the objective of this study is to quantitatively estimate the effect of medicare supplementation on use of health services by medicare beneficiaries . however , the extent of supplementary health insurance coverage is only one of many factors influencing the use of health services by medicare beneficiaries . previous studies of health services utilization have found such factors as age , sex , race , income , and health status to be capable of exerting independent influences on the use of health services ( leopold and langwell , 1978 ) . in order to isolate the influence of supplementary health insurance coverage , it is necessary to control for the variation in utilization arising from these other factors . accordingly , our empirical results are based upon a multivariate model that relates an individual 's use of either physician or hospital services to a variety of underlying determinants . in particular , the empirical specification for the model is : where the subscript i denotes the ith medicare beneficiary ; ui measures the person 's annual use of health services ( two alternative models are estimated : one for annual number of physician visits and one for annual number of hospital days ) ; privi is a binary variable indicating whether the ith beneficiary supplements medicare with some type of private health insurance ; caidi is a binary variable indicating whether the ith beneficiary received medicaid benefits during the past 12 months ; x3i through xni compose a set of variables to control for other factors influencing the ith person 's utilization ; and ei is a stochastic error term , assumed to have a truncated - normal distribution . the set of control variables in this model is designed to capture the influence of family income , race , sex , region of residence , education , family size , health status , age , marital status , labor - force status , veteran status , and the availability of medical resources . the primary data source is the 1976 health interview survey ( usdhew , 1977 ) . observations were excluded for persons for whom family income or education was unknown or not reported , reducing the sample for the analysis of hospital utilization to 8,325 . the elimination of observations pertaining to persons who failed to report the number of physician visits during the preceding 12 months further reduced the sample for analyzing physician utilization to 8,239 . for each of the dependent variables about 30 percent of the sample reported no use of physician services during the preceding 12 months , and approximately 80 percent did not use inpatient hospital services . accordingly , the tobit estimation technique ( tobin , 1958 ) was used for this study . covariance analyses revealed that our investigation of physician utilization should be conducted with data stratified according to the presence or absence of chronic health problems . thus , results from the analysis of physician utilization are reported separately for ( 1 ) elderly medicare beneficiaries who have no chronic health problems and ( 2 ) those who have one or more such conditions . in contrast , covariance tests for hospital utilization indicated that it was appropriate to pool over all health conditions . these tables highlight the influence of supplementary coverage on the utilization of health services by elderly medicare beneficiaries . table 1 reports the average utilization of health services among medicare beneficiaries by type of supplementation , both in absolute terms and relative to the average utilization by medicare beneficiaries who do not supplement ( shown in parentheses in the table ) . these average rates were tabulated directly from the health interview survey ( his ) data , and thus are unadjusted for other determinants of utilization . the differentials between these averages should not be interpreted as reliable indicators of the influence of supplementation on utilization . since we shall compare these unadjusted averages with utilization rates adjusted for other determinants , a brief examination of the apparent implications of the results in table 1 is merited . these unadjusted averages reveal that beneficiaries who supplement medicare with private health insurance generally make greater use of health services than those who do not supplement . the largest differential between those with private supplementation and those with only medicare arises in connection with physician visits by beneficiaries with no chronic health problems : those who have private supplementation in this group report 39 percent more visits to physicians than their counterparts who rely solely on medicare . private supplementation is also associated with somewhat greater use of hospital services ( 2.79 days per year ) , relative to the average utilization among those with no supplementation ( 2.51 days ) . in contrast , those with one or more chronic health problems and private supplementation tend to have fewer physician visits compared to those with no supplementary coverage . while the differential is small ( 6.23 visits versus 6.72 visits ) , it is nevertheless paradoxical . public supplementation of medicare is associated with relatively high rates of utilization of both physician and hospital services . for example , medicare beneficiaries with medicaid supplementation spent an average of 76 percent more days in the hospital than those with no supplementation and 58 percent more than those with private supplementation . based upon this type of evidence , one might be tempted to conclude that public supplementation