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A study of employee health plan choice and medical cost: Panel data probit regression and sample selection model

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A study of employee health plan choice and medical cost: Panel data probit regression and sample selection model

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, som e thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of th e copy subm itted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographicaliy in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, M l 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A Study of Employee Health Plan Choice and Medical Cost: Panel Data Probit Regression and Sample Selection Model by Jeonghoon Ahn A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA in Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) December 2000 Copyright 2000 Jeonghoon Ahn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3041429 __ ___ __( g ) UMI UMI Microform 3041429 Copyright 2002 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90007 This dissertation, written by ..................................................... under the direction of h. Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School in partial fulfillment of re quirements for the degree of DOCTOR OF PHILOSOPHY Dean of Graduate Studies Date ...^cem ber. „ 18A „2000 DISSERTATION COMMITTEE Chairperson m t s - o l . 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents List of T ab les.................................................................................................................. List of F ig u r e s ..................................................................................................................iv ABSTRACT.........................................................................................................................v 1 Health Care in United States ...................................................................................1 1.1 History o f Health Insurance and Medical S e r v i c e ............................................1 1.2 Health Insurance Organizations..................................................................... 4 1.3 Medicare and Capitation M e th o d ..................................................................6 1.4 Previous Studies on Employment Based Health Plan C h o ic e ................... 9 1.5 Previous Studies on Medicare C a p ita tio n ............................................ 11 R eferences............................................................................................................... 14 2 USC Employee Health Plan D a t a ................................................................... 17 3 An Analysis of Employee Health Plan Choice: HMO vs. PPO - Using Random Effect Panel Data Probit R egression ............................................... 27 3.1 Introduction.............................................................................................. 27 3.2 M o d el........................................................................................................ 32 3.3 Cross-sectional Probit Model Estimation Results ............................. 38 3.4 Panel Probit Model Estimation R e s u lts ............................................... 43 3.5 Concluding R e m a rk ............................................................................... 52 R eferences............................................................................................................... 53 4 Medical Expenditure and Sample S e le c tio n .................................................. 58 4.1 Introduction.............................................................................................. 58 4.2 M o d el........................................................................................................ 64 4.3 D ata............................................................................................................ 68 4.4 Estimation R esu lts................................................................................... 72 4.5 Concluding R em arks............................................................................... 77 R eferences............................................................................................................... 80 BIBLIO G RA PH Y ................................................................................................. 83 ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables Chapter 2 Table 1. Variables from the Employee Data....................................................... 22 Table 2. Employee Choice of Health Plans.........................................................24 Table 3. Change o f Plan Coverage....................................................................... 24 Table 4. Correlations o f Selected Variables.........................................................25 Table 5. Variables from the Claim Data...............................................................26 Chapter 3 Table 1. Estimation Result of Probit Switch models......................................... 42 Table 2. Estimation Result of Random Effect Panel Probit Model.................. 46 Table 3. Prediction Success Table (Based on Switch Model: Model 3)........ 47 Table 4. Prediction Success Table (Based on Panel Data Model: Model 6). .47 Table 5. Simulated Probabilities.......................................................................... 49 Chapter 4 Table 1. Summary Statistics for Claim Data Variables......................................69 Table 2. Correlations............................................................................................. 69 Table 3. PCG Design.............................................................................................70 Table 4. Summary Statistics by PCG Groups..................................................... 70 Table 5. PCG Changes.......................................................................................... 72 Table 6. Estimation Result for PCG and AAPCC Models................................ 74 Table 7. Panel Selection Model Medical Expenditure Estimation....................76 Table 8-1. Success Table for PCG (PCG2 Model)............................................. 76 Table 8-2. Success Table for PPCG (PPCG 3 Model)........................................77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures Figure 1. Predicted Probability of Switching Health Plan Type (Based on Switch Probit Model 3)................................................................................................................50 Figure 2. Predicted Probability of Switching Health Plan Type (Based on Panel Probit Model 6)................................................................................................................51 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT We develop a new way of estimating medical expenditures with Pure Cost Group (PCG) model and panel data selection model of Kyriazidou(1997). This method shows better explanatory power than current Adjusted Average Per Capita Cost (AAPCC) model of Medicare capitation, and this gain of explanatory power comes from the econometric consideration of selection bias in health plan type choice without a help of diagnostic information. Comparing to new Medicare capitation method of Princi pal In-Patient Diagnostic Cost Group (PIP-DCG) model, this methodology can avoid a serious violation of privacy issue of revealing medical diagnostic information but still guarantees better explanatory power than AAPCC model. Another gain we can achieve by this model is a correction of selection bias caused by the favorable selection of healthier enrollees on Health Maintenance Organization (HMO) type plans. Both AAPCC and PIP-DCG models are not free from this selection bias since they use only the data from fee for service type plan enrollees. This is a reason why AAPCC based Medicare capitation method set 5 percent differential between HMO plan rate and fee for service plan rate. PIP-DCG can alleviate this selection bias by considering some di agnostic information but still there exists a selection bias issue basically coming from the incomplete diagnostic information. Our methodology is composed of two parts; V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the first part relies upon a random effect panel data probit model of health plan type choice between HMO and Preferred Provider Organization (PPO), while the second part relies upon a panel data selection model with nonparametric kernel correction us ing the first part estimation result. This panel data modeling has a great advantage that we can control for unobserved heterogeneity. This advantage and a proper definition o f willingness to pay measure (defined as relative premium) result in a dramatic accu racy of health plan choice prediction in the first part. We used a data set of university employees throughout the paper. It would be, however, easy to apply our methodology to either Medicare data or Medicaid data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 Health Care in United States 1.1 History of Health Insurance and Medical Service Before World War II, health insurance and health service were not available to most Americans. Less than twenty percent of Americans were covered by any form of health insurance until the end of WWII.1 Mass mobilization during wartime ex posed millions of men and women to the well organized health services from the military and to the concept of health benefits as a part of employment. Another war, the Korean War in the fifties, also contributed to widen this type of exposure to the health industry. As a result, the percentage of Americans covered by any kind of health insurance rose to more than seventy percent by the early sixties. Also this be came an inevitable trend until today. Such a growth was largely supported by the fast growing American economy after the wartime. As more and more people use health services, the expenditures on medical services have also grown rapidly. The Health Care Financing Administration (HCFA) shows that the national health expenditures have grown from 26.9 billion US dollars and 5.1 percent of Gross Domestic Product 1 Williams and Torrens( 1999). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (GDP) in 1960 to more than 1.1 trillion US dollars and 13.5 percent of GDP in 1998.2 Also funding composition in the same period has changed from, 75 percent from pri vate funds, 11 percent from federal budget, and 14 percent from state and local funds in 1960, to 54.5 percent from private funds, 32.8 percent from federal budget and 12.7 percent from state and local funds in 1998. This rapid growth in health expen ditures and increased burden of federal government has generated a debate not only in the congress but also among the general public. In the last four decades, several major legislations and the Supreme Court deci sions changed the health service system dramatically. Traditionally, indemnity insur ance3 was the prevailing means of health insurance. In the sixties, competition was not there in the medical industry. Also there was no oversupply of physicians. Instead there was a shortage of medical schools and many students who could not get admis sion into the limited number of U.S. medical schools had to study abroad.4 Also no physician had an incentive to reduce health service utilization under the fee for service (FFS) reimbursement scheme, which prevailed at that time. Basically physicians had the freedom to set up a price for any treatment and the oath of Hippocrates was their 2 Health Care Financing Administration Internet site http://www.hcfa.gov/stats/nhe-oact/hilites.htm and the table I at http://www.hcfa.gov/stats/nhe-oact/tables/tI.htm. 3 Under an indemnity plan, an enrollee pays a premium and she gets a reimbursement from the insurance company for the health care. 4 This problem was a motivation o f the Health Professions Educational Assistance Act (HPEA) in 1963. Eventually, this act has driven up the physicians per 100,000 population ratio almost twice from 139 in 1960 to 251 in 1996 (from the Table 12.3 from P.J. Feldstein(1999), Health Care Economics, 5th ed., Delmar Publishers, Albany, New York). 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. only restraint. As a result, physicians discriminated prices according to a patient’s affordability. Furthermore, state and county medical associations formed a cartel to negotiate with indemnity insurance companies. The most important change of health insurance in this period was the birth of Medicare in 1965. After 1965, the federal government took a central role in the health insurance industry. The federal govern ment started to plan, finance, and monitor a big part of the health business. In the seventies, the enforcement of anti-trust laws against professional organizations, totally changed the health service market structure. Before 1975, when the Supreme Court ruled against the Virginia State bar association which enforced a minimum fee sched ule for its members, professionals such as lawyers or doctors were not considered as engaged in trade or business.5 In December of that year, the Federal Trade Commission (FTC) also charged the American Medical Association, the Connecticut State Medical Society and the New Haven County Medical Association with anticompetitive behav ior.6 After getting the final victory in 1982, the FTC made subsequent moves in the health care industry. These moves changed the health care market structure to the cur rent HMO versus PPO picture. These legal interventions, the HMO act of 1973, the 1979 Amendments to CON Legislation7 opened wide futures to HMO’s. This advan 5 Feldstein(1999) Chp 9. 6 According to Cantwell(1981), this anticompetitive behavior is “to prevent or hinder their members from (a) soliciting business by advertising or otherwise; (b) engaging in price competition; and (c) otherwise engaging in competitive practices.” 7 The National Health Planning and Resources Development Act (CON) in 1974 limited capital expenditures by hospitals to prevent existing hospitals’ anticompetitive behavior by the mean of capital expenditures. However, this legislation resulted in a limitation on HMOs to build new hospitals to 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. tage of HMO type plans made even the traditional indemnity insurance companies start their own HMO’s, and HMO’s began to flourish in most parts of America.8 HMO’s have a strong advantage in cost containment, but they are viewed by physicians as severely restrictive while PPO’s are much closer to physicians’ favorable indemnity plans. Even though physicians’ favorable choice between HMO and PPO was always the latter, there was not enough demand for the PPO market to satisfy all the doc tors. Finally, between 1997 and 1998, when the booming economy supported more demands on PPO type services, the market share of PPO plans caught up with HMO plans.9 1.2 Health Insurance Organizations Among the types o f health insurance, the easiest one to understand is the indem nity plan. It is similar to other insurances such as auto insurance or fire insurance. In the case of the event for which an enrollee and an insurance company contracted, the insurance company pays the contracted amount to the enrollee while the insurance company collects the premium from the enrollees. This type of insurance contract was well explained in microeconomics by the difference in the risk attitude between the compete with existing hospitals. Therefore the Congress amended the CON legislation in 1979 to loosen the restrictions on HMOs. 8 According to Fox(1997), there were only 6 million HMO enrollees in 1976 but it increased to 56 million enrollees in 1995. 9 Dalzell, M.(1999), “PPOs: A better brand of managed care?”. Managed Care June 1999. 