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Publications:
Recent developments in partial identification, with Elie Tamer. Identification strategies concern what can be learned about the value of a parameter based on the data and the model assumptions. The literature on partial identification is motivated by the fact that it is not possible to learn the exact value of the parameter for many empirically relevant cases. A typical result in the literature on partial identification is a statement about characterizing the identified set, which summarizes what can be learned about the parameter of interest given the data and model assumptions. For instance, this may mean that the value of the parameter can be learned to necessarily be within some set of values. First, the review surveys the general frameworks that have been developed for conducting a partial identification analysis. Second, the review surveys some of the more recent results on partial identification.
@article{klinetamer2023recent, author = "Brendan Kline and Elie Tamer", title = "Recent developments in partial identification", journal = "Annual Review of Economics", volume = "15 (forthcoming)", year = "2023", url = "http://www.brendankline.com/papers/KlineTamer-ARE-Aug2022.pdf" }
Bayes factors based on p-values and sets of priors with restricted strength. This paper focuses on the minimum Bayes factor compatible with a p-value, considering a set of priors with restricted strength. The resulting minimum Bayes factor depends on both the strength of the set of priors and the sample size. The results can be used to interpret the evidence for/against the hypothesis provided by a p-value in a way that accounts for the strength of the priors and the sample size. In particular, the results suggest further lowering the p-value cutoff for "statistical significance."
@article{kline2022Bayes, author = "Brendan Kline", title = "Bayes factors based on p-values and sets of priors with restricted strength", journal = "The American Statistician", volume = "76", number = "3", pages = "203-213", year = "2022", url = "http://dx.doi.org/10.1080/00031305.2021.1877815", doi = "10.1080/00031305.2021.1877815" } Moment inequalities and partial identification in industrial organization, with Ariel Pakes and Elie Tamer. in Handbook of Industrial Organization, vol. 4 (ed. Kate Ho, Ali Hortacsu and Alessandro Lizzeri): 345-431, 2021. We review approaches to identification and inference on models in Industrial Organization with partial identification and/or moment inequalities. Often, such approaches are intentionally built directly on assumptions of optimizing behavior that are credible in Industrial Organization settings, while avoiding the use of strong modeling and measurement assumptions that may not be warranted. The result is an identified set for the object of interest, reflecting what the econometrician can learn from the data and assumptions. The chapter formally defines identification, reviews the assumptions underlying the identification argument, and provides examples of their use in Industrial Organization settings. We then discuss the corresponding statistical inference problem paying particular attention to practical implementation issues.
@incollection{kpt2021handbook, author = "Brendan Kline and Ariel Pakes and Elie Tamer", title = "Moment inequalities and partial identification in industrial organization", booktitle = "Handbook of Industrial Organization", editor = "Kate Ho and Ali Hortacsu and Alessandro Lizzeri", chapter = "5", volume = "4", year = "2021", url = "http://dx.doi.org/10.1016/bs.hesind.2021.11.005", doi = "10.1016/bs.hesind.2021.11.005" } Econometric analysis of models with social interactions, with Elie Tamer. in The Econometric Analysis of Network Data (ed. Bryan Graham and Aureo de Paula): 149-181, 2020. [Presentation slides] This chapter discusses two main issues relating to the econometrics of models of social interactions. First, this chapter discusses the identification of models of social interactions. Models with social interactions are typically estimated with data on many small groups. For each group, the data typically consist of the outcome and treatment of each individual and perhaps other data like the demographic characteristics. The identification question asks whether it is possible to use such data to recover information about the underlying model that generated the data. And second, this chapter discusses the interpretation and policy relevance of models of social interactions. An important consideration in the application of models of social interactions concerns the adequacy of the specification of the model. Models of social interactions inevitably involve assumptions, either explicit or implicit, about the nature of the interactions. These assumptions often times entail significant restrictions on behavior that are not necessarily implied by economic theory for all applications. These assumptions also concern the relationship between the observed data and the underlying model that generated the data. Therefore, such assumptions are important considerations in the assessment of the adequacy of models of social interactions for particular applications.
