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Register a new userIdentification and Estimation of Weakly Separable Models Without Monotonicity
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We study the identification and estimation of treatment effect parameters in weakly separable models. In their seminal work, Vytlacil and Yildiz (2007) showed how to identify and estimate the average treatment effect of a dummy endogenous variable when the outcome is weakly separable in a single index. Their identification result builds on a monotonicity condition with respect to this single index. In comparison, we consider similar weakly separable models with multiple indices, and relax the monotonicity condition for identification. Unlike Vytlacil and Yildiz (2007), we exploit the full information in the distribution of the outcome variable, instead of just its mean. Indeed, when the outcome distribution function is more informative than the mean, our method is applicable to more general settings than theirs; in particular we do not rely on their monotonicity assumption and at the same time we also allow for multiple indices. To illustrate the advantage of our approach, we provide examples of models where our approach can identify parameters of interest whereas existing methods would fail. These examples include models with multiple unobserved disturbance terms such as the Roy model and multinomial choice models with dummy endogenous variables, as well as potential outcome models with endogenous random coefficients. Our method is easy to implement and can be applied to a wide class of models. We establish standard asymptotic properties such as consistency and asymptotic normality.
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This paper studies identification and estimation of a class of dynamic models in which the decision maker (DM) is uncertain about the data-generating process. The DM surrounds a benchmark model that he or she fears is misspecified by a set of models. Decisions are evaluated under a worst-case model delivering the lowest utility among all models in this set. The DMs benchmark model and preference parameters are jointly underidentified. With the benchmark model held fixed, primitive conditions are established for identification of the DMs worst-case model and preference parameters. The key step in the identification analysis is to establish existence and uniqueness of the DMs continuation value function allowing for unbounded statespace and unbounded utilities. To do so, fixed-point results are derived for monotone, convex operators that act on a Banach space of thin-tailed functions arising naturally from the structure of the continuation value recursion. The fixed-point results are quite general; applications to models with learning and Rust-type dynamic discrete choice models are also discussed. For estimation, a perturbation result is derived which provides a necessary and sufficient condition for consistent estimation of continuation values and the worst-case model. The result also allows convergence rates of estimators to be characterized. An empirical application studies an endowment economy where the DMs benchmark model may be interpreted as an aggregate of experts forecasting models. The application reveals time-variation in the way the DM pessimistically distorts benchmark probabilities. Consequences for asset pricing are explored and connections are drawn with the literature on macroeconomic uncertainty.
This paper explores the identification and estimation of nonseparable panel data models. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional distributions of unobservable variables do not change over time, and the joint support of explanatory variables satisfies some weak assumptions. To identify the target parameters, existing studies assume that the structural function does not change over time, and that there are stayers, namely individuals with the same regressor values in two time periods. Our approach, by contrast, allows the structural function to depend on the time period in an arbitrary manner and does not require the existence of stayers. In estimation part of the paper, we consider parametric models and develop an estimator that implements our identification results. We then show the consistency and asymptotic normality of our estimator. Monte Carlo studies indicate that our estimator performs well in finite samples. Finally, we extend our identification results to models with discrete outcomes, and show that the structural function is partially identified.
We study the impact of weak identification in discrete choice models, and provide insights into the determinants of identification strength in these models. Using these insights, we propose a novel test that can consistently detect weak identification in commonly applied discrete choice models, such as probit, logit, and many of their extensions. Furthermore, we demonstrate that when the null hypothesis of weak identification is rejected, Wald-based inference can be carried out using standard formulas and critical values. A Monte Carlo study compares our proposed testing approach against commonly applied weak identification tests. The results simultaneously demonstrate the good performance of our approach and the fundamental failure of using conventional weak identification tests for linear models in the discrete choice model context. Furthermore, we compare our approach against those commonly applied in the literature in two empirical examples: married women labor force participation, and US food aid and civil conflicts.
We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily implementable combinatorial methods are described to check them. In all normal form games, the identified set is characterized in terms of the value of a submodular or convex optimization program. Efficient algorithms are then given and compared to check inclusion of a parameter in this identified set. The latter are illustrated with family bargaining games and oligopoly entry games.
We study identification and estimation of causal effects in settings with panel data. Traditionally researchers follow model-based identification strategies relying on assumptions governing the relation between the potential outcomes and the unobserved confounders. We focus on a novel, complementary, approach to identification where assumptions are made about the relation between the treatment assignment and the unobserved confounders. We introduce different sets of assumptions that follow the two paths to identification, and develop a double robust approach. We propose estimation methods that build on these identification strategies.
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