidence: Shiller (1997a), (1997b) Related Psychological Biases: Shafir, Diamond, Tversky (1997), Genesove-Mayer (2001), ... framing effect, mental accounting, cognitive dissonance, self attribution bias

Stock market: Modigliani-Cohn (1979), Asness (2000, 2003), Ritter-Warr (2002),

Campbell-Vuolteenaho (2004), Cohen et al. (2005)

Stage 1: Focus on price-rent ratio (Pt/Lt )

● abstracts from movements of fundamentals that affect prices

and rents symmetrically (demographics, land cost etc.)

● not perfect substitutes: pride of ownership, . . .

Stage 2: Decompose price-rent ratio in:

● expected return (incl. risk premium)

● expected rent growth rate

● “mispricing”

Inflation effect on each part

PV of permanent service flow

tttt

t

t

rrE

L

P 1

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1

11

with money illusion

tttt

ttt

t

t

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rE

L

P 1

)1(

1

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1

11

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Regress Pt / Lt separately on 1/rt , 1/it, and πt

Regress Pt / Lt separately on 1/rt , 1/it, and πt

Persistence of Pt /Lt and regressors might lead to spurious results.

Regress forecasts error on 1/rt , 1/it, and πt

We explore whether it, rt, πt, 1/it and 1/rt have forecasting power for the price rent ratio.

In assessing the forecasting performance of these variables, one faces several econometric issues:

in-sample regression results may be spurious, and both R2 and statistical significance of the regressor are biased upward if both the expected part of the regressand and the predictive variable are highly persistent since Pt/Lt is highly persistent, this could lead to spurious results.

in exploring the forecastability of the price-rent ratio, the choice of the control variables is problematic and to some extent arbitrary since the literature on housing prices has suggested numerous predictors. Moreover, Poterba (1991) outlines that the relation between housing prices and forecasting variables often used in the literature has not been stable across sub-samples.

We address both issues jointly.

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

. |*******| . |*******| 1 0.968 0.968 78.708 0.0000 . |*******| .*| . | 2 0.929 -0.126 152.09 0.0000 . |*******| .*| . | 3 0.883 -0.109 219.31 0.0000 . |****** | .*| . | 4 0.834 -0.062 280.08 0.0000 . |****** | .*| . | 5 0.78 -0.095 333.91 0.0000

RATIO

0sfor ]/[

0sfor

1111

111,1

^

ttsttt

ttstt

LPELP

LP

]/[ 11 ttst LPE

For the first problem, we remove the persistent component of the price-rent ratio by constructing the forecasting errors:

where s is the forecasting horizon and is the (estimated) persistent component of the price-rent ratio.

Second, we estimate by fitting a reduced form vector auto regressive model (VAR) for P t/Lt, the log gross return

on housing, rh;t, the rent growth rate Δlt and the log real return on the twenty-year Government Bonds, r t (constructed as the nominal rate,

it, minus quarterly inflation)

This approach for constructing forecast errors, is parsimonious since it allows us to remove persistency from the dependent variable without assuming a structural model. It is also conservative since the reduced form VAR is likely to over-fit the price-rent ratio.

]/[ 11 ttst LPE

We use quarterly U.K. data over the sample period 1987:Q1:2007:Q1. The VAR is estimated with one lag since this is the optimal lag length suggested by both the Bayesian and Akaike information criteria.

Vector Autoregression Estimates Standard errors in ( ) & t-statistics in [ ]

RETURN_H RENT_GROWTH RATIO R

RETURN_H(-1) 1.0038 -0.0895 0.0205 0.2571[ 58.1189] [-1.69829] [ 0.83429] [ 2.13740]

RENT_GROWTH(-1) -0.0832 -0.3546 0.0601 -0.4360[-2.42667] [-3.38872] [ 1.23091] [-1.82591]

RATIO(-1) -0.0054 0.0390 1.0046 -0.1336[-0.52205] [ 1.22975] [ 67.8457] [-1.84559]

R(-1) 0.0008 0.0443 -0.0141 0.8856[ 0.09293] [ 1.79420] [-1.22382] [ 15.7070]

R-squared 28.75% 16.20% 98.74% 81.75% Adj. R-squared 25.90% 12.84% 98.69% 81.02%

Following Campbell and Shiller (1988), for small perturbations around the steady state,

the variables included in the VAR should capture most of the relevant information for the price-rent ratio.

