Asymptotics for Statistical Treatment Rules

This paper develops asymptotic optimality theory for statistical treatment rules in smooth parametric and semiparametric models. Manski (2000, 2002, 2004) and Dehejia (2005) have argued that the problem of choosing treatments to maximize social welfare is distinct from the point estimation and hypothesis testing problems usually considered in the treatment eects literature, and advocate formal analysis of decision procedures that map empirical data into treatment choices. We develop large-sample approximations to statistical treatment assignment problems in both randomized experiments and observational data settings in which treatment eects are identified. We derive a local asymptotic minmax regret bound on social welfare, and a local asymptotic risk bound for a two-point loss function. We show that certain natural treatment assignment rules attain these bounds.

[1]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[2]  Leonard J. Savage,et al.  The Theory of Statistical Decision , 1951 .

[3]  S. Karlin,et al.  The Theory of Decision Procedures for Distributions with Monotone Likelihood Ratio , 1956 .

[4]  D. Freedman,et al.  On the consistency of Bayes estimates , 1986 .

[5]  L. L. Cam,et al.  Asymptotic Methods In Statistical Decision Theory , 1986 .

[6]  Aad Van Der Vbart,et al.  ON DIFFERENTIABLE FUNCTIONALS , 1988 .

[7]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[8]  A. V. D. Vaart,et al.  On the Asymptotic Information Bound , 1989 .

[9]  A. V. D. Vaart,et al.  An Asymptotic Representation Theorem , 1991 .

[10]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[11]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[12]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[13]  M. Schervish.  Theory of Statistics , 1995 .

[14]  F. Y. Edgeworth,et al.  The theory of statistics , 1996 .

[15]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[16]  W. J. Hall,et al.  Asymptotically uniformly most powerful tests in parametric and semiparametric models , 1996 .

[17]  Anatolii A. Puhalskii,et al.  On large-deviation efficiency in statistical inference , 1998 .

[18]  M. Berger,et al.  Is the Threat of Training More Effective Than Training Itself? Experimental Evidence from the UI System , 1999 .

[19]  Charles F. Manski,et al.  Treatment Choice Under Ambiguity Induced by Inferential Problems , 2002, ISIPTA.

[20]  Gary Chamberlain,et al.  Econometrics and decision theory , 2000 .

[21]  M. Berger,et al.  Evaluating profiling as a means of allocating government services , 2000 .

[22]  Charles F. Manski,et al.  Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice , 2000 .

[23]  Rajeev H. Dehejiaa,et al.  Program evaluation as a decision problem , 2002 .

[24]  C. Manski.  Statistical treatment rules for heterogeneous populations , 2003 .

[25]  K. Schlag.  ELEVEN - Tests needed for a Recommendation , 2006 .

[26]  Rajeev Dehejia.  When is ATE enough? Risk aversion and inequality aversion in evaluating training programs , 2008 .