Supply and demand factors in the determination of Medicare expenditures.
Conspicuously absent, however, have been analyses that directly attempt to estimate the determinants of Medicare expenditures. Previous efforts to identify the source of Medicare expenditures have typically used accounting relationships to allocate changes in total Medicare expenditures to various components of the cost and utilization of Medicare services. (1) Furthermore, earlier research has not identified supply- and demand-side factors in the determination of Medicare expenditures. At present, it is not known to what extent Medicare expenditures are driven by supply-side considerations (such as reimbursement to hospitals or physicians) or reflect demand-side phenomena (such as the ability of beneficiaries to pay for services). It is also unclear whether and to what extent supply and demand factors differs in their effects on Medicare expenditures for hospital services (Part A) and expenditures for physician services (Part B). As a result, considerable uncertainty remains about the most effective means for controlling Medicare cost inflation.
Nevertheless, a variety of initiative have been implemented in recent years to control Medicare costs from the supply side. The prospective payment system (PPS) has been introduced to Medicare reimbursement for hospital services. At the same time, reimbursement for physician services has been adjusted by a variety of methods, with further changes, such as the use of relative value scales, in the offing.
Utilization review has also been implemented, as have changes in the rules relating to Medicare participation. Increasing beneficiary out-of-pocket payments or coinsurance rates, or both, has received considerable attention, but to date few adjustments have been made.
Statistical estimates of the determinants of Medicare expenditures could provide important input into the decision-making process regarding Medicare reform. This article attempts to provide such estimates. More specifically, it presents a multivariate analysis of the determinants of Medicare expenditures. This yields direct estimates of the extent to which Medicare expenditures are driven by demand-and supply-side factors.
The remainder of this article is divided into four sections. The first section reviews factors thought to determine Medicare expenditures and the resulting cost-containment initiatives that have been implemented. The empirical models to be estimated are presented next. The subsequent sectio presents the estimation results and calculates the responsiveness of Medicare expenditures to changes in supply-side and demand-side factors. A final section offers some concluding remarks about the results and their policy implications.
Almost since the advent of Medicare, policymakers have demonstrated a strong commitment to constrain its costs. Nevertheless, Medicare costs have continued to escalate. Previous initiatives to constrain costs may be conveniently delineated into efforts to constrain supply-side factors believe to have escalated Medicare costs, and efforts to limit demand-side factors. We turn not to a discussion of each.
Many have blamed the escalation in Medicare costs on growth in the costs of physician and hospital services. Early efforts to control Medicare costs appeared to be based on the philosophy that limits on reimbursement or physician discretion in utilizing hospital services, or both, could produce the desired effect. Beginning with the Social Security Amendment of 1972, early cost-containment initiatives included peer review of hospital admissions, limits on above-average costs per day for hospital stays, and cost-based limits on the rate of increase in payment rate ceilings for physicians (Congressional Budget Office 1986).
Although repeated efforts have been made to control Medicare Part B expenditures, including the freezing of payments to physicians (Iglehart 1988), expenditures continue to grow. In fact, Medicare expenditures on physician services grew by 17.9 percent annually from 1967 to 1985 (Gornick et al. 1985).
Considerable dispute exists regarding the desirability of imposing federal regulations on Medicare reimbursement. With respect to physician reimbursement, some have argued that price controls may have adverse consequences for the quantity and quality of physician services provided to beneficiaries. Adherents to the physician demand inducement hypothesis would likely point out that such controls would lead only to increases in physician services, with little resulting savings to Medicare. Both of these views argue against price controls, albeit for different reasons.
Yet still other views judge price to be an effective means of constraining Medicare costs without risking adverse consequences. Medicare's longstanding history of price regulation suggests that this view has been the more prevalent one among policymakers. Proponents of this view argue that the escalating supply of physicians serves to mitigate potential access problems posed by price controls on Medicare reimbursements. As Davis (1988) states:
The truth is that U.S. has a growing supply of physicians, and is not threatened with a physician shortage in the foreseeable future no matter what (emphasis added) the Medicare payment assignment policy might.. be. (p. 11)
Medicare reimbursement for hospital services has followed a similar pattern of repeated efforts to constrain costs on the supply side. These efforts culminated with the introduction of PPS in 1983, to replace the erstwhile retrospective cost-based reimbursement for inpatient services. Under PPS, hospitals are receiving a fixed amount per Medicare admission, based on each patient diagnosis at the time of discharge. Initially, 468 diagnosis-related groups (DRGs) were defined for reimbursement under PPS.