Indeed, the R2 of the VAR equation for Pt/Lt is about 98%, which is consistent with previous studies that

have outlined the high degree of predictability of housing prices.

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2 4 6 8 10 12 14 16 18

R_PATRAT_RPIR_PATRAT_IR_PATRAT_1_I

R_PATRAT_1_RR_PATRAT_R

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0

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T_STAT_RPIT_STAT_RT_STAT_1_R

T_STAT_IT_STAT_1_I

U.K R 2̂ U.K. t-statistic

1. For s =0 , the output is that of a standard forecasting regression, since

The real interest rt rate has little if any forecasting power, R2 aprox 2% and t-stat of 0.741, same thing for reciprocal with R2 at 0.3%, it has negative slope and explains 28% - consistent with fundamentals, also inflation, significant predictor, R2 22%, negative slope, consistent with Modigliani and Cohn (1979) – inflation causes a negative mispricing in assets.

2. For s > 0, we would expect the statistical significance and explanatory power to be reduced as now we eliminate the persistence of the regressand.

It is clear that the real rate and its reciprocal still have no forecasting power.To the contrary, the nominal rate and inflation are statistically significant forecasting variables and continue to explain between 14% and 10% of the movements in the price-rent ratio.

tttt LP 1,1

^

•Regress deltas for each forecasting horison s on it, rt, πt, 1/it and 1/rt

Case-Shiller (1989) house price changes are predictable

inefficiency ? What explains variation of changes in price-rent ratio?

lagged inflation and nominal interest rates explains 28 to22 percent

(significant regressors, consistent with money illusion)

real interest rate has no predictive power

Is inflation in pricing kernel/rent growth predictions for other reasons?

(risk-premium, growth prediction, frictions)

Log-linearize around steady state and iterate

• Subtract rf to obtain excess and excess returns re

•Take expectations: E (objective), (subjective)

Taking expectations and assuming that TVCs hold

Hence,

tte

tht barE

1,1

1 ~

Individuals fail to distinguish between nominal and real rates of returns. They mistakenlyattribute a decrease (increase) in inflation πt to a decline (increase) in real returns, rh,t

or equivalently ignore that a decrease in inflation also lowers nominal rent growth rate

As suggested in Campbell and Vuolteenaho (2004) I use as risk proxy the GARCH –estimate of the conditional volatility of an investment that is long on housing market and short on the 10 years government bonds.

Dependent Variable: LONG_SHORTMethod: ML - ARCHSample (adjusted): 1988Q1 2007Q1Included observations: 77 after adjustmentsConvergence achieved after 22 iterationsVariance backcast: ONGARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1)

Coefficient Std. Error z-Statistic Prob.

AR(1) 0.8577 0.0611 14.0291 0.0000AR(2) -0.3935 0.0846 -4.6532 0.0000AR(3) 0.3905 0.0747 5.2245 0.0000

Variance EquationC 0.0007 0.0002 4.1405 0.0000RESID(-1)^2 -0.1105 0.0336 -3.2872 0.0010GARCH(-1) 0.9866 0.0438 22.5300 0.0000

R-squared 0.5542 Mean dependent var 0.0563Adjusted R-squared 0.5228 S.D. dependent var 0.1308S.E. of regression 0.0903 Akaike info criterion -2.1930Sum squared resid 0.5793 Schwarz criterion -2.0104Log likelihood 90.4310 Durbin-Watson stat 1.9152

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LRATIO PSI PSI2

Variable Control Lagged)1( OLS from residual

)1( OLS from residual

1

12

1

1

,

,

VOLrE

VOLrE

et

et

th

th

Slope Coeff. R-squared Slope Coeff. R-squared Slope Coeff. R-squared

-1.3253 37.49% -0.0111 36.95% 0.1478 39.44%(0.0000) (0.0000) (0.0000)

-0.8224 21.85% -0.0064 17.24% 0.0430 16.45%(0.0000) (0.0000) (0.0004)

