Testing for Differences in Survey-Based Density Expectations: A Compositional Data Approach

We propose to treat survey-based density expectations as compositional data when testing either for heterogeneity in density forecasts across different groups of agents or for changes over time. Monte Carlo simulations show that the proposed test has more power relative to both a bootstrap approach based on the KLIC and an approach which involves multiple testing for differences of individual parts of the density. In addition, the test is computationally much faster than the KLIC-based one, which relies on simulations, and allows for comparisons across multiple groups. Using density expectations from the ECB Survey of Professional Forecasters and the U.S. Survey of Consumer Expectations, we show the usefulness of the test in detecting possible changes in density expectations over time and across different types of forecasters.