Jack Porter

How Dangerous Are Drinking Drivers

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

Asymptotics for Statistical Treatment Rules

8,000.

Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak

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.

Estimating the Effect of Alcohol on Driver Risk Using Only Fatal Accident Statistics

It is well-known that size-adjustments based on Edgeworth expansions for the t-statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable. This paper shows, however, that the lack of Edgeworth expansions and bootstrap validity are not tied to the weak instrument framework, but instead depends on which test statistic is examined. In particular, Edgeworth expansions are valid for the score and conditional likelihood ratio approaches, even when the instruments are uncorrelated with the endogenous explanatory variable. Furthermore, there is a belief that the bootstrap method fails when instruments are weak, since it replaces parameters with inconsistent estimators. Contrary to this notion, we provide a theoretical proof that guarantees the validity of the bootstrap for the score test, as well as the validity of the conditional bootstrap for many conditional tests. Monte Carlo simulations show that the bootstrap actually decreases size distortions in both cases.

Efficiency of Covariance Matrix Estimators for Maximum Likelihood Estimation

Measuring the relative likelihood of fatal crash involvement for different types of drivers would seem to require information on both the number of fatal crashes by driver type and the fraction of drivers on the road falling into each category. In this paper, however, we present a methodology for measuring fatal crash likelihood that relies solely on fatal crash data. The key to our identification strategy is the hidden richness inherent to two-car crashes. Crashes involving two drinking drivers are proportional to the square of the number of drinking drivers on the road; crashes with one drinking and one sober driver increase linearly in the number of drinking drivers. Imposing a limited set of assumptions (e.g. independence across crashes, equal mixing on the roads), we are able to estimate both the likelihood of causing a fatal crash and the fraction of drivers of each type on the road. Our estimates suggest that drivers with alcohol in their blood are at least eight times more likely to cause a fatal crash; legally drunk drivers pose a risk at least 15 times greater than sober drivers. Males, young drivers, and drivers with bad past driving records are all more dangerous, but the impact of these other factors is far less than that of alcohol.

Location Properties of Point Estimators in Linear Instrumental Variables and Related Models

When econometric models are estimated by maximum likelihood, the conditional information matrix variance estimator is usually avoided in choosing a method for estimating the variance of the parameter estimate. However, the conditional information matrix estimator attains the semiparametric efficiency bound for the variance estimation problem. Unfortunately, for even moderately complex models, the integral involved in computation of the conditional information matrix estimator is prohibitively difficult to solve. Simulation is suggested to approximate the integral, and two simulation variance estimators are proposed. Monte Carlo results suggest these estimators are attractive in providing accurate confidence interval coverage rates compared to the standard maximum likelihood variance estimators.

Panel Asymptotics and Statistical Decision Theory

We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.

Comment on “Simple Estimators for Invertible Index Models”

This paper develops some applications of asymptotic statistical decision theory in econometrics, focusing on settings where the data are organized into groups or cells with heterogeneous parameters. Even if the groups are of different sizes, local asymptotic normality holds under suitable regularity conditions, and this can greatly simplify analysis of different types of econometric problems. We apply these results to the analysis of treatment assignment rules, and to estimators of cell‐specific parameters that employ shrinkage towards parametric models.

Estimation in the Regression Discontinuity Model

Ahn, Ichimura, Powell, and Ruud have written an important contribution on identification and estimation of a quite general class of index models. Their setup allows a set of reduced form parameters to depend on an unknown function of one or more linear indices, and this mapping is assumed to be invertible so that the linear indices can be written as a function of the reduced form parameters. A pairwise matching argument yields identification of the parameters of the linear indices. In particular, any pair of observations with the same reduced form parameter values must have identical linear index values. So, given sufficient variation in the covariates of the linear indices conditional on the reduced form parameter values, the coefficient parameters of the linear indices are identified. This identification argument leads to a natural method of estimation. Pairs of observations are matched by the closeness of their nonparametrically estimated reduced form parameters. A quadratic form in the difference of the linear index covariates is formed and averaged over pairs of observations (weighted by the closeness of their estimated reduced form parameters). The eigenvalue of this average closest to zero is the estimate of the linear index parameters. True to the article’s title, this estimator is simple and straightforward for practitioners. Ahn, Ichimura, Powell, and Ruud show that the coefficient estimator has a parametric rate and provide the limiting distribution alongwith a consistent asymptotic variance estimator. The article shows that this approach works even in the “over-determined” case where the number of reduced form parameters exceed the number of linear index coefficients, and the effect on the asymptotic variance is highlighted. Finally, the choice of weight matrix in the quadratic form average is considered for improved efficiency. This is an intuitive and practical approach to commonly used semiparametric index models.