Health Care Reform and Health Insurance Selection in Chile

Transcription

1 Health Care Reform and Health Insurance Selection in Chile Cristian Pardo May 30, 2015 Abstract This paper builds and estimates a structural, dynamic choice model using panel data from Chile in order to examine the impact on health insurance selection of a major component of Chiles health care reform: the GES plan. This plan provides guarantees in coverage and benefits to several conditions in the context of a health insurance system where public and private health insurers co-exist. Differences in the structure of premiums, benefits and out-of-pocket medical costs imply that riskier individuals are more likely to choose public insurance (adverse selection). In addition, pre-existing condition restrictions in the private system imply that insurance selection is a dynamic process in that current insurance choices can affect future health insurance selections. The introduction of the GES plan may also affect health insurance choices due to differences in costs and benefits across insurance systems. Estimation results suggest that individuals affected by pre-existing condition restrictions would be willing to pay in order to gain access to private insurance and the GES plan seems to have significantly reduced out-of-pocket medical costs to people affected by the covered illnesses, even if they were contracted outside the private system. In addition, females, older individuals and the less educated are in fact less likely to choose private insurance. Simulations on the impact of the introduction of the GES plan on health insurance selection suggest an overall participation change towards the public system of about 5 percentage points, and it is stronger for the young and the healthy, as wells as for males and the higher educated. This result signals that the reform may have eased somewhat adverse selection problems in Chiles health care system as it has drawn low-risk individuals towards the public system. Keywords: Health insurance, adverse selection, public health. JEL Classification: I10; I11; I18. 1

2 1 Introduction Chile s health care system is one worth analyzing as it allows us to understand how a mature health insurance system where public and private health insurers co-exist performs. Workers in Chile are required to spend at least 7 percent of their income in health insurance and can choose from either the public insurer (Fondo Nacional de Salud or FONASA 1 ) or a private plan offered by a Instituto de Salud Previsional or ISAPRE, 2 though they cannot choose to remain uninsured since by law health insurance in Chile is mandatory. From an individual s perspective, the structure of insurance premiums, benefits and outof-pocket medical costs differ significantly between the two systems. In the private system, on the other hand, insurance companies offer a wide variety of plans, and benefits depend on the premium. At the same time, premiums reflect the individual s basic health risk indicators and of his or her dependents. In the public system, on the other hand, FONASA offers a fixed benefits package that is independent of the premium paid. Therefore, since individuals in FONASA also pay seven percent of their salaries for health insurance, premiums increase with income while benefits remain unchanged. Furthermore, the private system often has access to better technology and faster service, while the public system relies mostly on public hospitals and may have longer wait times. However, on average ISAPRE plans tend to be less affordable and more discriminatory than their public counterpart. Adverse selection may arise as a consequence of the described structure. Namely, riskier individuals may be more inclined to choose FONASA since its premium remains constant relative to their health risk or number of dependents, as well as due to possible lower out-ofpocket medical costs. In addition, individuals with higher income are more likely to select an ISAPRE, as the resulting higher premiums they must pay allow them to purchase a more comprehensive health plan. While individuals are allowed to move between systems, the Chilean health care system does contain some mobility restrictions as a consequence of the existence of preexisting condition clauses. Namely, by law, each member and his or her dependents must declare any pre-existing illness before joining an ISAPRE, especially if serious and/or chronic. Based on the information provided, ISAPREs are entitled to reject a household or substantially limit their health coverage. That is, the development of some illnesses while not covered by a private plan may be considered pre-existing conditions by ISAPREs, which may limit private future coverage. This practice exists in order to avoid strategic behavior such as joining an ISAPRE for treatment of a pre-existing illness and then, once recovered, switch to a lower cost plan or to FONASA. The public system, on the other hand, does no impose such restrictions. The described asymmetry in mobility between systems imply that (i) sicker individuals 1 National Health Fund. 2 Health Insurance Institution. 2