@incollection{klinetamer2019econometric, author = "Brendan Kline and Elie Tamer", title = "Econometric analysis of models with social interactions", booktitle = "The Econometric Analysis of Network Data", editor = "Bryan Graham and Aureo de Paula", chapter = "7", year = "2020", url = "http://doi.org/10.1016/B978-0-12-811771-2.00013-4" }
An empirical model of non-equilibrium behavior in games. This paper studies the identification and estimation of the decision rules that individuals use to determine their actions in games, based on a structural econometric model of non-equilibrium behavior in games. The model is based primarily on various notions of limited strategic reasoning, allowing multiple modes of strategic reasoning and heterogeneity in strategic reasoning across individuals and within individuals. The paper proposes the model, and provides sufficient conditions for point identification of the model. Then, the model is estimated on data from an experiment involving two-player guessing games. The application illustrates the empirical relevance of the main features of the model.
@article{kline2018empiricalmodel, author = "Brendan Kline", title = "An empirical model of non-equilibrium behavior in games", journal = "Quantitative Economics", volume = "9", number = "1", pages = "141-181", year = "2018", url = "http://dx.doi.org/10.3982/QE647", doi = "10.3982/QE647" }
Identification of treatment effects with selective participation in a randomized trial, with Elie Tamer. 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 are 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.
@article{klinetamer2018identification, author = "Brendan Kline and Elie Tamer", title = "Identification of treatment effects with selective participation in a randomized trial", journal = "The Econometrics Journal", volume = "21", number = "3", pages = "332-353", year = "2018", url = "http://dx.doi.org/10.1111/ectj.12114", doi = "10.1111/ectj.12114" }
Bayesian inference in a class of partially identified models, with Elie Tamer. 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.
@article{klinetamer2016bayesian, author = "Brendan Kline and Elie Tamer", title = "Bayesian inference in a class of partially identified models", journal = "Quantitative Economics", volume = "7", number = "2", pages = "329-366", year = "2016", url = "http://dx.doi.org/10.3982/QE399", doi = "10.3982/QE399" }
Identification of the direction of a causal effect by instrumental variables. This paper 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.
@article{kline2016identificationdirection, author = "Brendan Kline", title = "Identification of the direction of a causal effect by instrumental variables", journal = "Journal of Business and Economic Statistics", volume = "34", number = "2", pages = "176-184", year = "2016", url = "http://dx.doi.org/10.1080/07350015.2015.1021925", doi = "10.1080/07350015.2015.1021925" }
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.
@article{kline2016empirical, author = "Brendan Kline", title = "The empirical content of games with bounded regressors", journal = "Quantitative Economics", volume = "7", number = "1", pages = "37-81", year = "2016", url = "http://dx.doi.org/10.3982/QE444", doi = "10.3982/QE444" }
Identification of complete information games. This paper establishes sufficient conditions for point identification of the utility functions in generalized complete information game models. These models allow generalized interaction structures and generalized behavioral assumptions. The generalized interaction structures allow that the dependence of an agent's utility function on the other agents' actions can itself depend on characteristics of the agents, including an endogenous network of connections among the agents. The generalized behavioral assumptions relax the solution concept from Nash equilibrium play to weaker solution concepts like rationalizability. The results allow a non-parametric specification of the unobservables.
@article{kline2015identificationcomplete, author = "Brendan Kline", title = "Identification of complete information games", journal = "Journal of Econometrics", volume = "189", number = "1", pages = "117-131", year = "2015", url = "http://dx.doi.org/10.1016/j.jeconom.2015.06.023", doi = "10.1016/j.jeconom.2015.06.023" }
The price elasticity of demand for heroin: matched longitudinal and experimental evidence, with Todd Olmstead, Sheila M. Alessi, Rosalie L. Pacula, and Nancy M. Petry. 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.
@article{olmsteadetal2015price, author = "Todd Olmstead and Sheila M. Alessi and Brendan Kline and Rosalie L. Pacula and Nancy M. Petry", title = "The price elasticity of demand for heroin: matched longitudinal and experimental evidence", journal = "Journal of Health Economics", volume = "41", year = "2015", url = "http://dx.doi.org/10.1016/j.jhealeco.2015.01.008", doi = "10.1016/j.jhealeco.2015.01.008" }
Explaining trends in body mass index using demographic counterfactuals, with Justin L. Tobias. 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.
