Silviase/jgov_v1.4_full_ann huggingface dataset:
these idiosyncratic findings in mind when analyzing the survey data in the following sections.

### 4. Empirical Analysis

### 4.1 Can the Professional Forecasts Serve as an Anchor?

While Figure 1 suggests that the average of professional forecasts provides a more accurate prediction of actual inflation than average household expectations, we want to examine whether professional forecasters are indeed “more rational” than households in their inflation forecasts and whether the mean of professional forecasts can be used as an anchor for reasonable inflation expectations by households.

Using the three “remain the same” intervals discussed in Section 3.1, Table 2 shows the results of our comparison to see how accurate household expectations are (relative to the mean professional forecast). We first calculated the mean absolute errors (MAE) and the root mean square errors (RMSE), on the interval choice basis, for each household as well as for the mean professional forecast. Then, we compare the performance of individual households with that of the mean professional forecast in the same period. Table 2 reports the share of households that outperformed the mean professional forecast. Regardless of our choice of the “remain the same” interval, the majority of households appear to have underperformed the mean professional forecast. This pattern becomes clear especially when we compare the RMSE, indicating that household expectations are very erratic. Although this informal comparison is not conclusive, it suggests that for the majority of households, professional forecasts could serve as an anchor for the formation of more accurate inflation expectations.

The next question that naturally arises is whether professional forecasts have greater forecasting power for future inflation than household expectations. Table 3 presents the results of regressing the realized inflation rate over the next year on the mean of household
expectations from the MCCS and the mean of ESPF inflation forecasts, along with the most recent annual inflation statistics available at the time the two surveys were conducted. To take the above-mentioned measurement problem into account, we report both results based on actual percentage figures, which we used as long as they were available, and results based on the medians of intervals, in which case we used the median value even when actual figures were available. $ ^{12} $ The implications of the regressions are clear: both the mean of household expectations from the MCCS and that of the ESP forecasts are positively associated with future inflation even when controlling for past inflation, but only the mean of ESP forecasts is statistically significant. The regression results that include both household expectations and the professional forecasts indicate that household expectations contain almost no information, while the professional forecasts have very significant predictive power. Note that this finding implies that the household expectations in the MCCS are irrational (using the conventional definition of rational expectations), since it means that household expectations did not incorporate available information that could be used to make a superior forecast.

Another preliminary investigation suggested by the structure of the model is to examine the way professional forecasts affect household expectations. The results for regressing inflation expectations of individual households on professional forecasts are shown in Table 4. Even after controlling for past inflation and past values of the dependent variable, past professional forecasts still had a statistically significant impact on household inflation expectations. Moreover, the size of the coefficient suggests that the impact is also economically significant.

However, the finding that the professional forecasts are more accurate than household expectations does not necessarily imply that the professional forecasts are rational. A recent
study (Ashiya 2009) using the ESPF data to examine the rationality of the professional inflation forecasts reports that almost all forecasters and the consensus forecast failed either the unbiasedness test, the efficiency test, or the martingale test. Therefore, even the professional forecasts do not look fully rational in Japan. However, it is also correct to say that the ESP forecasts are “more rational” than household expectations in the sense that the former must be employing certain information (that households are not) to make professional forecasts superior to household expectations. Based on the superiority of the professional forecasts, we examine whether household expectations can be well modeled as updating toward the professional forecasts.

### 4.2 Estimating the Empirical Model

Let us turn to the regressions investigating whether the MCCS data can be well represented by the sticky information model. We begin examining the macro based (time series) model to explain the mean of household expectations by estimating

$$ M_{_{t}}[\pi_{_{t,t+12}}]=\alpha_{_{1}}N_{_{t}}[\pi_{_{t,t+12}}]+\alpha_{_{2}}M_{_{t-1}}[\pi_{_{t-1,t+11}}]+\alpha_{_{0}}+\varepsilon_{_{t}} $$

Comparing this to (2) provides the testable restrictions, i.e., $ \alpha_{1} + \alpha_{2} = 1 $ and $ \alpha_{0} = 0 $ . We used the mean of the ESPF inflation forecasts and the most recent annual inflation statistics available at the time the expectations were formed as our alternative proxies for $ N_{t}[\pi_{t,t+12}] $ .

The results are presented in Table 5. The estimates of $ \alpha_{1} $ are meaningful with a positive value only when we used the mean of the ESPF as our proxy. While the coefficient on the constant term, $ \alpha_{0} $ , is not significantly different from zero, the point estimates of $ \alpha_{1}=0.37 $ and $ \alpha_{2}=0.92 $ lead to the rejection of the restriction $ \alpha_{1}+\alpha_{2}=1 $ . Only when we included both of the two alternative proxies for $ N_{t}[\pi_{t,t+12}] $ in our regression, the expanded restriction of $ \alpha_{1-1}+\alpha_{1-2}+\alpha_{2}=0 $ was accepted. However, it is not easy to put a meaningful interpretation on this.
expanded regression. While the time series result here demonstrates that the professional forecast dominates the most recent inflation statistics, this provides only weak support for (or even rejects) the sticky information model, partly because we still have only a limited number of observations.

