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Connected Substitutes and Invertibility of Demand

Econometrica 2013 81(5), 2087-2111
We consider the invertibility (injectivity) of a nonparametric nonseparable demand system. Invertibility of demand is important in several contexts, including identification of demand, estimation of demand, testing of revealed preference, and economic theory exploiting existence of an inverse demand function or (in an exchange economy) uniqueness of Walrasian equilibrium prices. We introduce the notion of “connected substitutes” and show that this structure is sufficient for invertibility. The connected substitutes conditions require weak substitution between all goods and sufficient strict substitution to necessitate treating them in a single demand system. The connected substitutes conditions have transparent economic interpretation, are easily checked, and are satisfied in many standard models. They need only hold under some transformation of demand and can accommodate many models in which goods are complements. They allow one to show invertibility without strict gross substitutes, functional form restrictions, smoothness assumptions, or strong domain restrictions. When the restriction to weak substitutes is maintained, our sufficient conditions are also “nearly necessary” for even local invertibility.

Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market

Journal of Political Economy 2004 112(1), 68-105 open access
In this paper, we exploit new sources of cross-sectional data to estimate a detailed product-level demand system for new passenger vehicles. We use four data sources: on the characteristics of products, on the attributes of the U.S. population of households, on the match between the first and second vehicle choices of the household, and on the match between households attributes and first choice vehicles. We show that these data solve some, but not all, of the traditional problems in estimating differentiated products demand systems and indicate which data sources are important for which problem. The data is rich enough to reveal a rather complex substitution pattern, requiring a quite general modeling framework. Together the data and model make a detailed analysis of industry demand possible. 1 Introduction In Berry, Levinsohn, and Pakes (1995) (BLP) we provide an algorithm for obtaining estimates of demand parameters for a class of differentiated product models. Demand-side models ...

An Instrumental Variable Approach to Dynamic Models

Review of Economic Studies 2023 90(4), 1724-1758
We present a new class of methods for identification and inference in dynamic models with serially correlated unobservables, which typically imply that state variables are econometrically endogenous. In the context of Industrial Organization, these state variables often reflect econometrically endogenous market structure. We propose the use of Generalized Instrument Variables methods to identify those dynamic policy functions that are consistent with instrumental variable (IV) restrictions. Extending popular “two-step” methods, these policy functions then identify a set of structural parameters that are consistent with the dynamic model, the IV restrictions and the data. We provide computed illustrations to both single-agent and oligopoly examples. We also present a simple empirical analysis that, among other things, supports the counterfactual study of an environmental policy entailing an increase in sunk costs.