On the information content of households' probabilistic forecasts of inflation

Central banks frequently measure households’ inflation expectations by eliciting probabilistic forecasts. In this question format, respondents are given a response scale with prespecified intervals and are asked to assign probabilities to the intervals that best represent their beliefs about inflation. A well-documented feature of probabilistic surveys is that the response scale affects the responses. For example, shifting the scale shifts responses in the same direction. One interpretation of this phenomenon is that the treatment differences are the result of a rational cognitive process in which a household’s response is a weighted average between the household’s prior information and a signal (in this case, information coming from the response scale). Formally

Response = α×Signal+ (1-α)×Prior Information (1)

The research question behind our experiment focuses on the quantification of α, the weight assigned to the signal, as a measure of response informativeness. A low weight indicates that respondents are barely affected by the signal, allowing researchers to treat the answers as informative for their prior information. Conversely, a high weight indicates that the survey responses are less informative.

In the experiment, we are interested in the information content of the spread and the symmetry of households’ responses. The spread (e.g., the standard deviation of the response) is often interpreted as a measure of a household’s uncertainty. The question is how much of this reported uncertainty is genuine and reflects the respondent’s prior beliefs (formed prior to seeing the response scale), and how much is driven by the scale. A wide response scale may induce households to provide a wide answer. To study this question, we vary the width of the scale in two of our treatments and estimate the weights in Equation (1). A similar issue arises with the symmetry of the responses. Again, by varying the symmetry of the response scale in two of our treatments, we can estimate the corresponding weights in Equation (1).