Top to Bottom: Best-case Standard Errors for Calibrated Model Parameters

Abstract

Calibration is a moment-matching procedure that selects the parameters of a structural model to match empirical moments drawn from potentially many different data sources. However, if the moments are diversely sourced, then their underlying correlation structure, which is necessary for the computation of standard errors of calibrated model parameters, is likely unknown. This paper derives a lower bound on the standard errors of calibrated model parameters which corresponds to the best-case standard errors using only the readily estimable point estimates and marginal variances of the empirical moments. We prove that the problem of finding the best-case standard errors is equivalent to solving a simple semidefinite program. We then compare this methodology to a procedure by Cocci and Plagborg-Møller (2023) that derives the worst-case standard errors. We apply both methodologies to two empirical applications: a model of multiproduct firms facing a price setting decision under a fixed menu cost and a heterogenous agent New Keynesian model.