Testing the Grossman model of medical spending determinants with macroeconomic panel data

Cropper [8], Gerdtham et al. [18] and Gerdtham and Johannesson [17] did the opposite, testing only the demand for health sub-model.

Strulik [51] criticizes Eq. (2) for implying that the loss of health capital through depreciation is an increasing function of its stock. This means that people lose health fast when they are healthy and that the loss of health slows down as health deteriorates. “This creates an equilibrating force that allows individuals to use health investments to converge towards a fixed point of constant health” [51]. Since convergence towards constant health, i.e., immortality is a troubling prediction, Dalgaard and Strulik [9] and Strulik [52] suggest to model aging differently. Drawing on Mitnitski et al. [38] and more papers by these authors, Dalgaard and Strulik adopt the perspective supported by gerontology that aging is triggered by the accumulation of health deficits and that this process of increasing frailty is a positive function of the health deficits that are already present in an individual. This turns Grossman’s mechanism for individual aging upside down. Dalgaard and Strulik ([9]: 679) recognize, however, that in applications beyond individual aging, for instance as a macro representation of the law of motion of the health capital stock, Eq. (2) may be perfectly reasonable.

See Nocera and Zweifel ([41], Appendix A) for a derivation. We basically follow their notation in this section, which in turn is based on Wagstaff [57].

So do Cropper [8] and Erbsland et al. [15]. However, Wagstaff [57] finds “serious inconsistencies between the pure investment model and the data”. Likewise, Leu and Gerfin [34] find the PI model to be rejected by their data. Combining a bell-shaped boundary of production possibilities with negatively sloped indifference curves in the healthy days-consumption space, Zweifel [59] claims that the optimum (the tangent point) “cannot lie on the increasing portion of the frontier, where more investment in health also permits to increase consumption. Rather, it necessarily lies beyond the peak, indicating a trade-off between health and consumption. This insight also casts doubt on the relevance of the popular pure investment variant of the MGM (Michael Grossman Model)”.

Frailty indices are emerging for a number of European OECD countries that could be used to measure the health status at the population level [24, 46]. Currently, however, not enough observations are available in the time dimension for the purpose of this paper.

It should be noted that by estimating the reduced form demand function for medical care one accepts the assumption implicit in Eq. (14) that the coefficient on lnH_it is equal to + 1. Zweifel’s conjecture that this coefficient is rather negative is thereby sidelined.

The sign on education is negative because better educated individuals are hypothesized to be more efficient producers of their health, and hence need less medical care to achieve an increase in their stock of health capital.

Grossman suggests adding (initial) wealth to the regressors in the demand functions for medical care to discriminate between the PI and the PC model. “Computed wealth elasticities that do not differ significantly from zero would tend to support the investment model” [23].

Some of the studies reviewed by Martín et al. [37] focus on the question whether rising HCE with age is caused by aging as such or by ‘proximity to death’. These studies typically analyze micro datasets from health insurance companies to compare ex post the health care costs for survivors with costs for those who have died. As our focus is on the macroeconomic level, we leave aside those studies reviewed by Martín et al. [37] which focus on the micro-level.

As a robustness check, we treated all missing values as actually missing instead of imputing values. The results (available upon request from the authors) hardly change.

Our dataset covers all 34 OECD countries except Turkey, for which no data on the compensation of employees were available, and Chile, Estonia, Israel and Slovenia, for which no employment data were available.

This even implies that M more or less drops out of the individual’s investment function (9) since the individual faces no direct medical costs (see [57]). This feature is circumvented when working with macroeconomic data because the society must incur the costs.

See http://​sites.​google.​com/​site/​bassaxsite/​home/​files/​Solowlucasdata.​zip.

Another limitation is the lack of treatment for endogeneity. So, as Carmignani et al. [5] point out, “in using EBA, it is more appropriate to interpret the regressors as ‘predictors’ instead of ‘determinants’”. One admittedly crude solution for the endogeneity problem used in applied consumption analysis has been to take the budget share as the dependent variable, i.e., HCE relative to GDP in the present context. In the presence of endogeneity, the error terms in HCE and GDP are likely to move in parallel so tend to cancel in the ratio. As a further robustness check, we also estimated the Grossman model specified in shares. The results (not shown, but available from the authors on request) are qualitatively not different from those for the level and growth models.

The correlation coefficients of the variables used in the EBA are almost always well below 0.4, and therefore do not pose a serious problem in our set-up.

Sala-i-Martin [47] proposes using the (integrated) likelihood to construct a weighted CDF(0). However, the varying number of observations in the regressions due to missing observations in some of the variables poses a problem. Sturm and de Haan [54] show that this goodness of fit measure may not be a good indicator of the probability that a model is the true model, and the weights constructed in this way are not equivariant to linear transformations in the dependent variable. Hence, changing scales result in rather different outcomes and conclusions. We thus restrict our attention to the unweighted version.

Hauck and Zhang [28] use Bayesian Model Averaging to identify robust drivers of HCE growth. They work around the problem of missing observations by imputing missing values.

We excluded the relative price of medical care for lack of observations. Also, we had to drop eight countries when performing the panel cointegration tests because they had less than the required number of 14 observations for at least one time series.

We do not convert real per capita health expenditure and the real wage into purchasing power parities (PPPs) for the growth models because when comparing growth rates, data based on constant national prices is to be preferred. PPPs should be used when levels are the object of analysis across countries (see [1]). So dlhce and dlrwage stand for the log difference of real per capita health expenditure and the real wage per employee, respectively, in constant national prices.

Column 2 of Table 4 shows that the hypothesis that the coefficients on the real wage and the relative medical price have the same value with opposite signs is rejected only at the 10 percent level. In all other specifications reported in Tables 4, 7 and 8 though, this hypothesis is always very clearly rejected.

Tables 9 and 10 in the appendix report EBA results for the covariates. The variables in these tables are ordered based on their estimated CDF(0) results in the levels model. Because of concerns over reverse causality, we have lagged the government share (gsh)—as well as per-capita real insurance premiums (lins).

Docteur and Oxley [12] call GDP “the main driving force in all studies”.

This variable has been suggested as a driver of total health care expenditure by Karatzas [30]. We include it as a control variable in our preferred models, although this component of HCE is of course beyond the individual’s control.

Hartwig [26] also found a significantly positive correlation between the growth rate of per capita health expenditure and the growth rate of relative medical prices.