Essays on simulation-based methodology with many auxiliary statistics

The thesis focuses on simulation-based methods for estimation and inferences when many auxiliary statistics are available. In the first chapter, we establish the consistency of the simulated minimum distance estimator in such a situation and derive its asymptotic distribution. Our estimator contributes to the asymptotic theory for estimators obtained by simulated minimum distance in situations where the number of auxiliary statistics (or the number of matched moments) is large, which has not been covered in the existing literature. The estimator is easy to implement and allows us to exploit all the informational content of a large number of auxiliary statistics without having to, (i) know these functions explicitly, or (ii) choose a priori which functions are the most informative. This allows us to exploit, among other things, long-run information. In the second chapter, we illustrate the implementation of the proposed method through Monte-Carlo simulation experiments based on small- and medium-scale New Keynesian models. These examples illustrate how to exploit information from matching a large number of impulse responses including at long-run horizons. It is revealed that the utilization of many auxiliary statistics and data-driven regularization effectively improves estimation in terms of precision and coverage rate. In the third chapter, we propose tests of the null hypothesis of autoregressive models against ones with Markov-switching autoregressive components. The empirical simulation-based tests allow for unknown distributions and use Monte-Carlo test techniques. The approach is flexible and computationally simple. The designed test statistic allows for a large number of empirical moments and relies on simulations under the null hypothesis which permits the use of higher-order moments. Our simulation experiments demonstrate that more information can be harvested with more moments matched, with evidence of increased empirical power. The Monte-Carlo testing methodology is illustrated with a mean-variance switching model, an autoregressive coefficient switching model, and an application to US output growth modeling.