Session 2: Empirical Implementation of Theoretical Models of Strategic Interaction and Dynamic Behavior

This paper presents an algorithm that generates the conditional moment inequalities that characterize the identified set of the common parameter of various semi-parametric panel multi-nomial choice models. I consider both static and dynamic models, and consider various weak stochastic restrictions on the distribution of observed and unobserved components of the models. For a broad class of such stochastic restrictions, the paper demonstrates that the inequalities characterizing the identified set of the common parameter can be obtained as solutions of multiple objective linear programs (MOLPs), thereby transforming the task of finding these inequalities into a purely computational problem. The algorithm that I provide reproduces many well-known results, including the conditional moment inequalities derived in Manski 1987, Pakes and Porter 2023, and Khan, Ponomareva, and Tamer 2023. Moreover, I use the algorithm to generate some new results, by providing characterizations of the identified set in some cases that were left open in Pakes and Porter 2023 and Khan, Ponomareva, and Tamer 2023, as well as characterizations of the identified set under alternative stochastic restrictions.

One of the main challenges in partially-identified models is obtaining a tractable characterization of the sharp identified set, which exhausts all in-formation contained in the data and modeling assumptions. In a large class of models, the sharp identified sets can be described using the so-called Art-stein’s inequalities, which verify that the observed distribution of outcomes, given covariates, can be generated by the model for some parameter values. While theoretically convenient, this approach is often impractical because the total number of inequalities is too large. However, many of the inequalities may be redundant in the sense that excluding them from the analysis does not lose identifying information. In this paper, I characterize the smallest possible collection of inequalities that suffices to describe the sharp identified set and provide an efficient algorithm for obtaining these inequalities in practice. I apply the results to the models of static and dynamic market entry, discrete choice, selectively-observed data, and English auctions, and conduct a simulation study to demonstrate that the proposed method substantially improves upon ad hoc inequality selection.

This paper studies causal inference with observational network data. A challenging aspect of this setting is the possibility of interference in both potential outcomes and selection into treatment, for example due to peer effects in either stage. We therefore consider a nonparametric setup in which both stages are reduced forms of simultaneous-equations models. This results in high-dimensional network confounding, where the network and covariates of all units constitute sources of selection bias. The literature predominantly assumes that confounding can be summarized by a known, low-dimensional function of these objects, and it is unclear what selection models justify common choices of functions. We show that graph neural networks (GNNs) are well suited to adjust for high-dimensional network confounding. We establish a network analog of approximate sparsity under primitive conditions on interference. This demonstrates that the model has low-dimensional structure that makes estimation feasible and justifies the use of shallow GNN architectures.

A researcher can use a tightly parameterized structural model to obtain internally consistent estimates of a wide range of economically interesting targets. We ask how reliable these estimates are when the researcher's model may be misspecified. We focus on the case of multivariate, potentially nonlinear models where the causal variable of interest is endogenous. Reliable estimates require that the researcher's model is flexible enough to describe the effects of the endogenous variable approximately correctly. Reliable estimates do not require that the researcher has correctly specified the role of the exogenous controls in the model. However, if the role of the controls is misspecified, reliable estimates require a property we call strong exclusion. Strong exclusion depends on having sufficiently many instruments that are unrelated to the controls. We discuss how practitioners can achieve strong exclusion and illustrate our findings with an application to a differentiated goods model of demand for beer.

We propose an instrumental variable framework for identifying and estimating average and quantile effects of discrete and continuous treatments with binary instruments. The basis of our approach is a local copula representation of the joint distribution of the potential outcomes and unobservables determining treatment assignment. This representation allows us to introduce an identifying assumption, so-called copula invariance, that restricts the local dependence of the copula with respect to the treatment propensity. We show that copula invariance identifies treatment effects for the entire population and other subpopulations such as the treated. The identification results are constructive and lead to straightforward semiparametric estimation procedures based on distribution regression. An application to the effect of sleep on well-being uncovers interesting patterns of heterogeneity.