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. two sides; the insurance company is risk neutral while the enrollee is risk averse so there is a core region which can make both sides better off. The oldest organized form of health insurance alive in the United States is the Blues, which include Blue Cross and Blue Shield plans. Basically, the Blues are service-benefit plans. While indemnity plans reimburse monetary benefit to their en rollees when there is a claim, the Blues offer a service for their enrollees in the case of need. The Blues were the dominant figure in the health care industry until the managed care plans began to thrive. They had two major cost advantages over their competitors (the commercial indemnity insurance companies): premium tax exemption from fed eral and state taxes and the discount from the hospitals. Blue Cross and Blue Shield (BCBS) plans were started by different entities. Blue Cross was formed by hospital groups and Blue Shield was founded by medical societies. However, both entities are on the side of medical care suppliers. This fact results in a full reimbursement system o f physician’s care on enrollees and a regional monopoly of each BCBS plan. The Health Maintenance Organization (HMO) has been the most dominant power in the health care market for the last two decades. The HMO act of 1973 opened its future in the employment based health insurance market and subsequent legislations supported its growth. Wholey et al.(1997) show the rapid growth from 1985 to 1995. The enrollment in HMO’s increased from 18.77 millions in 1985 to 58.11 millions in 1995. Also they report that the premiums for HMO’s almost doubled in same period. 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The characteristics of HMO’s can be summarized as strong cost containment organiza tion. To contain rapidly growing medical expenditures, HMO’s use gate keepers called primary care physicians. Therefore, they cut unnecessary visits to the specialists and also provide preventive care education. The problem, however, is the restriction on the usage o f outside specialists. If there is no inside specialist for a rare disease, it is difficult to get appropriate care in an HMO environment. Preferred Provider Organization (PPO) is a mutation of traditional fee for ser vice plans. It provides a discounted fee schedule from its member physicians and still allows visits to outside physicians without any discount. So it leaves the limitation on the choice of outside physicians to financial incentives only. This is why it is consid ered as the better quality care organization, compared to HMO’s which strictly restrict unnecessary visits to specialists and do not reimburse visits to outside members. Point of Service plan (POS) is a new type of health care organization. It is typically just a mixture of HMO and PPO plans. The most general form is a HMO plan with the option to visit outside members. So it combines the merits of both types. 1.3 Medicare and Capitation Method Medicare was started by the 1965 legislation in the congress which provided health care access to any American citizen over 65 years old or disabled or with a fi nal stage renal disease. Basically, the Health Care Financing Administration (HCFA) 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reimburses medical costs to health plans under Medicare. This original retrospective payment method caused a rapid growth of expenditures in the Medicare program. As a response, the Social Security Amendments of 1972 introduced a risk based con tract option for the federally qualified HMO’s. Under this initial risk contract option, the actual medical costs of HMO’s were compared to a retrospectively calculated Ad justed Average Per Capita Cost (AAPCC)1 0 and HMO’s could share up to 10 percent of AAPCC in savings but were required to absorb all the losses. Before this risk con tract option, the federal government took all the risk of Medicare enrollees but this risk contract provides risk sharing between the federal government and HMO plans. Unfortunately, this risk contract was not welcomed by the qualified HMO’s. Accord ing to Langwell and Hadley(1986), there was only one plan, out of sixty-four plans signed with Medicare, that had a risk contract with Medicare at the end of 1979. The Tax Equity and Fiscal Responsibility Act of 1982 (TEFRA)1 1 introduced a full risk contract, which is applicable for only qualified HMO’s or Competitive Medical Plans (CMP: defined by the TEFRA). Under TEFRA risk contract, HMO’s receive up to 95 percent of AAPCC adjusted by each county factor. If the HMO’s actual cost is less than 95 percent of AAPCC, they are required to convert the difference into either ad ditional benefits or reduced cost sharing amount1 2 for the beneficiaries. Even though 1 0 This is a projected amount o f medical costs for the enrollee if she had been in the fee for service reimbursement plan. The regulations implementing the Social Security Amendment of 1972 define AAPCC. 1 1 This legislation went into effect April 1, 1985. 1 2 It can be a form of premiums, deductibles, etc. 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. there was a certain risk sharing concept in group practice prepayment plans of initial Medicare legislation (for Part B service) and risk contract option in the Social Secu rity Amendment of 1972 (for both Part A and Part B services) before TEFRA, it was a small number of plans only and risk contracting under TEFRA rules played a key role in the increase to 200 risk contracting HMO’s in Medicare in 1995.1 3 From the Bal anced Budget Act (BBA) of 1997, the traditional Medicare providers of HMO/CMP and FFS were modified to Medicare+Choice plans, which also include more variety of health care organizations such as PPO, Provider Sponsored Organization (PSO), Reli gious fraternal benefit society plan, and so on. This 1997 legislation also introduced a new Medicare capitation formula using diagnostic information. As explained above, AAPCC decides the rightful amount of payment schedule for those federally qualified Health Maintenance Organizations (HMO’s) and Compet itive Medical Plans (CMP’s) as 95 percent of an actuarially estimated medical expense which would have been incurred for an average Medicare beneficiary in the specific cell and county.1 4 This 5 percent differential was set to accommodate the cost effi ciency of HMO type organizations and favorable selection of healthier enrollees in HMO type plans. However, this capitation method only uses demographics and pos sible selection bias was pointed out by numerous authors. As a result, the Balanced Budget Act1 5 of 1997 introduced a new capitation model called Principal In-Patient 1 3 Zarabozo and LeMasurier( 1997). 1 4 There are 142 cells in AAPCC. 1 5 This legislation also introduces a new concept of Medicare+Choice (M+C) as an eligible organization 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Diagnostic Cost Group (PIP-DCG) model. This model used certain diagnostic infor mation o f patients with more than one day hospitalization to sort out high cost groups of patients. With the help of a panel of medical doctors, epidemiologists and health economists made 15 PIP-DCGs and a base category. By this grouping, a new cap itation method was imposed from 2000.1 6 The problem of this method is the base category, which not only includes the lowest cost group, but also includes new en rollees and undeterministic cost group patients. This problem plays a role in reducing the explanatory power of the PIP-DCG model. The report to the Congress1 7 says that AAPCC has only one percent explanatory power while the PIP-DCG model has six percent explanatory power. 1.4 Previous Studies on Employment Based Health Plan Choice Employment based health insurance was insignificant before the end of World War II. A series of legislations and changes in taxation resulted in a rapid diffusion of employee health benefit and fast growth of group health insurance plans in the forties. This trend has been accelerated by the strong union and labor movements in the sixties. for a risk contract. So the previous HMO/CMP eligibility are extended to include the PPO’s and other type o f health care plans. 1 6 It starts with 10% PIP-DCG and 90% AAPCC amount in 2000 but it would be 100% PIP-DCG in 2004. 17 Report to Congress: Proposed Method of Incorporating Health Status Risk Adjusters into Medicare + Choice Payments. 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. As a result, 65 percent of companies with 25 to 99 employees, 77 percent of compa nies with 100 to 499 employees and 86 percent of companies with more than 500 employees offered some kind of group health coverage to their employees in 1979.1 8 According to Kuttner(1999), 151.7 million people among 167.5 million nonelderly Americans with private health insurance belonged to employer provided health insur ance in 1997. Because of the increased burden in the employee side, actual take up rate fell from 88.3 percent in 1987 to 80.1 percent in 1996 even though the offering of health insurance percentage increased from 72.4 percent to 75.4 percent in the same period. As employment based health insurance expanded over time, private health in surance costs per enrollee also increased sharply. Kuttner(1999) says that costs per enrollee increased 218 percent in inflation adjusted dollars between 1980 and 1993. This sharp increase in medical expenditures made employers consider managed care organizations more seriously. There are many studies on employee health plan choice, but the following four papers are most closely related to this dissertation. Ellis( 1985) analyzed a large anony mous firm employees’ choices of health plans using a multinomial logit model and he found that previous health expenditure is a powerful predictor of future health plan choice. Another multinomial logit analysis by Barringer and Mitchellf 1994) found that inducing to enroll in HMO (tax exclusion for employer provided health insur 1 8 Whitted, G.(1999) “Chapter 7 Private health insurance and employee benefits,” in Introduction to Health Services, Williams, S.J. and P.R.Torrens eds., 5th ed., Delmar Publishers, Albany, New York. 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ance) is better than providing financial incentives for health care costs (personal in come tax credit). This policy conclusion was derived by a simulation of probabilities on choosing health plan between Fee for Service (FFS) and HMO plans. Buchmueller and Feidstein(1997) basically showed a strong response of employees with respect to the simulated moderate increase of premium using a cross-sectional probit model of switch. Feldman et al. (1989) is different from the above three studies in the sense that it is not an analysis confined to a single firm. They analyzed 17 firms in the Min neapolis metropolitan area using a nested logit model and each nest distinguished by the freedom to choose a doctor1 9 is shown to be the best model. Also they found that employees are very sensitive to the change of premium. All these analyses used cross-section data2 0 and utilized simulation of probabilities to draw their conclusions. 1.5 Previous Studies on Medicare Capitation Before the Balanced Budget Act of 1997, Medicare only offered two choices of plan types: fee for service type plans and HMO type plans. These two health care orga nizations were very different in fundamental operations and induced different groups of enrollees. Many authors expressed concerns about adverse selection between fee for service plans and HMO plans. They found large evidence that healthier enrollees 19 IPA(Independent Practice Association) and FFS vs. HMO 20 Buchmueller and Feldstein(1997) used a single year(1993) probit model o f switch but they utilized some data(switch dummy variable and premium increase) on two years(1993 and 1994). U Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. tend to select HMO plans and as a result higher risk enrollees remain in fee for service plans, this is so called “cream skimming.” From Medicare Current Beneficiary Survey (MCBS) data, Riley et al.(1996) showed HMO enrollees are less likely to report poor health status than FFS enrollees. Hellinger(1995) had a nice summary of this problem. Dowd et a/.(1996) were very interesting since they found exactly an opposite adverse selection in HMO’s of Twin cities in 1988. They found higher risk enrollees had cho sen HMO’s in 1988 data using an endogenous sample selection model. Also they said this opposite adverse selection is interesting since three of five risk contract2 1 HMO’s in the data switched to non-risk contract later, which supports the finding. There were many critiques on the AAPCC capitation method. AAPCC is still2 2 the back bone of Medicare system and allows risk contract and reimbursement schemes. Therefore, there has been a lot of attention to this method from both researchers and the federal government. Newhouse(1986) noted the low explanatory power of AAPCC, 0.6 percent in Lubitz et a/.(1985). Also he suggested four desirable characteristics for the new adjuster of AAPCC. Two most important desirable characteristics he empha sized, were the predictability of medical expenditures and the collection costs. These two characteristics become the selection criteria for the later studies and the HCFA. Even though there were numerous methods to improve AAPCC predictability, most of 21 See section on Medicare and capitation method for TEFRA. 22 It will be used until 2003. From 2004, PIP-DCG will determine the Medicare capitation by 100 percent. 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the papers took the strategy of adding new variables which is easy to get and improves the predictability o f medical expenditures. Newhouse et al.( 1989) suggested physiologic health status and prior year uti lization to improve AAPCC. Gruenberg et al.{ 1996) showed that including diagnos tic, perceived health and disability variable improved the predictability. Weiner et al.( 1996) developed the Ambulatory Care Group (ACG) algorithm and reported better predictability than AAPCC.2 3 . Ash(1986), Ash et al.( 1989), Ellis and Ash(1995) and Ellis et al.( 1996) suggest the DCG (Diagnostic Cost Group) model, a diagnosis based capitation method which can improve explanatory power. This line of studies has been well accepted by the HCFA and they have chosen the PIP-DCG model, a variation of DCG model, as a new method of capitation from January 2000. Generally, including more variables improves the predictability of medical expenditure but there is a trade off with collection costs. For example, possible violation of privacy is a very sensitive issue and the biggest challenge of utilizing diagnostic information. 23 Still the highest adjusted R square of their method was only 7.89 percent in Female and Age 65 - 69 group (R square of AAPCC for the same group was 1.22 percent). 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References Ash, A. (1986). Analysis of alternative AAPCC models using data from the continuous Medicare history sample [Final report prepared for Health Care Financing Administration]. Health Policy Research Consortium Brandeis/Boston University. Ash, A., Porell, F., Gruenberg, L., Sawitz, E. & Beiser, A. (1989). Adjusting Medicare capitation payments using prior hospitalization data. Health Care Financing Review, 10(4), 17-29. Barringer, M. W. & Mitchell, O. S. (1994). Workers’ preferences among company- provided health insurance plans. Industrial and Labor Relations Review, 48. 141-152. Buchmueller, T. C. (1995). Health risk and access to employer-provided health insurance. Inquiry, 32, 75-86. Buchmueller, T. C. & Feldstein, P. J. (1997). The effect of price on switching among health plans. Journal o f Health Economics, 16, 231 -247. Cantwell, J. R. (1981). Copayments and consumer search: increasing competition in Medicare and other insured medical markets. Health Care Financing Review, 3(2), 65-76. Dalzell, M. D. (1999). PPO’s: A better brand of managed care? Managed Care, 8(6). Dowd, B., Feldman, R., Moscovice, I., Wisner, C., Bland, P. & Finch, M. (1996). An analysis o f selectivity bias in the Medicare AAPCC. Health Care Financing Review, 77(3), 35-57. Ellis, R. P. (1985). The effect of prior-year health expenditures on health coverage plan choice. In R. M. Scheffler and L. F. Rossiter (Eds.), Advances in health economics and health services research (Vol. 6, pp.149-170). Greenwich, Connecticut: JAI Press. Ellis, R. P. & Ash, A. (1995). Refinement to the Diagnostic Cost Group (DCG) model. Inquiry, 32, 418-429. Ellis, R. P., Pope, G. C., Iezzoni, L. I., Ayanian, J. Z., Bates, D. W., Burstin, H. & Ash, A. S. (1996). Diagnosis-based risk adjustment for Medicare capitation payments. Health Care Financing Review, 77(3), 101-128. 