/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

This paper provides an introduction and "user guide" to Regression Discontinuity (RD) designs for empirical researchers. It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a "quasi-experimental" design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD.

Regression Discontinuity Designs in Economics

Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades, much research has been done on the econometric and statistical analysis of such causal effects. This recent theoreti- cal literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization, and other areas of empirical microeconomics. In this review, we discuss some of the recent developments. We focus primarily on practical issues for empirical research- ers, as well as provide a historical overview of the area and give references to more technical research.

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Recent developments in the econometrics of program evaluation

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

This paper provides an introduction and “user guide” to Regression Discontinuity (RD) designs for empirical researchers. It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a “quasi-experimental” design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD. ( JEL C21, C31)

/pdf/regression-discontinuity-designs-in-economics-5foiogfcmd.pdf

Regression discontinuity designs in economics

The regression discontinuity model has recently become a commonly applied framework for empirical work in economics. Hahn, Todd, and Van der Klaauw (2001) provide a formal development of the identification of a treatment effect in this framework and also note the potential bias problems in its estimation. This bias difficulty is the result of a particular feature of the regression discontinuity treatment effect estimation problem that distinguishes it from typical semiparametric estimation problems where smoothness is lacking. Here, the discontinuity is not simply an obstacle to overcome in estimation; instead, the size of discontinuity is itself the object of estimation interest. In this paper, I derive the optimal rate of convergence for estimation of the regression discontinuity treatment effect. The optimal rate suggests that with appropriate choice of estimator the bias difficulties are no worse than would be found in the usual nonparametric conditional mean estimation problem (at an interior point of the covariate support). Two estimators are proposed that attain the optimal rate under varying conditions. One new estimator is based on Robinson’s (1988) partially linear estimator. The other estimator uses local polynomial estimation and is optimal under a broader set of conditions.

/pdf/estimation-in-the-regression-discontinuity-model-6wy91gctw9.pdf

Estimation in the Regression Discontinuity Model

This paper provides conditions under which the inequality constraints generated by either single agent optimizing behavior, or by the Nash equilibria of multiple agent problems, can be used as a basis for estimation and inference We also add to the econometric literature on inference in models defined by inequality constraints by providing a new specification test and methods of inference for the boundaries of the model’s identified set Two applications illustrate how the use of inequality constraints can simplify the problem of obtaining estimators from complex behavioral models of substantial applied interest

/pdf/moment-inequalities-and-their-application-1bvd4yvbie.pdf

Moment Inequalities and Their Application

We present a methodology for measuring the risks posed by drinking drivers that relies solely on readily available data on fatal crashes. The key to our identification strategy is a hidden richness inherent in two‐car crashes. Drivers with alcohol in their blood are seven times more likely to cause a fatal crash; legally drunk drivers pose a risk 13 times greater than sober drivers. The externality per mile driven by a drunk driver is at least 30 cents. At current enforcement rates the punishment per arrest for drunk driving that internalizes this externality would be equivalent to a fine of $8,000.

/pdf/how-dangerous-are-drinking-drivers-4xiai0hbpv.pdf

How Dangerous Are Drinking Drivers

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.

/pdf/asymptotics-for-statistical-treatment-rules-1pxl3bjx8h.pdf

Asymptotics for Statistical Treatment Rules

This paper provides conditions under which the inequality constraints generated by either single agent optimizing behavior, or by the Nash equilibria of multiple agent problems, can be used as a basis for estimation and inference. We also add to the econometric literature on inference in models defined by inequality constraints by providing a new specification test and methods of inference for the boundaries of the model's identified set. Two applications illustrate how the use of inequality constraints can simplify the problem of obtaining estimators from complex behavioral models of substantial applied interest.

Jack Porter

Papers

Estimation in the Regression Discontinuity Model

Moment Inequalities and Their Application

How Dangerous Are Drinking Drivers

Asymptotics for Statistical Treatment Rules

Moment inequalities and their application