Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter August 8, 2014

Eliminating the Outside Good Bias in Logit Models of Demand with Aggregate Data

Dongling Huang EMAIL logo and Christian Rojas

Abstract

The logit model is the most popular tool in estimating demand for differentiated products. In this model, the outside good plays a crucial role because it allows consumers to stop buying the differentiated good altogether if all brands simultaneously become less attractive (e.g. if a simultaneous price increase occurs). But practitioners lack data on the outside good when only aggregate data are available. The currently accepted procedure is to assume a “market potential” that implicitly defines the size of the outside good (i.e. the number of consumers who considered the product but did not purchase); in practice, this means that an endogenous quantity is approximated by a reasonable guess thereby introducing the possibility of an additional source of error and, most importantly, bias. We provide two contributions in this paper. First, we show that structural parameters can be substantially biased when the assumed market potential does not approximate the outside option correctly. Second, we show how to use panel data techniques to produce unbiased structural estimates by treating the market potential as an unobservable in both the simple and the random coefficients logit demand model. We explore three possible solutions: (a) controlling for the unobservable with market fixed effects, (b) specifying the unobservable to be a linear function of product characteristics, and (c) using a “demeaned regression” approach. Solution (a) is feasible (and preferable) when the number of goods is large relative to the number of markets, whereas (b) and (c) are attractive when the number of markets is too large (as in most applications in Marketing). Importantly, we find that all three solutions are nearly as effective in removing the bias. We demonstrate our two contributions in the simple and random coefficients versions of the logit model via Monte Carlo experiments and with data from the automobile and breakfast cereals markets.

JEL Codes: C15; C82; D12; D43

Acknowledgments

We thank Jun Ishii, Charles Romeo, and Jeffrey Wooldridge for their very helpful suggestions and comments. We also thank Ron Cotterill and Jim Levinsohn for providing the data. The simple logit results in this paper were reported in a preliminary-results paper (Huang and Rojas 2013). In this paper, we extend the analysis to the random coefficients case and complement it with more extensive applications.

References

Armantier, O., and O.Richard.2008. “Domestic Airline Alliances and Consumer Welfare.” The RAND Journal of Economics39(3):875904.10.1111/j.1756-2171.2008.00042.xSearch in Google Scholar

Berry, S. T.1990. “Airport Presence as Product Differentiation.” The American Economic Review80(2):39499.Search in Google Scholar

Berry, S. T.1994. “Estimating Discrete Choice Models of Product Differentiation.” The RAND Journal of Economics25(2):24262.10.2307/2555829Search in Google Scholar

Berry, S. T., M.Carnall, and P.Spiller. 2006. “Airline Hubs: Costs, Markups and the Implications of Customer Heterogeneity.” In Advances in Airline Economics. Vol. 1 of Competition Policy and Anti-Trust, edited by D.Lee. Bingley, UK: Emerald Group Publishing LTD.Search in Google Scholar

Berry, S. T., J.Levinsohn, and A.Pakes.1995. “Automobile Price in Market EquilibriumEconometrica63(4):84190.10.2307/2171802Search in Google Scholar

Berry, S. T., J.Levinsohn, and A.Pakes.1999. “Voluntary Export Restraints on Automobiles: Evaluating a Trade Policy.”The American Economic Review89(3):40030.10.1257/aer.89.3.400Search in Google Scholar

Chamberlain, G.1982. “Multivariate Regression Models for Panel Data.” Journal of Econometrics1:546.10.1016/0304-4076(82)90094-XSearch in Google Scholar

Chu, C., P.Leslie, and A.Sorensen. 2011. “Bundle-Size Pricing as an Approximation to Mixed Bundling.” The American Economic Review101(1):263303.10.1257/aer.101.1.263Search in Google Scholar

Dube, J. P., J.Fox, and C.Su.2012. “Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation.”Econometrica80(5):223167.10.3982/ECTA8585Search in Google Scholar

Gorman, W. M.1959. “Separable Utility and Aggregation.”Econometrica27(3):46981.10.2307/1909472Search in Google Scholar

Hausman, J., G.Leonard, and J. D.Zona.1994. “Competitive Analysis with Differentiated Products.” Annals of Economics and Statistics34:15980.Search in Google Scholar

Huang, D., and C.Rojas.2013. “The Outside Good Bias in Logit Models of Demand with Aggregate Data.” Economics Bulletin33:198206.Search in Google Scholar

Kim, K., and A.Petrin.2010. “Control Function Corrections for Unobserved Factors in Differentiated Product Models.”Working Paper, University of Minnesota and NBER.Search in Google Scholar

Mundlak, Y.1978. “On the Pooling of Time Series and Cross Section Data.” Econometrica46:6985.10.2307/1913646Search in Google Scholar

Nevo, A.2000. “A Practitioner’s Guide to Estimation of Random Coefficients Logit Models of Demand.”Journal of Economics and Management Strategy9(4):51348.10.1162/105864000567954Search in Google Scholar

Nevo, A.2001. “Measuring Market Power in the Ready-to-Eat Cereal Industry.”Econometrica69(2):30742.10.1111/1468-0262.00194Search in Google Scholar

Park, S., and S.Gupta.2009. “Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data.”Journal of Marketing Research46(4):53142.10.1509/jmkr.46.4.531Search in Google Scholar

Petrin, A., and K.Train.2010. “A Control Function Approach to Endogeneity in Consumer Choice Models.”Journal of Marketing Research47(1):313.10.1509/jmkr.47.1.3Search in Google Scholar

Reiss, P. C., and F. A.Wolak.2007. “Structural Econometric Modeling: Rationales and Examples from Industrial Organizations.” In Handbook of Econometrics, Vol. 6A, edited by J.J.Heckman and L.Edward. Oxford, UK: Elsevier Press.10.1016/S1573-4412(07)06064-3Search in Google Scholar

Wooldridge, J.2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.Search in Google Scholar

Published Online: 2014-8-8
Published in Print: 2014-1-1

©2014 by De Gruyter

Downloaded on 30.1.2023 from https://www.degruyter.com/document/doi/10.1515/roms-2013-0016/html
Scroll Up Arrow