## Key messages

House price expectations play an important role in observed housing market dynamics. This note adds to a growing literature aimed at better understanding how expectations of future changes in house prices are formed and updated. Of particular interest is the extent to which households impart, or extrapolate, past house price changes into their expectations of future house price changes. Extrapolative expectations feature prominently in accounts of boom-bust cycles in housing markets, yet there is little direct evidence on the process through which house price expectations are formed.

Drawing on the recent work of Armona, Fuster and Zafar (2018), we conduct a randomized information experiment leveraging the Canadian Survey of Consumer Expectations (CSCE). We find the following:

- When asked about their perceptions of house price growth over the past one and five years, respondents tend to overestimate house price growth at the one-year horizon but underestimate it at the five-year horizon.
- Once presented with information about actual house price changes, households subsequently revise their expectations of future house price changes in an extrapolative manner.
- For year-ahead expectations, respondents extrapolate to a degree consistent with the observed persistence in house price growth, although they tend to underestimate the strength of persistence.
- However, respondents also extrapolate the information into five-year expectations, a horizon at which house price growth has historically reverted back to its mean.

- Our findings suggest it is important for policy-makers concerned about boom-bust cycles in house prices to monitor house price expectations, especially at longer horizons. This is particularly relevant in the Canadian context, where house prices in certain markets have displayed signs of “froth” in recent years.

## Experiment design

Our data come from an information experiment carried out in conjunction with the CSCE.1 We conduct the experiment in three steps (Figure 1).

First, we ask respondents about their perceptions of house price changes in their local area over the previous one and five years, and about their expectations of future local house price changes over the next one and five years.

In the second step, respondents are randomly distributed into three groups. The first two groups are the treated respondents: they are exposed to objective information about actual local house price changes over either (i) the past year (one-year treatment or “T1”) or (ii) the past five years (five-year treatment or “T5”). Specifically, we inform treated respondents about the percentage change in the Teranet house price index in their forward sortation area (i.e., the area identified by the first three digits of their postal code). The third group of respondents—the control group—are given no information.

In the third step, future house price expectations are re‑elicited at both time horizons from all respondents.

### Figure 1: Experiment design

#### Step 1

Elicit perceptions of past house price growth

Previous

1 and 5 years

Elicit perceptions of future house price growth

Next

1 and 5 years

#### Step 2

1-year treatment

Reveal house price growth over past year

5-year treatment

Reveal house price growth over past 5 years

Control group

No information provided

#### Step 3

Re-elicit expectations 1 and 5 years ahead

## Perceptions of past house price growth

We begin by looking at how respondents’ perceptions of changes in house prices over the past one and five years line up with observed house price changes over those same horizons. As shown in Chart 1a, a clear positive correlation exists between perceived and observed house price changes. In other words, respondents residing in areas that experienced higher (lower) rates of house price growth also report higher (lower) perceived house price growth, on average.

However, when asked about their perceptions of house price growth over the past year, most respondents tend to *overestimate* actual house price growth over the past year. The degree of overestimation is particularly large for those who experienced weak or negative house price growth. Quite a different picture emerges when it comes to house price growth over the past five years. In this case, perceptions are fairly accurate among respondents who experienced relatively low rates of house price growth. However, those who experienced higher rates of house price growth tend to *underestimate* by a wide margin.

Next, we define a “perception gap” as the difference between observed and perceived house price growth, and we plot the distribution of these gaps at both the one- and five-year horizons (Chart 1b). A positive (negative) gap reflects that respondents underestimated (overestimated) past house price changes relative to observed outcomes. Consistent with the observations from Chart 1a, one-year perception gaps have a negative skew, with respondents overestimating house price growth by an average of 3.2 percentage points. In contrast, a clear positive skew emerges in five-year perception gaps, with a mean underestimation of 2.4 percentage points.

Thus, while perceptions of past house price growth are correlated with reality, substantial perception gaps exist. This means that the information provided to a random subset of respondents in the second step of the experiment differs materially, on average, from their perceptions of past changes in house prices.

## Updating of house price expectations

Next, we investigate how respondents revise their house price expectations when presented with objective information on past house price changes in their forward sortation area.

