Session 1: Empirical Implementation of Theoretical Models of Strategic Interaction and Dynamic Behavior

When treatment effects are heterogeneous across units but auto-correlated over time, there is value to dynamic treatment rules that assign treatment status on the basis of past treatment outcomes. Treatment has an option value. The challenge is that correlation in estimated treatment effects may be driven by correlation in errors rather than correlation in treatment effects. This paper shows how to estimate the value of dynamic assignment rules in observational data, and applies the methodology to Operation Ceasefire, a widely adopted homicide reduction program. Using a newly constructed data-set of adoption events across the US, we argue that programs inspired by Operation Ceasefire generate statistically insignificant reductions in homicide rates on average, but that their effectiveness is significantly improved by dynamic adoption. A naive approach would considerably overestimate these benefits.

We propose a generalization of the synthetic control and interventions methods to the setting with dynamic treatment effects. We consider the estimation of unit-specific treatment effects from panel data collected under a general treatment sequence. Here, each unit receives multiple treatments sequentially, according to an adaptive policy that depends on a latent, endogenously time-varying confounding state. Under a low-rank latent factor model assumption, we develop an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be viewed as an identification strategy for structural nested mean models—a widely used framework for dynamic treatment effects—under a low-rank latent factor assumption on the blip effects. Unlike these models, however, it is more permissive in observational settings, thereby broadening its applicability. Our method, which we term synthetic blip effects, is a backwards induction process in which the blip effect of a treatment at each period for a target unit is recursively expressed as a linear combination of the blip effects of other units that received the designated treatment. This strategy avoids the combinatorial explosion in the number of units that would otherwise be required by a naive application of prior synthetic control and intervention methods in dynamic treatment settings. We provide estimation algorithms that are easy to implement in practice and yield estimators with desirable properties. Using unique Korean firm-level panel data, we demonstrate how the proposed framework can be used to estimate individualized dynamic treatment effects and to derive optimal treatment allocation rules in the context of financial support for exporting firms.

We propose a general approach for inference for a broad class of treatment effect parameters in a setting of a discrete valued treatment and instrument with a general outcome variable. The class of parameters considered are those that can be expressed as the expectation of a function of the response type conditional on a generalized principal stratum. Here, the response type refers to the vector of potential outcomes and potential treatments, and a generalized principal stratum is a set of possible values for the response type. In addition to instrument exogeneity, the main substantive restriction imposed rules out certain values for the response types in the sense that they are assumed to occur with probability zero. It is shown through a series of examples that this framework includes a wide variety of parameters and assumptions that have been considered in the previous literature. A key result in our analysis is a characterization of the identified set for such parameters under these assumptions in terms of existence of a non-negative solution to linear systems of equations with a special structure. We propose methods for inference exploiting this special structure and recent results in Fang et al. (2023).

Empirical models of demand for differentiated products rely on low-dimensional product representations to capture substitution patterns. These representations are increasingly proxied by applying ML methods to high-dimensional, unstructured data, including product descriptions and images. When proxies fail to capture the true dimensions of differentiation that drive substitution, standard workflows will deliver biased counterfactuals and invalid inference. We develop a practical toolkit that corrects this bias and ensures valid inference for a broad class of counterfactuals. Our approach applies to market-level and/or individual data, requires minimal additional computation, is efficient, delivers simple formulas for standard errors, and accommodates data-dependent proxies, including embeddings from fine-tuned ML models. It can also be used with standard quantitative attributes when mismeasurement is a concern. In addition, we propose diagnostics to assess the adequacy of the proxy construction and dimension. The approach yields meaningful improvements in predicting counterfactual substitution in both simulations and an empirical application.

Small firms obtain patents at significantly lower rates than large firms. To investigate the mechanisms behind this patent-grant gap, we develop and estimate a dynamic structural model of patent examination. We measure claim novelty as the minimum textual distance to prior art, computed from PatentBERT embeddings, and identify examiner behavior by observing the specific prior art cited in rejections. We find that the gap is mostly driven by the stricter and less predictable novelty standards faced by small firms, rather than by large differences in underlying novelty, patent value, prosecution costs, or prior art search. The strictness and the unpredictability of these standards are complements, with their joint effect concentrated in the revision stage: equalizing either alone closes little of the gap, while equalizing both closes most of it. We also show that more precise prior art search---the direction of the USPTO's recent AI-assisted tools---delivers its gains almost entirely to large firms, while extremely precise search harms both firm types. The policy lesson is legibility rather than leniency: making the standard applied to small-firm applications more predictable is more promising than lowering it or improving prior art search.