-18.7193 21.29% -0.2211 44.17% 1.6420 51.09%(0.0000) (0.0000) (0.0000)

0.7779 27.80% 0.0092 50.99% -0.0666 56.32%(0.0000) (0.0000) (0.0000)

it log(1/it)

RegressorsDependent Variables

PSI

PSI2

Obj_exp_ret_rent

πt

-Subj_exp_ret_h

Univariate regression outputs of the three components of the price-rent ratio on three possible explanatory variables

First row : univariate regression outputs of the mispricing measure and the proxies that are meant to capture inflation illusion .

regressors are statistically significant signs of coefficients are consistent with money illusion: the mispricing of the price/rent

ratio tends to rise as inflation and nominal interest rates decrease and the log of the reciprocal of the nominal rate rises.

proxies for inflation bias are able to explain between 37.5% and 39.5% of the variation. We plot the fitted value of inflation versus the psi mispricing below:

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10 20 30 40 50 60 70 80

FITTED_PSI_RPI PSI

The third row shows that the expected future real rent growth rates seem to be negatively correlated with inflation and nominal interest rate and positively correlated with the log reciprocal of the nominal rate.

The regressors explain between 21% and 51% of the time series variation

Consistent with Fama (1981) – high inflation proxies for worsening of future economic conditions

On the other hand, this could simply be the outcome of housing rents being more sticky than the general price level.

The fourth row outlines that there is a significant link between inflation and (subjectively expected) risk premia on the housing investment

The regressors explain between 27 percent and 56 percent of the time series variation

positive signs of the regressors imply that higher inflation is associated with a lower risk premium on housing investment (remember dependent variable is neg)

estimate of the elasticity of the price-rent ratio with respect to each regressor = sum of the slope coefficients associated with that regressors

On average, 1% increase in inflation

On average, 1% increase in nominal interest rates

19.26% decrease in the price of housing relative to rent largest contribution given by effect of inflation on objective expectations of rent growth rates,followed by psi

0.223% decrease of Pt/Lt, largest and second largest contribution same as above

Canada

The mispricing measure for Canada is computed in the same style using this time monthly data for house prices and rents from January 1980 to April 2007.

Housing and rent data was obtained from the BIS, with the latter being extracted as the rent component of the CPI.

As a measure of inflation we used the CPI excluding shelter.

As interest rate we used the 10-year par yields of Canadian governemnt bonds

Canada

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50 100 150 200 250 300

PSI_CANADA LRATIO

Slope Coeff. R-squared Slope Coeff. R-squared Slope Coeff. R-squared

-0.5854 13.62% -0.0094 42.79% 0.0818 47.17%(0.0000) (0.0000) (0.0000)

-3.2222 19.22% -0.0516 51.98% 0.4541 57.44%(0.0000) (0.0000) (0.0000)

0.1068 9.66% 0.0015 23.50% -0.0135 27.17%(0.0000) (0.0000) (0.0000)

Dependent Variables

Regressors

πt it log(1/it)

PSI

Obj_exp_ret_rent

-Subj_exp_ret_h

The measure of mispricing generally has the right pattern of correlation with the price-rent ratio as in chart

Inflation explains 13.26% of the variation ofthe estimated mispricing component, less than is explained by the nominal interest rate (42.8%)

The explanatory power of inflation on the subjective expectations of housing returns is weaker (only 9.66%) and 1% increase in inflation aproximates into a 3.7% decrease of Pt/Lt.

The correlation between the mispricing measures for U.K., Canada and

inflation and the nominal interest rate are negative, as in Modigliani-Cohn (the mispricing is greater in low inflation and low nominal interest environments)

Inflation impact on expected housing returns is significant and the sign contradicts rational channels through which inflation could impact on house prices.(if inflation made economy more risky, it would drive up the required risk premium on housing sign should have been positive.It is not. (in times of high inflation, housing investment is considered less risky).One explanation : we use a before tax measure of house returns, so an increase in inflation increases after-tax return on housing, therefore lowering tbe before-tax risk premium)

However, rational channels could explain inflation effects because– High inflation leads to lower expected rent growth (ex: stagflation caused by a cost-push shock)