This paper examines data on point and probabilistic forecasts of inflation from the Survey of Professional Forecasters. We use this data to evaluate current strategies for the empirical modeling of forecast behavior. In particular, the analysis principally focuses on the relationship between ex post forecast errors and ex ante measures of uncertainty in order to assess the reliability of using proxies based on predictive accuracy to describe changes in predictive confidence. After we adjust the data to account for certain features in the conduct and construct of the survey, we find a significant and robust correlation between observed heteroskedasticity in the consensus forecast errors and forecast uncertainty. We also document that significant compositional effects are present in the data that are economically important in the case of forecast uncertainty, and may be related to differences in respondents' access to information.

This paper is interested in the small sample properties of the indirect inference procedure which has been previously studied only from an asymptotic point of view. First, we highlight the fact that the Andrews (1993) median-bias correction procedure for the autoregressive parameter of an AR(1) process is closely related to indirect inference; we prove that the counterpart of the median-bias correction for indirect inference estimator is an exact bias correction in the sense of a generalized mean. Next, assuming that the auxiliary estimator admits an Edgeworth expansion, we prove that indirect inference operates automatically a second order bias correction. The latter is a well known property of the Bootstrap estimator; we therefore provide a precise comparison between these two simulation based estimators.

The possibility of exact maximum likelihood estimation of many observation-driven models remains an open question. Often only approximate maximum likelihood estimation is attempted, because the unconditional density needed for exact estimation is not known in closed form. Using simulation and nonparametric density estimation techniques that facilitate empirical likelihood evaluation, we develop an exact maximum likelihood procedure. We provide an illustrative application to the estimation of ARCH models, in which we compare the sampling properties of the exact estimator to those of several competitors. We find that, especially in situations of small samples and high persistence, efficiency gains are obtained.