Reputation is often important in markets for experience goods. New sellers commonly invest in reputation by offering introductory pricing or other incentives. By encouraging buyers to try new sellers, these investments generate information externalities for future buyers while diverting business from other sellers. I study reputation investment behavior by workers in the context of a large online labor platform. I show that employers value worker reputation and experience, and that new workers initially bid low wages but raise their bids after obtaining experience and public reviews. I estimate a dynamic equilibrium model where forward-looking workers bid anticipating the impact of reputation and experience on future employment outcomes. Compared to a counterfactual with bidding based only on immediate payoffs, forward-looking bidding increases the equilibrium number of reviewed workers by 52% and quadruples the number of matches on the platform. However, workers’ investments remain below the social optimum. The socially optimal platform-funded subsidy for hiring new workers raises total surplus by 22% while increasing platform profit. The subsidy level that maximizes platform profit is lower, but achieves 80% of the total surplus gain.

In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator using tools from geometric measure theory. Building on our Hadamard differentiability results, we apply the functional delta method to obtain the asymptotic properties of the value function process for the binary constrained optimal allocation problem and the plug-in ROC curve estimator. Moreover, the convexity of the optimal allocation value functions facilitates demonstrating the degeneracy of first order derivatives with respect to the policy. We then present a double / debiased estimator for the value functions. Importantly, the conditions that validate Hadamard differentiability justify the margin assumption from the statistical classification literature for the fast convergence rate of plug-in methods.

This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment (in)equality models, specification testing of such models, and inference for parameters bounded by linear programs. The new test uses a two-step test statistic and a chi-squared critical value with data-dependent degrees of freedom that can be calculated by an elementary formula. Its simple structure and tuning-parameter-free implementation make it attractive for practical use. We establish uniform asymptotic validity of the test, demonstrate its finite-sample size and power in simulations, and illustrate its use in an empirical application that analyzes women’s labor supply in response to a welfare policy reform.

This paper considers the problem of testing whether there exists a solution satisfying certain nonnegativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system of equations, including the slope coefficients, to be unknown. For this reason, we describe the linear system as having unknown (as opposed to known) coefficients. This hypothesis testing problem arises naturally when constructing confidence sets for possibly partially identified parameters in the analysis of nonparametric instrumental variables models, treatment effect models, and random coefficient models, among other settings. To rule out certain instances in which the testing problem is impossible, in the sense that the power of any test will be bounded by its size, we begin our analysis by characterizing the closure of the null hypothesis with respect to the total variation distance. We then use this characterization to develop novel testing procedures based on sample-splitting. We establish the validity of our testing procedures under weak and interpretable conditions on the linear system. An important feature of these conditions is that they permit the dimensionality of the problem to grow rapidly with the sample size. A further attractive property of our tests is that they do not require simulation to compute suitable critical values. We illustrate the practical relevance of our theoretical results in a simulation study.

We advance the proxy variable approach to production function estimation. We show that the invertibility assumption at its heart is testable. We characterize what goes wrong if invertibility fails and what can still be done. We show that rethinking how the estimation procedure is implemented either eliminates or mitigates the bias that arises if invertibility fails. In particular, a simple change to the first step of the estimation procedure provides a first-order bias correction for the GMM estimator in the second step. Furthermore, a modification of the moment condition in the second step ensures Neyman orthogonality and enhances efficiency and robustness by rendering the asymptotic distribution of the GMM estimator invariant to estimation noise from the rst step.

We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics (e.g. number of common friends) enter the link formation equation, while the mapping from model primitives to equilibrium network structure is generally intractable. Our approach sidesteps this difficulty using a “bounding-by-c” technique that treats endogenous co-variates as random variables and exploits monotonicity restrictions to obtain identifying information. A central contribution is to develop a spectrum of fixed-effects handling strategies based on subnetwork configurations: tetrad-based restrictions that difference out all individual fixed effects, triad-based and weighted restrictions that combine difference-out and integrate-out steps by differencing out some fixed effects and profiling over the remainder conditional on observed characteristics, and general weighted cycle-based restrictions that unify these cases. We also provide point identification results. Preliminary simulations show that the approach can deliver informative bounds on the structural parameters.

In the structural estimation of dynamic discrete choice games, misspecification of unobserved heterogeneity can introduce significant bias in two key categories of structural parameters: those related to dynamic state dependence, such as adjustment or switching costs, and those that reflect strategic interactions among players, like competitive or peer effects. This paper examines the identification of these parameters within models that account for unobserved heterogeneity using a fixed-effects framework, and with short panel data. Drawing on recent advances in functional differencing techniques, we establish identification results for different game types, including distinctions between simultaneous versus sequential moves, myopic versus forward-looking decision-makers, and one-directional versus two-directional strategic interactions. We illustrate the applicability of these findings through an empirical study of a dynamic game of price competition.