Prior to the introduction of PPS, Medicare expenditures for inpatient services grew rapidly--at an average annual rate of 16.1 percent between 1967 and 1984 (Gornick et al. 1985). PPS gives hospitals the incentive to constrain costs by limiting either lenght of stay or the costs of services provided, or both. Recent findings suggest that PPS has indeed limited the growth in hospital costs relative to retrospective cost-based reimbursement (Iglehart 1988; Feder, Hadley, and Zuckerman 1987), although the implications for quality of care are still unclear.
Consumers have also been blamed for increasing Medicare costs. Two arguments are generally presented in support of this contention. First, it is argued that the income of the elderly has risen substantially. Pauly (1988) notes that increases in Social Security payments have exceeded increases in income for the nonelderly, improving the economic situation of the elderly in both absolute terms and relative to the rest of the population.
Second, government expenditures on Medicare have risen substantially while the cost burden borne by the elderly has been relatively modest (Pauly 1988). Indeed, throughout much of Medicare's history, little action has been taken to constrain Medicare Part B expenditures by directly increasing beneficiary liability. As Iglehart (1988) points out, the Social Security Amendments of 1972 (the same amendments that led to significant efforts to constrain Medicare costs on the supply side) have limited premium increases for Part B to be annual increment in Social Security benifits, resulting in a net decrease in the proportion of expenditures financed through premium revenues from 54.5 percent in 1973 to 22.3 percent in 1983.
In an effort to limit government spending, the Reagan administration successfully promoted legislation that allowed premiums to grow more rapidly than Social Security payments. However, by 1989 Part B premiums were once again limited by the cost-of-living increase in Social Security cash benefits. As a result, it is projected that the Part B premium will finance only about 17 percent of the program's outlays by 1993 (Iglehart 1988).
Part A reveals a similar pattern of cost-sharing leniency on beneficiaries. While inpatient hospital coinsurance has risen substantially in percentage terms, it still reflects a small portion costs. Moon (1988) notes that although direct changes in Medicare cost sharing increased beneficiaries' cost-sharing responsibility, these changes were of a lesser magnitude than the legislative initiatives aimed at altering reimbursement to the service provider.
While most efforts to constrain costs have been directed at the supply side, these changes may also have implications for beneficiary liability (demand side) as well. For example, Moon (1988) has argued that PPS may indirectly raise beneficiary liability under Medicare Part A. In particular, the shorter hospital stays induced by PPS have also served to increase the average cost of a hospital visit since more tests and procedures are conducted in less time. Since deductibles and coinsurance rates are based on average daily costs, PPS may have indirectly served to increase beneficiary liability. Consistent with this view, Moon notes that the Part A deductible rose from $400 in 1985 to $492 in 1986--an increase of 23 percent.
Of course, other efforts to limit reimbursement on the supply side may serve to limit beneficiary liability. We merely wish to point out that, while most efforts to constrain Medicare costs have sought to avoid affecting beneficiary liability, such impacts are in many cases inevitable, and may even serve to raise benficiary liability.
At least two other factors that may have contributed substantially to the growth in Medicare costs bear mention. these are the development of new technologies, and what Baumol (1988) has termed Medicare's "cost disease."
The relationship between the use of new technologies and Medicare costs is straightforward. Sophisticated equipment is costly. This probably has played a more important role in raising Part A expenditures.
The problem to which Baumol refers, however, is more subtle, and has primarily affected Part B expenditures. Baumol argues that in labor-intensive industries, such as the physician services industry, the opportunities for cost-reducing technological developments are limited. Over time, therefore, prices can be expected to rise more steeply in these industries than in other sectors of the economy.
Important research topics that go beyond the scope of the present analysis include estimating the effects of adopting new technology and of bearing with slow productivity growth in the field of physician services. These factors are dynamic in nature, and must therefore be studied over time. We present a cross-sectional anlysis that will shed light on demand-and supply-side effects on Medicare expenditures, but we do not address dynamics.