of medicare has greatly stimulated the use of health services . however , while such a conclusion may be correct , it does not necessarily follow from the evidence in table 1 . the high utilization rates in the medicaid category may simply reflect the relatively poor health status of persons in this group . table 2 contains the key findings of this study , namely , the predicted utilization rates by type of supplementation , adjusted for other determinants . these estimates are derived from a multivariate model that controls for a variety of determinants of utilization and thus isolates the influence of supplementation on utilization from the influence of other factors such as health status . the values reported in table 2 represent predicted utilization rates for  typical  medicare beneficiaries ; that is , they are derived under the assumption that all of the determinants of utilization ( except the supplementation variables ) equal their mean values . what do these predicted utilization rates imply about the influence of supplementation on the use of health services by elderly medicare beneficiaries ? first , other things equal , supplementation always stimulates use of health services , generally by statistically significant amounts . in particular , the paradox of relatively low demand for ambulatory care by those chronically ill beneficiaries with private supplementation disappears once the utilization rates are adjusted for other determinants . second , public supplementation always stimulates more utilization of health services than does private supplementation . however , in no instance is the differential in utilization rates between those with private supplementation and those qualifying for medicaid statistically significant . we are justified in concluding only that , other things equal , medicaid supplementation of medicare permits elderly beneficiaries to use physician and hospital services at least as often as those who purchase private supplementary health insurance . this conclusion contrasts sharply with the one implied by the unadjusted average utilization rates in table 1 : those estimates suggest that the influence of public supplementation on the demand for health services far outweighs the influence of private supplementation . a final important implication of the estimates reported in table 2 pertains to the differential effectiveness of supplementary coverage at stimulating demand for health services . supplementation greatly increases the use of both hospital services and physician services among elderly persons with no chronic health problems . however , among those elderly beneficiaries with one or more chronic health problems ( about 78 percent of the beneficiary population ) , persons with some type of supplementation have only slightly more physician visits than those with no additional coverage . apparently the deductibles and coinsurance provisions of medicare 's part b medical insurance do not represent an important barrier to ambulatory medical care for those beneficiaries who suffer from chronic health problems . for these individuals , supplementation  particularly through medicaid  serves mainly to redistribute income to the chronically ill medicare beneficiaries . conclusion that public supplementation was very effective at stimulating demand for ambulatory care among those with chronic illnesses . the estimates presented in table 3 provide an additional perspective on supplementation 's role in determining utilization rates among elderly medicare beneficiaries . mean utilization for a group , u , can be defined as : where p is the probability that a person with mean characteristics will use a particular health service and u is the mean utilization rate among those who actually use the health service . thus , any change in a group 's utilization rate ( u ) can be divided along the following lines : this relationship can be restated in percentage terms as table 3 partitions the percentage increase in utilization arising from supplementation into the three components identified in equation 3 : the percentage increase in the probability of using a particular health service , the percentage increase in the utilization rate among those that make use of the health service , and the interaction between these two factors . the estimates in table 3 reveal that supplementation raises a group 's mean utilization rate ( adjusted for other determinants ) largely by increasing the proportion of the group that uses medical services . when compared to no supplementation for example , medicaid supplementation raises the use of hospital services by 47 percent . most of this gain ( 29 percent out of the 47 percent ) arises from the hospitalization of persons who , in the absence of medicaid supplementation , would not have received treatment on an inpatient basis . private supplementation has a similar influence on the utilization of hospital services : most of the gain comes from more people being admitted to hospitals rather than from an increase in average length of stay . these results suggest that the part a deductible ( approximately equal to the average charge for an inpatient hospital day ) represents a significant barrier to the utilization of hospital services by the elderly . supplementation increases utilization by persons in this group mainly by permitting a larger fraction of the group to visit a physician than would otherwise be the case . the part b deductible ( $ 60 ) thus appears to also serve as an important barrier to the use of ambulatory medical services by