In a rollover lottery, buyers pick their own numbers, and a jackpot not won adds to the next draw. We develop an equilibrium model of this lottery, since it is a major source of government revenue. Buyers differ in their lottery enjoyment levels, and the market-clearing price is the expected monetary loss on a lottery ticket — namely, ticket face value less expected winnings. The supply curve captures the relation between tickets sold and expected loss implied by the rules of the game. We use this equilibrium model in two empirical applications. First, we test the model’s predictions on the optimal relationship between odds and population size using data from many countries, and across U.S. states. Second, we propose a structural empirical implementation of the model and nonpara- metrically estimate demand for U.S. national rollover lotteries by exploiting the randomness inherent in the rollover mechanism. We find that the model predicts well out of sample and show how to use it to inform lottery design.

A growing number of central authorities use assignment mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms incentivize students to strategically misreport their preferences. In this paper, we provide an approach for identifying the causal effects of school assignment on future outcomes that accounts for strategic misreporting. Misreporting may invalidate existing point-identification approaches, and we derive sharp bounds for causal effects that are robust to strategic behavior. Our approach applies to any mechanism as long as there exist placement scores and cutoffs that characterize that mechanism's allocation rule. We use data from a deferred acceptance mechanism that assigns students to more than 1,000 university-major combinations in Chile. Matching theory predicts that students' behavior in Chile should be strategic because they can list only up to eight options, and we find empirical evidence consistent with such behavior. Our bounds are informative enough to reveal significant heterogeneity in graduation success with respect to preferences and school assignment.

We study the role of selection into treatment in difference-in-differences (DiD) designs. We derive necessary and sufficient conditions for parallel trends assumptions under general classes of selection mechanisms. These conditions characterize the empirical content of parallel trends. For settings where the necessary conditions are questionable, we propose tools for selection-based sensitivity analysis. We also provide templates for justifying DiD in applications with and without covariates. A reanalysis of the causal effect of NSW training programs demonstrates the usefulness of our selection-based approach to sensitivity analysis.

Social disruption occurs when a policy creates or destroys many network connections between agents. It is a costly side effect of many interventions and so a growing empirical literature recommends measuring and accounting for social disruption when evaluating the welfare impact of a policy. However, there is currently little work characterizing what can actually be learned about social disruption from data in practice. In this paper, we consider the problem of identifying social disruption in a research design that is popular in the literature. We provide two sets of identification results. First, we show that social disruption is not generally point identified, but informative bounds can be constructed using the eigenvalues of the network adjacency matrices observed by the researcher. Second, we show that point identification follows from a theoretically motivated monotonicity condition, and we derive a closed form representation. We apply our methods in two empirical illustrations and find large policy effects that otherwise might be missed by alternatives in the literature.

We develop asymptotic approximation results that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and other statistical decision problems that involve multiple decision nodes with structured and possibly endogenous information sets. Our results extend the classic asymptotic representation theorem used extensively in efficiency bound theory and local power analysis. In adaptive settings where the decision at one stage can affect the observation of variables in later stages, we show that a limiting data environment characterizes all limit distributions attainable through a joint choice of an adaptive design rule and statistics applied to the adaptively generated data, under local alternatives. We illustrate how the theory can be applied to study the choice of adaptive rules and end-of-sample statistical inference in batched (groupwise) sequential adaptive experiments.

Empirical methods for transferable-utility matching games have previously been developed using the key outcome of the matches formed in equilibrium. We explore identification and estimation of match production functions and agent valuation functions using data on two additional outcomes of such matching games: monetary transfers (prices) and profits. We provide identification results for nonparametric models for the case of data on profits and for more parametric models for the case of data on prices. We provide estimators paralleling the identification results for both profit data and price data. Importantly, our identification results allow for agents to have valuations defined over the unmeasured characteristics of potential partners.

We study the identification and estimation of a multidimensional screening model, where a monopolist sells a multi-attribute product to consumers with private information about their multidimensional preferences. Under optimal screening, the seller designs product and payment rules that exclude “low-type” consumers, bunches the “medium types” at “medium-quality” products, and perfectly screens the “high types.” We determine sufficient conditions to identify the joint distribution of preferences and the marginal costs from data on optimal individual choices and payments. Then, we propose estimators for these objects, establish their asymptotic properties, and assess their small-sample performance using Monte Carlo experiments.