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Feldman, R., Finch, M., Dowd, B. & Cassou, S. (1989). The demand for employment-based health insurance plans. The Journal o f Human Resources 24(1), 115-142. Feldstein, P. J. (1999). Health care economics (5th ed.). Albany, New York: Delmar Publishers. Fox, P. D. (1997). An overview of managed care. In P. R. Kongstvedt (Ed.), Essentials o f managed health care (2nd ed., pp. 3-16). Gaithersburg, MD: Aspen Publishers, Inc. Gruenberg, L., Kaganova, E. & Hombrook, M. C. (1996). Improving the AAPCC with health-status measures from the MCBS. Health Care Financing Review; 77(3), 59-75. Hellinger, F. J. (1995). Selection bias in HMO’s and PPO’s: a review of the evidence. Inquiry, 32, 135-142. Kuttner, R. (1999). The American health care system-employer sponsored health coverage [Health policy report]. New England Journal o f Medicine 340(3). Langwell, K. M. & Hadley, J. P. (1986). Capitation and the Medicare program: history, issues, and evidence [Annual supplement]. Health Care Financing Review, pp. 9-20. Lubitz, J., Beebe, J. & Riley, G. (1985). Improving the Medicare HMO payment formula to deal with biased selection. In R. M. Scheffler & L. F. Rossiter (Eds.), Advances In health economics & health services research (Vol. 6, pp. 101-122). Greenwich, Connecticut: JAI Press. Newhouse, J. P. (1986). Rate adjusters for Medicare under capitation [Annual supplement]. Health Care Financing Review, pp. 45-55. Newhouse, J. P., Manning, W. G., Keeler, E. B. & Sloss, E. M. (1989). Adjusting capitation rates using objective health measures and prior utilization. Health Care Financing Review, 10(3), 41-54. Riley, G., Tudor, C., Chiang, Y. & Ingber, M. (1996). Health status of Medicare enrollees in HMO’s and fee for service in 1994. Health Care Financing Review, 77(4), 65-76. Weiner, J. P., Dobson, A., Maxwell, S. L., Coleman, K., Starfield, B. H. & Anderson, G. F. (1996). Risk-adjusted Medicare capitation rates using ambulatory and inpatient diagnoses. Health Care Financing Review, 17(3), 77-99. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Wholey, D. R., Christianson, J. B., Engberg, J. & Bryce, C. (1997). HMO market structure and performance: 1985 - 1995. Health Affairs, 16(6), 75-84. Williams, S. J. & Torrens, P. R. (1999). Introduction to Health Services (5th ed.). Albany, New York: Delmar Publishers. Zarabozo, C. & LeMasurier, J. (1997). Medicare and managed care. In P. Kongstvedt (Ed.), Essentials o f managed health care (2nd ed., pp. 405-431). Gaithersburg, MD: Aspen Publishers, Inc. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 USC Employee Health Plan Data The data set, we use in this dissertation, is provided by the University of South ern California (USC) benefit office. It includes two subsets - employee data and claim data - they can be connected through encoded ID number. We have the data for two years 1996 and 1997. There are 8,543 employees for the year 1996 and 8,596 em ployees for the year 1997. These are all the employees of USC in each year. After deleting alternative plan choice data and coding error data, we get 7,743 employee data and 7,761 data for year 1996 and 1997, respectively.2 4 This data set contains 6,644 employees in a two year balanced panel and 1,099 employees for the single year 1996 only and 1,117 employees for the single year 1997. Available health plans are three HMO plans and two PPO plans, offered in both years. The two PPO plans are offered by the university network, which includes the services by USC faculty physicians at the USC hospitals2 5 , while the three HMO plans are all outside organizations: Kaiser Permanente (KP), CalifomiaCare (CC)2 6 and PacifiCare (PC). The university network plans are both PPO type plans but the coverage and the preferred rates are different: one is a basic coverage plan (NET 24 There were seven coding errors for the age variable, two coding errors for the experience variable and one data for 1998 which might be a coding error o f the date variable. 25 USC hospitals have more than 2000 beds and it is one of the biggest teaching hospital. 26 This is a Blue Cross/ Blue Shield(BCBS) descendent. 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1) and the other is a more extensive coverage plan (NET 2). Also employee can choose outside insurance and take one of the supplemental coverage plans for free: alternative plan A and alternative plan B. This choice of an alternative plan is highly dependent on outside option characteristics such as spouse health plan characteristics. So we cannot consider these choices in our analysis as long as we do not observe those outside plan characteristics. There were two major changes in the design of health plans offered by the uni versity in 1997. Both changes were applicable to university network plan2 7 holders only. The first change was made on the deductible of university network plans (PPO): there was no deductible for the direct services from the university2 8 in 1996 but $100 per person and $300 per family annual deductible was introduced from 1997. Also the annual deductible of services rendered by all the other preferred provider groups in the university network plan, was increased from $100 to $150 per person and from $300 to $450 per family. The second change was the increase in premiums of the basic cov erage university network plan (NET 1) while all the other plan premiums stayed the same. These changes can be interpreted as an out of pocket expense increase for the employee who chose a university network plan over any of the HMO plans. 27 This is the only PPO type plan in the analysis. 28 These services are defined as services rendered by USC School of Medicine faculty physicians and inpatient and outpatient services provided at USC University Hospital, Children’s Hospital Los Angeles, Estelle Doheny Eye Hospital, Kenneth Norris Jr. Cancer Hospital, the USC Acute Care Center and the Faculty/Staff Clinic in the University Park Health Center. 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. There are originally ten variables in the employee data set: encoded ID, health plan choice, dental plan choice, date o f birth, gender, pay grade, encoded department code, hire date, percentage of working time and residential ZIP code. Also there are six variables in the claim data set: encoded ID number, date of the claim, total charge o f the claim, deductible applied, coinsurance amount, and inpatient days. It is, how ever, incomplete since the claim data set includes only the PPO plan holders. Since HMO medical cost structure is very different from PPO, especially in this case of the Academic Health Center (AHC) involved, we cannot even approximate HMO claim charges by the given PPO plan claim data. One defect of this data set is it does not in clude salary information but as previous studies show the income effect of observed salary is significantly small.2 9 Instead, we have the pay grade information which is approximately proportional to the salary. However, all the faculty members have the same pay grade code regardless of their salary, so we could not use it as a proxy for the salary. From the raw data, we constructed several dummy variables: one for faculty (Dfa c u lty) since we expect difference in the choice of health plan between faculty and nonfaculty employee, one for HMO or PPO (D//a/o), one for switching between HMO plans and PPO plans from 1996 to 1997 (P sw itc h ), one for residential zip code being the same as any of the university hospitals zip codes (DunivHOSp)zai one 29 Probably, household wealth is a more accurate estimate. Barringer and Mitchell(1994) found the coefficient of salaryfin thousand dollars) to the choice probability of each FFS or HMO plan is -0.03 to -0.02.(all statistically significant) While Wolfe and Goddeeris(1991) found strong positive wealth effect on the supplemental health insurance purchase among senior citizens. 30 We used the directories of providers and hospitals from each health plan to compare the difference in 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for male P m a le), one for different zip code from 1996 to 1997 (Dm o v e) and finally dummies for each coverage category (P sin g le for single person coverage, Dplus for employee plus one dependent coverage, Df a m il y for employee plus two or more de pendent coverage) Next we generated age (AGE) and experience (EX) variable from date of birth and hire date. AGE variable was defined as the actual age at the initial day of plan coverage, January 1st of each year. Experience variable was defined by the formula of the total months at USC (until the initial day of plan coverage) divided by twelve. This experience variable has different meaning from usual labor economics since actually it is experience at USC. So we can view this variable in health plan choice as a proxy showing persistence.3 1 Most importantly, we generated a monthly premium variable (PREM) from the university booklet distributed to each employee for useful information about choice of health plan. Also we generated relative pre mium (RPrem) which is defined as own premium minus the minimum premium o f the other type of plans for given coverage type. This variable has an asymmetric effect on HMO and PPO plans: this is a major part of switching cost for HMO plans since they have to pay more to switch into PPO type plans unless they reduce the number of people covered and it is a kind of measure of willingness to pay more to stay in enrollment o f hospitals among plans and we found only university hospitals are not available to the other HMO plans and there is no difference between California Care and PacifiCare except only for one hospital. So we only generated a dummy for university hospital in our comparison between HMO and PPO plans. Kaiser health plan uses its captive provider Permanente group(closed panel HMO). 31 The best variable to show persistence is the years in the specific health plan but we did not get this data either. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PPO type plans for PPO plan holders. More detailed explanation is provided in the next chapter. In the estimation, all the plan characteristics of each plan are represented by premium of each health plan since they are perfectly correlated with each other for given number of dependent coverage. This was pointed out as a defect of using single firm analysis in Feldman et al.(1989). So we cannot consider separately price elastic ity and cross price elasticity typically in this kind of single firm data. This is why we need to generate a relative premium variable which is a combination of both own pre mium and the other type plan premium. The reason we use the minimum of the other type plan premium is based on the fact that HMO choosers care more about the price of the health plan and PPO choosers care more about the quality of service they can get when other things remain the same. As a result, switching cost for HMO plan hold ers can be defined as own premium minus minimum PPO plan premium and, when we assume the quality of health care services are the same among HMO plans (or at least employee does not have enough information to distinguish high quality and low quality), the highest utility level from the choice of HMO plan will be from the low est premium plan and relative premium can be viewed as the amount o f monetary gain PPO plan holders are willing to pay to stay in PPO plan (or not to switch to any other HMO plan since this was compared to highest utility HMO plan). All these variables from the employee data are tabulated in Table 1. 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1. Variables from the Employee Data3 2 Variable Description Whole Data Balanced Panel 96Data {N =7743) 97Data (T V =7761) 96Data (JV=6644) 97Data (N=6644) D HMO Dummy variable for HMO 0.502 (0.500) 0.497 (0.500) 0.502 (0.500) 0.493 (0.500) AGE Age o f employee 42.278 (11.640) 42.335 (11.637) 42.698 (11.353) 43.698 (11.353) Working% Working Status (full time = 100) 97.230 (11.560) 96.459 (12.705) 97.393 (11.373) 96.502 (12.728) EX Experience in USC 10.073 (8.280) 10.166 (8.362) 10.424 (8.221) 11.424 (8.221) EX2 Square o f EX 170.009 (256.303) 173.265 (260.489) 176.250 (256.302) 198.099 (271.734) Coverage Number o f people covered (up to three including self) 1.959 (0.864) 1.973 (0.870) 2.003 (0.863) 2.024 (0.861) D PLUS Dummy for 2-person coverage 0.252 (0.434) 0.248 (0.432) 0.255 (0.436) 0.258 (0.437) DF A M IL Y Dummy for 3-person coverage 0.354 (0.478) 0.362 (0.481) 0.374 (0.484) 0.383 (0.486) PREM Monthly Premium 48.373 (37.975) 50.586 (35.805) 49.531 (38.436) 52.212 (36.980) RPrcm Relative Premium 5.492 (38.574) 4.967 (38.948) 5.804 (39.281) 5.557 (40.559) RPrcm2 Square o f RPrcm 1517.947 (12346.92) 1541.393 (11084.26) 1576.413 (12611.36) 1675.694 (11685.89) VU nivH OSP Dummy variable for living near University Network Hospitals 0.075 (0.263) 0.075 (0.263) 0.074 (0.262) 0.072 (0.260) Variable Description Switch model ^Switch Dummy variable for switching 0.024 (0.154) APremium Difference o f premiums 2.680 (13.482) A Premium^ Square o f APremium 188.909 (3687.852) ACovcragc Difference o f coverage 0.020 (0.271) D M A LE Dummy variable for male = I 0.526 (0.499) DF A CU LTY Dummy variable for faculty member = I 0.312 (0.463) D M O VE Dummy variable for moving residence 0.120 (0.325) 32 Mean is rounded at 1/1000 and standard Deviation is in the parentheses. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In Table 1, we can see that there is not much difference in means between whole data and balanced panel data. Only one notable difference is the mean of the Dhmo variable in the 1997 whole sample and the mean of the 1997 balanced sample, which indicates that the dominant number of newly hired employees of 1997 data chose HMO as their first health plan to start at USC. This makes sense since if they do not have enough information about each health plan then why not start with a less expensive plan? Also Table 2 shows the basic structure o f health plan choice for the balanced panel we are considering. Only 3.3 percent of employees switched their plans to an other plan and 2.4 percent of employees switched the type of the plan (i.e. HMO vs. PPO). From Table 3, we can see the coverage structure is very stable for those who use this health benefit (94% of employee did not change coverage type), the biggest two changes are from single coverage (1,SINGLE) to employee plus one dependent coverage (2,PLUS ONE) and employee plus one dependent coverage category to fam ily coverage (3,FAMILY). This can happen when employee get married or married employee gets the first baby and so on. Table 4 shows the correlation structure of the variables we used in estimation. One notable thing is that the relative premium (RPrem) is more highly correlated with D h m o variable than premium (PREM) so we get a better fit of the model when we use RPrem as an independent variable and we also expect to get a better prediction.3 3 33 We did not include any estimation result (See the Next Chapter) using PREM for panel data model but we found a significant difference in prediction success table of the models using PREM instead of 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2. Employee Choice o f Health Plans3 4 ’97 Plans ’96 Plans Net 1 Net 2 Kaiser PacifiCare CA Care Total Net 1 3157 0 29 11 12 3209 (98.3) (0-9) (0.4) (0.4) (100.0) Net 2 5 98 0 0 0 103 (4.9) (95.1) (100.0) Kaiser 67 0 2470 11 7 2555 (2.6) (96.7) (0.4) (0.3) (100.0) PacifiCare 25 0 6 568 9 608 (4.1) (1.0) (93.4) (1.5) (100.0) CA Care 17 0 4 2 134 157 (10.8) (2.5) (1.3) (■85.4) (100.0) Cygna 1 0 3 6 2 12 (8.3) (25.0) (50.0) (16.7) (100.0) Total 3272 98 2512 598 164 6644 Note: 162 employee changed type of plan (2.4% of 6644 employee) and 217 employee changed their plan to different plan. (3.3%) Table 3. C hange o f Plan C overage3 5 ’97 Coverage ’96 Coverage Single Plus One Family Total Single 2319 120 25 2464 (94.1) (4.9) (1.0) (100.0) Plus One 61 1520 112 1693 (3.6) (89.8) (6 .6 ) (100.0) Family 7 71 2409 2487 (0.2) (2.9) (96.9) (100.) Total 2387 1711 2546 6644 RPrem. 34 Percentage of 1997 plan choice for given 1996 plan are in parentheses. 35 Percentage of 1997 plan coverage category for given 1996 plan coverage are in parentheses. 