Econometric Models for Industrial Organization by Matthew Shum

By Matthew Shum

Fiscal types for business association makes a speciality of the specification and estimation of econometric types for examine in commercial association. In contemporary many years, empirical paintings in commercial association has moved in the direction of dynamic and equilibrium versions, regarding econometric equipment that have positive aspects designated from these utilized in different parts of utilized economics. those lecture notes, aimed for a primary or second-year PhD direction, encourage and clarify those econometric equipment, ranging from easy types and construction to types with the complexity saw in usual study papers. The lined subject matters comprise discrete-choice call for research, types of dynamic habit and dynamic video games, a number of equilibria in access video games and partial identity, and public sale types.

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6) is called the William–Daly–Zachary theorem, and analogous to the Shepard/Hotelling lemmas, for the random utility model. 7) is a precise statement of the “inverse mapping” from choice probabilities to utilities for discrete choice models, and thus 2 See Gelfand and Fomin (1965), Rockafellar (1971), Chiong, Galichon, and Shum (2013). 3 Indeed, in the special case where ∇H(·) is one-to-one, then we have U = (∇H(p)). This is the case of the classical Legendre transform. November 17, 2016 26 9:38 Econometric Models for Industrial Organization - 9in x 6in b2555-ch01 Econometric Models for Industrial Organization reformulates (and is a more general statement of) the “inversion” result in Berry (1994) and Berry, Levinshon, and Pakes (1995).

Here u(x, i; θ) denotes the per-period utility of taking choice i at state x, without the additive logit error. Note that the knowledge of i |x 3 Note that the distribution (x , i , |x, i) can be factored, via the conditional independence assumption, into ( |i , x )(i |x )(x |x, i). November 17, 2016 42 9:38 Econometric Models for Industrial Organization - 9in x 6in b2555-ch03 page 42 Econometric Models for Industrial Organization is crucial to being able to forward-simulate the choice-specific value functions.

Let the i-th element of q(p1 (X), . . , pK (X)), denoted qi (X), be equal to ∆i (X). The known mapping q derives just from F ( ), the known distribution of the utility shocks. Hence, since the choice probabilities can be identified from the data, and the mapping q is known, the value function differences ∆1 (X), . . , ∆K (X) is also known. Next, we note that the choice-specific value function also satisfies a Bellman-like equation: Vd (X) = ud (X) + βEX |X,D E max(Vd (X ) + d ∈D d ) = ud (X) + βEX |X,D V0 (X ) + E max(∆d (X ) + d ∈D d ) = ud (X) + βEX |X,D H(∆1 (X ), .

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