We provide simple tests for selection on unobserved variables in the Vytlacil-Imbens-Angrist framework for Local Average Treatment Effects (LATEs). Our setup allows researchers not only to test for selection on either or both of the treated and untreated outcomes, but also to assess the magnitude of the selection effect. We show that it applies to the standard binary instrument case, as well as to experiments with imperfect compliance and fuzzy regression discontinuity designs, and we link it to broader discussions regarding instrumental variables. We illustrate the substantive value-added by our framework with three empirical applications drawn from the literature.
Although typically overlooked, many purchase datasets exhibit a high incidence of products with zero sales. We propose a new estimator for the Random-Coefficients Logit demand system for purchase datasets with zero-valued market shares. The identification of the demand parameters is based on a pairwise-differencing approach that constructs moment conditions based on differences in demand between pairs of products. The corresponding estimator corrects nonparametrically for the potential selection of the incidence of zeros on unobserved aspects of demand. The estimator also corrects for the potential endogeneity of marketing variables both in demand and in the selection propensities. Monte Carlo simulations show that our proposed estimator provides reliable small-sample inference both with and without selection-onunobservables. In an empirical case study, the proposed estimator not only generates different demand estimates than approaches that ignore selection in the incidence of zero shares, it also generates better out-of-sample fit of observed retail contribution margins.
Although typically overlooked, many purchase datasets exhibit a high incidence of products with zero sales. We propose a new estimator for the Random-Coefficients Logit demand system for purchase datasets with zero-valued market shares. The identification of the demand parameters is based on a pairwise-differencing approach that constructs moment conditions based on differences in demand between pairs of products. The corresponding estimator corrects nonparametrically for the potential selection of the incidence of zeros on unobserved aspects of demand. The estimator also corrects for the potential endogeneity of marketing variables both in demand and in the selection propensities. Monte Carlo simulations show that our proposed estimator provides reliable small-sample inference both with and without selection-onunobservables. In an empirical case study, the proposed estimator not only generates different demand estimates than approaches that ignore selection in the incidence of zero shares, it also generates better out-of-sample fit of observed retail contribution margins.
The conventional discrete-choice model of demand assumes consumers are fully informed about every available product alternative. This assumption is at odds with the long literature studying incomplete information and the role of the consumer’s “evoked set” or “consideration set.” The author develops a novel empirical discrete-choice demand model derived from an underlying theory of consumer’s rational inattention. The model distinguishes between factors that shift demand through the utility function, such as prices and product attributes, and factors that shift demand through the consumer’s information “evaluation costs.” The author conducts an empirical case study of the laundry detergent category. Using a set of exclusion restrictions based on retail promotional instruments, specification tests select the rational inattention model over the conventional full-information discrete-choice model. Exploiting the launch of Tide Pods midway through the sample, the author demonstrates the role of evaluation costs for the measured value creation from a new product. A conventional discrete-choice model always assigns positive incremental consumer value from new products. However, the rational inattention model developed herein finds a decrease in overall consumer welfare from the new Pods products’ entry, with the increased friction in information associated with the larger choice set offsetting the potential gains from higher match value.
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