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. Table 4. Correlations o f Selected Variables Invariant DSwitch A Premium ACoverege D MALE DFACULTY D MOVE VUnivHOSP EX AGE 0 Switch 1.0000 A Premium 0.0563 1.0000 ACovcragc -0.0119 0.4657 1.0000 °MALE -0.0023 -0.0158 0.0016 1.0000 DFACULTY -0.0389 0.0377 -0.0004 0.3010 1.0000 &MOVE 0.0288 0.0096 0.0405 -0.0256 -0.0590 1.0000 VUnivHOSP 0.0087 -0.0088 -0.0146 -0.0238 -0.0986 0.0277 1.0000 EX -0.0523 -0.0940 -0.0967 0.1360 0.2060 -0.1342 -0.0432 1.0000 AGE -0.0597 -0.0740 -0.1333 0.1521 0.3122 -0.1694 -0.0751 0.6147 1.0000 96 Data D HMO RPrcm PREM DSwitch D HMO 1.0000 RPrem -0.5397 1.0000 PREM -0.2388 0.8458 1.0000 ^Switch 0.0561 -0.0333 -0.0264 1.0000 97 Data D HMO RPrcm PREM DSwitch Dh m o 1.0000 RPrem -0.6569 1.0000 PREM -0.3183 0.8191 1.0000 DSujitc/i 0.0543 0.0206 •0.0069 1.0000 The claim data is related to medical expenditures for the two years 1996 and 1997. We aggregate this claim data by year to get annual charges for each individual and we get total annual charges (TOTAL), annual deductible paid (DEDUCT), annual coinsurance3 6 amount (COINS), and annual inpatient days (InDays), as a result. Fur ther we generate out of pocket payment variable (Op) as the addition of deductible and coinsurance. More detailed information on this data set is available in Chapter 4. Table 5. Variables from the C laim D ata ’96 Data ’97 Data. Variable Mean S.D. Mean S.D. TOTAL 9347.49 36498.43 9775.64 40916.66 DEDUCT 91.39 102.93 198.83 132.66 COINS 246.28 1065.35 271.39 1159.00 InDays 0.64 4.50 0.65 5.61 Op 337.66 1092.98 470.22 1191.18 36 For the PPO plan, a discounted rate is applied to the patient after deductible, so the coinsurance is the amount the patient pays over the deductible for the health service. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 An Analysis of Employee Health Plan Choice: HMO vs. PPO - Using Random Effect Panel Data Probit Regression 3.1 Introduction After the Health Maintenance Organization (HMO) act of 1973 (PL 93-222)3 7 , HMO’s have grown rapidly in the employment based health insurance market. Ac cording to Wholey, Christianson, Engberg and Bryce(1997), there were 571 HMO’s in operation covering more than 58 million Americans in 1995. However, this rapid growth has slowed down because of the emergence of new alternatives such as PPO (Preferred Provider Organization) and POS (Point of Service) managed care. As the American economy continues to get stronger, the labor market gets tighter as a re sult; employers go for better benefits packages which may include “luxurious” PPO type plans. Between 1997 and 1998, HMO-type plans lost some market share to PPO type plans for the first time3 8 . PPO’s are getting more popular among employ ers since they tend to offer a more luxurious benefit package to stay competitive in 37 This legislation required employers to offer HMO as an option at least and to contribute equally between indemnity plan premiums and HMO premiums. However, equal contribution requirement has been changed to no financial discrimination requirement in 1988 amendment(PL 100-517).(See Wrightson, Jr.(1990) for detail) 38 Dalzell, M.(1999), “PPOs: A better brand of managed care?”. Managed Care June 1999 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a tight labor market. Generally speaking, HMO plans are designed to lower med ical costs, so they use extensive cost containment measures to keep medical costs down. As a result each member pays only a small copayment ($5 to $ 15 per visit). However, the organization authority closely monitors the performance o f physician as well as requiring each member to see her primary care doctor so called a “gate keeper” first and get a referral to a specialist, so it may cause consumer dissatisfac tion from this system. On the other hand, PPO plans are similar to fee for service (FFS) plans in most aspects but they also offer a discounted rate for the providers be longing to the plan network. These plans allow patients to choose any specialist but they set a higher rate of charge for a specialist outside the network where the patient belongs. The POS plan is a hybrid o f these two models, the most common form be ing HMO with an option to visit a physician outside the network without any referral from the primary care doctor. The payment structure of POS is a small copayment for the physicians within the network, similar to HMO plans, but changes to indem nity type proportional payments for the outside physicians. These different medical cost payment structures play a key role not only in policy holders’ health service utilizing behavior but also in the choice of specific type of plans. Generally speak ing, HMO plans have strong advantages in keeping medical costs down whereas PPO plans have advantages of the quality o f medical services (highly dependent upon free dom of choice for physician). There is an additional characteristic of our specific data 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. set which makes this cost versus quality comparison much stronger. In our data, PPO plans are offered by an academic health center (AHC) based network. As Reuter and Gadkin(1997) show, AHC’s have higher quality of care with advanced medical tech nology while they also have higher costs for each case, resulting from the graduate medical education.3 9 Also Solit and Nash(1997) pointed out that most managed care plans do not put much importance on research or education while AHC is the cen terpiece of promoting the industrial revolution in medicine. So AHC combined PPO plans have superior quality against typical HMO type plans. There are numerous analyses of the managed care market as managed care be came a dominant form of health insurance within an employment package. However, as the survey of Miller and Luft(1997) shows, it is difficult to answer which is ab solutely the best type of health insurance organization since it is critically dependent upon which aspect of comparison we are interested in. Therefore, a typical cost-benefit analysis on health care organization more likely focuses on specific disease-care cost- benefit comparison between two types of plans. Also there is an important future un certainty which makes it difficult to judge the superiority of plan types. According to Dalzell(1999), sharply increasing medical costs can be an important slow-down factor for the current thriving PPO type plans since PPO’s discounted fee-for-service struc ture is more vulnerable to cost increases. The difference in organizational structure 39 Their study includes metropolitan areas in California. Also USC hospital is one o f the biggest teaching hospitals in the US. 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. makes it more important to keep medical costs down for HMO type plans. Therefore, as soon as the premium differential between PPO and HMO gets greater than people’s willingness to pay for the quality, PPO will be in danger to keep the current grow ing trend. Hence, the strategy of this chapter is to focus on the effects of changes in health insurance structure on the choice of health plan types and an appropriate mea sure of willingness to pay for the quality from the switching and continuing health plan types. Also we extend it to a parallel comparison of the previous analyses of em ployees’ health plan choice and an analysis of employees’ switching behavior of health plans and their implication on willingness to pay. Among others, Ellis( 1985), Feldman et a l (1989), Barringer and Mitchell(1994) and Buchmueller and Feldstein(1997) are considered in this chapter. Ellis(l985) analyzed a large anonymous firm’s employees’ choices of health plans using a multinomial logit model and found that the previous health expenditure is a powerful predictor of future health plan choice. Another multi nomial logit analysis by Barringer and Mitchell( 1994) found that inducing to enroll in HMO (tax exclusion for employer provided health insurance) is better than providing financial incentives for health care costs (personal income tax credit) through a sim ulation of probabilities on choosing health plan between Fee for Service (FFS) and HMO plans. Buchmueller and Feldstein(l997) basically showed a strong response of employees with respect to the simulated moderate increase o f premiums using a cross- sectional probit model of switch. Feldman et al. (1989) is different from the above 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. three studies in the sense that it is not an analysis confined to a single firm. They an alyzed 17 firms in the Minneapolis metropolitan area using a nested logit model; and each nest distinguished by the freedom to choose a doctor4 0 is shown to be the best model. They also found that employees are very sensitive to the change of premiums. All these studies used cross-sectional data4 1 and utilized simulation of probabilities upon which to draw conclusions. In this chapter, we extend this type of analysis to a more general panel data probit model and we show that there is a valid4 2 hetero geneity in the model through a likelihood ratio test between the unrestricted panel data model and the pooled probit model as a restricted model. After controlling for this unobserved heterogeneity and introducing relative premium concept, we find that still ceteris paribus price sensitive behavior can be observed in this framework while cross-sectional study does not show this sensitive behavior of employee. This sensitive behavior makes more sense in the Southern California region since this is the region showing the nation’s highest managed care penetration rate and the most competitive health care market. This chapter is organized as follows. A brief explanation about several models of health plan choice are available in section 2. The estimation results of switch model 40 IPA(Independent Practice Association) and FFS vs. HMO 41 Buchmueller and Feldstein( 1997) used a single year (1993) probit model o f switch but they utilized some data (switch dummy variable and premium increase) on two years (1993 and 1994). 42 Random effect parameter can be tested by various specification test depending on the model setup. For example, Hausman specification test (Hausman( 1978)). 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are presented in section 3; the estimation results of panel data probit model are showed in section 4; and section 5 concludes. 3.2 Model We consider the following health plan type choice, y*t = /3xit + £it, i = 1,.... N :t = 1,.... Ti (1) yit = 1 if y*t > 0 = 0 otherwise, (2) where y*t is the unobserved propensity to join a HMO type plan by individual i at time t, and yu.= E ^hmo denotes the choice of health plan type whether HMO (D//A /0 = l) or PPO (DW A /o=0), x it is a fc-dimensional vector of observable variables including de mographics and eit is an error term. Tx = 1 for all i implies usual cross-section Limited Dependent Variable (LDV) model, which is most commonly used in health economics literature. Ellis(1985) used a logit model to analyze employee plan choice, Hombrook et al. (1989) examined selectivity and selection bias using a probit version; Buch- mueller(1995) used a probit model for comparing the effects of employer provided health insurance types on health status. Also Buchmueller and Feldstein( 1997), which is discussed in the next section, employed a probit model to study employees’ behav- 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ior of switching health plans. As we can see, our model is more general than all the above studies, since we consider each individual’s previous history. Also note that this is not just a stack of cross-sections as we can find in some cohort studies of epidemiol ogy or longitudinal studies in health economics (there is an important individual index i present above). This is called a panel data analysis or time-series cross-section anal ysis in econometrics and is classified in two models; random effect models and fixed effect models. To see the difference between these two models, let us assume the fol lowing error structure on Eu for a probit panel data random effect model4 3 Eit = U i + Vit H i ~ 7V(0,0 -^), v it ~ iid N (0 ,1), ux J_ uit (3) where ti^ is an unobserved heterogeneity among individuals (which is time invariant), i)it denotes an underlying innovation, and JL indicates independent relationship. Ran dom effect models consider individual specific term (which does not vary with the time index t) Ui as random while fixed effect models consider it as nonrandom or fixed with certain normalization (such as sum up to one or zero). There is a good comparison of these two models in Hsiao(1986). The simplest way to see the conceptual difference between these two models is whether we can permute ux over i. Random effect mod els allow us to do it while fixed effect models do not. Hence, we can choose either 43 In this paper, identifying restrictions are already imposed on the variance o f innovations (rr^ = 1). Alternative identifying assumption can be made as <r„ + a \ = 1. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. model depending on the question we are interested in. If we are interested in the av erage individual behavior after controlling for unobserved heterogeneity, we can use a random effect model; if we have to control for nonchangeable individual unobserved characteristic then a fixed effect model would be the better choice. There are also special considerations needed for panel data probit modeling. Hsiao(1986) and Cham berlain 1984) explain that a fixed effect probit model does not provide a consistent estimator of /3 since there is an incidental parameter Ui in the model. This notorious incidental parameter problem resulted from the fact that the number of parameter to estimate increases faster or at the same rate as the sample size N increases. Generally, increasing the sample size N to a large enough number yields an efficiency gain, but the incidental parameter problem is an exception. To solve this incidental parameter problem, Chamberlain( 1980) suggests Conditional Maximum Likelihood Estimation (CMLE) in a fixed effect logit model. Basically his idea is to condition the likelihood function on the minimum sufficient statistic Ylt Vit- It Is a consistent estimator. How ever, it is inefficient under the usual homogeneity hypothesis (Ui = u) since does not use this information in the estimation and it does not utilize the observations which do not contribute to the conditional likelihood function, (i.e. the conditional density is degenerate when Ylt Vu = 0 or Ylt Va = Ti is given: yx are either all zeros or all ones.)4 4 44 Hausman(1978) considered specification test between random effect versus fixed effect model in linear panel data model. It is possible to extend this in logit specification. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Both Ui and v it are normally independently distributed; thus, we can transform the panel data univariate probit model in the balanced panel (T, = T for all i) case, to a multivariate probit model as follows, For each i, yit = 1 if /3xit + eit > 0 = 0 if (3xu + Sn 5 ~ 0, t = 1 , T. Ei = (e*i, Ei2, ~ N ( 0 , I t + iff) Corr[eis, eit] = p = c t 2 J { 1 + <r*), for s ± t (4) where I t is T -dimensional identity matrix, t is a T-dimensional vector of ones, and l ' is its transpose. It is obvious that there exists a intertemporal correlation structure among the error terms belonging to the same individual4 5 . This correlation is differ ent from the usual serial correlation since it does not change for all the time periods, hence the term “equicorrelation.”4 6 One problem with the usual multivariate probit model is that we cannot obtain a Maximum Likelihood Estimator (MLE) for T > 4, since the evaluation of a higher order multivariate normal integral is not satisfactory. In addition, there is a critical difference between the usual multivariate probit model and this panel data probit model. There are (T — l ) x k constraints, i.e. the equality of the coefficients (i.e. (3t = /3), in our random effect panel data probit model. Be 45 CoTx{£it,£ia) =<ri/0- + (Tu) f o r t / s . 46 In our model setup this equicorrelation can be interpreted as time preference rate equal to one and serial correlation can be interpreted as discounting factor (reciprocal of time preference rate) is constant over time after applying change of variables appropriately. 