讲座题目：Double Boosting for High Dimensional IV Regression Models
主 讲 人：Tae Hwy Lee 教授
加州大学河滨分校经济系教授，1990年6月毕业于加州大学圣地亚哥分校，获得经济学博士学位，导师为Halbert White Jr和诺贝尔经济学奖获得者Clive W.J. Granger先生。研究方向涵盖时间序列、金融风险分析、大数据、机器学习等方面。为American Economic Review，Econometric Theory，Journal of Econometrics，Economics Letters等顶级期刊杂志匿名审稿人。获得The Bank of Korea Research Award和Tjalling C. Koopmans Econometric Theory Prize等奖项。
Endogeneity in a regression model for the automobile demand equation leads to inconsistent estimation of the price elasticity parameter. The standard solutions are the two stage least squares (2SLS) and generalized method of moments (GMM). These methods face challenges when instruments are high dimensional and when some are irrelevant and/or invalid. It is critical to select relevant and valid instruments for the consistent estimation. In this paper, we introduce a new method that will select relevant and valid instruments simultaneously using boosting algorithm, which we call Double Boosting (DB). We show that the DB consistently selects relevant and valid instruments. In particular, we consider the case when the endogenous variables X (price) are unknown nonlinear functions of observable instruments W (the product characteristics), which can be approximated by some sieve functions such as polynomials. The sieve approximation captures nonlinearity between endogenous variables X and instruments W , while however it produces high dimensional instruments Z=f(W). Monte Carlo simulation demonstrates the DB procedure, and compares its performance relative to other methods such as penalized GMM (Cheng and Liao 2015) and the standard Boosting (Ng and Bai 2008). In the application to estimating the BLP-type automobile demand function (Berry, Levinson and Pakes 1995) with price being endogenous and instruments being high dimensional functions of product characteristics, we find that the DB estimators indicate that automobiles demands are more consistent with the profit maximization compared to other estimators.