those with no chronic health problems . in addition , the part b coinsurance rate ( 20 percent of covered services ) apparently serves as an important deterrent to physician utilization by those elderly persons with no chronic conditions . this conclusion follows from the relatively large positive effect of supplementation on utilization among those who , in the absence of supplementary coverage , would have still made some use of physician services . to illustrate , private supplementation leads to a 42 percent increase in physician visits by persons in this health - status group . of this increase , 16 percent is due directly to greater utilization among those who would have seen a physician even without supplementary coverage . as we noted earlier , supplementation stimulates physician utilization only to a small degree among those elderly with chronic health problems . table 3 reveals the two underlying components of mean utilization to be about equally responsible for this small gain in the use of physician services . apparently neither the deductible nor the coinsurance provisions of part b represent important barriers to physician utilization among those elderly beneficiaries with chronic health problems . our principal finding is that beneficiaries ' utilization of health care services rises when medicare is supplemented by private insurance coverage or by medicaid , though in varying amounts depending on individuals ' health status . to turn the conclusion around , we find that medicare cost - sharing ( when not vitiated by private or medicaid supplementation ) leads to significantly lower levels of hospital and physician utilization than would have prevailed in the absence of the program 's deductibles and coinsurance . the estimates we report allow for an illustrative calculation of the magnitude of the cost savings owing to medicare cost - sharing . cost - sharing under parts a and b is an effective economic incentive for the 29 percent of the 24 million elderly beneficiaries ( about 7 million ) who have neither private nor public supplementary health insurance . the predicted hospital utilization rates in table 2 imply a utilization reduction of between 630 and 890 days per thousand beneficiaries per year when cost - sharing is effective ( compared to private supplementation and medicaid , respectively ) . therefore , the part a cost - sharing provisions result in 4.4 million to 6.2 million fewer days of hospital care for the elderly . assuming a cost per day of $ 160 ( the part a hospital inpatient deductible for calendar year 1979 ) , medicare cost - sharing results in a reduction in total hospital expenditures by the elderly of between $ 700 million and $ 1 billion . of course , only part of these savings accrue to the medicare program since some of the reduced utilization would have been subject to the part a deductible . however , cost control is not the sole goal of the medicare program . it has been argued that medicare cost - sharing is particularly perverse because it largely reduces the health services utilization of certain disadvantaged groups  the medicaid - ineligible low income and nonwhite populations  for whom medicare was designed to equalize access to medical care ( gornick , 1976 ; davis and schoen , 1978 ) . thus it is conceivable that the advantage of cost - sharing in controlling health expenditures might be outweighed by the disproportionate reduction in utilization among certain population groups . to test the hypothesis that the availability of private health insurance supplementation leads to inequitable utilization advantages for whites and higher income groups , we re - estimated the above - described model after omitting the private insurance variable . examination of the changes in the coefficients on the race and income variables , respectively , will reveal unequal access afforded by the private market availability of supplementary insurance , if any . in all three regressions  physician visits for chronics and non - chronics and hospital days the coefficients for southern and non - southern blacks changed insignificantly . similarly , as reported in link , long , and settle ( 1980 ) , the variables representing income classes did not change significantly . whatever inequitable access to services exists for medicare beneficiaries is apparently caused by factors other than the availability of private supplementary insurance . in summary , we conclude that medicare cost - sharing , in the absence of private or public supplementation , reduces medical care utilization and , therefore , costs to the program . moreover , it appears that the burden of this cost - sharing is not so concentrated among race and income groups as to cause uniformly inequitable access to medical care . however ,  fine - tuning  among these competing objectives remains in the province of policymakers , not researchers .
this paper investigates the extent to which private supplementary insurance and medicaid , which vitiate the effect of medicare cost - sharing , encourage elderly beneficiaries to seek additional medical care . a multivariate model of health services utilization 
 is estimated with the tobit technique , using the 1976 health interview survey . 
 we find that either private or public supplementation induces greater use of hospital and physician services , though in amounts that vary considerably according to health status . 
 the paper closes with observations on cost savings brought about by medicare cost - sharing and some implications for equity among beneficiaries .