Shrinkage Methods for Automated Econometric Model Determination

Shrinkage Methods for Automated Econometric Model Determination Zhipeng Liao 2012 The rst chapter of my dissertation proposes a GMM shrinkage method to e¢ ciently estimate the unknown parameters o identi ed by some moment restrictions, when there is another set of possibly misspeci ed moment conditions. I show that my method enjoys oracle-like properties, i.e. it consistently selects the correct moment conditions in the second set and at the same time, its estimator achieves the semiparametric e¢ ciency bound implied by all correct moment conditions. For empirical implementation, I provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. Several extensions are also studied. First, I establish the oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the rst set fail to strongly identify o. Second, I show that this shrinkage technique can be used in GMM to perform grouped variable selection and moment selection simultaneously. The simulation results show that the method works remarkably well in terms of correct moment selection and the nite sample properties of its estimators. As an empirical illustration, I apply my method to estimate the life-cycle labor supply equation studied in MaCurdy (1981) and Altonji (1986). My empirical ndings support the validity of the IVs used in both papers and con rm that wage is an endogenous variable in the labor supply equation. Moreover, my estimate of the labor supply elasticity enjoys the smallest standard error with its value being very close to those in the literature. The moment selection methods proposed in the rst chapter focus only on the orthogonality restriction of a moment condition. As a result, the moment conditions which satisfy the orthogonality restriction but fail to improve the e¢ ciency of the GMM estimate may be selected by the GMM shrinkage estimation with high probability in the nite samples. Such moment conditions are called irrelevant moment conditions. Irrelevant moment conditions may enlarge the nite sample bias of the GMM estimate, although they do not a¤ect its asymptotic properties. Chapter 2 provides a new adaptive penalty that serves as the basis for which the GMM shrinkage estimation can consistently select the correctly speci ed and relevant moment conditions. As a result, misspeci ed and irrelevant moment conditions are not selected with probability approaching 1 and the GMM shrinkage estimate is not only asymptotically e¢ cient but also robust against the irrelevant moment conditions in nite samples. The third chapter studies the joint determination of cointegrating rank and autoregressive lag order in vector error correction (VEC) models. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This chapter proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate VEC models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like e¢ cient estimation of the cointegrating matrix and transient dynamics. As such, they o¤er considerable advantages to the practitioner as an automated approach to the estimation of cointegrated systems. This chapter develops the new methods, derives their limit theory and reports simulation results.