We can also look at medians of various percentiles of the individual distributions.27 We measure aggregate forecast uncertainty as the median across respondents of the individual IQRs. We also monitor the probability that respondents attach to extreme inflation outcomes by computing, for instance, the median probability of deflation: in other words, the median of the individual subjective probabilities assigned to outcomes with inflation less than zero. Finally, to characterize the variation in inflation expectations across respondents, we compute the dispersion of expected values: the IQR of individual density means. Again, we can look at other percentiles of the distribution across respondents to detect possible clustering and polarization.28 We publish at a monthly frequency many of the aggregate measures of inflation expectations, as well as measures for a broad range of labor market  25  Delavande et al. (2011b). 26  See Bruine de Bruin et al. (2011b). 27  By tracking the same individuals over time, we can in principle study the extent to which respondents update their expectations in response to new information. For instance, if respondents receive information that deviates from their priors, their density forecasts could initially exhibit greater uncertainty and even become bimodal until they converge to a new value for their central tendency. 28  For example, in the immediate aftermath of the financial crisis, we detected a certain amount of polarization in the distribution of inflation expectations, with some consumers expecting relatively high inflation, and some expecting deflation.

In nearly all cases considered to date, this leads to the conclusion that expectations of economic agents are identical or will converge over time. While this approach has given us invaluable insights in a multitude of models and applications, it faces a major empirical problem: in practice, economic agents hold widely  1  Guiso, Jappelli, and Terlizzese (1994). 2  Guiso and Parigi (1999). 3  Manski (2002). BIS central bankers’ speeches  1  differing views about the future path of economic variables, as I will illustrate throughout these remarks. Thus, recent research has focused on alternative assumptions regarding the nature of expectations held by economic agents. Measuring subjective expectations directly can inform our modeling assumptions on the information sets available to agents, and on the nature of the expectations formation and updating process.4 There are many Bayesians in the audience today. However, for the benefit of those who are not as familiar with Bayesian terminology, let me quickly define what I mean by “subjective expectations” or beliefs. This term refers to the personal probability distributions that individuals hold over uncertain events. Apart from the laws of probability and rules about how beliefs are updated with the arrival of information, there are no restrictions on these probability distributions, hence the use of the word “subjective.”5 Further, individuals might act according to their subjective beliefs without being able to fully articulate in standard forms their underlying probability distribution. Thus, a need arises to elicit these views in order to understand behavior more fully.