Essays on Estimation, Calibration and Inference for Simulation Models

The last century has seen a growing interest in complexity in economics and social sciences. The need to model the complex and emergent dynamics of a system has spurred many researchers towards the exploration of estimation techniques that could be used for increasingly complex models, fostering the rise of simulation-based econometric methods. This dissertation aims at contributing to the blossoming literature concerning estimation, calibration and inference for simulated models. Chapter 1, jointly written with Raffaello Seri and Davide Secchi, gives a historical review of the different simulation methods, from the first experiments with early computers to sophisticated agent-based models (ABM). In this chapter we focus on three fundamental aspect governing the dynamics of the system: randomness, causation and emergence. Chapter 2 critically review the different approaches developed for the estimation, calibration and validation of simulation models. We begin clarifying the concept of identification and estimation and we expose the problems related to the dependence of the simulated data on the parameters to be estimated. Then, we formalize the meaning of calibration, estimation and validation of simulated models. Subsequently, considering the classical simulation-based econometric frameworks, we detail the characteristics of the most popular techniques (e.g., indirect inference, method of simulated moments, simulated minimum-distance, simulated maximum likelihood, and approximate Bayesian computation). We then make a comparison of the different methods, explaining their main advantages and weaknesses. In the last section of the chapter, we shift our attention on the estimation, calibration and validation of ABM. Chapter 3, co-authored with Raffaello Seri, Davide Secchi and Samuele Centorrino, considers the issues of calibrating and validating a theoretical model. We aim at selecting the parameters that better approximate the data when the researcher has to choose among a finite number of alternatives. Given a pre-specified loss function, we propose to build a Model Confidence Sets (MCS, see [223]) to restrict the number of plausible alternatives, and measure the uncertainty associated to the preferred model. We further suggest an asymptotically exact logarithmic approximation of the probability of choosing a certain configuration of parameters. A numerical procedure for the computation of the latter is provided and its results are shown to be consistent with Model Confidence Sets. The implementation of our framework is showcased using a model of inquisitiveness in ad hoc teams (see [30]). The similarity between simulated and real-world observations is generally computed minimizing their statistical distance (see Chapter 2 of this thesis). Therefore, a natural implication of estimation and calibration concerns the study of the asymptotic properties of divergence measures. Chapter 4, that is jointly written with Raffaello Seri, is devoted to the estimation of the entropy of a discretely supported time series through a plug-in estimator. We demonstrate the almost-sure convergence of the observed entropy HN to a limit H∞. We show that the widely used bias correction proposed by [418] is incorrect and we fix it in order to remove the O