Analyzing Probabilistic House Price Expectations in Spain: Insights from Household Surveys

2. Introduction • Present new evidence on probabilistic expectations on house price change from the Spanish Survey of Household Finances (EFF) • Evidence from a new question in the EFF where households are asked to assign probabilities to different scenarios of house price changes • Analysing the answers • modelling densities • how heterogeneity in the estimated individual distributions relate to differences in housing properties and household characteristics • How subjective expectations matter for predicting consumption behaviour • Housing investment, car purchases etc.

3. Outline • Subjective probabilities of future house prices in the EFF: the question and pattern of answers to assess coherency • Fitting a probability distribution for each respondent • Relating heterogeneity in expectations to housing and household characteristics • Relating expectations to local housing and labour markets • House price expectations and spending behaviour • Conclusions

4. 1. Subjective probabilities of future house prices in the EFF • The EFF is a representative survey of the Spanish population that contains detailed information on household assets, debts, income, and consumption (and demographics) • Has been conducted on 5 occasions (2002, 2005, 2008, 2011, 2014) to around 6,000 households • Two distinctive characteristics • Oversampling of wealthy households • Panel component with refreshment to maintain representativity • New question to elicit household house price probabilistic expectations in the EFF2011 (and subsequent waves)

5. 1. Subjective probabilities of future HPs • One motivation: Importance of real estate in household wealth • 80% of the value of household assets • all along the wealth distribution: 88% bottom quartile 68% top decile • 83% of owner occupiers, 36% of Spanish households hold other real estate property • Also timely: housing market collapse that shattered HP exp. after 2007 • nº buying housing: 2.3% (annually) 2002-2005 1.1% in 2011 • EFF2011: 23% of hh expect drop over 6% in price of their homes; among hh expecting such large drops the fraction who bought a car was half the fraction in the total population (4.5% vs. 9.4%) • Aggregate expectations about rates of return on housing found to be an important determinant of house purchase (Bover, 2010); Uncertainty/Volatility about these returns also found to play a role • Learning about house price expectations at the individual level may be useful in understanding portfolio composition and consumption

6. 1. Subjective probabilities of future HPs • Other surveys eliciting probabilistic expectations about HP • HRS, the NYFed survey and the American Life Panel, SHIW • Introduced very recently (2010, 2011, 2012) • vary: price of their home, of a typical home in their zip code… • Very few attempts to analyze the answers to such probabilistic HP question • This paper is one of the first empirical studies to document the beliefs of households about the future value of their homes and the first one that uses a representative sample of households

7. 1. Subjective probabilities of future HPs • Subjects answering the 2011 EFF questionnaire were asked the following: • “We are interested in knowing how you think the price of your home will evolve in the next 12 months: • Distribute 10 points among the following 5 possibilities, assigning more points to the scenarios you think are more likely (assign 0 if a scenario looks impossible) • Large drop (more than 6%) • Moderate drop (around 3%) • Approximately stable • Moderate increase (around 3%) • Large increase (more than 6%) • DK • NA”

8. 1. Subjective probabilities of future HPs • Comments about the formulation of the EFF question • Small test pilot conducted beforehand • Refers to price of household main residence • Households have better information about their own house • Sentiment about HP nationwide could be inferred by aggregating individual expectations • Conveying the concept of probability • “Percent chance”, “how likely”, beans/balls to distribute • The respondent is offered 10 points to distribute as opposed to 100 because it is cognitively less demanding • Ranges • predetermined as opposed to self-reported • number: trade-off between more precise stats vs. less cognitively demanding • Numerical answers are linked with verbal expressions (Juster, 1966) • We chose to elicit a density formulation rather than a cumulative distribution formulation (evidence that easier to deal with) • Automatic prompt appears on the screen in case answers do not add up to 10

9. 1. Subjective probabilities of future HPs Item non-response • Only 4.3% of EFF2011 participants did not answer the question 10.5% if non-owner, 3.4% if owner Provides an indication of the extent of ignorance (mixed with unwillingness to respond) • Men are more prone to answering this question than women 2.8% vs. 6.4% non-response • Non-response rates decrease with education (7.1%, 2.5%, 1.5%) • Non-response of over 64 stands out (6.3%) • Significantly negative correlation with the fraction of monetary questions answered

10. 1. Subjective probabilities of future HPs Coherency analysis • Number of intervals used • 60% of respondents express uncertainty and put probability mass in more than one interval; 25% use more than two; 2.5% use all five • Bruine de Bruin et al. (2011) report 70% using more than two bins in answering about their own wage expectation in the NYFed survey • Very small fraction assigning non-zero probabilities to non-adjacent bins • 1.68% • Bunching in the middle of the scale (all 10 points to middle interval) 19.6% • In principle, this group may mix ignorants and strong believers • Lack of specific characteristics in this group suggests that it is not dominated by ignorants Uncertainty • Large fraction of respondents hold their beliefs with certainty: • 10% drop around 3% with certainty • 9.6 % drop over 6% with certainty

