Essays in instrumental variables estimators

This PhD thesis focuses on instrumental variable models. Often, econometric models are based on orthogonality conditions used to estimate parameters of interest. The literature on such models is vast, and numerous approaches have provided consistent and asymptotically normal estimators. The three chapters presented here consider different models featuring moment conditions that are estimated. In particular, it is aimed to study the finite performances of various estimators in different contexts, in order to provide guidelines on which procedure to select according to the problem at hand. The first chapter considers Euler equations, fundamental equation in dynamic stochastic macroeconomic models. I solve a generic stochastic growth model and use its solutions to generate samples in order to study the performances of moment based estimators. The second chapter studies the widely used linear model in a context where the variable of interest is endogenous. Given one has a valid instrument that satisfies the conditional moment restriction, many different estimators can be used based on the linear projection of the endogenous variable on the instrument, and transformations of it. I propose an approximate Mean Squared Error (MSE) criterion function to minimize over a set of transformations supplied by the researcher and show it is asymptotically optimal in the sense that the true MSE of the estimator using the optimal number of transformations converges in probability towards the minimum of the true MSE over the set of transformations proposed. In a simulation study, I show the competitive performance of this estimator compared to a variety of estimators used in the literature. I find that it proves particularly competitive when the degree of endogeneity is low, and when the relationship between the endogenous variable and the instrument is highly nonlinear. In other settings, its performance is roughly equivalent to that of the Two Stage Least Squares (2SLS) estimator. In the last chapter, I propose another alternative to instrumental variable estimators that considers the use of kernel based estimators when regressing the endogenous variable on the instruments. I show the resulting estimator is consistent and asymptotically normal, and includes the 2SLS estimator as a special case. Similarly to the second chapter, a simulation study is conducted to show its finite sample behavior.