A Near Minimax Risk Bound: Adaptive Lasso with Heteroskedastic Data In Instrumental Variable Selection

In this paper we use adaptive lasso estimator select between relevant and irrelevant instruments in heteroskedastic and non Gaussian data. To do so limit theory of Zou (2006) is extended from univariate iid case. Next, it is shown that adaptive lasso estimator can achieve near minimax risk bound even in the case of heteroskedastic data. To achieve that a new proof is used that benefits from Stein’s Lemma. This is a new result and extends the iid Gaussian case. It is also shown in the paper that Lasso estimators are not model selection consistent whereas adaptive lasso can select the correct model in fixed number of instruments case. The case of weak versus strong instruments are also handled by adaptive lasso. Simulations show that compared to alternatives in econometrics it does well in terms of bias. ∗Mehmet Caner: Department of Economics, 4168 Nelson Hall, Raleigh, NC 27518. email: [email protected]. Michael Fan: Department of Economics, North Carolina State University, Raleigh, NC 27695.