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. cause of these restrictions, the classical gradient based maximum likelihood method is computationally intractable in the parlance of Hajivassiliou and Ruud(1994).4 7 This technical difficulty was the main motivation of developing logistic distribution based models or introducing the simulation based estimation methods.4 8 There are many dif ferent simulation methods that can be applied in this case. Among others, Gouneroux and Monfort(1993) explain how to apply Simulated Maximum Likelihood (SML) in this case by relevant conditioning4 9 and Keane(1993) explains different ways to solve this problem by using a Geweke-Hajivassiliou-Keane (GHK) simulator which does not use conditioning on u and directly simulates the transitional probability over time5 0 . A recent publication by Hyslop(1999) shows that we do not need many simulations for simulated maximum likelihood by Monte Carlo integration in the appendix of his pa per (H = 20 simulations are sufficient). These two methods can be applied even in the presence of a serially correlated error structure, which is especially important in the health plan choice literature since state dependence is frequently observed in this field. However, in the case of T = 2 , introducing serial correlation does not change the ba- 47 These equality constraints make the gradient very complicated because all the arguments of multivariate normal distribution function have /? in it (if we combine these constraints into the likelihood function) or increase the number o f equations to be evaluated (if we include these constraints as separate equations). 48 Chamberlain( 1984) suggests a minimum distance estimator which actually utilizing these restrictions. In addition, he also considers the correlation between Ui and Xi as an additional set o f restrictions. 49 L = 52 H i log[jfsu/(:r|u)] = 52*11 1°s[t7 12h=i nt:V =i$(/3xit + r T uUi)>< n t:V =o4>(— /3xu — rruUi)j 50 This is a different conditioning. It is conditioning on current time t and simulating probability from t to t 1 period. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sic autocovariance structure much but adds one more parameter.5' This is a limitation o f our data set which has only two years o f data. Another popular method which can avoid multivariate normal integral was de veloped by Butler and Moffit(1982). This method utilizes Gauss-Hermite quadrature5 2 to evaluate inner integrals in the following likelihood function.5 3 L = nil = nf= = nf= = n i l = = n i l = nil P[yn = da, U i2 = di2 ,..., U iTx = diTi) / {2 d n -l)0 x n r[ •oo « / — ' fe (£il ■ si2i -iT, ) d£iTt...d£ii •oo r(2dii — \)p x ii r(2diTi — ^ ) ^ x T i r+ oo j * • • j j fs\u(^tt|^t) ./u(^t) dU xdSi*px^..dSi\ J — oo J — oo J — oo •oo ” - 1 - 0 0 / +oo / u(ut)n ^ = 1[Fe|u{(2dif - l)(3xit\ui) - Fe|u(-oo|i^)]c£ui •o o / +oo 0(uI)n ^ :1[< l>{(2£Zi£ - 1 )(3xit + Ui\ - 0] dui ■ o o / +oo 1 e - a /2 K u ,/ ^ ) 2u T L i^ 2dit _ 1 ) ( f e + U .)J d u . ■ o o ^ uV27T 1 f+°° 2 — / e r'g{ri)dri V * J-oo 1 * —= V Wkgicik) ■ Gaussian-Hermite Integration (5) where di£ = 0 or 1 only, f w and Fw are the density and the distribution function of the subscript variable w, respectively. 0 and $ denote the standard normal density 51 Var(v.i) = Y X p ^ * j ^ + au L L > f°r v it = p v u - 1+ white 52 Gaussian-Hermite Integration formula: J Z o e~r2g(r)dr S £ £ =1 wkg(ak) 53 From (3) and (4), e,£| ux ~ IN (u x, 1). noise term. 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and distribution function, respectively. r{ = Ui/rru\/2, dr{ — 1 /(rru\/2) dv^, g{rx) = n ^ :1$[(2dit — 1) {(3xit + a-uy/2ri)\, wk is a quadrature weight and ak is called a quadrature abscissa.5 4 Once wk s and ak s are provided, this likelihood function can be easily maximized with respect to (3. Generally, we need higher K to achieve good approximation as T * grows higher and p = <r„/(l -I- < r 2 u) gets larger. There is a finite sample Monte Carlo simulation result by Guilkey and Murphy(1993) which shows that K = 8 points is enough for the most of the cases. Butler and Moffit(1982) method has a simple implication on testing the existence of random effect. Since there exists an equicorrelation parameter due to the random effect coefficient (< rft in equation (4)), we can test the significance o f this equicorrelation parameter to judge whether in fact there exists random effect.S 5 3.3 Cross-sectional Probit Model Estimation Results We follow the employee switching health plan probit model of Buchmueller and Feldstein(1997) here. They define5 6 54 The tabulated values o f iuk and ak can be found in Table 25.10 of Abramovitz and Stegun( 1972). 55 In our model setup, this test is equivalent to testing whether there is an omitted time invariant variable. 56 In the original model o f Buchmueller and Feldstein( 1997), they considered the sign o f APremiumi as a separate dummy variable, but we did not find much difference in our result whether we separate it or not. 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S* = a 0 + a^APremiurr^ + a 3 APremium^ + /3DEM, 4- 7 PLANi (6) Dswitch = 1 if S* > 0 = 0 otherwise, (7) where S* is an unobserved net benefit of switching plans (whether HMO to PPO or PPO to HMO) and Dswitch is the dichotomous analog of S*, APremium1 is the differ ence in premiums from year 1996 to 1997, APremium? is the square of that variable, DEMj is individual demographics and PLAN* is plan characteristics for individual i. In our data, we use ACoverage, Working %, AGE, EX, Dfacu lty, DjjmvHOSP, Dm ale and Dmove as DEM variables and D//A /0 9 6, Dplus, ®fam and PREM as PLAN variables. We can see that this type of model has a clear advantage in terms of the variables that we can use. In panel models, we cannot identify any time invariant variable from the random effect coefficient so we cannot include any variable which does not vary over time such as gender, dummy for faculty (Dfac u lty), and so on. Also we cannot use certain difference variables such as dummy for moving (DA iove)5 difference of coverage (ACoverage) variable in panel data setup, since this will re duce to T — 1 period panel data model if we use any of these difference variables. We have only two years of panel data so it will end up becoming a cross-sectional analy sis. Estimation results of switch probit models are in Table 1. Model 3 turns out to be the best model and shows similar results as in Buchmueller and Feldstein(1997). The 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. difference in premiums has a positive sign as in their model but has a much weaker effect on switching plans. This is mainly because we do not observe much switch ing behavior in our data, with no structural change occurring, while those authors used data where a systematic change occurred. Their data is between 1993 to 1994 on the University of California’s (UC) nine campuses, three laboratories and one stand alone law school, while the contribution policy of UC to each health plan was changed from 1993 to 1994. Until 1993, UC contributed equally to the cost of the four largest mem bership plans, and the high option indemnity plan was included among the four plans so the contribution to each plan exceeded the premium required for all HMO plans. However, UC changed its contribution policy limiting the contribution amount to the least expensive plan available in all locations. Therefore, more than half the people who were in the expensive FFS plan holders and about 30% of expensive HMO plan holders switched into other plans5 7 while only 5% and 6% of each cheaper HMO and FFS plan holders (who are not affected by this systematic change) switched. In our data, there was a minor plan characteristic change; only small increase in PPO pre miums and deductibles. Hence we have only 3.3% of people switching and 2.4% of people switching their type of plan. The effect of the difference of coverage variable (ACoverage) is very critical. It shows an employee is more likely to switch to a differ ent type of plan when she or he reduces the number of dependent covered. The role of 57 The switch, they are considering is a switch o f plan not a switch of type of plan. 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the dummy variable of HMO plan (D/^a/o) is to capture the difference in switching be havior between HMO plan holders and PPO plan holders. We observe from Table 2 of the previous chapter that the switch from HMO plans to PPO plans (left lower triangu lar components) is almost twice the switch from PPO plan to HMO plans (right upper triangular components). Again this supports our notion of asymmetry between HMO plan choosers and PPO plan choosers. PPO plan holders are not much affected by their increased premium. Or simply their willingness to pay is still higher than the cur rent price difference. The effects from working status and age are significantly small, 0.0082 and -0.0094, respectively. Also experience at USC has a small negative effect on the probability of switching; thus, it is sensible that people who have stayed at USC longer have a higher chance of finding the type of plan they prefer. All three cross- section models have very low pseudo R 2 values58 suggesting that these cross-section probit models are not adequate for our data. 58 Pseudo R 2 —\ - ( L i / L 0) where L\ is the full m odel likelihood and LQ is the likelihood o f the m odel w ith a constant only. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1. Estimation Result o f Probit Switch models5 9 Dependent VariabIe:D5 u^tc/l = 1 for switching between HMO and PPO. N = 6644. Switch Models Variable MODEL 1 Estimate p-value MODEL 2 Estimate p-value MODEL 3 Estimate p-value Constant -2.5736 (-5.370) 0.001 -2.4939 (-5.290) 0.001 -2.5220 (-5.363) 0.001 APremium 0.0321 (8.658) 0.001 0.0318 (8.704) 0.001 0.0312 (8.568) 0.001 A Premium^ 0 . 0 0 0 1 (8.446) 0.001 0 . 0 0 0 1 (8.874) 0.001 0 . 0 0 0 1 (8.699) 0.001 ACoverage -0.8741 (-6.222) 0.001 -0.8657 (-6.208) 0.001 -0.8324 (-6.034) 0.001 D //A f096 0.2646 (3.372) 0.001 0.2555 (3.454) 0.001 0.2701 (3.803) 0.001 Working % 0.0081 (1.799) 0.072 0.0080 (1.794) 0.073 0.0082 (1.843) 0.065 AGE -0.0075 (-1.797) 0.072 -0.0080 (-1.951) 0.051 -0.0094 (-2.326) 0.020 EX -0.0156 (-1.104) 0.270 -0.0133 (-2.173) 0.030 -0.0135 (-2.195) 0.028 DFAC U LT Y -0.1380 (-1.464) 0.143 -0.1092 (-1.209) 0.227 D F A M I L Y -0.1457 (-1.393; 0.164 -0.1008 (-1.347) 0.178 D PLUS -0.0434 (-0.441) 0.659 PREM 0.0007 (0.499) 0.618 DUnivHosp 0.0197 (0.155) 0.877 D M A L E 0.0798 (1.099) 0.272 D M O V E 0.0939 (0.971) 0.332 * 1 EX 0 . 0 0 0 1 (0.193) 0.847 Log Likelihood -692.19906 -693.47533 -695.33565 LR test 138.91 > x U 136.36 > x t 132.64 > X t Pseudo R2 0.0912 0.0895 0.0871 59 All the estimates are rounded up at 1/10000 and t-values are in parentheses. Minimum precision of p-value is at 1/1000. 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.4 Panel Probit Model Estimation Results The next model we are considering is the random effect panel data probit model in (4). If we had more than T > 3, then it would be worth considering a model with serial correlation in the error term and estimate it by a simulated maximum likeli hood method. Keane(1993) pointed out that it helps for prediction if we consider a more general model of serial correlation than the equicorrelation model. Also it would be better in a modeling sense, since the consumer's choice reveals the state depen dence in many cases.60 We estimate (4) with the x vector composed of RPrem, Dp lu s, ^FAMt EX and AGE6 1 . RPrem is the key variable in explaining health plan choice. It is defined as RPremppo = P R E M ppo — min{PREM/7 A rc > for given coverage cat egory} for PPO plan holders and RPrempjuo = PREM//a/o — min{PREMppo f°r given coverage category} for HMO plan holders. This variable represents the mone tary gain for an employee to select PPO type plan. For PPO plan holders, this relative premium is the amount that they are willing to give up from their budget to stay in their PPO plans, while it is the negative amount HMO plan holders saved in premi ums. Hence, this variable is expected to have a negative relationship with the choice of HMO type regardless of the plan choice. This is one reason why this variable is not endogenous.62 Also it is a parallel to the switching cost of Buchmueller and Feld- 60 This can be also modeled with a lagged dependent variable. 61 We considered also DunivHOSP, PREM, AGE2 and EX2 but they are all insignificant. 62 The strict exogeneity of RPrem variable could be examined by the Granger causality test (D p A /o => RPrem) if we have enough T periods. Still non causality result of the dependent variable to 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. stein(1997). One difference from their definition is that this variable has been defined asymmetrically, since PPO plan holders care more about the quality of service, given that other things are equal. Hence, this RPrem variable can be viewed as a revealed amount of an employee’s monetary benefit by choosing her plan type. In the view of microeconomics, this variable is designed to capture an income effect. If we consider (4) as a demand function, RPrem variable can be viewed as a relative price. Accord ing to Feldman et al. (1989), the disadvantage of using data from one company is the correlation between plan characteristics such as deductible, copayment structure and premiums. A company normally offers a menu of coverages which comes with a spe cific premium amount, deductible amount, copayment structure and so on. Thus, there is a lack of variability in distinguishing the effect from deductible change from the ef fect of premium increase, since they are generally correlated. We chose premiums as a representative plan characteristic but PPO premiums and HMO premiums are also highly correlated with each other for each given coverage category (Single, Plus One, and Family). Therefore, we had to combine two premiums; also this combination al lows economic interpretations as opportunity cost and willingness to pay. We tried three different type of quadrature approximation points; K = 12, 26, 30 (see equation (5) ) 63 are used to estimate the panel data probit model. The estimation RPrem variable does not guarantee the strict exogeneity o f RPrem variable, instead it would refute the strict exogeneity if the dependent variable causes RPrem in Granger sense. For more detail, see Geweke(1982). 63 Actually, we tried all possible quadrature points from 8 to 30 (STATA 6.0 does not support higher points) and the effect o f increasing approximation points is monotonic. Also the results with less than 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. results are in Table 2. All three configurations show that there is a significant random effect coefficient existing in the model. This is not surprising since we have only a small number o f variables available for this panel data model. The estimates are quite different from 12-point approximation to 30-point approximation, thus we believe it is caused by the approximation error. So we used a 30-point approximation as the model for prediction. The effect of relative premium is negative, as expected, and the square term is positive but significantly small. The experience term shows a small preference for HMO plans among employees with longer experience at USC. The effect of AGE is negative, i.e. aged employees prefer PPO type plans. The effect of number of covered persons clearly indicates a preference for HMO plans. To summarize, young employees with a large number of dependents prefer HMO type plans. This is also found in Ellis(1985) and other literature. For the random effect, we can test it by LM test on the significance of p, which is an autocorrelation of the error term in (4). The difference between a random effect panel data probit model like (4) and a usual probit model on the pooled data can be characterized as a correlation structure of error term: the former has equicorrelation while the latter has no intertemporal correlation. This is the intuition behind the LM test on p. If p is significantly different from zero, this supports the existence of random effect. We found that all three approximations indicate the existence of random effect. 20 points are confirmed by a program based on GAUSS 3.2 using Table 25.10 in Abramowitz and Stegun (1972). 