We now turn to our micro data based regression (7), which examines whether the sticky information model represents the MCCS inflation expectations reasonably well. The testable restrictions here are $ \beta_{1}=0 $ , which examines a necessary condition for rational expectations, and $ \beta_{1}=\beta_{2}=1 $ , which implies that the sticky information model describes inflation expectation dynamics. Table 6 presents the regression results. The most indisputable finding from these regressions is the fact that household expectations are far from rational. The restriction $ \beta_{1}=0 $ is overwhelmingly rejected irrespective of our choice of data type and specification. The joint hypothesis that $ \beta_{1}=0 $ and $ \beta_{2}=1 $ , meaning that household expectations exactly track the mean of professional forecasts, is also unanimously rejected. The results regarding the relevance of the sticky information model, i.e., the restriction $ \beta_{1}=\beta_{2}=1 $ , look somewhat inconclusive. While the hypothesis $ \beta_{1}=\beta_{2}=1 $ is again strongly rejected, probably due to our large sample of more than a hundred thousand observations, the point estimates of $ \beta_{1}\cong\beta_{2}\cong0.7 $ yield the impression that the model is not necessarily a bad approximation of inflation expectation dynamics.

When we tried replacing the mean of the professional forecast variable with the most recent observed inflation rate (column [2] of Table 6) to check whether professional forecasts can serve as an anchor, the point estimates became smaller. And in the “horserace” regression (column [3]) that includes both variables, we obtain larger positive coefficients on the professional forecast based variables and negative coefficients on the most recent inflation based variables. We also expanded our regression specification to include a constant term and
obtained significant positive constants. This result again deviates from the baseline sticky information model. However, the estimated size of the coefficients of key interest, $ \beta_{1} $ and $ \beta_{2} $ , continues to be not far from 1, even after expanding the model to include the constant term. Therefore, the micro data based regressions suggest that the sticky information model captures some real world aspects not captured by the rational expectations model.

### 4.3 Can Sticky Information Explain Disagreement About Inflation Expectations?

One implication of the simple sticky information model is that inflation expectations vary based only on the time since households' last opportunity to update their expectations. Mankiw et al. (2004) argue that the sticky information model broadly explains the observed disagreement among households about inflation expectations. Therefore, one simple way to examine the usefulness of the model is to estimate a model with dummy variables to capture the date of the last update by individual households. Table 7 reports the results. Row [1] of the table shows the result for this model with time dummies only, which captures the mean of inflation expectations for each expectation period $ (t) $ . However, the result of main interest is that shown in row [2], in which additional dummy variables are included in the model to control for the date of the last update. This indicates that although the dummies are significant, suggesting that the timing of the updating of expectations plays a role, the explanatory power of the extended model in terms of explaining disagreement among households about inflation expectations increased only modestly. That is, there seem to be some factors other than sticky information that bring about such disagreement.

Another testable issue raised by the sticky information model is the size and determinants of $ \lambda $ , the fraction of the population that obtain new information and update their expectations. The seminal model by Mankiw and Reis (2002) assumes a Poisson process in
which $ \lambda $ , the probability that a household changes its inflation expectation, is given as an exogenous constant, regardless of how long it has been since the last update. Early studies using the U.S. data and employing different identification schemes report that households update their information sets on average once a year ( $ \lambda $ is estimated to be around 0.083). However, the probability (or the share of households that change their responses to the inflation expectation question in a survey from their responses in the previous survey) that is directly observable in the Japanese MCCS data set is 0.48, indicating very fickle expectations that, on average, are updated every 2.1 month. $ ^{13} $ Moreover, the observational distribution of the average interval between the expectation updates among individual households is more long-tailed than the pattern generated by the theoretical Poisson process of $ \lambda=0.48 $ (see Figure 2), suggesting that $ \lambda $ may vary in accordance with the type of household or with the time since the last update.