Starting with respondents who were shown data on house price growth over the past year, Chart 2a depicts a positive relationship between revisions of year-ahead expectations and perception gaps. Respondents who initially underestimated (overestimated) past house price changes subsequently revised their year‑ahead house price expectations upward (downward). In other words, respondents extrapolated the information they were given on past house price changes into their expectations of future house price growth.2

Surprisingly, some revisions are also evident among respondents who were *not* provided any information (Chart 2b). Nevertheless, respondents in the treated group revised their expectations to a greater extent, on average, than those in the control group (about three times more). Importantly, we find the differences in revisions between the two groups to be statistically significant, as shown in Table A-1 in Appendix A.

### Chart 2: Relationship between one-year revisions and one-year perception gaps

#### a. Treatment group (T1)

#### b. Control group

Turning to respondents who were provided data on house price growth over the past five years, we see a similar pattern of revisions. Chart 3a shows that the respondents in the treated group materially revised their expectations and that these revisions were positively correlated with their initial perception gaps. In this case, though, we see virtually no revision by the control group (Chart 3b), which is to be expected since the five‑year perception gap is never revealed to them.

To sum up the relationships depicted in Chart 2 and Chart 3, treated respondents significantly revised their house price expectations relative to the control group upon being provided relevant information about past changes in house prices.3 They made these revisions in an extrapolative manner, with greater underestimation of past house price changes leading to a larger upward revision of future expectations. This was true at both the one- and five-year horizons. Thus, because of (i) the experiment’s design (Figure 1) and (ii) the random selection of respondents who are exposed to the information treatment, we provide a causal relationship between past house price changes and expectations of future changes.

### Chart 3: Relationship between five-year revisions and five-year perception gaps

#### a. Treatment group (T5)

#### b. Control group

Next, we ask whether the updating behaviour we observe is reasonable given the empirical properties of house prices. Of particular interest is measuring how the degree of extrapolation from past information compares with the observed persistence in house price growth.

### Chart 4: Comparison of updating behaviour with historical persistence of house price growth

Chart 4 plots estimates of the degree of extrapolation alongside empirical estimates (obtained from autoregressions) of the observed persistence in house price growth at both one- and five-year horizons. Note that these autoregressions are estimated for each of over 1,600 forward sortation areas, so the numbers reported in the chart are averages.

In the case of one-year expectations, the estimate of 0.24 means that for each percentage point of underestimation (overestimation) of past one-year house price growth, treated respondents revise up (down) their expectations by 0.24 percentage points.4 In comparison, the mean estimated autoregressive coefficient for one‑year house price growth is 0.46. Said differently, house price growth at the one-year horizon is quite persistent, so the extrapolation evident in our experiment is not unreasonable. In fact, these estimates suggest respondents do not extrapolate enough at short horizons. This is consistent with results using data for the United States.5

However, the picture is quite different at the five-year horizon. For each percentage point underestimation (overestimation) of past five-year house price growth, treated respondents revise up (down) their expectations by 0.14 percentage points. In contrast, the mean autoregressive coefficient for the five-year horizon is negative, indicating that house price growth reverts to its mean over longer horizons. Thus, the extrapolation of the provided information into longer-term expectations is not easily justifiable based on the empirical properties of house prices.6

## Implications

To the extent that house price expectations influence housing market outcomes, our findings have important implications. Extrapolation (particularly at long horizons) can lead to self-perpetuating increases in house prices that may not be supported by economic fundamentals. This factor could have been at play in Canada in recent years, as house prices in Toronto and Vancouver rose at a rapid rate.

The results of our experiment suggest that policy-makers concerned about boom-bust cycles in house prices should pay close attention to house price expectations, especially at longer horizons. Unfortunately, no such data for Canada have been readily available. Even the CSCE, when first designed, elicited house price expectations only at the one-year horizon. Recently, further questions have been added to elicit house price expectations at the five-year horizon, so tracking these data will be possible going forward.

## Appendix A

### Regression analysis of the treatment effects

Our main regression model for updating house price expectations is as follows:

\( Δy_{i,h}\) \(=\,β_{0}\) \(+\,β_{1} T_{1,i}\) \(+\,β_{2} T_{5,i}\) \(+\,β_{3} x_{i,1} \) \(+\, β_{4} x_{i,5} \) \(+\, β_{5} (T_{1,i}*x_{i,1})\) \(+\, β_{6} (T_{5,i}*x_{i,5})\) \(+\,ε_{i,h}, (1)\)

where \(Δy_{i,h}\) is the revision in house price expectations, either for the one-year horizon (h = 1) or the five year horizon (h = 5). \(T_{1,i} (T_{5,i})\) is an indicator that equals one if respondent i is assigned to treatment T1 (T5); \(x_{i,1}\) is i’s perception gap for the past H years, where H = {1, 5}. The *β*s are the parameters of interest.

