Alternatively, the difference might reflect the disparity between the subjective probability distributions of the marginal investor and the average survey respondent – and therefore measure the dispersion in beliefs between the two. Under this interpretation, the marginal investor in the futures market was much more pessimistic – in other words, placed more probability on low rate outcomes – than the average survey respondent in December, while by January the average survey respondent revised her beliefs downward. Note that the marginal investor in the futures market likely changes over time, and this change can be an additional source of fluctuations in the gap between market-implied rates and mean projections. Unfortunately, we have no direct measure of the beliefs of the marginal investor. But we can obtain evidence on whether the dispersion in beliefs fell from December to March by looking at the dispersion of beliefs among survey respondents. One measure of such dispersion in beliefs is the extent to which the KLIC varies across respondents. A high (low) KLIC means that the respondent’s forecast distribution requires substantial (little) tilting to deliver the market-implied rate. Slide 14 shows, in the bars outlined in light blue, the KLIC distribution  53  Brodsky et al. (2016b). 54  Note that this distribution is constructed by tilting the average of respondents’ probability distributions. Alternatively, we could have tilted the probability distribution for each respondent and then averaged across these tilted distributions. While the two approaches do not, in general, deliver the same answer, in this case they almost do.

To our knowledge, these results provide the first direct evidence regarding a meaningful link between survey-based inflation expectations and actual behavior.32 In the second experiment, we studied the formation process of inflation expectations by looking at whether and how survey respondents updated their inflation expectations when they received relevant new information.33 Specifically, we first elicited inflation expectations. We then randomly provided information to a subset of respondents on either past food price inflation, or professional economists’ forecasts of future inflation from the SPF. Finally, we reelicited respondents’ inflation expectations, and studied whether they were correlated with the information content of the signal they received.34 We found that respondents, on average, updated their inflation expectations in response to the information provided, and they did so sensibly and in a direction consistent with Bayesian updating – with larger revisions for less informed respondents and for those with greater baseline uncertainty. Further, there was significant heterogeneity both in how fully informed respondents were about objective inflation measures and in their updating behavior. This finding points to the potential importance of allowing for heterogeneous informationprocessing rules in our economic models. These findings are also consistent with existing sticky-information models of expectations formation, since cross-sectional disagreement falls after the provision of information.35 Results from the experiment also indicate that expectations about changes in the “prices you pay,” like the similar Michigan survey question about “prices in general,” are more responsive to information about food prices than expectations about the rate of inflation.