3 may tend to accumulate in the public system due to the restricted public to private movement, and/or (ii) workers may suboptimally select to remain or trapped in the private system due to the concern that unforeseen negative future health shocks while in FONASA may prevent them to move to a private plan in the future. Consequently, mobility restrictions due to pre-existing conditions suggest that the insurance selection process is fundamentally dynamic as current insurance choices may affect future health insurance selections. Namely, the existence of these clauses imply that some individuals may get stuck in one system or the other due to unexpected negative changes in their health status, restricting their ability to make more active insurance choices in the future. Therefore, given the important future repercussions of current health insurance decisions, individuals are likely to want to use all available information in order to select the optimal health insurance system, so that in the event of getting trapped in one system, that happens where they would consider at that time the better of the two systems. An important purpose behind analyzing insurance choices in Chile is to draw lessons on the impact of health care policy changes for countries considering reform in their health care systems. Chile began introducing important changes in several areas of social security since the beginning of the 2000s. A major component in Chile s health care reform is the introduction of the Plan de Garantias Explicitas en Salud or GES Plan 3 starting in 2005, which provides guarantees in coverage and access to benefits to several conditions. GES benefits are offered system-wide and coverage is restricted to closed networks of practices and hospitals that each ISAPRE or FONASA offers. While GES benefits are included at no extra cost to FONASA enrollees, private insurers charge a single price to all their subscribers, regardless of their health risks. A newly-created Fondo de Compensacion Solidario (solidarity compensation fund) shares health risks included in the GES plan among ISAPRE users. The introduction of the GES plan may have several repercussions on the selection of health insurance by individuals. For instance, the fact that GES benefits are included in FONASA at no extra cost increases the relative attractiveness of the public system, all else equal. At the same time, however, the fact that ISAPREs are mandated to offer GES benefits may imply that FONASA could be used less as catastrophic insurance, increasing the relative attractiveness of private plans. Private coverage on non-ges illnesses continues to depend on the amount of monetary contribution by workers. New legislation, however, has provided limits to ISAPREs ability to offer plans that provide less coverage than FONASA, effectively eliminating lower-cost private plans. Consequently, some low-risk and/or low-income individuals could move away from ISAPREs if the current cheapest plan in the private system costs more than they are willing and/or able to pay. On the other hand, the aforementioned reduction in the variety of plans offered by ISAPREs, and their reduced ability to increase prices and/or discriminate among groups can increasing ISAPRE s attractiveness due to lower uncertainty 3 Explicit Guarantees in Health Care Plan. 3

4 and possibly lower prices if competition among private insurers increases as a consequence of lower information costs due to greater transparency. Using a structural approach for modeling the behavior of individuals making forwardlooking decisions on health insurance types would allow us to estimate some of the underlying parameters driving such dynamic behavior. In addition, the estimated parameters can be used to perform simulations and ex-ante program evaluation. For instance, in the context of this study, this method would enable us to predict the impact of a policy reform on health insurance choices. That is, we can use simulations in order to evaluate the impact of policy changes introduced in the past by simulating decisions with and without the reform. In this case, the impact of the introduction of the GES plan on health insurance choices. Consequently, the objective and contribution of this paper is to build and estimate a simple structural, dynamic choice model using panel data from Chile s Encuesta de Proteccion Social (EPS) survey 4 in order to conduct an evaluation of the impact of the GES plan on health insurance selection. The proposed dynamic model is such where past choices (type of insurance) and current states (mainly, health status) can affect individuals present and future utility (say, due to changes in out-of-pocket medical costs), in order to predict what decision individuals of certain characteristics are more likely to make and under certain circumstances. In addition, in this paper we will be able to empirically test whether higherrisk and poorer individuals are more likely to choose FONASA, whether the asymmetry in restrictions on health insurance mobility may affect health insurance choices, whether individuals health insurance decisions would change if the restrictions on pre-existing conditions were to be eliminated, and whether any of the above characteristics can be affected by the introduction of the GES plan, by simulating individuals health insurance choices with and without the reform. The paper is structured as follows. Section 2 provides a description of the data and summary statistics of the estimation sample. Section 3 includes a brief description of the Chilean health care system. Section 4 presents the theoretical model and estimation method. Section 5 provides the results of the estimation and section 6 presents the simulation exercise of the impact of the health care reform on insurance choice. We conclude with a discussion of the findings in section 7. 2 DATA This analysis relies on data from Chile s Encuesta de Proteccion Social (EPS) survey for 2002, 2004, 2006 and 2009, which follows a panel of individuals over time. The survey includes questions on health and insurance status, as well as household demographic characteristics, labor market status, and income. 4 Social Security Survey. 4