11. 1. Subjective probabilities of future HPs . % probability mass in each of the 5 pre-defined intervals . Respondents overwhelmingly put most of the probability mass in the expected drop-in-price region

12. 1. Subjective probabilities of future HPs

13. 2. Fitting a probability distribution for each respondent • Subjects are asked to distribute 10 points among 5 possible changes to the price of their homes over the next year • We use the subject responses to fit a saturated probability distribution • This is useful because it facilitates the calculation of comparable measures of position, uncertainty, and quantiles for all individuals • Using a saturated distribution avoids placing restrictions in the form of the distribution relative to the information in the data (fitting the distribution)

14. 3. Relating heterogeneity in expectations to housing and household characteristics • Quantile regressions from subjective quantile variables • Measured quantiles q𝝉iare to be interpreted as conditional quantiles given characteristics of the individual and the house, both observable and unobservable • To look at the variability in these distributions, we estimate LS regressions of individual quantiles on measured characteristics and postal code dummies (within-postal code quantile estimates) • These quantile regressions are very different from ordinary QR where one fits a quantile model to data that are sample draws from the distribution • Here the left hand side variable consists of direct measures of the conditional quantiles

15. 3. Relating heterogeneity in expectations to housing and household characteristics • Examine the association between quantiles at various points of the estimated individual densities and demographics, within postal codes • In particular I consider the individual median and the 10th, 25th, 75th, and 90th percentiles as distributional measures for each respondent • The regression equations are of the form: • q𝝉i = Xi 𝜷𝝉 + Zi γ𝝉 + u𝝉I • Xi is a vector of household characteristics such as age, education, gender, income and wealth • Zi is a vector of house characteristics, which includes postal code dummies, log (price/square meter) and in some cases also an indicator of age of the house • There are 1,094 postal codes in our data, 212 of them have only one household and 71 have 10 or more.

16. 3. Relating heterogeneity in expectations to housing and household characteristics Table 5. Quantiles of subjective probability distributions of house prices (within postal codes estimates)

17. 3. Relating heterogeneity in expectations to housing and household characteristics Table 6. Uncertainty in subjective probability distributions of house prices (within postal codes estimates)

18. 3. Relating heterogeneity in expectations to housing and household characteristics • P/m2 (self-assessed) • joint distribution of self-assessed HP and expectations (interestingly not a predictor given controls) • Age • lower declines in the lower part of the distribution as age increases • progressively lower uncertainty with age • Occupation (relative to white collar) • Blue collar workers: more optimistic expectations all over the distribution • Self-employed: negative shift upper part of the distribution; less optimistic • Bought recently (last 6 years) • more optimistic; similar over the distribution but more precise in upper part • same results if “House built in the last 6 years” so does not seem to reflect reverse causality; results unchanged if omitted

19. 3. Relating heterogeneity in expectations to housing and household characteristics • Result on gender stands out • Being a woman produces a positive shift particularly at the median and top wealth quantile • difficult to explain in terms of differences in information as one may do with education, occupation, age • does not seem to be related to risk aversion either • An Abadie-Imbens matching estimator of the gender average treatment effect, which uses the controls in a non-parametric way, produces similar results (both in magnitude and significance); also weighting on the propensity score • further evidence on potential differences in valuations by gender → regressed self-assessed values of different assets reported in the EFF on same controls (Table A2) → women tend to provide higher estimates for the value of their house but lower ones for their financial assets • Affect heuristics? Preferences affecting judgement?

20. 3. Relating heterogeneity in expectations to housing and household characteristics • What these results say is that there is a difference by gender among respondents to the survey (controlling for postal code and other covariates), who are meant to be the most knowledgeable about household finances • Are women more optimistic or simply more realistic? • Aggregate of counterfactual point predictions of house price changes across all households as if all were male/female respondents: • Actual aggregate house price change between 2011 and 2012 around -10 percent • The counterfactual aggregate male and female point forecasts are -3 and -2.6 percent respectively. Even if the position of the subjective probability distribution may be affected by framing, the distance between actual and predicted changes is sufficiently large to conclude that women were more optimistic rather than more realistic by comparison with men.

