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Estimating log models: to transform or not to transform?

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  • Manning, Willard G.
  • Mullahy, John

Abstract

Data on health care expenditures, length of stay, utilization of health services, consumption of unhealthy commodities, etc. are typically characterized by: (a) nonnegative outcomes; (b) nontrivial fractions of zero outcomes in the population (and sample); and (c) positively-skewed distributions of the nonzero realizations. Similar data structures are encountered in labor economics as well. This paper provides simulation-based evidence on the finite-sample behavior of two sets of estimators designed to look at the effect of a set of covariates x on the expected outcome, E(y|x), under a range of data problems encountered in every day practice: generalized linear models (GLM), a subset of which can simply be viewed as differentially weighted nonlinear least-squares estimators, and those derived from least-squares estimators for the ln(y). We consider the first- and second- order behavior of these candidate estimators under alternative assumptions on the data generating processes. Our results indicate that the choice of estimator for models of ln(E(x|y)) can have major implications for empirical results if the estimator is not designed to deal with the specific data generating mechanism. Garden-variety statistical problems - skewness, kurtosis, and heteroscedasticity - can lead to an appreciable bias for some estimators or appreciable losses in precision for others.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Health Economics.

Volume (Year): 20 (2001)
Issue (Month): 4 (July)
Pages: 461-494

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Handle: RePEc:eee:jhecon:v:20:y:2001:i:4:p:461-494

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Web page: http://www.elsevier.com/locate/inca/505560

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  1. Manning, Willard G, et al, 1987. "Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment," American Economic Review, American Economic Association, vol. 77(3), pages 251-77, June.
  2. Mullahy, John, 1998. "Much ado about two: reconsidering retransformation and the two-part model in health econometrics," Journal of Health Economics, Elsevier, vol. 17(3), pages 247-281, June.
  3. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
  4. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-26, April.
  5. Kennedy, Peter E, 1981. "Estimation with Correctly Interpreted Dummy Variables in Semilogarithmic Equations [The Interpretation of Dummy Variables in Semilogarithmic Equations]," American Economic Review, American Economic Association, vol. 71(4), pages 801, September.
  6. Manning, W. G. & Duan, N. & Rogers, W. H., 1987. "Monte Carlo evidence on the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 35(1), pages 59-82, May.
  7. Blough, David K. & Madden, Carolyn W. & Hornbrook, Mark C., 1999. "Modeling risk using generalized linear models," Journal of Health Economics, Elsevier, vol. 18(2), pages 153-171, April.
  8. Gourieroux Christian & Monfort Alain & Trognon A, 1982. "Pseudo maximum lilelihood methods : applications to poisson models," CEPREMAP Working Papers (Couverture Orange) 8203, CEPREMAP.
  9. Jones, Andrew M., 2000. "Health econometrics," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 6, pages 265-344 Elsevier.
  10. Manning, Willard G., 1998. "The logged dependent variable, heteroscedasticity, and the retransformation problem," Journal of Health Economics, Elsevier, vol. 17(3), pages 283-295, June.
  11. Kennedy, Peter, 1983. "Logarithmic Dependent Variables and Prediction Bias," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 45(4), pages 389-92, November.
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