This course addresses the statistical challenges behind three issues that are central in applied economics, namely heterogeneity, endogeneity and missing or incomplete data. The aim is to present the economic motivations behind these themes, the identification issues that they raise and inference in these settings. We consider mostly estimation of models with no parametric restrictions, since these restrictions are rarely justified by economic theory, contrary to exclusion restrictions for instance. We present several estimation methods in such non or semiparametric settings : M-estimators, Generalized Empirical Likelihood estimators, semiparametric two-step estimators, nonparametric estimators…
After completion of this course students are expected to be able to: – understand and make use of estimation techniques that are at the frontier of econometric theory; – understand the main ideas for proving asymptotic results for these estimation methods; – understand the identification problem in semi or nonparametric models; – develop estimation methods for econometric models that are similar to the ones analyzed during the course; – apply the estimation methods presented in class to make inference in economic models of practical interest.
Part I. A) Estimation based on unconditional moment restrictions : GMM (brief review and its finite sample properties) ; Empirical Likelihood (EL) and Generalized Minimum Contrast estimation ; Generalized EL (GEL) and higer-order properties ; weak identification ; misspecification and ETEL. B) Estimation based on conditional moment restrictions.
Part II. Quantile regression : Motivation, Estimation, Asymptotic results. Quantile restrictions in nonlinear models, panel data, quantile treatment effects. Instrumental variables in nonlinear and nonparametric models A benchmark: the linear model. The estimating equation approach. Application to quantile IV models. The control function approach. Estimation of semi or nonparametric models Estimation without nuisance parameters. Semiparametric two steps estimators. Partially identified models. Examples of partially identified models: missing data, incomplete models. Inference on parameters or the identification region.
Chernozhukov V., H. Hong and E. Tamer (2007), Estimation and Confidence Regions for Parameter Sets in Econometric Models, Econometrica, 75, 1243-1284.
Imbens, G. and Newey, W. K. (2009), Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity, Econometrica, 77; 481-512.
Y. Kitamura (2007), Empirical likelihood methods in econometrics: Theory and practice. In R. Blundell, W. Newey, and T. Persson, editors, Advances in Economics and Econometrics, volume 3, pages 174-237. Cambridge University Press.
Y. Kitamura, G. Tripathi, and Ahn, H. (2004), Empirical likelihood-based inference in conditional moment restriction models, Econometrics, Vol. 72, 1667-1714.
Koenker, R. (2005), Quantile Regression, Econometric Society Monograph Series, Cambridge University Press.
Manski, C. (2003), Partial Identification of Probability Distributions, Springer.
Newey, W. K. and Smith, R. (2004), Higher order properties of GMM and Generalized Empirical Likelihood estimators, Econometrica, vol.72, 219-255.
Powell, J.L. (1994), Estimation of Semiparametric Models, in: Handbook of Econometrics, Vol.IV, eds. R.F. Engle and D.L. McFadden, North-Holland.
Schennach, S. (2007), Point estimation with exponentially tilted empirical likelihood, Annals of Statistics, vol. 35, 634-672.
van de Geer, S. (2009), Empirical Processes in M-Estimation, Cambridge University Press.
Wooldridge, J. W. (2002), Econometric Analysis of Cross Section and Panel Data.