@article{klinetobias2014explaining, author = "Brendan Kline and Justin L. Tobias", title = "Explaining trends in body mass index using demographic counterfactuals", journal = "Econometric Reviews", volume = "33", number = "1-4", pages = "172-196", year = "2014", url = "http://dx.doi.org/10.1080/07474938.2013.807155", doi = "10.1080/07474938.2013.807155" }
Comment on ``Social networks and the identification of peer effects'' by Paul Goldsmith-Pinkham and Guido W. Imbens, with Elie Tamer. @article{klinetamer2013comment, author = "Brendan Kline and Elie Tamer", title = "Comment on ``{Social} networks and the identification of peer effects'' by {Paul Goldsmith-Pinkham and Guido W. Imbens}", journal = "Journal of Business and Economic Statistics", volume = "31", number = "3", pages = "276-279", year = "2013", url = "http://dx.doi.org/10.1080/07350015.2013.792264", doi = "10.1080/07350015.2013.792264" }
Bounds for best response functions in binary games, with Elie Tamer. 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.
@article{klinetamer2012bounds, author = "Brendan Kline and Elie Tamer", title = "Bounds for best response functions in binary games", journal = "Journal of Econometrics", volume = "166", number = "1", pages = "92-105", year = "2012", url = "http://dx.doi.org/10.1016/j.jeconom.2011.06.008", doi = "10.1016/j.jeconom.2011.06.008" }
The Bayesian and frequentist approaches to testing a one-sided hypothesis about a multivariate mean. 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.
@article{kline2011bayesian, author = "Brendan Kline", title = "The {Bayesian} and frequentist approaches to testing a one-sided hypothesis about a multivariate mean", journal = "Journal of Statistical Planning and Inference", volume = "141", number = "9", pages = "3131-3141", year = "2011", url = "http://dx.doi.org/10.1016/j.jspi.2011.03.034", doi = "10.1016/j.jspi.2011.03.034" }
A restriction on lobbyist donations. 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.
@article{kline2009restriction, author = "Brendan Kline", title = "A restriction on lobbyist donations", journal = "Economics Letters", volume = "104", number = "3", pages = "129-132", year = "2009", url = "http://dx.doi.org/10.1016/j.econlet.2009.04.021", doi = "10.1016/j.econlet.2009.04.021" }
The wages of BMI: Bayesian analysis of a skewed treatment-response model with nonparametric endogeneity, with Justin L. Tobias. 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.
@article{klinetobias2008wages, author = "Brendan Kline and Justin L. Tobias", title = "The wages of {BMI}: Bayesian analysis of a skewed treatment-response model with nonparametric endogeneity", journal = "Journal of Applied Econometrics", volume = "23", number = "6", pages = "767-793", year = "2008", url = "http://dx.doi.org/10.1002/jae.1028", doi = "10.1002/jae.1028" } Working Papers:
Classical p-values and the Bayesian posterior probability that the hypothesis is approximately true. 2022. This paper relates p-values for the hypothesis that θ = c to the Bayesian posterior probability that the hypothesis is approximately true, in the sense that θ ∈ [c - ε, c + ε] for a selected ε > 0. In a setup with a continuous prior for θ, the results show that a larger (respectively, smaller) p-value does not necessarily correspond to a higher (respectively, lower) probability that θ is close to c. Therefore, the results suggest caution about common ways of using p-values, specifically the use of small p-values as a key standard in empirical research.
@unpublished{kline2022Bayesian, author = "Brendan Kline", title = "Classical p-values and the {Bayesian} posterior probability that the hypothesis is approximately true", year = "2022" } Identification of incomplete information games in monotone equilibrium. 2017. This paper develops identification results for a class of incomplete information games. These games determine an allocation of units of a valuable object and arrangement of monetary transfers on the basis of the actions taken by the players. The identification strategy is based on the assumption of monotone equilibrium, in which players use strategies that are weakly increasing functions of their valuations for the object being allocated. Such equilibria are known from the economic theory literature to exist under general conditions. The identification result concerns recovering the distribution of valuations for a unit of the object. The identification results flexibly deliver either point identification or partial identification, as appropriate based on the identifying content of the data. The partial identification results are stated as "bounds" on the distribution of valuations in the sense of the usual multivariate stochastic order. The identification results allow for dependent valuations. Moreover, the identification results can apply to an incomplete model that does not necessarily involve a complete specification of all of the details of the game.
@unpublished{kline2017identification, author = "Brendan Kline", title = "Identification of incomplete information games in monotone equilibrium", year = "2017" } |