Brendan Kline

Bayesian inference in a class of partially identified models

This paper develops a Bayesian approach to inference in a class of partially identified econometric models. Models in this class are characterized by a known mapping between a point identified reduced‐form parameter μ and the identified set for a partially identified parameter θ. The approach maps posterior inference about μ to various posterior inference statements concerning the identified set for θ, without the specification of a prior for θ. Many posterior inference statements are considered, including the posterior probability that a particular parameter value (or a set of parameter values) is in the identified set. The approach applies also to functions of θ. The paper develops general results on large sample approximations, which illustrate how the posterior probabilities over the identified set are revised by the data, and establishes conditions under which the Bayesian credible sets also are valid frequentist confidence sets. The approach is computationally attractive even in high‐dimensional models, in that the approach avoids an exhaustive search over the parameter space. The performance of the approach is illustrated via Monte Carlo experiments and an empirical application to a binary entry game involving airlines.

The empirical content of games with bounded regressors

This paper develops a strategy for identification and estimation of complete information games that does not require a regressor that has large support or a parametric specification for the distribution of the unobservables. The identification result uses a nonstandard but plausible condition on the unobservables: the assumption that the joint density of the unobservables of all agents is unimodal in the sense of achieving the global maximum at a unique point. Also, a three‐step semiparametric estimator is proposed. Under mild regularity conditions, the estimator is consistent and asymptotically normally distributed. The estimator is nonstandard in the sense that the estimators of the intercept and interaction effect parameters converge at slower than the parametric rate. An intermediate result concerns identification and estimation of the direction of the interaction effect.

The price elasticity of demand for heroin: Matched longitudinal and experimental evidence

This paper reports estimates of the price elasticity of demand for heroin based on a newly constructed dataset. The dataset has two matched components concerning the same sample of regular heroin users: longitudinal information about real-world heroin demand (actual price and actual quantity at daily intervals for each heroin user in the sample) and experimental information about laboratory heroin demand (elicited by presenting the same heroin users with scenarios in a laboratory setting). Two empirical strategies are used to estimate the price elasticity of demand for heroin. The first strategy exploits the idiosyncratic variation in the price experienced by a heroin user over time that occurs in markets for illegal drugs. The second strategy exploits the experimentally induced variation in price experienced by a heroin user across experimental scenarios. Both empirical strategies result in the estimate that the conditional price elasticity of demand for heroin is approximately -0.80.

Using Observational vs. Randomized Controlled Trial Data to Learn About Treatment Effects

Randomized controlled trials (RCTs) are routinely used in medicine and are becoming more popular in economics. Data from RCTs are used to learn about treatment eects of interest. This paper studies what one can learn about the average treatment response (ATR) and average treatment eect (ATE) from RCT data under various assumptions and compares that to using observational data. We nd that data from an RCT need not point identify the ATR or ATE because of selection into an RCT, as subjects are not randomly assigned from the population of interest to participate in the RCT. This problem relating to external validity is the primary problem we study. So, assuming internal validity of the RCT, we study the identied features of these treatment eects under a variety of weak assumptions such as: mean independence of response from participation, an instrumental variable assumption, or that there is a linear eect of participation on response. In particular we provide assumptions sucient to point identify the ATR or the ATE from RCT data and also shed light on when the sign of the ATE can be identied. We then

Identification of the Direction of a Causal Effect by Instrumental Variables

This article provides a strategy to identify the existence and direction of a causal effect in a generalized nonparametric and nonseparable model identified by instrumental variables. The causal effect concerns how the outcome depends on the endogenous treatment variable. The outcome variable, treatment variable, other explanatory variables, and the instrumental variable can be essentially any combination of continuous, discrete, or “other” variables. 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 treatment variable and/or outcome is continuous. The outcome can be mismeasured or interval-measured, and the endogenous treatment variable need not even be observed. The identification results are constructive, and can be empirically implemented using standard estimation results.

Identification of treatment effects with selective participation in a randomized trial

Randomized trials (RTs) are used to learn about treatment effects. This paper studies identification of average treatment response (ATR) and average treatment effect (ATE) from RT data under various assumptions. The focus is the problem of external validity of the RT. RT data need not point identify the ATR or ATE because of selective participation in the RT. The paper reports partial‐identification and point‐identification results for the ATR and ATE based on RT data under a variety of assumptions. The results include assumptions sufficient to point identify the ATR or ATE from RT data. Under weaker assumptions, the ATR or ATE is partially identified. Further, attention is given to identification of the sign of the ATE and identification of whether participation in the RT is selective. Finally, identification from RT data is compared to identification from observational data.

Explaining Trends in Body Mass Index Using Demographic Counterfactuals

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.