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Linear and non-linear models for national health expenditures in the USA

Published online by Cambridge University Press:  18 June 2018

Allan J. Kroopnick*
Affiliation:
University of Maryland University College, The Graduate School, Adelphi, Maryland 20783USA e-mail: allan.kroopnick@faculty.umuc.edu

Extract

In this brief Article, using the elementary theory of differential equations as well as some basic economic theory, we will develop several estimates for national health expenditures for the United States: one using a linear model and three using non-linear models. We will derive the nonlinear models first and then compare them to the linear one in order to see if they differ significantly. While these estimates are for the United States, the methods used here, because they are robust, could be used for any country. Statistical information may be obtained from the World Bank databases which store health statistics by country [1].

What we will do here is estimate the total health costs as a percentage of gross domestic product (GDP) if no further copayments are required. In other words, we are seeking to estimate the total cost of health care as a percentage of GDP when all health care costs are covered by insurance and government subsidy. Several models will be discussed here since such estimates may be made using a variety of assumptions. There is no ‘best’ model, although such a decision is possible when comparing the estimates to actual data.

Type
Articles
Copyright
Copyright © Mathematical Association 2018 

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References

1. The World Bank, Health expenditure, total (% of GDP), accessed January 2018 at: http://data.worldbank.org/indicator/SH.XPD.TOTL.ZSGoogle Scholar
2. Scitovsky, A. A. and Snyder, N. M., Effect of coinsurance on use of physician services, Social Security Bulletin, (June 1972) pp. 319.Google Scholar
3. Trowbridge, C. L., Quality-Price relationships in health insurance, Actuarial Note Number 79, Social Security Administration, DHEW Publication Number (SSA)73-11507 (November 1972).Google Scholar
4. Analysis of health insurance proposals introduced in the 92nd congress, Ways and Means Committee Print, United States Government Printing Office (5270-1176) (August 1972).Google Scholar