Does money illusion explain house price movements?

1. Doctoral School of Finance DOFIN Does money illusion explain house price movements? MSc Student: Secuesu Andrei Supervisor: Professor Dr. MOISA ALTAR

2. 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).

3. 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 BUT future mortgage payments arelarger in realterms (mortgage is not inflated away.)

4. Money illusion - Related literature • U.K. evidence Real versus nominal - A first-cut Decomposing inflation effects Empirical evidence • Canada evidence

5. “An economic theorist can, of course, commit no greater crimethan to assume money illusion.” Tobin (1972) • Money Illusion: Patinkin (1965), Leontief (1936), Fisher (1928) “That shirt I sold you will cost me just as muchto replace as Iam 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)

6. 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

7. PV of permanent service flow with money illusion Regress Pt / Ltseparately on 1/rt, 1/it, and πt

8. Regress Pt / Ltseparately on 1/rt, 1/it, and πt Persistence ofPt /Ltand 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.

9. 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 Pt/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, rt (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.

10. 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. • 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.

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

12. 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)

13. Log-linearize around steady state and iterate • Subtractrf to obtain excess and excess returns re • Take expectations:E (objective),(subjective)

14. Taking expectations and assuming that TVCs hold Hence,

15. Individualsfail to distinguish between nominal and real rates of returns. They mistakenly attribute 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

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

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

20. 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:

21. The third rowshows 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)

22. 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

23. 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

24. Canada 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.

25. 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)