Another testable implication of the Carroll (2003) type sticky information model is that in periods when there are more news stories on inflation, the speed of updating should be faster. To examine this point, we run a few probit regressions to investigate the relationship between the updating of inflation expectations (the dependent variable takes one when a household revised its inflation expectation and takes zero when it does not) and the number of price related news stories. Table 8 reports the regression results. First, news stories, especially an increase in the number of news stories, raise the probability that households update their inflation expectations, as predicted by the Carroll model. However, the probability of updating seems to depend more on other, non-news variables. First, the gap between the professional forecast and household expectations before an update appears to have a larger effect on the update probability than the number of news articles (column [2]). Second, the time since the last update also appears to play a role. We tried to capture this by including a variable for the
number of months since the last update, expecting that the length of time since the last update would raise the update probability. However, the estimated coefficient on this variable turned out to be significantly negative (column [3]). Given this counterintuitive result, we additionally included the average number of months between updates for each household $ (i) $ , thereby allowing for the possibility that the average number of months varies across households. The result, shown in column [4], looks reasonable; that is, the coefficient on the average number of months is negative while that on the number of months since the last update is positive. In other words, households which tend to update their expectations less frequently are less likely to update in each period. Moreover, after controlling for the household-idiosyncratic average number of months between updates, the number of months since the last update term has a positive effect, indicating that the probability differs depending on where the household is in its adjustment cycle.

### 5. Conclusion

Given the agreement among economists that macroeconomic outcomes depend critically on agents' expectations, it is surprising that efforts to test models of expectations using available survey data have been very limited. Following in the spirit of Carroll (2003), and considering the lack of empirical studies on expectation formation in Japan, this paper attempted to examine the properties of inflation expectations by Japanese households, using micro level data that has become available in recent years from the MCCS and the ESPF. Based on the setting of the Carroll model, we derived a micro data based empirical specification to examine both the sticky information model and the rational expectations model.

Our analysis showed that Japanese household expectations are not rational in the sense that they are biased, at least ex post, and that households appear not to instantaneously
incorporate information that is freely available from news reports on the views of professional forecasters into their expectations. While the sticky information model seems to partially explain inflation expectation dynamics among Japanese households, the part of expectation disagreement among households that can be explained by the model is not necessarily large, i.e., real world inflation expectation dynamics are more complex than in the simple setting of a standard sticky information model.

Given that our empirical findings are not necessarily consistent with mainstream economic theory, which assumes a representative rational agent, it seems advisable to be prudent in interpreting subjective responses to survey questions. However, a preliminary examination of the micro data from the MCCS we conducted did not show any systematic patterns that would indicate that the responses of some survey participants were unreliable. $ ^{14} $ In addition, we cleaned the data based on several criteria, dropping any anomalous observations. The sample size decreased by half as a result, but our empirical findings remained qualitatively unaffected. Therefore, while the quality of the MCCS data could certainly be improved, such as by the introduction of a question that asks respondents for a numerical value of the inflation rate they expect, the findings of this paper – although based on somewhat less than perfect data – reveal novel and interesting facets on the nature of inflation expectations.
## References

Ashiya, Masahiro (2009) “Japanese CPI Forecasters: Homogeneity, Accuracy, and Rationality,” unpublished manuscripts presented at the “Expectation Formation” part of the Tokyo meeting for the ESRI International Collaboration Projects 2008.

Batchelor, Roy, and Pami Dua (1991) “Blue Chip Rationality Test,” Journal of Money, Credit and Banking, Vol. 23, pp. 692-705.

Carroll, Christopher D. (2003) “Macroeconomic Expectations of Households and Professional Forecasters,” Quarterly Journal of Economics, Vol. 118, pp. 269-298.

Curtin, Richard (2005) “Inflation Expectations: Theoretical Models and Empirical Tests,” unpublished paper downloadable from https://ssl.nbp.pl/Konferencje/BBM/curtin.pdf.

Hashimoto, Yukari (2007) “On Answer Deviations Due to Different Implementations of the Monthly Consumer Confidence Survey Covering All of Japan and Making of Reference Series,” ESRI Research Note, No.1, Economic and Social Research Institute, Cabinet Office, Government of Japan (in Japanese).

Hori, Masahiro, and Satoshi Shimizutani (2005) “Price Expectations and Consumption under Deflation: Evidence from Japanese Household Survey Data,” International Economics and Economic Policy, Vol. 2, No. 2-3, pp. 127-151.

Kahn, Shulamit (1997) “Evidence of Nominal Wage Stickiness from Microdata,” American Economic Review, Vol. 87, pp. 993-1008.

Kamada, Koichirou (2008) “Downward Stickiness of Households’ Inflation Expectations: An Analysis Using the ‘Opinion Survey of the General Public’s Views and Behavior’,” Bank of Japan Working Paper Series, No.08-J-8 (in Japanese).

Kawagoe, Masaaki (2007) “Is the Consensus Forecast Just the Average?—Re-examining an Evaluation of the ESP Forecast,” ESRI Discussion Paper Series, No.180, Economic and Social Research Institute, Cabinet Office, Government of Japan (in Japanese).