21. 3. Relating heterogeneity in expectations to housing and household characteristics • Are people with more certain expectations more accurate? Age is the main observable associated with differences in the degree of certainty in expectations • Age does not have a significant effect on point-forecasts as measured by the subjective median • →ie no evidence of differences in predictive accuracy according to the degree of certainty as captured by age Another indicator of the potential association between accuracy and certainty: • Correlation between the median and the inter-quartile range of the individual subjective distributions: -0.4 • → iemore certain individuals tend to predict lower falls in house prices. Given the actual declines described above, such negative correlation would suggest that more certain expectations are less accurate • (this result is consistent with recent evidence in psychology that superforecasters are more uncertain about their forecasts - Tetlockand Gardner, 2015)

22. 3. Relating heterogeneity in expectations to housing and household characteristics Importance of location of the house On q50 • % of explained variation due to postal code dummies 96.6% • % of postal code variation explained • by municipality dummies 63.7% • by province dummies 29.2% On q75-q25 • % of explained variation due to postal code dummies 94.7% • % of postal code variation explained • by municipality dummies 75.4% • by province dummies 29.3%

23. 3. Relating heterogeneity in expectations to housing and household characteristics Importance of location of the house • Estimated effects of other variables may be misleading in the absence of location information Eg. gender effect would not be found (Table A3)

24. 4. Relating expectations to local housing and labour markets . Respondents expect the price of their home to grow more in areas where HP are already high

25. 4. Relating expectations to local housing and labour markets Table 8. Postal code dummies on housing and labour market variables (province). Quantiles • when forming their HP expectations respondents extrapolate the recent evolution of the province labour and housing markets • Change in unemployment rate in 2010 wrt 2009 of +1 pp implies -0.18 pp on expected median HP change • Rate of return on housing in 2009 of -1% implies -0.17pp on expected median HP change

26. 4. Relating expectations to local housing and labour markets Table 9. Postal code dummies on housing and labour market variables (province). Uncertainty • Change in unemployment rate in 2010 wrt 2009 of +1 pp implies +0.10pp on expected interquartile HP change • Change in rate of return on housing in 2009 wrt 2009 of +1pp implies 0.04pp on expected interquartile HP change

27. 5. House price expectations and consumption decisions • One of the main purposes of collecting subjective expectations data is to help understand behavior • → whether HP expectations predict household expenditure decisions • Large unexpected shocks to HP expectations in Spain after 2007 • - Large drop in % of households buying second house • 1.7% a year between 2002 and 2005 • 0.6% in 2011 • (owner occupied housing from 0.6 to 0.5%) • - 9.4% of the population of households bought a car in the last 12 months • Among the 7.2% of households (490 households) who expect a large drop in HP with certainty this rate is 4.5%

28. 5. House price expectations and consumption decisions • Expenditure questions in the EFF • Car purchase in last 12 months (if purchase; and amount if purchased) • Housing equipment (furniture, washing mashine, etc.) (if; amount) • Amounts spent on food expenditure (at home and outside) as well as on other non-durables also collected • Purchase of secondary housing • both investment and consumption • evidence in Bover (2010): large positive effect of aggregate expected returns on housing on the hazards of purchasing a house • may mask individual differences (both in household and house attributes)

29. 5. House price expectations and consumption decisions • Probit models for the probability of • Buying secondary housing • Buying a car • Buying other big ticket items • To analyze expenditure • Tobit estimates for the amounts spent on • Other housing • Cars • Other big ticket items • Multivariate regressions • Amount spent on food and other non-durables • [to check restrictiveness of tobit estimates assumption –same relationship for decision to purchase and amount- implied tobit probabilities for the various purchase probabilities also provided and compared to probit ones]

30. 5. House price expectations and consumption decisions • 2 variables measuring household beliefs about future HP • Location of expectations: 0/1 dummy taking value 1 for people expecting a large certain drop with certainty (ie all ten points to more than 6% drop) • Uncertainty about expectation location: 0/1 dummy taking value 1 for respondents assigning points to more than one option • → constructed directly from household responses • Importantly, able to control for expectations about future household income (qualitative question) • Information about occurrence of positive or negative income shocks • Other controls: log net wealth, interactions of it with HP expectations, respondent gender, age (6 intervals), dummies nº persons, couple, children, labour status respondent and partner • Location variables: postal codes or municipality size (7 categories)

31. 5. House price expectations and consumption decisions • About the timing of subjective expectations and expenditure outcomes: • Ideally, how expectations held at t about the future influence decisions at t • Expectation data correspond to beliefs held at the time of the interview, while the expenditure data refer to purchases during the last 12 months → good timing approximation, specially for durables • Potential concern of reverse causality is that the uncertainty about the future price of the main residence may be reduced by investment in information associated with the purchase of other housing • However, the results in Table 6 indicate a lack of association between uncertainty and having bought the main residence recently → suggests that endogenous reductions in uncertainty may not be very important

32. 5. House price expectations and consumption decisions • Most pessimistic households have a significantly lower probability of buying a house than the rest -0.8 pp at the median, -1.24 pp at the 80th percentile • Uncertainty about the evolution of house prices also associated with reductions in the probability of buying a house -0.63 pp at the median, -0.8 at the 80th percentile • Expecting a large drop in HP also associated with smaller probability of buying a car -4.5 pp at the median but not for wealthier households • However, uncertain expectations are positively correlated with the probability of buying a car and, mostly with other big ticket items → could reflect some substitution effects • Probabilities of purchase from tobit are very much in line, can be obtained controlling for postal code for the whole sample and confirm the results (Table 11B)

