Unbiased Analysis of Today's Healthcare Issues

Dynamic Analysis of Market Shares and Health Insurance Choice

Written By: Jason Shafrin - Mar• 15•07

Consumer-directed health plans (CDHP) have been a topic of much interest in the United States of late. In order to increase competition between health plans, in 1996 the German government began a program to allow consumers to have a free choice of their social health insurers plan. Since the federal government sets a high minimum benefit level for each insurance company, 95% of the benefits are equivalent across plans. Thus, the only main difference is price. In Germany, the insurance premium paid by the worker is equal to a set contribution rate multiplied by their salary. If benefits are truly identical, one would expect an infinite elasticity of demand for health plans with respect to price (i.e.: the contribution rate). A paper by Tamm, Tauchmann, Wasem and Greß (2007) aim to estimate these price elasticities in Germany using a panel data between 2001 and 2004.


The basic econometric specification is to use a conditional logit model (McFadden Frontier in Econometrics 1973). The authors wisely realize, however, that there are likely transaction and information costs to change insurance plans and thus there may be some persistence in the data. Thus a more general dynamic model is estimated of the form:

  • log(sit)=αlog(sit-1)+βxitiit

The variable s represents the insurance plan’s market share, x gives the contribution rate, γ is a fixed effects term and ε is the error term, distributed Type I extreme value. If α=0 then this model is the same as the static case, and if α=1 then market shares are non-stationary and follow a random walk. Since using a lagged dependent variable often means that the lagged term is correlated with the error term, the authors use the Arellano and Bond (1991) GMM estimator.


The authors find that there is significant persistence, (i.e.: α is approximately one). The elasticity of market shares with respect to contribution rates is found to be either -0.55 or -1.09 depending on the specification. These results are similar to those found by studies in Switzerland, but much less than the -2.90 elasticity found by the Schut et al. (2003) study also analyzing German data, but in a static setting.


The two major points of criticism is that this paper only analyzes individuals who are enrolled in the social insurance scheme. Individuals with salaries above a certain threshold, the self-employed, and civil servants can all opt-out of social insurance scheme in order to purchase private insurance. Also, although the benefits are relatively constant across the insurers, there is no attempt to control for doctor quality or any other quality measure of the insurance plan. Plan quality may explain why the price elasticity is much lower than expected.

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