Econ 483 Advanced Econometrics Methods Fall 2013 Lecture: M.W 1:30PM{3:30PM, AAH 3204 Instructor: Ivan Canay Office: 331 Andersen Hall Phone: 847-491-2929 Email: [email protected] Web Page: http://faculty.wcas.northwestern.edu/~iac879 Office Hours: by appointment Course Description: This course of the graduate econometrics sequence mixes technical topics with tools that are useful for applied work. The structure of the course consists of three parts: the first one introduces empirical likelihood, the second one presents new inference tools in models with dependent and heterogeneous data, and the third one presents tools for empirical analysis in randomized controlled experiments. Grading: There will be no exams in this class. Grading will consist on weakly reports (submitted via Blackboard), three problem sets (with due dates TBD, submitted via Black- board, and typed in LATEX) and a topic presentation (on one of the topics of marked with a star in the Course Outline). Weakly reports should avoid displays and formulas and be limited to a maximum of two pages. For the topic presentation you must prepare lecture notes (in LATEX, maximum 8 pages, and in a similar format of my lecture notes) and a slide presentation. The weighting scheme for the final grade will be: Weakly Reports: 20% Problem Sets: 30% Topic Presentation: 50% Lecture Notes: I will provide lecture notes every week with related references you are supposed to read. The readings listed below include most of the articles we will discuss in class. 1 Course Outline Part I: Empirical Likelihood 1. Intro to Empirical Likelihood. 2. More on Empirical Likelihood. 3. Generalized Empirical Likelihood. 4. Higher Order Expansions of Estimators. 5. Higher Order Properties of Empirical Likelihood. 6. EL for Moment Inequalities. 7. Self-Concordance for EL. Part II: Inference with Dependent and Heterogeneous Data 8. Randomization Tests 9. t-test Heterogeneity Robust Inference? 10. Inference with Dependent Data using Cluster Covariance Estimators? 11. Randomization Tests under a Weak Convergence Assumption Part III: Treatment Assignment in RCE 12. The Treatment Assignment Problem 13. Restricted Randomization: Permuted Blocks and Bias Coin Design 14. Generalized Bias Coin Designs 15. Stratification and Covariate-Adaptive Randomization 16. Optimal Design Based on a Linear Model 17. Inference under Covariate-Adaptive Randomization 18. Balance by Re-Randomization? 19. Response Adaptive Randomization? 2 Readings [1] Atkinson, A. Optimum biased coin designs for sequential clinical trials with prognostic factors. Biometrika 69, 1 (1982), 61{67. [2] Atkinson, A. The comparison of designs for sequential clinical trials with covariate information. Journal of the Royal Statistical Society: Series A (Statistics in Society) 165, 2 (2002), 349{373. [3] Baldi Antognini, A. A theoretical analysis of the power of biased coin designs. Journal of Statistical Planning and Inference 138, 6 (2008), 1792{1798. [4] Baldi Antognini, A., and Giovagnoli, A. A new biased coin design for the sequential allocation of two treatments. Journal of the Royal Statistical Society: Series C (Applied Statistics) 53, 4 (2004), 651{664. [5] Baldi Antognini, A., and Zagoraiou, M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors. Biometrika 98, 3 (Sep 2011), 519{535. [6] Bester, C. A., Conley, T. G., and Hansen, C. B. Inference with dependent data using cluster covariance estimators. Journal of Econometrics 165, 2 (2011), 137{151. [7] Blackwell, D., and Hodges, J. Design for the control of selection bias. The Annals of mathematical statistics 28, 2 (1957), 449{460. [8] Bugni, F. A., Canay, I. A., and Shaikh, A. M. On inference under covariate adaptive randomization. manuscript, November 2013. [9] Bugni, F. A., Canay, I. A., and Shi, X. Specification tests for partially identified models defined by moment inequalities. CeMMAP working paper CWP01/13., January 2013. [10] Canay, I. A. El inference for partially identified models: Large deviations optimality and bootstrap validity. Journal of Econometrics 156, 2 (June 2010), 408{425. [11] Chen, Y. The power of efron's biased coin design. Journal of statistical planning and inference 136, 6 (2006), 1824{1835. [12] Efron, B. Forcing a sequential experiment to be balanced. Biometrika 58, 3 (1971), 403{417. [13] Hoeffding, W. The large-sample power of tests based on permutations of observa- tions. The Annals of Mathematical Statistics 23, 2 (1952), pp. 169{192. [14] Hu, Y., and Hu, F. Asymptotic properties of covariate-adaptive randomization. Annals of Statistics, forthcoming (2012). 3 [15] Ibragimov, R., and Muller,¨ U. K. t-statistic based correlation and heterogeneity robust inference. Journal of Business & Economic Statistics 28, 4 (2010), 453{468. [16] Ibragimov, R., and Muller,¨ U. K. Inference with few heterogenous clusters. Manuscript (2013). [17] Imbens, G., Spady, R. H., and Johnson, P. Information theoretic approaches to inference in moment condition models. Econometrica 66, 2 (March 1998), 333{357. [18] Kitamura, Y. Asymptotic optimality of empirical likelihood for testing moment re- strictions. Econometrica 69, 6 (September 2001), 1661{1672. [19] Kitamura, Y. Empirical likelihood methods in econometrics: Theory and practice. Cowles Foundation Discussion Paper 1569 (June 2006). [20] Lock Morgan, K., and Rubin, D. Rerandomization to improve covariate balance in experiments. The Annals of Statistics 40, 2 (2012), 1263{1282. [21] Manski, C., and Tetenov, A. Admissible treatment rules for a risk-averse planner with experimental data on an innovation. Journal of Statistical Planning and Inference 137, 6 (2007), 1998{2010. [22] Markaryan, T., and Rosenberger, W. Exact properties of efron's biased coin randomization procedure. The Annals of Statistics 38, 3 (2010), 1546{1567. [23] Newey, W. K., and Smith, R. J. Higher order properties of gmm and generalized empirical likelihood estimators. Econometrica 72, 1 (January 2004), 219{255. [24] Owen, A. Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 (1988), 237{249. [25] Owen, A. Empirical likelihood for confidence regions. Annals of Statistics 18, 1 (March 1990), 90{120. [26] Owen, A. Empirical likelihood for linear models. Annals of Statistics 19, 4 (December 1991), 1725{1747. [27] Owen, A. Self-concordance for empirical likelihood. Working Paper (2012). [28] Pocock, S., and Simon, R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial. Biometrics (1975), 103{115. [29] Qin, B. J., and Lawless, J. Empirical likelihood and general estimating equations. Annals of Statistics 22, 1 (1994), 300{325. [30] Romano, J. P. Bootstrap and randomization tests of some nonparametric hypotheses. Ann. Statist. 17, 1 (1989), 141{159. 4 [31] Romano, J. P. On the behavior of randomization tests without a group invariance assumption. Journal of the American Statistical Association 85, 411 (1990), pp. 686{ 692. [32] Romano, J. P., and Lehmann, E. Testing Statistical Hypothesis. Springer, New York, 2005. [33] Schennach, S. M. Point estimation with exponentially tilted empirical likelihood. Annals of Statistics 32, 2 (April 2007), 634{672. [34] Serfling, R. J. Approximation Theorems of Mathematical Statistics. John Wiley, New York, 1980. [35] Shao, J., Yu, X., and Zhong, B. A theory for testing hypotheses under covariate- adaptive randomization. Biometrika 97, 2 (2010), 347{360. [36] Smith, R. Properties of biased coin designs in sequential clinical trials. The Annals of Statistics (1984), 1018{1034. [37] Smith, R. L. Sequential treatment allocation using biased coin designs. Journal of the Royal Statistical Society. Series B 46, 3 (1984), 519{543. [38] van der Vaart, A. W. Asymptotic Statistics. Cambridge University Press, Cam- bridge, 1998. [39] van der Vaart, A. W., and Wellner, J. A. Weak Convergence and Empirical Processes. Springer-Verlag, New York, 1996. [40] Wei, L. The adaptive biased coin design for sequential experiments. The Annals of Statistics 6, 1 (1978), 92{100. 5.