Standard Errors for Calibrated Parameters

TL;DR

This paper develops conservative standard error formulas for calibrated parameters in structural models, valid without needing the correlation structure of empirical moments, and applies them to economic models.

Contribution

It introduces a method to compute conservative standard errors using only variances of moments, avoiding the need for correlation estimates, and provides new tests for model restrictions.

Findings

Derived conservative standard errors valid under worst-case correlation.

Identified a simple moment selection scheme minimizing worst-case variance.

Applied methods successfully to economic models of pricing and macroeconomics.

Abstract

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive 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 tests of over-identifying or parameter restrictions. We apply our methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model.