In specifying the empirical model, demand and supply factors will be separated in order to ferret out their relative importance. Previous studies have failed to do this. For example, Juba and Sulvetta (1986) used a statistical analysis to estimate the determinants of Medicare expenditures. They estimated the effects of enrollment, services per enrollee, real payments per service, and general inflation on Medicare costs. The researchers noted that growth in services per enrollee was an important determinant of Medicare cost inflation. Whether this apparent relationship is a supply- or demand-side phenomenon is not clear, however: this pattern could reflect more services provided by the physician or a higher propensity to seek care among beneficiaries, or both.
We seek to estimate these effects separately. The analysis includes supply and demand variables to accomplish this objective. Physician and hospital costs (described more fully below) are measures of supply variables. They are considered supply variables because they measure payments to suppliers of medical care services and, as such, are expected to affect Medicare expenditures directly, independent of any effects they may have on consumer propensity to seek care. For instance, if suppliers of medical care services cost more per unit of their service, then the overall cost of those should be higher, even if consumer propensity to seek care is insentive to these costs. By contrast, demand variables should affect Medicare expenditures only to the extent that they affect consumer propensity to seek care: they are not expected to have any direct effects on expenditures. Demand-side variables (described more fully later) include measures of elderly income and the extent of elderly out-of-pocket liability.
The first step in this analysis is to examine patient demand for medical care. Since physicians typically decide the medical treatment that may be required, they are likely to exercise considerable influence over the consumer's decision-making process. As Farley (1986) notes: "The fundamental peculiarity of the physician market is the fact that physicians directly influence consumption decisions" (p. 318). While conceding this application, Farley also notes that physicians do not share in all aspects of patient decision making, since patients independently select physicians and decide whether to contact the physician for an episode of illness. Once such decisions are made, however, physicians primarily decide the course of treatment.
Following Farley, we assume that consumers decide whether to receive care or not, but the physicians determine the appropriate treatment regimen. The variable we use to measure the consumer's decision to seek care is the proportion of enrollees in a state served during the year of our analysis (1984). We consider the proportion served under Parts A and/or B (ALLSERV), Part B only (SMISERV), and Part A only (HISERV).
The use of a state-level analysis was dictated by data availability. (2) There is a long and as yet unresolved controversy in the literature (i.e., Aigner and Goldfeld 1974) on the relative merits of aggregated versus disaggregated data when, as is often the case, disaggregated data are subject to greater measurement error. The reason for this controversy is that, while aggregation may introduce aggregation bias in the coefficient estimates, it may also reduce measurement error, which is another source of bias.
Because the value of the dependent variable must lie between 0 and 1, we specify a logit model. (3,4) More specifically, consumer demand for care covered under Part A or Part B is estimated as: [Mathematical Expression Ommited] where:
LN (*) = Natural logarithm function;
PREVCHGi = An index of Medicare prevailing charges for state i in 1984;
HOSCOSTi = Average daily hospital room cost in state i in 1984;
PCT80i = Percent of over-65 population aged 80 and above in state i in 1984;
PCTMETi = Percent of population located in a metropolitan area in state i in 1984;
UNBENi = Percent of Medicare beneficiaries unassigned in state i in 1982; and
OLDINCi = Median income of elderly in state i in 1984. (5)
Equations of the form indicated by Equation 1 are also estimated separately for Part A utilization and Part B utilization.
The variables UNBEN and OLDINC are included as measures of, respectively, patient out-of-pocket liability and patient ability to pay. These are demand variables. A higher value of UNBEN suggests that a higher proportion of the estate's Medicare population will be balance-billed by physicians. This should act to decrease utilization. On the other hand, a higher value of OLDINC indicates greater ability to pay. Hence, we accept OLDINC to be positively related to utilization.
The variables PREVCHG and HOSCOST are included to measure, respectively, the cost of physician and hospital services. These are supply variables. To the extent that insurance coverage is incomplete, consumers may be less likely to seek care as the costs of these services increase.
