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Health Expenditure Estimation and Functional Form: Applications of Generalized Gamma and Extended General Linear Models

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Abstract:

Rationale: Health care expenditure regressions are used in a wide variety of economic analyses including risk adjustment and program and treatment evaluations. Two recent articles have demonstrated that generalized gamma models with heteroskedasticity (GGM-het) and extended general linear models (EGLM) provide flexible approaches to deal with a variety of data problems commonly encountered in expenditure estimation. To date, however, there have been few empirical applications of these models to expenditures.

Objective: We use nationally representative data from the first six panels of the U.S. Medical Expenditure Panel Survey (MEPS) to compare the bias and predictive accuracy of GGM-het and EGLM models with other regression models in a cross-validation study design.

Methodology: We estimate models of prescription drug, ambulatory and total health care expenditures conditional on having any expenditure. Models are estimated separately for the elderly and other privately insured adults. Since expenditure distributions vary by type of service and population, the appropriate functional form is also likely to vary. In estimating expenditures, we focus on two recently developed modeling approaches that flexibly accommodate skewness, kurtosis, heteroskedasticity and other data problems. The GGM-het model, proposed by Manning, Basu, and Mullahy (2005), uses a log-link like many standard GLM models. However, the GGM-het model is more flexible than standard models because the generalized gamma distribution has a scale parameter and two shape parameters and variance is explicitly modeled as a function of explanatory variables. In the EGLM model, proposed by Basu and Rathouz (2005), the link function is not specified prior to estimation. Instead, both the link and variance functions are simultaneously estimated along with the coefficients.

Our models use socioeconomic characteristics and condition information from the first year of each MEPS panel to predict expenditures in the second year. We use a split-sample cross validation design to compare results from GGM-het, EGLM, log OLS with heteroskedasticity (log-het), linear OLS, Poisson and Gamma models. We use the validation sample to test for over-fitting and to examine predictive ratios and mean prediction errors in the entire sample, in the tails of the distribution and for persons with chronic conditions.

Results: In our preliminary analysis we focused on total expenditures and estimated all types of models except EGLM. We found that the expenditure distribution for the elderly was more kurtotic than the distribution for other adults and the distributions varied in the extent of heteroskedasticity beyond simple functions of the mean. Overall, the GGM-het and log-het models fit the data for privately insured adults very well. However, none of our models was clearly superior for the elderly.

Conclusions: Our preliminary analysis confirms that GGM-het models are robust to a wide variety of common data problems. For some distributions, however, an even more flexible estimator, such as the EGLM model, may be required.
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Association:
Name: Economics of Population Health: Inaugural Conference of the American Society of Health Economists
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http://healtheconomics.us


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MLA Citation:

Miller, Edward. and Hill, Steven. "Health Expenditure Estimation and Functional Form: Applications of Generalized Gamma and Extended General Linear Models" Paper presented at the annual meeting of the Economics of Population Health: Inaugural Conference of the American Society of Health Economists, TBA, Madison, WI, USA, Jun 04, 2006 <Not Available>. 2013-12-17 <http://citation.allacademic.com/meta/p93417_index.html>

APA Citation:

Miller, E. and Hill, S. C. , 2006-06-04 "Health Expenditure Estimation and Functional Form: Applications of Generalized Gamma and Extended General Linear Models" Paper presented at the annual meeting of the Economics of Population Health: Inaugural Conference of the American Society of Health Economists, TBA, Madison, WI, USA <Not Available>. 2013-12-17 from http://citation.allacademic.com/meta/p93417_index.html

Publication Type: Abstract
Abstract: Rationale: Health care expenditure regressions are used in a wide variety of economic analyses including risk adjustment and program and treatment evaluations. Two recent articles have demonstrated that generalized gamma models with heteroskedasticity (GGM-het) and extended general linear models (EGLM) provide flexible approaches to deal with a variety of data problems commonly encountered in expenditure estimation. To date, however, there have been few empirical applications of these models to expenditures.

Objective: We use nationally representative data from the first six panels of the U.S. Medical Expenditure Panel Survey (MEPS) to compare the bias and predictive accuracy of GGM-het and EGLM models with other regression models in a cross-validation study design.

Methodology: We estimate models of prescription drug, ambulatory and total health care expenditures conditional on having any expenditure. Models are estimated separately for the elderly and other privately insured adults. Since expenditure distributions vary by type of service and population, the appropriate functional form is also likely to vary. In estimating expenditures, we focus on two recently developed modeling approaches that flexibly accommodate skewness, kurtosis, heteroskedasticity and other data problems. The GGM-het model, proposed by Manning, Basu, and Mullahy (2005), uses a log-link like many standard GLM models. However, the GGM-het model is more flexible than standard models because the generalized gamma distribution has a scale parameter and two shape parameters and variance is explicitly modeled as a function of explanatory variables. In the EGLM model, proposed by Basu and Rathouz (2005), the link function is not specified prior to estimation. Instead, both the link and variance functions are simultaneously estimated along with the coefficients.

Our models use socioeconomic characteristics and condition information from the first year of each MEPS panel to predict expenditures in the second year. We use a split-sample cross validation design to compare results from GGM-het, EGLM, log OLS with heteroskedasticity (log-het), linear OLS, Poisson and Gamma models. We use the validation sample to test for over-fitting and to examine predictive ratios and mean prediction errors in the entire sample, in the tails of the distribution and for persons with chronic conditions.

Results: In our preliminary analysis we focused on total expenditures and estimated all types of models except EGLM. We found that the expenditure distribution for the elderly was more kurtotic than the distribution for other adults and the distributions varied in the extent of heteroskedasticity beyond simple functions of the mean. Overall, the GGM-het and log-het models fit the data for privately insured adults very well. However, none of our models was clearly superior for the elderly.

Conclusions: Our preliminary analysis confirms that GGM-het models are robust to a wide variety of common data problems. For some distributions, however, an even more flexible estimator, such as the EGLM model, may be required.

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