The constant term, \(β_{0}\), captures the average revision for the control group when the perception gap is zero. \(β_{1}\) represents the difference in average revisions between respondents in the T1 group and in the control group, also when the perception gap is zero. Likewise, \(β_{2}\) represents the difference in average revision between respondents in the T5 and in the control groups. \(β_{3}\) and \(β_{4}\) capture revisions related to the one-year and five-year perception gaps, respectively, for respondents in the control group.

The main coefficients of interest are \(β_{5}\) and \(β_{6}\). For example, the estimate of \(β_{5}\) shows the causal effect of the past one-year information treatment on T1 respondents’ revisions of expected house price growth. In other words, it measures the sensitivity of expected house price growth with respect to the one-year perception gap for the T1 group. \(β_{5}\) and \(β_{6}\) will be different from zero if revisions are systematically driven by the difference between the revealed information and a respondent’s prior perceptions about past changes in house prices.

We estimate equation (1) using ordinary least squares.7 Columns 1 and 2 of Table A-1 show the estimates for the one- and five-year expectation revisions, respectively. In column 1, we see that the estimate of \(β_{5}\) is positive and significant (5 percent level): the estimate of 0.10 implies that, for each percentage point underestimation (overestimation) of past one-year house price changes, T1 respondents revise up (down) their year-ahead expectations by 0.10 percentage points. That is, T1 respondents revise their year-ahead expectation by an additional 0.10 percentage points relative to respondents in the control group, who, even though they are not provided any new information between the baseline and the final stage of the survey, systematically revise their one-year ahead expectations by 0.14 percentage points. This highlights the importance of having a control group to account for the effect that completing a survey focused on house prices may have on expectations. Column 1 shows that the estimate of \(β_{6}\) is also positive, significant (1 percent level) and larger than \(β_{5}\). For each percentage point underestimation (overestimation) of past one-year house price changes, T5 respondents revise up (down) their year-ahead expectations by 0.43 percentage points.

Turning to column 2 in Table A-1, we see a positive relationship between five-year expectation revisions and perception gaps. Estimates of \(β_{5}\) and \(β_{6}\), in addition to those of \(β_{3}\) and \(β_{4}\), imply that individuals in the treatment groups revise up (down) their five-year expectations by 0.05 to 0.14 percentage points per percentage point of underestimation (overestimation) of past house price changes.

### Table A-1: Home price expectation revisions

Home price expectation revisions at horizon: | 1 year | 5 years^{†} |

(1) | (2) | |

T1 (β_{1}) |
-0.544^{*} |
0.0371 |

(0.283) | (0.0849) | |

T5 (β_{2}) |
-0.724^{*} |
-0.207^{**} |

(0.406) | (0.104) | |

1-year perception gap (β_{3}) |
0.143^{***} |
0.0213^{***} |

(0.0252) | (0.00688) | |

5-year perception gap^{a} (β_{4}) |
0.0362 | 0.0212^{**} |

(0.0425) | (0.0107) | |

T1 ^{*} 1-year perception gap (β_{5}) |
0.101^{**} |
0.0305^{**} |

(0.0493) | (0.0130) | |

T5 ^{*} 5-year perception gap (β_{6}) |
0.433^{***} |
0.122^{***} |

(0.101) | (0.0218) | |

Constant (β_{0}) |
-0.00966 | -0.0741 |

(0.229) | (0.0681) | |

Observations | 1,887 | 1,887 |

R-squared | 0.151 | 0.107 |

Joint significance of covariates^{‡} |
0 | 0 |

Mean of dependent variable | -0.63 | -0.1 |

SD of dependent variable | 6.53 | 1.76 |

Sample | All | All |

Notes: Ordinary least squares estimates reported. Robust standard errors in parentheses. Significant at ^{*}p<0.10, ^{**}p<0.05, ^{***}p<0.01.

^{†} Annualized

^{‡} F-test on equality of all covariates to zero (excluding constant). P-value shown.

## Appendix B

### Data

Our data come from an information experiment embedded in an online survey fielded by a large national polling firm on our behalf. It is a nationally representative sample of 2,128 Canadians aged 18 years or older. The survey assesses how house price expectations are formed and updated, given their importance for observed housing dynamics. Respondents’ socio-economic characteristics and numeracy aptitudes are recorded during the survey. Respondents are also asked a series of broader questions related to their expectations about the Canadian economy (e.g., interest rates, inflation, income).