33. 5. House price expectations and consumption decisions • Effects of HP expectations on average probabilities of purchase

34. 5. House price expectations and consumption decisions • Estimates for the various expenditures • Again, the larger and most significant effects are the reduction in the amounts spent when buying second housing for households expecting a large drop in the price of their home or for those being uncertain about the evolution of the value of their home • For these households the amounts spent when buying a car are also significantly lower (-13,000€ at the median level of wealth) • Similarly, some evidence of substitution effects for expenditures on other big ticket items and on food and other non-durables among wealthy households uncertain about future house prices (but these do not hold when controlling for postal code)

35. 5. House price expectations and consumption decisions Table 11A. Effects of house price expectations on expenditures

36. 6. Conclusions • The evidence on the HP question in the EFF is very encouraging since an important fraction of people seems to understand it and to provide meaningful answers (as long as respondents are familiar with the subject matter) • There is substantial heterogeneity in probabilistic HP expectations both in the location of such expectations as well as for the amount of uncertainty around them Women and blue collar workers more optimistic; older more certain • Results provide valuable information about heterogeneity in the housing market Location at the postal code explains most of the observed heterogeneity Past returns to housing and unemployment rates are found to be strong determinants of the estimated effects of location

37. 6. Conclusions • Novel findings about the association between house price probabilistic expectations and various durable expenditures • Pessimistic expectations households have significantly lower probabilities of buying a house and of buying a car (and amounts spent smaller) • However, no association between HP expectations and expenditure on other big ticket items, nor on food and other non-durable expenditure • Greater uncertainty in HP expectations is associated with lower probability of buying a secondary house (and smaller amounts spent) but not with the purchase or the amount spent in other goods • The previous results vary with wealth

38. 6. Conclusions • Is it a temporary effect (just postponing) or not? • Housing: (S,s) model estimates for house purchases in Bover (2010) show that the effect of predicted returns on housing on the hazards of purchasing a house comes through a decrease in the desired proportion of housing wealth as opposed to postponing transactions (no effect on the inaction range)

39. THANK YOU

41. Ten most frequent answers

42. 2. Fitting a probability distribution for each respondent • We assume that the probability distributions have a pre-specified support and a pre-specified neighbourhood around zero for the no change category

43. 2. Fitting a probability distribution for each respondent { 0.1 0.7 0.8 0.9 1} 1 0.9 0.8 0.7 0.1 -6 -3 0 3 6 Change in HP (%)

44. 2. Fitting a probability distribution for each respondent { 0.1 0.7 0.8 0.9 1} 1 0.9 0.8 0.7 0.1 -15 -6 -3 -1 0 1 3 6 15 Change in HP (%)

45. 2. Fitting a probability distribution for each respondent { 0.1 0.7 0.8 0.9 1} 1 0.9 0.8 0.7 0.1 -15 -6 -3 -1 0 1 3 6 15 Change in HP (%)

46. 2. Fitting a probability distribution for each respondent { 0.1 0.7 0.8 0.9 1} 1 0.9 0.8 0.7 0.1 -15 -6 -3 -1 0 1 3 6 15 Change in HP (%)

47. 2. Fitting a probability distribution for each respondent { 0.1 0.7 0.8 0.9 1} 1 0.9 0.8 0.7 0.5 0.1 -15 -6 -3 -1 0 1 3 6 15 q50 Change in HP (%)

48. 2. Fitting a probability distribution for each respondent { 0.1 0.7 0.8 0.9 1} 1 0.9 0.8 0.7 0.25 0.1 -15 -6 -3 -1 0 1 3 6 15 q25 Change in HP (%)

49. 2. Fitting a probability distribution for each respondent • Having specified end-points and an interval around zero, to get a full cdf we simply connect the points we observe using straight lines • so that the cdf is piece-wise linear and the density is flat within segments • This allows to calculate all quantiles by simple linear extrapolation • To obtain q𝝉i for some 𝝉 ∊ (zli , z(l+1)i ) we use • q𝝉i = qzli + [(𝝉 - zl i )/(z(l +1)i - zl i )](qz(l+1)i- qzli) • where the zl i are cumulative probabilities and qzli the corresponding quantiles given by (-15, -6, -1, 1, 6, 15) for l = 0, 1, …, 5 • (back)

50. 3. Relating heterogeneity in expectations to housing and household characteristics • Unobserved heterogeneity in the previous quantile models is large but not explained by any other observables • e.g. risk aversion • Results are qualitatively robust to the way of fitting the distribution • e.g. alternative cut-off points