Standard Errors for Calibrated Parameters

Calibration; a popular way to discipline the parameters of structural models using data; can be viewed as a version of moment matching (minimum distance) estimation. Existing standard error formulas for such estimators require knowledge of the correlation structure of the matched empirical moments; which is often unavailable in practice. Given knowledge of only the variances of the individual empirical moments; we develop conservative standard errors and confidence intervals for the structural parameters that are valid even under the worst-case correlation structure. In the over-identified case; we show that the moment weighting scheme that minimizes the worst-case estimator variance amounts to a moment selection problem with a simple solution. Finally; we develop an over-identification test and a joint test of parameter restrictions. All procedures are quickly and easily computable in standard software packages.