Structural Breaks, Model Selection, and Overidentification in Dynamic Factor Models

The first chapter develops tests for structural breaks of factor loadings in dynamic factor models. We focus on the joint null hypothesis that all factor loadings are constant over time. Because the number of factor loading parameters goes to infinity as the sample size grows, the conventional test cannot be used. Based on the fact that the estimated factors will demonstrate a higher dimension under the alternative hypothesis than under the null, we reduce the infinite-dimensional problem into a finite-dimensional one and our statistic compares the pre- and post-break subsample second moments of estimated factors. Our test is consistent under the alternative hypothesis in which a fraction of or all factor loadings have structural changes. The Monte Carlo results show that our test has good finite-sample size and power. In an empirical illustration, we find some evidence of structural break in the factor loadings in early 1980s in the United States.;The second chapter develops methods to estimate the number of factors in dynamic factor models where the idiosyncratic shocks have potentially strong correlation in the cross-sectional dimension. Existing methods, such as Bai and Ng (2002) and Onatski (2010), assume that the cross-sectional correlation in the idiosyncratic shocks is weak. Violation of such weak correlation assumption can lead to inconsistent estimates of the number of factors. This chapter establishes a data dependent estimator that is consistent whether the idiosyncratic shocks are weakly or strongly correlated in the cross-sectional dimension. Monte Carlo results show that our estimator has similar performance to existing methods in the case where the conventional weak correlation assumption is satisfied. When the idiosyncratic shocks have strong cross-sectional correlation, our estimator outperforms the existing methods.;This chapter develops tests for overidentifying restrictions in Factor-Augmented Vector Autoregressive (FAVAR) models. The identification of structural shocks in FAVAR can lead to restrictions on the factor loadings of many variables, so it can involve infinitely many identifying restrictions as the number of cross sections goes to infinity. Our focus is to test the joint null hypothesis that all the restrictions are satisfied. Conventional tests cannot be used due to the large dimension. We transform the infinite-dimensional problem into a finite-dimensional one by combining the individual statistics across the cross section dimension. We find the limit distribution of our joint test statistic under the null hypothesis and prove that it is consistent against the alternative that a fraction of or all identifying restrictions are violated. The Monte Carlo results show that the joint test statistic has good finite-sample size and power. We implement our tests to an updated version of Stock and Watson’s (2005) data set. The proposed test rejects the null hypotheses that the number of fast shocks is two or more, but does not reject the null that there is only one fast shock, which is the monetary policy shock. This result is further confirmed by the impulse responses of major macroeconomic variables to the monetary policy shock: the impulse responses based on one fast shock are generally more economically plausible than those based on two or more fast shocks; and the price puzzle is either considerably reduced or entirely solved for all price indexes when only one fast shock is used.