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2. Estim ation R esult o f R andom E ffect Panel Probit M o d el (G au ssian Quadrature A p proxim ation)6 4 Dependent Variable:D/f a / q = 1 for choosing HMO type plan and PffAfO = 0 f o r PPO type. Panel Models MODEL 4 (quadrature approximation with 12 points) MODEL 5 (quadrature approximation with 26 points) MODEL 6 (quadrature approximation with 30 points) Variable Estimate p-value Estimate p-value Estimate p-value Constant 0.3496 (2.954) 0.003 0.5061 (2.965) 0.003 0.5346 (2.940) 0.003 RPrem -0.1470 (-43.387) 0.001 -0.1934 (-25.729) 0.001 -0.2039 (-23.447) 0.001 R P rem 2 0.0003 (41.656) 0.001 0.0004 (24.897) 0.001 0.0004 (22.794) 0.001 EX 0.0297 (6.172) 0.001 0.0410 (5.864) 0.001 0.0432 (5.799) 0.001 D PLUS 0.2974 (3.291) 0.001 0.3504 (2.836) 0.005 0.3670 (2.795) 0.005 Df a m i l y 1.8118 (14.743) 0.001 2.2583 (12.931) 0.001 2.3525 (12.464) 0.001 AGE - 0 . 0 1 2 0 (-3.535) 0.001 -0.0174 (-3.553) 0.001 -0.0184 (-3.515) 0.001 p (random effect) 0.2641 [0.0369| LR-test 0.6157 [0.0369] LR-test 0.6552 [0.03484] LR-test N = 6644 Log Likelihood -1 191.2616 -1164.2466 -1161.2354 Wald test 1963.54 > x i 682.95 > X6 563.37 > *6 LR test: p = 0 1266.76 > X i 1212.73 > Xi 1206.70 > X \ Guilkey and Murphy(1993) reported that a pooled probit model with corrected asymptotic errors performed quite well for many parametric configurations in their Monte Carlo simulation. We did a model selection search for probit models with pooled data using robust standard errors. The resulting model has very similar esti mates as the panel probit model with 1 2 -point quadrature approximation; therefore we did not report this result. 64 t-values are in parentheses and standard error is in brackets for p. Minimum precision o f p-values is at 1/ 1000. 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T able 3. Prediction S u ccess Table (Based on Switch Model: Model 3 from Table 1) Predicted Choice observed count Observed Choice No Switch Switch No Switch 6480 2 6482 Switch 162 0 162 Predicted Count 6642 2 6644 T able 4. Prediction S u ccess Table (Based on Panel Data Model: Model 6 from Table 2) Predicted Choice observed count Observed Choice PPO HMO PPO 6682 0 6682 HMO 1 2 “ 6594 6606 Predicted Count 6694 6594 13288 a.All twelve wrong predictions are from year 1996 sample. No wrong prediction at all for 1997 sample. Now we can compare switch probit model and panel data probit model. Table 3 and Table 4 show the prediction success tables of two models (MODEL 3 vs. MODEL 6 ). We can see that the panel data probit model predicts almost perfectly whether the choice of health plan type is PPO or HMO. Table 5 shows the effect of a premium in crease on the switching probability. Switching probabilities in the panel data model are calculated as the probability of choosing the other plan type given the choice of plan type in 1996. One important remark is that these probabilities are evaluated at the mean of the random effect coefficient which is zero. This might be a weakness in us ing a random effect specification; however, a fixed effect probit model does not give Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. consistent estimators. 65 The probabilities of the switch probit model are calculated as in Buchmueller and Feldstein(1997). For each given change of premium we averaged the choice probabilities for three different categories: All plans, PPO plan holders only and HMO plan holders only. These results are in the first three columns o f Table 5. We can see that the predicted probabilities of switching plan types are very small. Even with $360 annual premium increase ($30 monthly increase), only 13.3% of HMO plan holders and 8.3% of PPO plan holders changed their plan type. Also a continuous pre mium change simulation is depicted in Figure 1. We can see slowly increasing curves of probability to switch. This price inelastic behavior of health plan choice is very dif ferent from previous studies. Buchmueller and Feldstein(1997) predicted 26.4% will change for just a $10 increase in monthly premium. If we consider the panel data pro bit model, we obtain a price elastic behavior of health plan switch. Figure 2 shows a dramatic difference from the cross-section probit model. The probability to switch is almost 64.3% of HMO plan holders for $360 annual premium increase, given that other things are equal (no chronic disease persistency or adverse retention of Altman et al.{ 1998)). The interpretation for PPO plan holder needs more attention; if we re duce every PPO plan holders’ willingness to pay by $30 per month, then almost 96% of them will switch. In other words, 96% of PPO plan holders’ willingness to pay amount ranges from $0 to $30. 65 To get a consistent estim ator for fixed effect m odel, w e m ay consider Cham berlain’s C M L E on logit m odel. 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 5. Simulated6 6 Probabilities6 7 (By using the estimates of Switch Model 3 from Table 3 (columns (1) - (3)) and the estimates of Panel Probit Model 6 from Table 4) Plans Increase of Premium ( 1) (2 ) (3) (4) (5) (6 ) All APrem = 0 1.9% 1 .2 % 2.5% 1.9% 1.7% 2 .0 % All APrem = $ 10/Month 3.8% 2 .6 % 4.9% 1.9% 1.7% 2 .0 % All APrem = $20/Month 6.7% 4.9% 8.5% 1.9% 1.7% 2 .0 % All APrem = $3 0/Month 1 0 .8 % 8.3% 13.4% 1.9% 1.7% 2 .0 % PPO APrem = $ 10/Month 2 .6 % 2 .6 % 2.5% 13.0% 25.8% 0 . 1% PPO APrem = $20/Month 3.7% 4.9% 2.5% 36.9% 73.4% 0 . 1% PPO APrem = $3 0/Month 5.4% 8.3% 2.5% 48.1% 95.8% 0 .1% HMO APrem = $ 10/Month 3.1% 1 .2 % 4.9% 1 1 .2 % 0.5% 2 2 .0 % HMO APrem = $20/Month 4.9% 1 .2 % 8.5% 25.3% 0.5% 50.2% HMO APrem = $3 0/Month 7.3% 1 .2 % 13.4% 32.3% 0.5% 64.3% (1) Probability o f Switch (all plans average) (2) Probability o f Switch (PPO plans average) (3) Probability of Switch (HMO plans average) (4) Probability o f Switch (sum o f probabilities to choose the other plan, all plan average) (5) Probability of Switch (sum of probabilities to choose the other plan. PPO plans average) (6) Probability o f Switch (sum o f probabilities to choose the other plan. HMO plans average) 66 Since the effect o f a relative premium increase in PPO plans is not the sam e as in HMO plans, w e sim ulate the probabilities by decreasing the w illingness to pay to stay in the PPO plan. 67 Probabilities are calculated on ly for people who did not change the coverage category' nor belonged to the disappeared Cygna plans. This restriction is needed to see the pure effect o f premium and it slightly reduces the probability o f sw itch less than 0.1% (So w e consider sam ple o f 6 ,2 4 8 people here). 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Figure 1.Predicted probability of switching health plan type (Based on Switch Probit Model 3) T o C N J All plan holders average PPO plan holders average HMO plan holders average o s i u 5 o J2 O JO o CL C N ° 0 12 8 16 4 20 24 28 32 Increase of prem ium Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission Figure 2.Predicted probability of switching health plan type (Based on Panel Probit Model 6) o C O All plan holders average — — PPO plan holders average HMO plan holders average _ c o o > N o o -1 0 0 -20 - 3 0 20 10 30 D e crea se of willingness to sta y in PPO In crea se of HMO premium 3.5 Concluding Remark In this chapter, we introduced two new concepts to analyze a relatively simple choice problem between HMO and PPO. The first one is the relative premium and how it helps to show a price sensitive behavior of consumer health plan choice. This is consistent with the general perception of HMO plans and PPO plans. HMO plan holders care more about medical costs while PPO plan holders care more about the quality of service. Our situation is that PPO plans are offered by an Academic Health Center, which is generally believed to offer a better quality service in terms of tech nology. Therefore this strengthens our model of quality versus cost containment com parison. This chapter also introduces a new concept of relative premium which makes a dramatic difference in simulated probability of switching. Another difference in our model is the panel data setup, which helps to obtain better prediction of the model. These two new tools have not been used in health economics literature so far. Our methodology has its strength in its applicability. It is still applicable for the data without a large systematic change. Even with this kind of data, we can trace a reasonable level of willingness to pay. We recommend that other researchers apply our new methodology to various health plan choice data. 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Further reproduction prohibited without permission. Chamberlain, G. (1984). Panel data. In Z. Griliches & M. Intriligator (Eds.), Handbook o f econometrics. (Vol. 2, pp. 1247-1318). Amsterdam, The Netherlands: North Holland. Chemew, M. (1998). Health plan report cards and insurance choice. Unpublished manuscript, University of Michigan. Chemew, M., Frick, K. & McLaughlin, C. G. (1997). Worker demand for health insurance in the non-group market: a note on the calculation of welfare loss. Journal o f Health Economics, 16, 375-380. Chiappori, P. A., Durand, F. & Geoffard, P. Y. (1997). Moral hazard and the demand for physician services: first lessons from a French natural experiment. Unpublished manuscript, University of Chicago. Chiappori, P. A., Salanie, B. (1997). Testing for asymmetric information in insurance markets. Unpublished manuscript, University of Chicago. Clark, D. & Olsen, J. A. (1994). Agency in health care with an endogenous budget constraint. 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Health Care Financing Review, 77(3), 171-189. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Geweke, J. (1982). Causality, exogeneity and inference. In W. Hildenbrand (Ed.), Advances in econometrics (pp. 209-235). New York: Cambridge University Press. Gibbs, D. A., Sangl, J. A. & Burrus, B. (1996). Consumer perspectives on information needs for health plan choice. Health Care Financing Review, 18(1), 55-73. Goldman, D. P., Hosek, S. D., Dixon, L. S. & Sloss, E. M. (1995). The effects of benefit design and managed care on health care costs. Journal o f Health Economics, 14, 401-418. Gourieroux, C. & Monfort, A. (1993). Simulation-based inference. Journal o f Econometrics, 59, 5 -33. Guilkey, D. K. & Murphy, J. L. (1993). Estimation and testing in the random effects probit model. Journal o f Econometrics, 59, 301-317. Hajivassiliou, V. A. & Ruud, P. A. (1994). Classical estimation methods for LDV models using simulation. In R. F. Engle & D. L. McFadden (Eds.), Handbook o f econometrics (Vol. 4, pp. 2383-2441). Amsterdam, The Netherlands: North Holland. Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46, 1251-1271. Henriet, D. & Rochet, J. C. (1998). The political economy of public health insurance. Unpublished manuscript, GREMAQ, Universite de Toulouse. Hill, S. C. & Wolfe, B. L. (1997). Testing the HMO competitive strategy: an analysis of its impact on medical care resources. Journal o f Health Economics, 16, 261-286. Hsiao, C. (1986). Analysis o f panel data (1st ed.). New York: Cambridge University Press. Hurd, M. D. & McGarry, K. (1997). Medical insurance and the use of health care services by the elderly. Journal o f Health Economics, 16, 129-154. Hyslop, D. (1999). State dependence, serial correlation and heterogeneity in intertemporal labor force participation of married women. Econometrica, 67, 1255-1294. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Keane, M. P. (1993). Simulation estimation for panel data models with limited dependent variables. In G. S. Maddala, C. R. Rao & H. D. Vinod (Eds.), Handbook o f statistics (Vol. 11, pp. 545-571). Amsterdam, The Netherlands: Elsevier Science Publishers B.V. Kominski, G. F. & Long, S. H. (1997). Medicare's disproportionate share adjustment and the cost of low-income patients. Journal o f Health Economics, 16, 177-190. Leigh, J. P. & Ward, M. M. (1997). Medical costs in workers' compensation insurance [Comment]. Journal o f Health Economics, 16, 619-622. Long, S. H., Marquis, M. S. & Rodgers, J. (1998). Do people shift their use of health services over time to take advantage of insurance? Journal o f Health Economics, 17, 105-115. Luft, H. S. (1995). HMO’s, market competition. & premium cost [Editorial]. Journal o f Health Economics, 14, 115-119. Manning, W.G. & Marquis, M. S. (1996). Health insurance: the tradeoff between risk pooling and moral hazard. Journal o f Health Economics, 15, 609 - 639. McFadden, D. (1974). The measurement of urban travel demand. Journal o f Public Economics, 3, 303-328. Miller, R. H. & Luft, H. S. (1997). Does managed care lead to better or worse quality of care? Health Affairs, 16(5), 7-25. Neudeck, W. & Podczeck, K. ( 1996). Adverse selection and regulation in health insurance markets. Journal o f Health Economics, 15, 387-408. Pauly, M. V. (1990). The rational nonpurchase of long-term-care insurance. Journal o f Political Economy, 98, 153-168. Reuter, J. & Gaskin, D. (1997). Academic health centers in competitive market. Health Affairs, 16, 242-252. Sainfort, F. & Booske, B. C. (1996). Role of information in consumer selection of health plans. Health Care Financing Review, 18(\), 31 -54. Schauffler, H. H., Howland, J. & Cobb, J. (1992). Using chronic disease risk factors to adjust Medicare capitation payments. Health Care Financing Review, 14(\), 79-90. 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Solit, R. L. & Nash, D. B. (1997). Academic health centers and managed care. In P. R. Kongstvedt (Ed.), Essentials o f managed health care (2nd ed., pp. 178-196). Gaithersburg, MD: Aspen Publishers, Inc. Van de Ven, W. P. & van Vliet, R. C. J. A. (1995). Consumer information surplus and adverse selection in competitive health insurance markets: an empirical study. Journal o f Health Economics, 14, 149-169. Wholey, D. R., Christianson, J. B., Engberg, J. & Bryce. C. (1997). HMO market structure and performance: 1985 - 1995. Health Affairs. 16(6), 75-84. Wholey, D., Feldstein, R. & Christianson, J. B. (1995). The effect of market structure on HMO premiums. Journal o f Health Economics. 14, 81-105. Wolfe, J. R. & Goddeeris, J. H. (1991). Adverse selection, moral hazard and wealth effects in the Medigap insurance market. Journal o f Health Economics, 10, 433-459. Woodbury, S. A. (1983). Substitution between wage and nonwage benefits. American Economic Review, 73, 166-182. Wrightson, Jr., C. W. ( 1990). HMO - Rate setting andfinancial strategy. Ann Arbor, MI: Health Administration Press Perspectives. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 Medical Expenditure and Sample Selection 4.1 Introduction How much money would be incurred for an individual’s annual medical expen diture or a group’s annual medical expenditure? This is an interesting question for many health care related decision makers. For example, actuaries in the Health Care Financing Administration (HCFA) would love to know how much medical costs will be charged for a senior citizen with specific demographics. Also university benefit office staffs would be interested in the projected medical expenditure of an average university employee. This necessity for an actuarial model was the reason why the Adjusted Average Per Capita Cost (AAPCC) formula68 was created and many insur ance companies or company benefit office staffs are seeking for the better model to use for making premium and deductible design. In the traditional statistics frame work, this question could be answered by a simple regression analysis. This may be true when all the information is available; however, it becomes a complex selection bias problem when you can only observe the medical expenditures of one specific type of plan and have no idea about the other types of plans. This selection bias 68 See Chapter 1. 