Komine, Takao, Kanemi Ban, Masaaki Kawagoe, and Hiroshi Yoshida (2009) “What Have We Learned from a Survey of Japanese Professional Forecasters? Taking Stock of Four Years of ESP Forecast Experience,” ESRI Discussion Paper Series, No. 214, Economic and Social Research Institute, Cabinet Office, Government of Japan.

Mankiw, N. Gregory, and Ricardo Reis (2002) “Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” Quarterly Journal of Economics, Vol. 117, No. 4, pp. 1295-1328.

Mankiw, N. Gregory, Ricardo Reis, and Justin Wolfers (2004) “Disagreement about Inflation Expectations,” in Mark Gertler and Kenneth Rogoff, eds., NBER Macroeconomics Annual 2003, pp. 209-248.

Thomas, Lloyd B. Jr. (1999) “Survey Measures of Expected U.S. Inflation,” Journal of
### Appendix A. The Monthly Consumer Confidence Survey Covering All of Japan (MCCS)

#### A.1. General Information

The MCCS is a nationally representative survey that has been conducted monthly since April 2004. The main purpose of the survey is to gain a quick understanding of shifts in consumer perceptions as a way to evaluate economic trends. The survey covers 6,720 households, sampled using a three-level stratified random sampling method of city/town/village, local unit, and household. The Prime Minister is in charge of the MCCS and has delegated the implementation of the survey to Shin Joho Center, Inc. $ ^{A1-1} $ Shin Joho Center distributes questionnaires to sample households around the $ 10^{th} $ of each month, which are expected to fill in the survey by the $ 15^{th} $ , and Shin Joho Center then collects the questionnaires by the $ 20^{th} $ . Each sample household is surveyed for 15 consecutive months.

#### A.2. The Questionnaire

Monthly survey questions are broadly classified into three categories: (1) consumer perceptions, (2) price expectations, and (3) household characteristics.

The following five questions in the consumer perception category are used to calculate the consumer confidence index, assigning values from zero to one to the allowed responses shown in brackets:

QOL (Overall Standard of Living): Looking ahead, do you think that half a year from now you will be better off, worse off, or about the same as now? – (1) will be better off, (2) will be somewhat better off, (3) about the same, (4) will be somewhat worse off, or (5) will be worse off.

QIG (Income Growth): Do you think that half a year from now the pace of income growth of your household will increase, decrease, or remain unchanged? – (1) will increase, (2) will somewhat increase, (3) will not change, (4) will somewhat decrease, or (5) will decrease.

QEO (Employment Opportunities): Do you think that half a year from now employment opportunities will be better, worse, or unchanged? – (1) will be better, (2) somewhat better, (3) about the same as now, (4) somewhat worse, or (5) worse.

QDGP (Durable Goods Purchases): Do you think that half a year from now will be a better time or a worse time to buy consumer durable goods? – (1) will be better, (2) somewhat better, (3) about the same as now, (4) somewhat worse, or (5) worse.

QVA (Value of Assets): Do you think that half a year from now the value of your family assets (stocks, real estate, and other assets) will have increased, decreased, or remained the
same? – (1) will have increased, (2) will have marginally increased, (3) will be about the same as now, (4) will have marginally decreased, or (5) will have decreased.

The question on price expectations, which used to fall under the questions on consumer perceptions and offer five choices, now is a category in its own right and, to gain a quantitative flavor, offers the eight choices mentioned in Section 3.1.

The third category of questions focuses on the following household characteristics, with the number of choices shown in parentheses: gender of the household head (2), occupation of the household head (5), age of the household head (9), number of household members (5), annual income of the household (7), type of main income source (4), type of residence (5), whether the household has a mortgage (2), etc.

In addition to the regular monthly questions in the three categories above, the following additional questions are included in the survey every three months (March, June, September, and December): (1) planned expenditure on courses, leisure activities, and services; (2) expenditure on travel made or planned; and (3) purchases and possession of principal consumer durables (conducted only in the March survey).

#### A.3. Characteristics of Respondents

The characteristics of households in the survey are summarized in Table A.1. Eight out of ten household heads are male. Another notable feature is that the surveyed households are rather old: the median age of the household head is 60 compared with an average for Japan – according to the 2005 Census – of 43. This probably also explains why a large share of household heads are “not working” and for a large share the main source of income is “pension benefits.” The fact that surveyed households are rather old may also mean that the household size, the number of working members, and the household income are below the national averages. In addition, the table manifests the aging of the population, as indicated by the growing share of households with a head aged over 70.

#### A.4. Change in the Survey Method

The survey method changed in April 2007. From its inception in April 2004 to March 2007, the survey was conducted in the current manner – consisting of direct visits and self-completion questionnaires – only four times a year, in March, June, September, and December. In the other months, the survey was conducted by telephone. The impact of this change in the survey method on the calculation of the consumer confidence index is discussed by Hashimoto (2007).