Finally, differences in health status and urban/rural location may also affect the propensity to seek care. The variable PCT80 is included as a measure of health status. Moon (1988) presents evidence indicating that the propensity either to use inpatient hospital services or physician services, or both, is substantially higher among Medicare beneficiaries aged 80 and above relative to their younger Medicare counterparts. Hence, we expect PCT80 to be positively related to Medicare utilization. Finally, the variable PCTMET is included to measure urban-rural differences in utilization.
The second-stage estimates use the predicted values of the dependent variables from Equation 1 together with other variables thought to influence the supply of services to Medicare beneficiaries. In particular, we estimate: [Mathematical Expression Ommited] where:
REMALLi = Medicare reimbursement under Parts A and/or B per enrollee in state i in 1984; and PREDALLi = Predicted value of proportion of enrollees served under Medicare Parts A and/or B in state i; other variables are as defined earlier.
Equations of the form indicated by Equation 2 are also estimated separately for Part A expenditures per enrollee (REMHI) and Part B expenditures (REMSMI). Note that the supply variables PREVCHG and HOSCOST are entered directly into Equation 2. The demand variables UNBEN and OLDINC do not appear explicitly in that equation, however, because these variables should affect Medicare expenditures only indirectly, through their impact on PREDALL.
Table 1 shows the regression results of the estimated logit model for utilization. The variable PREVCHG is not significantly related to any of the utilization measures. This result may reflect two conflicting factors. First, the higher the PREVCHG value, the higher the expected out-of-pocket copayment: this factor should tend to decrease utilization. On the other hand, the probability that a physician will balance-bill patients may be inversely related to PREVCHG: this would tend to encourage utilization.
HOSCOST also shows no significant relationship to beneficiary propensity to seek care. Apparently, consumers are not very price sensitive when seeking treatment covered under Medicare. No significant relationship was found between the degree of urbanization (PCTMET) and utilization, although the coefficient on PCTMET is positive in all three cases.
By contrast, variables that measure beneficiary characteristics are more strongly related to utilization. A significant positive relationship [tdo] is observed between PCT80 and the propensity to use services covered by Medicare Part A. The coefficients on PCT80 are also positive in the other two regressions, although they are not statistically significant. The stronger relationship between PCT80 and the propensity to use services covered under Part A is consistent with evidence presented by Moon (1988), which indicates that the use of Medicare for inpatient hospital services in addition to their Part B copayments.
The variable OLDINC is positively related to utilization of physician services and to overall utilization, but negatively related to use of hospital services. One possible explanation for the negative sign in the hospital services equation follows from the observation that an elderly individual's health status may be positively related to his or her income. In fact, a recent study by the Commonwealth Fund Commission (1987) indicates a strong positive correlation between income and health status among the elderly. That study found that 44.4 percent of elderly poor reported being in fair or poor health while 22.2 percent of those with moderate or high incomes reported poor health. Low-income elderly were also substantially more likely to have chronic medical conditions. Use of hospital services may depend primarily on health status, not income, since most hospital-related care is not elective in nature. If, as the Commonwealth Fund Commission study suggests, low-income elderly have poorer health status, then they can be expected to use hospital services more frequently than individuals with higher incomes.
Many physicians services, however, are not a matter of life and death, but are elective in nature. Use of elective services may be much more dependent upon one's ability to pay than upon health status. Hence, a positive relationship between income and utilization of physician services might be expected.
Furthermore, high-income elderly may prefer to opt for outpatient services (which are covered under Part B) because adequate home care is more readily accessible to them. But low-income elderly may have greater difficulty in obtaining adequate home care and, as a result, may be more likely to require hospitalization. In this regard, Pauly (1981) mentions a Rhode Island study indicating that "for some kinds of illness, low income is likely to lead to more frequent hospitalization (e.g., for pneumonia and bronchitis) because desirable home-care alternatives are less readily available" (pp. 61-62). These factors may also help to explain why income is inversely related to use of hospital services but directly related to use of physician services.