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. problem is not confined to health economics or to any insurance company’s problem. Any field of science using collected or observed data has the potential problem that data collections or data observations might have been selected by a certain nonran dom decision process. If this is the case, then the data set is subject to selection bias. Therefore, we need to adjust any estimation result using this kind of selected data set by the probability of selecting it. Heckman(1976) is the most well known procedure to correct this selection bias problem in a cross-sectional data. In the field of health economics, the Medicare capitation formula is an exten sively researched application of medical expenditure forecasting and selection bias. Medicare provides health insurance to the people who are 65 and older, those who have permanent kidney failure, and certain people with disabilities. There were two differ ent types of health service approaches available to Medicare beneficiaries: HMO69 and Fee For Service (FFS). The HCFA reimbursed FFS directly so they could observe the medical bill of a beneficiary while HMO’s had two options: to ask for direct re imbursement or to sign for a risk contract. For the latter, a fixed fee schedule was calculated by a capitation formula called Adjusted Average Per Capita Cost (AAPCC) at HCFA every year. This traditional Medicare structure has been changed by the Bal anced Budget Act (BBA) of 1997. This legislation introduced a new entity called Medicare+Choice plans, which extended the available choice of health care organiza 69 This plan should be a federally qualified Health Maintenance Organization (HMO) or Competitive Medical Plan (CMP: defined in Tax Equity and Fiscal Responsibility Act (TEFRA)). 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. tion types to the various health care organizations including PPO, Provider Sponsored Organization (PSO), Religious fraternal benefit society plan, and so on. This 1997 legislation also introduced a new Medicare capitation formula called PIP-DCG.70 Medicare is the nation’s largest health insurance program, which covers approx imately 39 million Americans according to the HCFA. According to McClellan(2000), Medicare spending in 1999 was $213 billion, which is 12 percent of the federal bud get and 2.3 percent of Gross Domestic Product (GDP). This is the strong motivation for the fact that there have been much attention on AAPCC and extensive research on the medical expenditure forecasting using the Medicare database. AAPCC was cal culated as follows: for each county, 142 different cells were determined by 6 criteria: age, sex, Medicaid eligibility, institutional status, working aged status, and whether a person has both parts of Medicare (part A covers mostly inpatient services and part B covers all other services such as physician and outpatient services). The HCFA de termined an appropriate payment schedule for each cell, as the 95% of an actuarially estimated medical expense which would have been incurred for an average Medicare beneficiary in the corresponding cell of the observable data. This observable data was from the direct reimbursement system. Finally, the HCFA adjusted county specific fac tor by multiplying a constant for each county. 71 This simplicity of AAPCC, which is 70 This legislation introduces the PIP-DCG model from the year 2000, but it will be blended with the existing AAPCC for the time being (until 2003). The 100 percent PIP-DCG model capitation is scheduled from 2004. 71 These cell values and each county specific factors are annually updated and available at the HCFA website (http://www.hcfa.gov). 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. basically a deficiency o f the health status of enrollees, was a main target of its critiques for selection bias. Many previous studies showed there was a favorable selection of healthier enrollees into HMO type plans. Using Medicare Current Beneficiary Sur vey (MCBS) data, Riley et al.(1996) showed that HMO enrollees were less likely to report poor health status than FFS enrollees. Hellinger(1995) has a nice summary of this problem. In contrast, Dowd et al. (1996) found adverse selection for the choice of Medicare HMO’s. They used an endogenous sample selection model, which is simi lar to our methodology but it is a cross-sectional model. Their finding was supported by the fact that some HMO’s in the analysis converted their risk contracts with the HCFA to non-risk contracts in the following period. If this finding was valid, HMO’s should have been paid more than AAPCC calculations (i.e. some percentage greater than 100% not 95%). Also this suggests that there exists a regional difference in the pool of Medicare HMO beneficiaries. Ash(I986), Ellis and Ash(1995) and Ellis et al.( 1996) showed the diagnosis based capitation method can excel the AAPCC in the explanatory power. The Di agnostic Cost Group (DCG) methodology was originally developed by Ash(1986) and further refined by Ellis and Ash(1995) and Ellis et al.( 1996) under the support of the HCFA. This method utilizes each Medicare enrollee’s diagnosis code (ICD9) of the previous year to group them into several risk categories and estimate their expendi tures using the ordinary least square method. This type of method is preferred by 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. physicians and epidemiologists because they believe diagnosis related research is the only solution to control for the difference of health status among the Medicare HMO beneficiaries. On the other hand, this method brought a debate on the violation of pri vacy issue. The idea of using an individual’s medical record was not welcomed by the public, since many people believed that these data are vulnerable to usage against their interests. After a public debate, the Balanced Budget Act (BBA) was finally initiated in 1997. The final version included a new method of calculating Medicare capitation called the PIP-DCG (Principal In-Patient Diagnostic Cost Group) model and the ex tension of available choice of health care organization types. The PIP-DCG model is a restricted version of the DCG model since this model only utilizes more than one day inpatient diagnosis records, to determine a cost group for each enrollee. However, a report72 to congress said, the PIP-DCG model explained about 6 percent of individ ual variation in health spending while AAPCC explained about 1 percent variation. These numbers reflect the difficulty of forecasting medical expenditures. Basically the observable variables are so limited that forecasting power on the individual level is very low. This problem can be viewed as an appeal for a panel data analysis. At least theoretically, panel data analysis can control for unobserved heterogeneity. Also an average level of medical expenditure is the one we need to know about, not an in 72 Report to Congress: Proposed Method o f Incorporating Health Status Risk Adjusters into Medicare+Choice Payments, HCFA (Health Care Financing Administration), Office o f Strategic Planning, Research and Evaluation Group, Division o f Payment Research, Mar. 1, 1999. 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dividual level.73 This necessity fits well to the random effect panel data models. As explained earlier, the HCFA used FFS reimbursement data to determine HMO reim bursement schedule74 since they cannot observe the actual medical expenditures in curred for Medicare HMO enrollees. This observability issue, the selection bias, is still remaining under the PIP-DCG model, but the ambiguity is whether this selection bias can be corrected by a grouping of people based on their one year history of diag nosis. The selection bias which comes from the difference in health status that might be mitigated by the correct grouping, but it might be still present if the bias resulted from the other factors such as the HMO’s organizational efficiency. Except for the fact that Medicare is for the sake of high risk people7 5 , this observ ability structure of the expenditure data is similar to our data set. 76 This is an rationale to apply AAPCC or the PIP-DCG model in estimating medical expenditures in our em ployee data set. We will extend this to a panel data selection model and show a result of the better explanatory power. This improvement in the explanatory power can also be found in other literature; Lamers( 1999) showed that the inclusion of previous his tory of DCG (not just one previous year) helps to improve explanatory power in Dutch sickness fund data. Even though Lamers did not use panel data modeling, it is clear 73 This was the main issue, which many people concerned as a serious violation o f privacy. 74 Under the assumption that HMO plans would have lower medical expenditure at only 95 percent of FFS plans. 75 The senior citizens, the disabled people, and the severe renal disease patients are considered as high risk group for the health care organizations. 76 We have a claim data for the PPO plan holders only. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. that the longer history would help to estimate the future medical costs. The health care expenditure estimation using panel data modeling is very rare; however, Baker(1997) used a fixed effect model to examine the effect of the HMO market share on the fee for service health care expenditures in a Medicare data. This chapter is organized as follows: section 2 will introduce Kyriazidou(1997) panel data selection model in medical expenditure setup; section 3 has a discussion about the claim data set we used; the various estimation results of medical expenditures are presented in section 4; and section 5 will conclude with some remarks. We used Kyriazidou( 1997) panel data selection model in our medical expendi ture estimation as follows, 77 4.2 Model log Eit = ditE*t d it(w * n + < 5 * + Ch) Wit! + 6i + €u, i = l —N , t = 1 , 2 (8) dit = I{ x it& + t t i - v it > 0 } (9) 77 It can be generalized to t > 2. 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Eit is the medical expenditure of individual i at time t. dit is the health plan type choice variable (=1-D//a,/o). E*t * s a latent variable only observed for dit = 1. * > it and xit are vectors o f explanatory variables, which may have common variables. 8* and U i are unobserved heterogeneity coefficients but we assume < 5 * to be a fixed effect coefficient while we keep ux as a random effect coefficient the same as in the previous chapter. 78 The logic behind this is simple; we considered the interchangeable individual specific effect in the choice of health plan type previously; however, a med ical expenditure variable is well known for its high skewness79 so it is unreasonable to assume a symmetric distribution for the individual specific effect. Another possible consideration is the case in which both 8* and ux are random effect coefficients, and also (£*t, v it) is from a bivariate normal distribution. For this case, Hsiao(1999) and Verbeek and Nijman(1992) showed that the sensitivity of parameter estimates from the misspecification is much higher than the fixed effect model. We can rewrite (8 ) as log E it = w u l + t> i + A u + u it ( 1 0 ) where ujit = £it — A u and it satisfies E (u > u \dn = I, di2 — 1, x n , x i2. , w * 2, Ui, 6*) = 0. If this was a cross-section version, Heckman(1976) can be applied and we substitute 78 This is different from Kyriazidou(1997). Her original model assumes fixed effect for both individual specific coefficients. Consequently, her conditional exchangeability condition should be modified as the distribution o f (£Ji,£i2 ,f*i| «»i,vt- 2 | wt2) is identical for same vector of (xn,Xi2,u!'l ,w^2,Ui,5“). 79 This is why we are taking logarithm. 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A by the inverse Mill’s ratio. To estimate 7 consistently, Kyriazidou(1997) proposed following two step estimation; Step 1. a consistent estimator of /3 is obtained from (9) In step 2, ^ is a trimming dummy defined as(pi = dzidl2 so 0f = 1 for individual i chooses PPO type plans for both years. xpiN is a weight estimated nonparametrically where K is a univariate kernel density function and hN is a bandwidth parameter which satisfies liminfw _ 00 fijv = 0. The intuition of this estimator is “differencing out nuisance parameter nonparametrically” according to Kyriazidou. This two step procedure can be easily done; we already have a candidate for /3 from the Model 6 softwares. Specifically, the second step can be done by a weighted least square re gression with weights being equal to iN and using only the people who enrolled in PPO plans for both years8 0 . An important remark is that we have to use the White het- eroskedasticity consistent standard errors in this step. Another remark from nonpara- metrics is that the choice of kernel type is less important than the choice of bandwidth 80 From Table 2 (upper left com er) in Chapter 2, there are 3260 em ployees stayed in PPO plan for 2 years. Step 2. 7 = ipiff Aw'Aw ^ ] M Z rli Aw'A log E ^ ] as it declines to zero as the difference A increases. More specifically, ( 11) in the previous chapter, and the kernel density can be calculated by many statistical 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. parameter for the estimation result sensitivity. Hence, the choice of derives the re sult. For example, if we set hN as infinity, then it is the same as running the regression on observed data only, which is believed to be subject to selection bias when the selec tion process is nonrandom. One disadvantage of using this kernel density estimation is that the desired 7 is asymptotically biased. To deal with this bias, Kyriazidou suggests a “plug-in” method similar to Bierens(1987).S I N - ( 1- i ) ( r + 1) / ( 2 ( r + l ) + l ) ^ 7 = 1 _ jV - ( l - * ) ( r + I ) / ( 2 ( r + l ) + l ) ( 1 2 ) where 7 is from the step 2 with hN = h N ~ i/(2(r+i)+i)^ ^ js ^ g estimator with window width = h N ~6/(2(r+1)+1) instead of hN, 8 € (0 , l ) . 82 One of the big advantage of this model is that it does not require a parametric specification of selection process (9); instead it only requires a consistent estimator for the selection process. This consistent estimator can be obtained by other methods such as the nonparametric methods of Manski(1987) or Horowitz(1992). Even though the Kyriazidou two step estimator is arbitrarily close to but slower than \Z~N ~rate, the orig inal version of Horowitz(1992) achieved N ~ 2/10 rate. Chen et al. (1998) is also in this line of study. They used a semiparametric method to achieve \fN consistency. Other noted literatures on this topic are: Verbeek and Nijman(1992) developed a Hausman 81 T he problem with this method is that the ch oice o f initial h changes the results. We follow K yriazidou(1997) and use h = 1 for the initial value. 82 In our estim ation, w e used the density o f standard normal distribution as a (a second order bias-reducing) kernel K (•), h = 1, 8 = 0.1 as in her original paper. 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. type test using a variable addition scheme which does not involve much computational burden than LM test; Nijman and Verbeek(1992) used a Hausman type test for the selectivity of attrition bias by comparing a balanced panel and an unbalanced panel; Zabel(1992) modified the idea of Verbeek(1990) to deal with the inconsistency re sulting from the correlation between random effect coefficient and the regressors; and WooIdridge( 1995) suggested a testing and a correcting method for the sample selection bias in a fixed effect panel data model with serial correlation. 4.3 Data We used the same data as the previous chapter, however, more interests are on the claim data in this chapter. We aggregated this claim data by year to pull out the annual charges for each individual and we got total annual charges (TOTAL), annual deductible paid (DEDUCT), annual coinsurance amount (COINS), and annual inpa tient days (InDays), as a result. Further we generated an out of pocket payment vari able (Op) as the addition of deductible and coinsurance. The summary statistics and correlations are in Table 1 and Table2. Our dependent variable in the analysis is the TOTAL variable, which is expected to be intrinsically different from HMO plans to PPO plans.83 83 There are other preferences on the daily charge variable for the analysis. This variable is generally m ore stable than the total charge variable. H owever, w e used the total charge variable, w hich is also used in A A PC C and PIP-DCG , for the com parison purpose. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1. Summary Statistics for Claim Data Variables ’96 Data ’97 Data. Variable Mean S.D. Mean S.D. TOTAL 9347.49 36498.43 9775.64 40916.66 DEDUCT 91.39 102.93 198.83 132.66 COINS 246.28 1065.35 271.39 1159.00 InDays 0.64 4.50 0.65 5.61 Op 337.66 1092.98 470.22 1191.18 Table 2. C orrelations TOTAL (’96) InDays (’96) Op (’96) TOTAL (’97) InDays (’97) Op ( 97) TOTAL (’96) 1.0000 InDays (’96) 0.8115 1.0000 Op (’96) 0.2064 0.1743 1.0000 TOTAL ( ’97) 0.1650 0.1584 0.0684 1.0000 InDays (’97) 0.0947 0.1100 0.0182 0.7183 1.0000 Op (’97) 0.1585 0.1074 0.1921 0.4121 0.6514 1.0000 Also we constructed a Pure Cost Group (PCG) variable, similarly to a Diagnostic Cost Group (DCG) variable using total expenditure of each year .We group each PCG by quartiles of total expenditure as in Table 3. PCG is different from DCG since it does not use any diagnostic information to assign enrollees to each group. DCG was designed by very complex categorization procedure; first, all the ICD9 codes are ranked by their associated expenditure and then a panel of doctors determine each group. If a code is difficult to judge its appropriate rank, it is assigned to the base group zero. So the base group zero contains both lowest expenditure group and undecided ICD9 code group. Newhouse et al.{ 1989) considered the prior year utilizations such as inpatient expense and outpatient expense to improve AAPCC formula and found significant increase in the explanatory power of medical expenditure regression. We Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. used a categorical variable instead of a continuous variable o f prior use and still get a similar result. Table 3. PCG design PCG 1996 1997 0 TOTAL96 < 428.00 TOTAL97 < 640.85 1 428.00 < TOTAL96 < 2010.775 640.85 < TOTAL97 < 2348.92 2 2010.775 < TOTAL96 < 6628.415 2348.92 < TOTAL97 < 7851.875 3 6628.415 < TOTAL96 7851.875 < TOTAL97 From Table 3, we can see the total expenditures increased from year 1996 to year 1997 but it increased monotonically for all four PCG's. To see the relationships between this PCG grouping and other variables, we present the following summary statistics table by PCG groups in both years. Table 4. Sum m ary Statistics B y PC G G roups8 4 ’96 Data '97 Data PCG 0 1 2 3 0 1 2 - > N 814 816 815 815 815 815 815 815 AGE 39.98 (11.05) 43.25 (11.35) 46.21 (10.50) 48.30 (11.06) 41.47 (10.92) 44.78 (10.79) 47.33 (11.23) 48.17 (11.57) D a m l e 0.55 (0.50) 0.49 (0.50) 0.53 (0.50) 0.56 (0.50) 0.54 (0.50) 0.50 (0.50) 0.54 (0.50) 0.54 (0.50) Prem 47.47 (43.53) 54.23 (41.65) 63.96 (51.20) 69.83 (57.21) 50.40 (40.23) 63.55 (50.75) 68.78 (39.11) 73.38 (52.77) EX 8.08 (7.62) 9.78 (8.50) 11.62 (8.63) 13.14 (9.81) 9.49 (7.40) 11.36 (8.69) 12.57 (9.25) 13.20 (9.57) D SIN G L E 0.67 (0.47) 0.45 (0.50) 0.29 (0.46) 0.19 (0.39) 0 . 6 8 (0.46) 0.41 (0.49) 0.26 (0.44) 0 . 2 0 (0.40) D PLUS 0.18 (0.39) 0.28 (0.45) 0.30 (0.46) 0.34 (0.47) 0.19 (0.39) 0.26 (0.44) 0.32 (0.46) 0.36 (0.48) D F A M IL Y 0.15 (0.35) 0.27 (0.44) 0.40 (0.49) 0.47 (0.50) 0.13 (0.33) 0.33 (0.47) 0.43 (0.50) 0.44 (0.50) D UnivHOSP 0.07 (0.26) 0.07 (0.25) 0.04 (0.20) 0.05 (0.22) 0.07 (0.25) 0.05 (0.22) 0.05 (0.22) 0.05 (0.22) RPrem 22.41 (39.92) 23.98 (37.07) 29.52 (47.69) 32.83 (54.52) 25.85 (36.42) 31.99 (46.19) 33.41 (35.40) 36.84 (49.83) 84 Mean is shown in each cell and standard deviation is in the parentheses below. 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. As we can find from Table 4, the higher medical expenditure groups have elder employees, the employees who are more experienced at USC, and the employees with more covered dependents than lower expenditure groups. This distinction is very clear for both years. On the other hand, gender and living near university hospitals do not have much relationship with the medical expenditures. The most important observa tion which we can find in this table, is the premium and the relative premium increase on the higher PCG. The effect of premium increase affects the PCG 1 group the most, not the highest risk group PCG 3. The interesting question for a university benefit of fice is how to reduce the number of high risk employees from the school sponsored plan. This can be answered by highly progressive premium setting on coverage types. After the premium increase in 1997, PCG 3 still has three times FAMILY coverage enrollees and two times PLUS ONE coverage enrollees than the base PCG. So the premium increasing strategy was not progressive enough to kick out more high risk enrollees from the school sponsored plan. Another interesting aspect of the PCG grouping is the following cross table of 1996 PCG groups and 1997 PCG groups. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 5. PCG Changes Correlation = 0.4736 1997 PCG 0 1 2 3 Total 1996 PCG 0 454 184 93 83 814 1 224 288 174 130 816 2 8 6 2 0 0 292 237 815 3 51 143 256 365 815 Total 815 815 815 815 3260 We can see that there is a positive correlation between the 1996 medical ex penditures and the 1997 medical expenditures; 0.4736. The diagonal cells show the people who stayed in the same group and the percentage of this remaining population is roughly 43 %. The percentage of the people with two PCG change (e.g. from PCG 0 to PCG 2) is 6 .8 % for the upward and 7% for the downward. The percentage of three PCG change is 2.5% for the upward and 1.5% for the downward. Hence, these percentages show PCG variable is a quite useful proxy for the medical expenditures. 4.4 Estimation Results Table 6 shows the selected85 regression results of the AAPCC model and the PCG model. AAPCC 1 is the one closest to the original AAPCC definition, 86 since we used employee data, we needed to control for the coverage differences (AAPCC2). 85 We analyzed both 1996 and 1997 data, but explanatory power of 1996 data is slightly higher for AAPCC models and PCG models and they are almost identical, so we report only 1996 results. 86 The original AAPCC includes four more variables and a county adjuster but none of them are applicable to our data since this data has only few overlapping population with the Medicare data except for the county adjuster. Still the county adjuster does not affect much since there are less than four counties around campus. 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Also we included some variables we used in the panel data model for the comparison purpose. For PCG1 regression and PCG2 regression, the former was a current infor mation based model and the latter was a year lagged forecasting model, which was based on 1996 information. As we can see, the explanatory power of PCG based re gressions (0.80 and 0.29) are higher than the AAPCC based regressions (the highest R 2 of AAPCC model is about 0.22). However, it drops dramatically when we try to forecast (PCG2). This is the exact same result we can find in Ellis and Ash(1995). For the individual variables, there were fewer expenses incurred for male enrollees87 and higher expenditure was incurred for elderly enrollees in all five regressions. The em ployees with higher number of covered persons show positive relationship with their expenditure. The higher PCG groups also show stronger positive relationship with the total expenditure. Then we compared above results with our proposed panel data based model esti mation results. In Medicare, the age groups are different between the elderly enrollees and the disabled enrollees since the former start with age greater than 65 while the lat ter do not. Hence, it is difficult to apply an age grouping to the non-Medicare data unless the data has a large enough subsample population with the Medicare eligibil ity.88 Instead, we applied a gender based stratification and compared the explanatory 87 Ellis and Ash(1995) reported elder male group is predicted to have higher medical cost than female group. This conflict with our result seems to be come from the fact that age population is totally difFerent(current employee versus over 65 people). 88 We have only 124 people older than 65 years in 1996 and 156 people in 1997. 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. power of the results. These results are from the second step of the Kyriazidou model after corrcting the bias. For the first step, we used Model 6 (with 30 points quadrature approximation) from the previous chapter for constructing (10) and (11). For the un biased estimator ( 1 2 ), we used the density o f standard normal distribution as a kernel89 with an initial bandwidth hN = N ~ 1 /5 and 8 = 0.1 for correcting the asymptotic bias as in Kyriazidou(1997). Table 6. Estim ation R esu lt for P C G and A A P C C M o d els9 0 AAPCC PCG Model AAPCC 1 AAPCC 2 AAPCC 3 PCG 1 PCG2 Variables lnTOTAL96 lnTOTAL96 lnTOTAL96 lnTOTAL96 lnTOTAL97 Constant 3.9087 (18.311) 2.2924 (10.432) 2.7955 (12.325) 2.2134 (20.189) 3.4478 (18.056) D m a l e -0.4124 (-3.819) -0.7862 (-7.533) -0.8101 (-8.026) -0.1161 (-2.267) -0.4954 (-5.738) AGE 0.0704 (14.930) 0.0611 (13.585) 0.0458 (8.299) 0.0029 (1.277) 0.0186 (4.866) Coverage 1.1581 (18.980) 1.0239 (17.239) 0.0387 (1.220) 0.7244 (13.645) EX 0.0206 (2.920) InDays 0.0005 (10.461) Op 0.1082 (9.870) DpCGl 4.5617 (64.614) 1.7057 (14.336) D pcC 2 5.8069 (79.060) 2.4677 (19.938) DpCG3 7.4765 (98.371) 2.9566 (23.147) & 0.0644 0.1576 0 . 2 2 0 2 0.8008 0.2919 Adj. R? 0.0638 0.1568 0.2188 0.8005 0.2905 F-statistic 112.04 203.01 153.12 2180.06 223.45 89 According to Bierens( 1987), this is a second order bias-reducing kernel. 90 t-values are in parentheses. 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In Table 7, we have a result that all the regressions based on the panel data se lection model show the higher explanatory power than corresponding cross-sectional model results. For example, AAPCC 3 versus Panel 1 and Panel 2 comparison, panel data based model show roughly 15 percent more explanatory power even though less number of explanatory variables are included. This fact can be also found in the com parison between PCG based model results. One noticeable thing in the panel data results is the difference between the male strata and the female strata. While the male employees show the strong negative effect between age increase and medical expen ditures, the female employees show the positive relationship. This strange negative relationship is mitigated when we introduce PCG groups in panel data model. As a re sult whole sample effect become positive between age and the expenditures. Out of pocket cost increases show a significant but very small influence on the total expendi tures. Also the negative relationship between inpatient days and the total expenditures is stronger for males. We also find the same positive relationship of the higher PCGs and the total expenditures. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 7. Panel Selection Model Medical Expenditure Estimation9 1 Data Female Male Whole Female Male Whole Model Panel 1 Panel 2 Panel 3 PPCG 1 PPCG 2 PPCG 3 AAGE* 0.2510 (9.070) -.5525 (-20.958) -0.0455 (-2.350) 0.4421 (20.287) -0.2497 (-9.162) 0.1213 (7.360) AOp* -0.0003 (-6.768) - 0 . 0 0 2 0 (-26.619) -0.0007 (-18.057) 0.0004 (8.768) -0.0014 (-19.105) - 0 . 0 0 0 2 (-4.468) AlnDays* -0.0623 (-2.744) -0.8322 (-18.776) -0.1613 (-7.579) -0.0576 (-3.339) 0.1047 (1.791) ACoverage* -0.6204 (-9.060) 0.5076 (7.737) -0.0925 (-1.644) 0.1204 (2.550) APCG* 0.8762 (33.340) 0.9019 (21.659) 0.8294 (39.252) 0.3730 0.3619 0.2457 0.6382 0.4978 0.4789 Adj FP 0.3714 0.3608 0.2448 0.6370 0.4966 0.4783 F- statistic 225.78 327.97 265.14 535.08 429.62 748.21 N 1522 1738 3260 1522 1738 3260 We also compared PCG model and panel data PCG model by the following suc cess tables. Table 8-1. S u ccess Table for PCG (P C G 2) Correlation = 0.4236 Actual 1997 PCG 0 1 2 3 Total Estimated 1997 PCG 0 467 180 8 8 76 811 1 224 279 179 135 817 2 93 2 1 0 277 246 826 3 31 146 271 358 806 Total 815 815 815 815 3260 91 A InTotal is dependent variable for all six models and t-values are in parentheses. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 8-2. Success Table for PPCG (PPCG3) Correlation = 0.4291 Actual 1997 PCG 0 1 2 3 Total Estimated 1997 PCG 0 454 184 92 85 815 1 2 2 0 286 177 132 815 2 91 195 295 234 815 3 50 150 251 364 815 Total 815 815 815 815 3260 This result shows that the panel data based PCG model has slightly better predic tion success than the cross-section data PCG model. Even though this small difference exists, the panel data based PCG model dominates in predicting the more important high PCG’s. This observation might be a data specific characteristic, but still it is in teresting to apply this model to other data. 4.5 Concluding Remarks The traditional issue of selection bias was discussed in terms of the different risk levels between different types of health care plans. When HMO’s started to become popular, there was a concern that HMO’s were accepting the lower risk group of people and as a result, an employer does not save medical cost.92 This is exactly the same concern for the HCFA; they set 5 percent differential between FFS reimbursement and HMO payment schedule, which can be also interpreted as 5 percent efficiency of HMO’s. Basically this type of selection bias is difficult to test or to estimate because 92 They called this phenomenon as “cream skimming.” 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o f the data availability. Because of this availability of data, what people did was either compare health status between two types of plans as Riley et al.(l996) did or analyze the choice of health plan types as we did in chapter three. Generally, a health related data set has a panel data structure and is composed of a poor set of explanatory variables. Naturally, these facts fit for the motivation of the panel data analysis. The omitted individual specific (time invariant) explanatory vari able can be controlled by either a fixed effect model or a random effect model. After controlling for these effects, the estimated coefficients for the available variables would have better predictive power than the popular cross-sectional approaches in health eco nomics. Also it is the natural way to go in the Medicare capitation research since there will be a new data set o f DCG group history for each individual available from 2000. Therefore, the HCFA should utilize this new available history for the future capitation calculation. Another issue for the current Medicare capitation method of PIP-DCG is the possible violation of privacy. The general American public does not welcome the idea of a federal agency keeping the personal medical information. DCG is based on personal diagnostic information which is very sensitive information in many social as pects. If we can substitute these diagnostic information with less sensitive medical cost information,93 without losing much explanatory power, then it would be a valu- 93 One reason we used a categorical variable of PCG instead of a continuous variable o f past medical expenditure is to minimize private information needed for the capitation. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. able alternative. This is why we introduced Pure Cost Group (PCG) to the medical expenditure estimation. Newhouse et a/.( 1989) already showed the result that the prior medical expenses improve explanatory power in the medical expenditure estimation. It is left to the other researchers to apply the methodology in this dissertation to the actual Medicare database. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References Ash, A. (1986). Analysis of alternative AAPCC models using data from the continuous Medicare history sample [Final report prepared for Health Care Financing Administration]. Health Policy Research Consortium Brandeis/Boston University. Baker, L. C. (1997). The effect o f HMO’s on fee-for-service health care expenditures: evidence from Medicare. Journal o f Health Economics, 16,453-481. Bierens, H. J. (1987). Kernel estimators of regression functions. In T. F. Bewley (Ed.), Advances in Econometrics: Fifth World Congress (Vol. 1). New York: Cambridge University Press. Chamberlain, G. (1984). Panel data. In Z. 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Asset Metadata

Creator Ahn, Jeonghoon (author)

Core Title A study of employee health plan choice and medical cost: Panel data probit regression and sample selection model

School Graduate School

Degree Doctor of Philosophy

Degree Program Economics

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Economics, Commerce-Business,health sciences, health care management,health sciences, public health,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor [illegible] (committee chair), [illegible] (committee member), Steece, Bert (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-116614

Unique identifier UC11334916

Identifier 3041429.pdf (filename),usctheses-c16-116614 (legacy record id)

Legacy Identifier 3041429.pdf

Dmrecord 116614

Document Type Dissertation

Rights Ahn, Jeonghoon

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA