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Register a new userEstimating High-Dimensional Discrete Choice Model of Differentiated Products with Random Coefficients
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We propose an estimation procedure for discrete choice models of differentiated products with possibly high-dimensional product attributes. In our model, high-dimensional attributes can be determinants of both mean and variance of the indirect utility of a product. The key restriction in our model is that the high-dimensional attributes affect the variance of indirect utilities only through finitely many indices. In a framework of the random-coefficients logit model, we show a bound on the error rate of a $l_1$-regularized minimum distance estimator and prove the asymptotic linearity of the de-biased estimator.
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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.
In nonlinear panel data models, fixed effects methods are often criticized because they cannot identify average marginal effects (AMEs) in short panels. The common argument is that the identification of AMEs requires knowledge of the distribution of unobserved heterogeneity, but this distribution is not identified in a fixed effects model with a short panel. In this paper, we derive identification results that contradict this argument. In a panel data dynamic logic model, and for T as small as four, we prove the point identification of different AMEs, including causal effects of changes in the lagged dependent variable or in the duration in last choice. Our proofs are constructive and provide simple closed-form expressions for the AMEs in terms of probabilities of choice histories. We illustrate our results using Monte Carlo experiments and with an empirical application of a dynamic structural model of consumer brand choice with state dependence.
The Random Utility Maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behavior, such as halo effects, that are incompatible with this framework. Models belonging to the Random Utility Maximization family may therefore not accurately capture such irrational behavior. Hence, more general choice models, overcoming such limitations, have been proposed. However, the flexibility of such models comes at the price of increased risk of overfitting. As such, estimating such models remains a challenge. In this work, we propose an estimation method for the recently proposed Generalized Stochastic Preference choice model, which subsumes the family of Random Utility Maximization models and is capable of capturing halo effects. Specifically, we show how to use partially-ranked preferences to efficiently model rational and irrational customer types from transaction data. Our estimation procedure is based on column generation, where relevant customer types are efficiently extracted by expanding a tree-like data structure containing the customer behaviors. Further, we propose a new dominance rule among customer types whose effect is to prioritize low orders of interactions among products. An extensive set of experiments assesses the predictive accuracy of the proposed approach. Our results show that accounting for irrational preferences can boost predictive accuracy by 12.5% on average, when tested on a real-world dataset from a large chain of grocery and drug stores.
Credible counterfactual analysis requires high-dimensional controls. This paper considers estimation and inference for heterogeneous counterfactual effects with high-dimensional data. We propose a novel doubly robust score for double/debiased estimation and inference for the unconditional quantile regression (Firpo, Fortin, and Lemieux, 2009) as a measure of heterogeneous counterfactual marginal effects. We propose a multiplier bootstrap inference for the Lasso double/debiased estimator, and develop asymptotic theories to guarantee that the bootstrap works. Simulation studies support our theories. Applying the proposed method to Job Corps survey data, we find that i) marginal effects of counterfactually extending the duration of the exposure to the Job Corps program are globally positive across quantiles regardless of definitions of the treatment and outcome variables, and that ii) these counterfactual effects are larger for higher potential earners than lower potential earners regardless of whether we define the outcome as the level or its logarithm.
Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. The second stage consists of a low-dimensional local linear regression, reducing CATE to a function of the covariate(s) of interest. We consider two variants of the estimator depending on whether the nuisance functions are estimated over the full sample or over a hold-out sample. Building on Belloni at al. (2017) and Chernozhukov et al. (2018), we derive functional limit theory for the estimators and provide an easy-to-implement procedure for uniform inference based on the multiplier bootstrap. The empirical application revisits the effect of maternal smoking on a babys birth weight as a function of the mothers age.
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