Finally, overall utilization may be positively related to income because individuals utilize physician services more frequently than hospital services. Hence, the positive relationship between income and utilization dominates the negative. (6)
Table 2 shows the estimation results for the determinants of Medicare expenditures. PREVCHG is a direct and significant determinant of expenditures per enrollee under Part B (REMSMI), but is insignificant in the other two regressions. By contrast, all three measures of Medicare expenditures are significantly related to hospital costs (HOSCOST). PCTMET is also directly related to Medicare expenditures. To some extent, the positive relationship between PCTMET and Medicare expenditures may reflect higher reimbursement [tdo] by Medicare in urban settings. There is also a positive and significant relationship between PCT80 and Part A expenditures.
The propensity to use services covered under Medicare has apparently played a very substantial role in raising Part B expenditures and, as a result of this, overall expenditures as well. For example, the positive coefficient on PREDSMI is large and significant--even after controlling for the cost of medical services, degree of urbanization, and age composition of the Medicare population. This suggests that utilization increases that are correlated with demand factors (UNBEN and OLDINC) have tended to increase Part B expenditures. (7)
By contrast, expenditures for hospital services do not appear to be strongly related to demand factors. The reason for this are unclear. Possibly, in states where the utilization of hospital services is relatively high, the average severity of illness among patients is relatively low, and this may serve to offset, at least in part, the higher average costs per enrollee one would expect to observe from a greater propensity to use the system. Furthermore, to the extent that states with a high propensity to utilize hospital services under Medicare tend to be low-income states (recall the inverse relationship between OLDINC and
Table 3: Medicare Utilization Elasticities Demand Measures Independent Parts A Variables and/or B Part B Part A PREVCHG .03 .03 -.01 HOSCOST -.08 -.07 .08 PCTMET .04 .03 .01 UNBEN -.27 (*) -.29 (*) -.02 OLDINC .24 (*) .27 (*) -.56 (*) PCT80 .13 .09 .39 (*) (*) Elasticity measures are derived from statistically significant coefficient estimates.
[TABULAR DATA OMITTED]
the proportion of individuals served under Part A), DRG reimbursemets for hospital services may be relatively low. This could also serve to offset higher per enrollee expenditures resulting from greater use of the system. More information about state-level variations in DRG reimbursement is required, however, if these remarks are to be taken as more than simply conjecture.
UTILIZATION AND EXPENDITURE ELASTICITIES
To get a better feel for the responsiveness of Medicare utilization and expenditures to changes in the explanatory variables employed by this study, Table 3 and Table 4 show utilization and expenditure elasticities, respectively. All elasticities are computed at the mean values of the explanatory variables.
Turning first to utilization elasticities. Table 3 indicates that a 1 percent increase in elderly income will raise the propensity to use physician services by 0.27 percent. On the other hand, a 1 percent increase in income is associated with a 0.56 percent decline in the use of hospital services. Changes in assignment status also exhibit a substantial effect on utilization. In particular, a 1 percent rise in the proportion of Medicare beneficiaries unassigned in a state lowers overall utilization by 0.27 percent, and utilization of physician services by 0.29 percent.
Table 4 indicates that changes both in Medicare reimbursement and in beneficiary liability and ability to pay affect Medicare expenditures substantially. For example, the direct effect of a 1 percent increase in the prevailing charge index raises Part B expenditures by 0.43 percent. Part B expenditures are similarly responsive to changes in assignments status and elderly income. More specifically, the elasticity of Part B expenditures per enrollee with respect to Medicare assignment is -0.49, while the corresponding elasticity with respect to elderly income is 0.45.
This article has examined some of the major factors thought to determine Medicare expenditures. We have explicitly attempted to separate the influence of demand-side factors and supply-side factors. As policy-makers grapple with the difficult issues of containing costs while preserving access, quantitative evidence on the roles played by demand and supply factors can provide an important input into the decision-making process.
Demand factors appear to play an important role in raising Medicare Part B expenditures. In particular, as elderly income or the percent of the elderly population with assigned claims rises, the propensity to use the system increases significantly. These results suggest that a tax on the income of the elderly will be effective in restraining Medicare expenditures per enrollee by significantly reducing the propensity to use physician services (Part B).
It was also found that lower Medicare prevailing charges and daily hospital costs are associated with lower Medicare expenditures per enrollee. This suggests that limits on the Medicare reimbursement and changes in reimbursement that give providers the incentive to constrain costs (such as the prospective payment system) will lead to significant and substantial savings for Medicare.
Although the results suggest that significant cost savings to Medicare may be realized either by constraining reimbursement (supply-side constraints) or by increasing beneficiary liability (demand-side constraints), it is unclear which of these options for controlling Medicare costs is prefarable. While supply-side constraints have been favored in the past (presumably because they do not have a direct impact on beneficiary out-of-pocket costs), such efforts may work to increase beneficiary liability indirectly, as Moon (1988) has noted.
That demand factors apparently have played a significant role in raising Medicare expenditures does not imply that efforts to increase beneficiary liability serve the public interest. Medicare assignment, for example, was implemented to promot access to care among those in greatest need of financial assistance. Its success in this role would seem to be good news from a societal perspective. Furthermore, many would argue that direct efforts to constrain beneficiary use by increasing out-of-pocket expenditures may place a crushing financial burden on many of the elderly, about 28 percent of whom are considered poor or near-poor, according to a recent study (Commonwealth Fund Commission 1987). At the very least, initiatives to constrain costs by increasing beneficiary liability must take into account beneficiaries' differential ability to pay.
Utilization review may be a promising alternative to increasing beneficiary liability. Ideally, this process would limit unnecessary care without imposing undue financial burdens on the low-income elderly. A recent study by Feldstein, Wickizer, and Wheeler (1988), which examined utilization review programs implemented by a large private insurer, indicates that utilization review can be a very effective means of controlling hospital admissions as well as expenditures. The results presented here suggest that such programs would also be successful in constraining Medicare expenditures. Of course, any utilization review program would need to be carefully monitored to avoid potential adverse consequences on the health status of beneficiaries.
In deciding among these alternatives, it must be recognized that the manner in which cost savings are achieved is fundamentally different under each. Demand-side constraints will limit the beneficiary propensity to use the system. Supply-side constraints will have relatively little effect on the likelihood that beneficiaries will use the system. Instead, supply-side constraints will achieve savings through lower reimbursement for services and, possibly, by inducing the system to lower the supply of services per enrollee.
Another important consideration in developing optimal Medicare cost-control policies is whether to employ "command and control" means, such as price and/or utilization controls, or to create financial incentives for consumers to seek and providers to furnish cost-effective care. Such incentives could include, for example, altering Medicare's copayment structure to discourage excessive use of the system. Zeckhauser and Zook (1981) suggest that providing incentives is preparable to direct control, arguing that direct regulation in the medical care sector has not been successful: that such efforts have failed because the structure of the medical care field is inappropriate for price/quantity controls. In some cases, command and control regulation and financial incentives to seek (provide) cost-effective care may not be mutually exclusive. Thus, the utilization review program analyzed by Feldstein, Wickizer, and Wheeler (1988) imposed financial penalties on patients who did not follow specified utilization review producers.
Identifying the "best" among the variety of alternatives for reforming the Medicare system goes well beyond the scope of the present analysis. As policymakers continue to address these complex issues, however, difficult choices will have to be made. It is hoped that the present study, as well as future research attempting to quantify the likely effects of these potential choices, will lead to a better-informed decision-making process.
The author thanks the editor, two anonymous referees, Glenn Melnick, and Randi Siegel for helpful comments and suggestions.
1. A study by Juba and Sulvetta (1986) did employ multivariate analysis. As discussed later in this article, however, their study did not estimate the influence of supply and demand factors separately.
Christensen, Long, and Rodgers (1987) provide a careful analysis of beneficiary characteristics associated with the use of Medicare services. Since that study was concerned with the demand-side determinants of Medicare use, however, the role of supply-side factors such as the cost of physician and hospital services was not examined. A futher difference between Christensen, Long, and Rodgers and the present study is that we directly estimate the relationship between demand-generated used of the Medicare system and average Medicare expenditures per enrolle.
2. More detailed data on patient-level utilization uder Medicare Part A exists on the Medicare Provider Analysis and Review (MEDPAR) files. However, that data set includes information only on actual users; no enrollee information is provided. Therefore, one cannot obtain measures of the propensity to use Medicare Part A, which is needed for estimating the extent to which higher Medicare expenditures reflect a greater propensity to use the system. In addition, one cannot measure Medicare expenditures per enrollee. Similarly, the Part B Medicare Annual Data files (BMAD) also exclude information on enrollees, so that the propensity to use Part B services and Part B expenditures per enrollee cannot be obtained from that source.
