Publications:
Explaining trends in body mass index using demographic counterfactuals. Econometric Reviews 33(1-4): 172-196, 2014. (with Tobias, Justin L.)
The United States is experiencing a major public health problem relating to increasing levels of excess body fat. This paper is about the relationship in the United States between trends in the distribution of body mass index (BMI), including trends in overweight and obesity, and demographic change. We provide estimates of the counterfactual distribution of BMI that would have been observed in 2003-2008 had demographics remained fixed at 1980 values, roughly the beginning of the period of increasing overweight and obesity. We find that changes in demographics are partly responsible for the changes in the population distribution of BMI and are capable of explaining about 8.6% of the increase in the combined rate of overweight and obesity among women and about 7.2% of the increase among men. We also use demographic projections to predict a BMI distribution and corresponding rates of overweight and obesity for 2050.
Bounds for best response functions in binary games. Journal of Econometrics 166(1): 92-105, 2012. (with Tamer, Elie)
This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment-response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment-response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.
The Bayesian and frequentist approaches to testing a one-sided hypothesis about a multivariate mean. Journal of Statistical Planning and Inference 141(9): 3131-3141, 2011.
This paper compares the Bayesian and frequentist approaches to testing a one-sided hypothesis about a multivariate mean. First, this paper proposes a simple way to assign a Bayesian posterior probability to one-sided hypotheses about a multivariate mean. The approach is to use (almost) the exact posterior probability under the assumption that the data has multivariate normal distribution, under either a conjugate prior in large samples or under a vague Jeffreys prior. This is also approximately the Bayesian posterior probability of the hypothesis based on a suitably flat Dirichlet process prior over an unknown distribution generating the data. Then, the Bayesian approach and a frequentist approach to testing the one-sided hypothesis are compared, with results that show a major difference between Bayesian reasoning and frequentist reasoning. The Bayesian posterior probability can be substantially smaller than the frequentist p-value. A class of example is given where the Bayesian posterior probability is basically 0, while the frequentist p-value is basically 1. The Bayesian posterior probability in these examples seems to be more reasonable. Other drawbacks of the frequentist p-value as a measure of whether the one-sided hypothesis is true are also discussed.
A restriction on lobbyist donations. Economics Letters 104(3): 129-132, 2009.
This paper studies the consequences of a fine for violating a ceiling on permissible donations in a competition for a political prize. Increasing the fine can increase or decrease the amount of expected donations in equilibrium.
The wages of BMI: Bayesian analysis of a skewed treatment-response model with nonparametric endogeneity. Journal of Applied Econometrics 23(6): 767-793, 2008. (with Tobias, Justin L.)
We generalize the specifications used in previous studies of the effect of body mass index (BMI) on earnings by allowing the potentially endogenous BMI variable to enter the log wage equation nonparametrically. We introduce a Bayesian posterior simulator for fitting our model that permits a nonparametric treatment of the endogenous BMI variable, flexibly accommodates skew in the BMI distribution, and whose implementation requires only Gibbs steps. Using data from the 1970 British Cohort Study, our results indicate the presence of nonlinearities in the relationships between BMI and log wages that differ across men and women, and also suggest the importance of unobserved confounding for our sample of males.
Completed Working Papers:
The empirical content of games with bounded regressors, 2014.
This paper develops a strategy for identification and estimation of complete information games that does not require a regressor that has large support, nor a parametric specification for the distribution of the unobservables. The identification result is a consequence of the fact that the complete information game framework has substantial empirical content for all values of the explanatory variables. The identification and estimation of the interaction effect parameter uses a non-standard but plausible condition on the unobservables: the assumption that the joint distribution of the unobservables of all agents is unimodal in the sense of achieving the global maximum at a unique point. A three-step semiparametric estimator is proposed that is based on this identification result. Under mild regularity conditions, the estimator is consistent and asymptotically normally distributed. The estimator is non-standard in the sense that the estimator of the interaction effect parameter converges at slower than the parametric rate. An intermediate result of this paper, potentially of independent interest, concerns identification and estimation of the direction of the interaction effect.
Default Bayesian inference in a class of partially identified models, 2013. (with Tamer, Elie)
We develop a Bayesian approach to inference in a class of partially identified econometric models. Models in this class have a point identified parameter mu (e.g., characteristics of the distribution of the data) and a partially identified parameter of interest theta (e.g., parameters of the model); further, if mu is known then the identified set for theta is known. Many instances of this class are commonly used in empirical work. Our approach maps, via the mapping between mu and theta, and without the specification of a prior for theta, the posterior for the point identified parameter mu to posterior probability statements about the identified set for theta, which is the quantity about which the data are informative. Thus, among other examples, we can report the posterior probability that a particular parameter value (or a set of parameter values, or a function of the parameter) is in the identified set. The paper develops general results on large sample approximations to these posterior probabilities, which illustrate how the posterior probabilities over the identified set are revised by the data. The paper establishes conditions under which the credible sets for the identified set also are valid frequentist confidence sets, providing a connection between Bayesian and frequentist inference in partially identified models (including for functions of the partially identified parameter). The approach is computationally attractive even in high-dimensional models: the approach avoids an exhaustive search over the parameter space (or "guess and verify"), partly by using existing MCMC methods to simulate draws from the posterior for mu. The paper also considers issues related to specification testing and estimation of misspecified models. We illustrate our approach via a set of Monte Carlo experiments and an empirical application to a binary entry game involving airlines.
Identification of complete information games (supersedes Identification of semiparametric games on networks with application to social interactions), 2013.
This paper provides sufficient conditions for the point identification of the utility functions in a class of generalized complete information game models. This class of models generalizes the standard model in two main areas: the structure of the interaction and how the agents "react" to that structure. The first generalization is that these models have a generalized interaction structure, which characterizes how the utility functions depend on the actions of other agents. This generalized interaction structure allows that the way that a given agent's utility function depends on the other agents' actions can itself depend on observable or unobservable characteristics of the agents. Further, this generalized interaction structure allows that there is a network of connections among the agents, as in a network of friendships in social interactions or more generally a network of inter-agent connections in a network game. This network determines whether a given agent's utility function has any dependence on another agent's action according to whether those agents are connected to each other in the network. This network can be endogenous, which corresponds to homophily in models of social interactions and related situations. The second generalization is that these models generalize the assumptions about how the agents "react" to this interaction structure, by relaxing the solution concept from Nash equilibrium play to weaker solution concepts like rationalizability. Further, the identification results allow a non-parametric specification of the unobservables. Indeed, as an extension, stronger sufficient conditions for the point identification of the distribution of the unobservables and the selection mechanism are established.
Identification of the direction of a causal effect by instrumental variables, 2013.
This paper provides a strategy to identify the existence and direction of a causal effect in a generalized nonparametric model that is identified by instrumental variables. The causal effect concerns how the outcome depends on the endogenous explanatory variable of interest. The model is nonparametric and nonseparable, so the causal effect can depend in a general way on the explanatory variables and unobservables. The outcome variable, explanatory variables, and the instrumental variable can be essentially any combination of continuous, discrete, or "other" variables, due to the use of a generalized regression framework. In particular, it is not necessary to have any continuous variables, none of the variables need to have large support, and the instrument can be binary even if the corresponding endogenous explanatory variable and/or outcome is continuous. The outcome can be mismeasured or interval-measured, and the endogenous explanatory variable of interest need not even be observed by the econometrician. The unobservables can be nonparametric, high dimensional, and not independent of the explanatory variables. In particular, this allows multiple endogenous explanatory variables, requiring an instrument only for the endogenous explanatory variable of interest. The identification results are constructive, and can be empirically implemented using standard estimation results.