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This article considers the invertibility problem of the optimal weighting matrix encountered during Impulse Response Function Matching Estimation (IRFME) of Dynamic Stochastic General Equilibrium (DSGE) Models. We propose to use a regularized inverse and derive the asymptotic properties of the estimator. We show that the asymptotic distribution of our estimator converges to that of the optimal estimator which has important implications for testing the fit of the model. We demonstrate the small sample properties of the estimator by Monte Carlo simulation exercises. Finally, we use our estimator to estimate the model in Altig et al.

A regularization approach to the minimum distance estimation: application to structural macroeconomic estimation using IRFs