3. An alternative is to estimate a linear probability model using ordinary least squares (OLS). As Heckman (1878) notes, however, such estimates will be inconsistent. If one were interested solely in obtaining reliable estimates of the Medicare expenditure equation, but not of the propensity to seek care, a linear probability model would be quite acceptable. This is so beause, as Heckman (1978) notes, "it is unnecessary to obtain consistent estimators of the parameters of the reduced form equations in order to consistently estimate structural relationships" (p. 947). The present study, however, focuses both of estimating expenditures. Thus, the approach taken in the text seems somewha preferable to estimating a linear probability model.
4. Disturbance terms are known to be heteroskedastic under the logit model. For the model specified in Equation 1, the variance of the disturbance term e will be given by:
Var (e) = 1 / ALLSERV(1-ALLSERV)
This problem is corrected by using weighted least squares. The weights are obtained by running an OLS regression on Equation 1 and using the resulting estimates of ALLSERV. While this procedure is frequently used for grouped data, it may also be applied in cases as in the text, where the dependent variable is a proportion and thus confined to the unit interval. See Maddala (1983) and Greene (1985) for further details on this estimation procedure.
5. All data pertaining to Medicare were obtained from Medicare Program Statistics for 1984, published by the Health Care Financing Administration. This source contains state-level data of Medicare enrollment, reimbursement, and utilization. The variables HOSCOST and PCTMET were constructed from data provided in the Statistical Abstract of the United States, 1987. OLDINC was constructed using several types of data. First, 1980 state-level incomes for elderly (those 65 and over) and nonelderly age groups were obtained from Bureau of the Census data. These data were used to obtain measures of the elderly population's share of total state income for each state in 1980. State-levle population data for the elderly were also obtained from the Bureau of the Census for the years 1980 and 1984. For 1984, only state-level income for all ages groups was available from the Bureau of Economic Analysis. The elderly group's share of state income from the 1980 data, adjusted for changes in the elderly population in each state between 1980 and 1984, was used to construct the share of total income belonging to the elderly in that state in 1984. Elderly income in 1984 was then obtained as the product of the total state income in 1984 and the elderly share of income in that state. OLDINC was constructured by Woods and Poole Economics, Inc. of Washington, DC, which can provide the interested reader with further details on this variable.
6. The variable PCT80 controls to some extent for health status effects. However, it is likely to be an incomplete control. To the extent that OLDINC is correlated with variations in health status that have not been controlled for, some caution must be exercised in interpreting the effects of elderly income on the propensity to use services covered by Medicare.
If, as evidence discussed in the text indicates, elderly income is directly related to health status, then the positive relationship observed between elderly income and the propensity to use physician services and physician and/or hospital services (see Table 1) probably understates the true effect of income on the propensity to use these services. This is so because the higher health status fo the high-income elderly may serve to offset, at least in part, their greater propensity to use these services.
Similarly, if health status were completely controlled for, we would expect to observe a less negative (or even a positive) relationship between elderly income and the propensity to use hospital services. These observations suggest, then, that the true relationship between elderly income and the propensity to use Medicare Parts A and/or B may be even stronger than estimates reported in the text. Our estimates may provide a lower bound on the true relationhsip between elderly income and the propensity to use services covered by Medicare.
7. Some caution must be exercised in interpreting the estimated coefficients on the predicted values of the propensity to use Medicare reported in Table 2. The assumption (discussed earlier in the text) that beneficiaries choose whether or not to seek care and physicians decide on the course of treatment is intended to be a reasonable approximation of reality, not an absolute truth. To some extent, beneficiaries who are more likely to use the system may also demand more services per episode of care. Thus, for example, high-income beneficiaries may be more likely to seek physician care and may also demand more services. To the extent that this is true, the estimated coefficients on the predicted values of Medicare use not only reflect demand factors associated with the propensity to use the system, but also those demand factors associated with the amount of services sought per episode of care.
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