Working Paper: NBER ID: w14080
Authors: Christopher R. Knittel; Konstantinos Metaxoglou
Abstract: 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.
Keywords: Random Coefficient Demand Models; Nonlinear Optimization; Consumer Welfare; Elasticities; Mergers
JEL Codes: C1; C6; C8; L1; L4
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Choice of optimization algorithm and starting values (C61) | Variations in parameter estimates (C51) |
| Choice of optimization algorithm and starting values (C61) | Variations in economic variables of interest (E39) |
| Variations in parameter estimates (C51) | Variations in own and cross-price elasticities (D11) |
| Choice of parameter estimates (C51) | Consumer welfare effects (D69) |
| Design of the optimization exercise (C61) | Large effects on economic variables of interest (E19) |
| Convergence at local extrema (C62) | Misrepresentation of true uncertainty regarding parameter estimates (C51) |
| Need to verify first and second-order conditions (C62) | Reliable parameter estimates (C51) |