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Dynamic Selection and Distributional Bounds on Search Costs in Dynamic Unit-Demand Models

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Dynamic Selection and Distributional Bounds on Search Costs in Dynamic Unit-Demand Models

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Abstract

This paper develops a dynamic model of consumer search that, despite placing very little structure on the dynamic problem faced by consumers, allows us to exploit intertemporal variation in within-period price and search cost distributions to estimate the population distribution from which consumers' search costs are initially drawn. We show that static approaches to estimating this distribution generally suffer from a dynamic sample selection bias because forward-looking consumers with unit demand for a good may delay their purchase in a way that depends on their individual search cost. We analyze identification of the population search cost distribution using only price data and develop estimable nonparametric upper and lower bounds on the distribution function and a nonlinear least squares estimator for parametric models. We also consider the additional identifying power of weak assumptions such as monotonicity of purchase probabilities in search costs. We apply our estimators to analyze the online market for two widely used econometrics textbooks. Our results suggest that static estimates of the search cost distribution are biased upwards, in a distributional sense, relative to the true population distribution. In a small-scale simulation study, we show that this is typical in a dynamic setting where consumers with high search costs are more likely to delay purchase than those with lower search costs.

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1. Introduction 2. Causal and non-causal models 3. Microeconomic data structures 4. Linear models 5. ML and NLS estimation 6. GMM and systems estimation 7. Hypothesis tests 8. Specification tests and model selection 9. Semiparametric methods 10. Numerical optimization 11. Bootstrap methods 12. Simulation-based methods 13. Bayesian methods 14. Binary outcome models 15. Multinomial models 16. Tobit and selection models 17. Transition data: survival analysis 18. Mixture models and unobserved heterogeneity 19. Models of multiple hazards 20. Models of count data 21. Linear panel models: basics 22. Linear panel models: extensions 23. Nonlinear panel models 24. Stratified and clustered samples 25. Treatment evaluation 26. Measurement error models 27. Missing data and imputation A. Asymptotic theory B. Making pseudo-random draw.
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