### Survey questions on households’ house price perceptions and expectations

*“***Over the past 5 years**, by about what percent do you think the average home price**in your area**[increased/decreased]?"

**Over the past 5 years**, I think the average home price **in my area** [increased/decreased] by a total of__ %

*“***Over the last 12 months**, by about what percent do you think the average home price**in your area**[increased/decreased]?"

**Over the last 12 months**, I think the average home price **in my area** [increased/decreased] by __ %

*“***Over the next 12 months**, by about what percent do you expect the average home price**in your area**to [increase/decrease]?"

**Over the next 12 months**, I expect the average home price **in my area** to [increase/decrease] by __ %

*“***Over the next 5 years**, by about what percent do you expect the average home price**in your area**to [increase/decrease]?"

**Over the next 5 years**, I expect the average home price **in my area** to [increase/decrease] by a total of__%

## Appendix C

### Definitions

While the average respondents seem to update their expectations in a way consistent with a belief in momentum, some respondents may not update their expectations at all, and others may update in a fashion consistent with mean reversion.

We denote the individual’s updating type by \(v_{i,h}\), where *h* denotes the horizon over which the respondent is forecasting (one year or five years ahead). The following definitions come from Armona, Fuster and Zafar (2018).

There are three update types:

**Non-updater (NU)**: This type does not update following treatment:

\(v_{i,h}\) \(=\,NU\,\,if Δy_{i,h}\) \(=\,0, \)

where

\(Δy_{i}\) = updated house price expectation (%) - initial house price expectation (%).

**Extrapolative expectations (EE):**This type updates in a way consistent with momentum in house prices. If the perception gap, \(x_{i}\), is positive (negative)—that is, the respondents underestimated (overestimated) past house price changes relative to the Teranet index—the respondents revise up (down) their house price expectations. Formally, the definition is

\(v_{i,h}\) \(=\,EE\,\,if (x_{i}>0,Δy_{i,h}>0) or (x_{i}<0,Δy_{i,h}<0). \)

**Mean-reverting expectations (MRE):**This type updates in a way consistent with mean reversion in house prices. For example, if the respondents learn that prices in the past actually increased by more than previously thought (that is, \(x_{i}\) >0), they revise their future forecast downward. Formally, the definition is

\(v_{i,h}\) \(=\,MRE\,\,if (x_{i}>0,Δy_{i,h}<0) or (x_{i}<0,Δy_{i,h}>0). \)

## Endnotes

- 1. See Appendix B for more details on the data and the house price questions.[←]
- 2. The definition of “extrapolative expectations” provided here is what is called “adaptive learning” in the macro-finance literature: the reaction to a too-high (low) initial forecast is met with a lower (higher) subsequent forecast. See Appendix C for a formal definition of extrapolative expectations.[←]
- 3. We conduct regression analysis to more precisely estimate the relationships depicted in Chart 2 and Chart 3 (full details are in Appendix A).[←]
- 4. The estimate of 0.24 percentage points is the addition of (i) the average revision by the one‑year treated group (0.10), i.e., the treatment effect, and (ii) the average revision by the control group (0.14) (see Table A-1, column 1).[←]
- 5. Armona, Fuster and Zafar (2018) find that one‑year treated respondents adjust their expectations by 0.20 percentage points versus a one‑year autoregressive coefficient of 0.53 for house price growth in the United States.[←]
- 6. One caveat is that the updating behaviour of some respondents may reflect the fact that they revise their view of mean house price growth in light of the information provided, so that what appears to be extrapolation may not necessarily be inconsistent with an expectation of mean reversion.[←]
- 7. Demographics are not included in the specification because random assignment to treatment groups should ensure demographics are irrelevant to treatment effects. Indeed, when we control for demographics (not shown), there is no notable difference in estimates.[←]

## Reference

- Armona, L., A. Fuster and B. Zafar. 2018. “Home Price Expectations and Behavior: Evidence from a Randomized Information Experiment.”
*The Review of Economic Studies*(forthcoming).

## Disclaimer

Bank of Canada staff analytical notes are short articles that focus on topical issues relevant to the current economic and financial context, produced independently from the Bank’s Governing Council. This work may support or challenge prevailing policy orthodoxy. Therefore, the views expressed in this note are solely those of the authors and may differ from official Bank of Canada views. No responsibility for them should be attributed to the Bank.