Fast, "Robust", and Approximately Correct: Estimating Mixed Demand Systems
Many econometric models used in applied work integrate over unobserved heterogeneity. We show that a class of these models that includes many random coefficients demand systems can be approximated by a “small-σ” expansion that yields a linear two-stage least squares estimator. We study in detail the models of product market shares and prices popular in empirical IO. Our estimator is only approximately correct, but it performs very well in practice. It is extremely fast and easy to implement, and it is “robust” to changes in the higher moments of the distribution of the random coefficients. At the very least, it provides excellent starting values for more commonly used estimators of these models.
We are grateful to Dan Ackerberg, John Asker, Steve Berry, Xiaohong Chen, Chris Conlon, Pierre Dubois, Jeremy Fox, Han Hong, Guy Laroque, Simon Lee, Arthur Lewbel, Thierry Magnac, Lars Nesheim, Ariel Pakes, Mathias Reynaert, Tobias Salz, Richard Smith, Pedro Souza, Frank Verboven, Martin Weidner, and Ken Wolpin for their useful comments, as well as to seminar audiences at NYU, Rice, UCL, and the Stanford Institute for Theoretical Economics (SITE). We also thank Zeyu Wang for excellent research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.