Essays on Least Squares Model Averaging

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Xie, Tian
model averaging , cross country economic growth models
This dissertation adds to the literature on least squares model averaging by studying and extending current least squares model averaging techniques. The first chapter reviews existing literature and discusses the contributions of this dissertation. The second chapter proposes a new estimator for least squares model averaging. A model average estimator is a weighted average of common estimates obtained from a set of models. I propose computing weights by minimizing a model average prediction criterion (MAPC). I prove that the MAPC estimator is asymptotically optimal in the sense of achieving the lowest possible mean squared error. For statistical inference, I derive asymptotic tests on the average coefficients for the "core" regressors. These regressors are of primary interest to researchers and are included in every approximation model. In Chapter Three, two empirical applications for the MAPC method are conducted. I revisit the economic growth models in Barro (1991) in the first application. My results provide significant evidence to support Barro's (1991) findings. In the second application, I revisit the work by Durlauf, Kourtellos and Tan (2008) (hereafter DKT). Many of my results are consistent with DKT's findings and some of my results provide an alternative explanation to those outlined by DKT. In the fourth chapter, I propose using the model averaging method to construct optimal instruments for IV estimation when there are many potential instrument sets. The empirical weights are computed by minimizing the model averaging IV (MAIV) criterion through convex optimization. I propose a new loss function to evaluate the performance of the estimator. I prove that the instrument set obtained by the MAIV estimator is asymptotically optimal in the sense of achieving the lowest possible value of the loss function. The fifth chapter develops a new forecast combination method based on MAPC. The empirical weights are obtained through a convex optimization of MAPC. I prove that with stationary observations, the MAPC estimator is asymptotically optimal for forecast combination in that it achieves the lowest possible one-step-ahead second-order mean squared forecast error (MSFE). I also show that MAPC is asymptotically equivalent to the in-sample mean squared error (MSE) and MSFE.
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