College of Food, Ag & Nat Res Sci
This project characterizes the numerical errors in the differentiated product demand model by Berry (1994) and Berry, Levinsohn, and Pakes (1995) in terms of the estimated market share error. Such characterization proposes a criterion to compare the exponentially transformed fixed-point iteration and the iteration in linear form. The researchers are demonstrating numerically that the exponential iteration introduces larger error and gains no convergence speed than the linear form. In addition, the error characterization suggests that the mathematical program with equality constraint (MPEC) approach by Dubé, Fox, and Su (2012) is equivalent in precision compared to the nested fixed-point (NFP) approach, but only if the equality constraint bound estimated market share error is as tight as the fixed-point iteration. However, under the recommendation of a tight fixed-point tolerance, it is very difficult for the MPEC approach to match the precision level of the NFP.