Canonical Correlations and Instrument Selection in Econometrics

This dissertation relates to three recent methods of instrument selection in econometrics, namely, the Canonical Correlations Information Criterion (CCIC), the Relevant Moments Selection Criterion (RMSC) and the approximate Mean Square Error Criterion (MSE). Usual canonical correlations measure the degree of association between two random vectors and provide the basis for construction of the CCIC. A new kind of canonical correlations called Long Run Canonical Correlations (LRCC) has recently emerged in econometrics and provides the basis for construction of the RMSC. Although the concept of LRCC has emerged in the literature, methods of their estimation and inference have not been developed. Developing these methods constitutes the first chapter of the dissertation. In addition, this chapter illustrates the usefulness of LRCC beyond their usefulness in relevant moments selection for GMM models in dynamic nonlinear settings. In particular, it demonstrates how LRCC can be used to develop econometric tests that play a role in (i) structural stability testing, and (ii) exogeneity testing of regressors in time series models where the regressors are nonstationary.Although the properties of each of the above three methods of instrument selection have been explored by their proponents, there have been no comparative studies of these methods to date. The second chapter of this dissertation fills that gap.The final and third chapter extends the statistical theory of the CCIC by considering the case where the number of instruments tends to infinity at an appropriate rate as the sample size tends to infinity. The importance of this extension stems from the fact that this can lead to a further gain in efficiency of the estimator by systematically capturing all relevant instruments from the growing candidate set.