arXiv 14 Sep 2026 · Econometrics
arXiv:2609.15736 · PDF · Extracted main text
The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Berry, Steven and Levinsohn, James and Pakes, Ariel (1995) Automobile prices in market equilibrium | 0.928 | 4 | 3 | 100% |
| 2 | Berry, Steven and Levinsohn, James and Pakes, Ariel (1999) Voluntary export restraints on automobiles: Evaluating a trade policy | 0.874 | 6 | 2 | 100% |
| 3 | Ai, Chunrong and Chen, Xiaohong (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions | 0.737 | 3 | 2 | 100% |
| 4 | Berry, Steven (1994) Estimating Discrete-Choice Models of Product Differentiation | 0.511 | 2 | 1 | 100% |
| 5 | Dom\'inguez, Manuel A and Lobato, Ignacio N (2004) Consistent estimation of models defined by conditional moment restrictions | 0.511 | 2 | 1 | 100% |
| 6 | Antoine, Bertille and Lavergne, Pascal (2014) Conditional moment models under semi-strong identification | 0.405 | 1 | 1 | 100% |
| 7 | Berry, Steven T and Haile, Philip A (2014) Identification in differentiated products markets using market level data | 0.405 | 1 | 1 | 100% |
| 8 | Berry, Steven T and Haile, Philip A (2021) Foundations of demand estimation | 0.405 | 1 | 1 | 100% |
| 9 | Bierens, Herman J (1982) Consistent model specification tests | 0.405 | 1 | 1 | 100% |
| 10 | Chamberlain, Gary (1987) Asymptotic efficiency in estimation with conditional moment restrictions | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 33 scored citations.