Empirical exercises in economics frequently involve estimation of highly nonlinear models. The criterion function may not be globally concave or convex and exhibit many local extrema. Choosing among these local extrema is non-trivial for a variety of reasons. In this paper, we analyze the sensitivity of parameter estimates, and most importantly of economic variables of interest, to both starting values and the type of non-linear optimization algorithm employed. We focus on a class of demand models for differentiated products that have been used extensively in industrial organization, and more recently in public and labor. We find that convergence may occur at a number of local extrema, at saddles and in regions of the objective function where the first-order conditions are not satisfied. We find own- and cross-price elasticities that differ by a factor of over 100 depending on the set of candidate parameter estimates. In an attempt to evaluate the welfare effects of a change in an industry's structure, we undertake a hypothetical merger exercise. Our calculations indicate consumer welfare effects can vary between positive values to negative seventy billion dollars depending on the set of parameter estimates used.
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number
14080.
Length: Date of creation: Jun 2008 Date of revision: Handle: RePEc:nbr:nberwo:14080
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Find related papers by JEL classification: C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Microeconomic Data L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance L4 - Industrial Organization - - Antitrust Issues and Policies
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