Chapter 1: Robust inference in short linear panels with fixed effects with endogenous covari-ates in a spatial setting In this chapter, I propose a simple way to obtain robust standard errors in linear panels in a spatial context with endogenous covariates where the number of time periods is small relative to the cross sectional dimension. The method is based on applying a Spatial HAC to an average of moment con- ditions across time to obtain a covariance estimator that is robust to both spatial and serial correlation (HACSC). I also present a control function approach (CF) alternative to estimate the parameters and extend the HACSC estimator to this case, where the standard errors require an adjustment to account for the sampling variability induced by the first stage estimation. In addition, I derive the Fixed Effects-Random Effects equivalence under a Correlated Random Effects framework in the presence of a spatial lag of the dependent variable to obtain a fully-robust Hausman-type test using the HACSC estimator. I run a Monte Carlo experiment and show that the HACSC estimator is robust to strong patterns of serial and spatial correlation. Furthermore, I also find that whenever the CF assumptions hold, the CF approach is more efficient than Two-Stage Least Squares. Finally, I estimate the effect of school district spending on the performance of fourth-grade students in Michigan, allowing for spillovers across districts. I find that the expenditure from neighboring districts has a positive and non-negligible impact on test passing rates. Chapter 2: Estimation of models with spatial panels and missing observations in the covariates Missing data problems are more serious en spatial models with spillover effects as the efficiency loss induced by using estimators that only use the complete cases is larger. In this paper I present a GMM estimator that uses the information on both the complete and incomplete observations for models with spatial spillover effects and missing data on the potentially endogenous variables to obtain potential efficiency gains. I also derive the Fixed Effects and Random Effects equivalence for spatial panels with missing data and I also develop an alternative GMM estimator in this Correlated Random Effects framework. The Monte-Carlo simulations show significant efficiency gains of the GMM estimator compared to estimators that only use the complete cases. Chapter 3: Estimation of models with multiple fixed effects and endogenous variables: a correlated random effects approach The inclusion of multiple individual heterogeneities and time effects, more commonly referred as “fixed effects,” is a common practice in panel data. A common approach to deal with these is to estimate the model using the fixed effects estimator by applying the within transformation, which has the disadvantage of removing all the variables that are constant across one of the dimensions of the data set. An alternative method to estimate the model is the correlated random effects approach using the Mundlak device, which restricts the dependence between the heterogeneities and the covariates in a particular way. In this paper, I show that the fixed effects estimates can be recovered using the Mundlak approach in models with three sets of heterogeneities and in the presence of endogenous variables. Furthermore, I prove that this equivalence can be obtained using two different sets of covariates.
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