02877cam a22003017 4500001000700000003000500007005001700012008004100029100002800070245016600098260006600264490004200330500001500372520123800387530006101625538007201686538003601758690011001794690012301904690014202027690010402169690007802273700003002351710004202381830007702423856003802500856003702538w14080NBER20160209141523.0160209s2008 mau||||fs|||| 000 0 eng d1 aKnittel, Christopher R.10aEstimation of Random Coefficient Demand Modelsh[electronic resource]:bChallenges, Difficulties and Warnings /cChristopher R. Knittel, Konstantinos Metaxoglou. aCambridge, Mass.bNational Bureau of Economic Researchc2008.1 aNBER working paper seriesvno. w14080 aJune 2008.3 aEmpirical 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC1 - Econometric and Statistical Methods and Methodology: General2Journal of Economic Literature class. 7aC61 - Optimization Techniques • Programming Models • Dynamic Analysis2Journal of Economic Literature class. 7aC81 - Methodology for Collecting, Estimating, and Organizing Microeconomic Data • Data Access2Journal of Economic Literature class. 7aL1 - Market Structure, Firm Strategy, and Market Performance2Journal of Economic Literature class. 7aL4 - Antitrust Issues and Policies2Journal of Economic Literature class.1 aMetaxoglou, Konstantinos.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w14080.4 uhttp://www.nber.org/papers/w1408041uhttp://dx.doi.org/10.3386/w14080