5 Health status is measured by a self-reported general health status question, rated on a 6-point scale, from very poor to excellent. As in Blau and Gilleskie (2000), for simplicity, we dichotomize this variable to health being either good to excellent (the top three categories) or fair to very poor (the bottom three categories). While the survey contains other measures of health, such as past medical usage, including more variables to construct the health status variable would increase the number of parameters and computational burden significantly. The combined panel consists of 19,807 individuals. Out of them, we have data for 15,183 individuals for whom there are at least two waves of observations with positive income. Then, we limit the sample to adults between the ages of 24 and 65, which further reduces the sample to 12,824 individuals. We do this in order to focus on adults who have likely completed schooling and who are likely to have already made insurance changes. 5 Second, as in Gilleskie and Mroz (2004), we keep only individuals with zero dependents in all years, reducing the sample to 7,579. That is, in our sample, other household members, if any, have either their own insurance plan or no insurance. We take this path for tractability, comparability and due to some data limitations. To model a household with dependents requires more complex joint modeling of fertility and health status over time for each household member (and his or her probability to continue to belong to the family in the future). Since the main scope of this paper is to focus on choices in the individual health insurance market, we leave adding dependents to the analysis for future research. Finally, we exclude individuals who report having either no insurance ( none ) or some other insurance in one of the two years, as there is no choice to be modeled in these cases for the following reasons. First, health insurance in Chile is mandatory for salaried workers, so having no health insurance is not a relevant option. Second, the response other corresponds mostly to health insurance provided by the armed forces and police exclusively to their members. That is, only the civilian population makes health insurance choices and the only relevant options are the public provider (FONASA) or any of the private providers (ISAPRE). Therefore, the elimination of observations that present no choice relevant to the model should not produce biased results. These restrictions imply that our final sample size is of 5,882 individuals. Descriptive data suggest that the transition from public to private insurance is less frequent than a transition from private to public. Table II shows the transition matrix for individuals changing insurance status between 2006 and 2009 for the full EPS sample. The vast majority (almost 92 percent) of individuals with public insurance in 2006 maintains public insurance in 2009, and just over two percent switch to private insurance. Of individuals with private insurance in 2006, less than three-quarters maintain this insurance status in 2009, while 20 percent move to public insurance. There are some differences by age and sex in the likelihood of transitioning between 5 After age 65, premiums for private insurance do not change and income is not likely to change, as most individuals have retired. 5

6 Table I: Variable Means, Full Sample versus Estimation Sample Insurance Type Full sample Estimation sample % public % private % none/other Observations 16,727 16,443 14,463 4,453 4,259 3,717 Other Variables Mean Std dev Mean Std dev Mean Std dev Full sample Age Female (%) Years schooling Regular or worse health (%) Poor or worse health (%) Income (thousand) , , ,815 Estimation sample Age Female (%) Years schooling Regular or worse health (%) Poor or worse health (%) Income (thousand) , Source: Authors calculations, EPS 2004, 2006, Calculations for EPS 2002 were omitted here due to space restrictions Note: The Other category includes individuals covered by the armed forces and those who do not know which insurance type they have; * signifies that the full sample and estimation sample means are statistically different. systems (Table III, panel a). Both men and women are most likely to move from public to private insurance when they are younger than 35 years old, suggesting that private insurance is more attractive to healthier individuals. Women tend to show a spike in the move from private to public coverage in older ages, while men are most likely to move from private to public at younger ages. Possibly, women move to public coverage when their spouse passes, 6

7 Table II: Insurance Status Transitions, Full Sample Status 2006 Status 2009 Public Private Other/None Total Public Private Other/None Total Source: Authors calculations, EPS 2006, Note: The Other category includes individuals covered by the armed forces and those who do not know which insurance type they have. and/or move to public coverage when chronic disease or disability takes effect. Meanwhile, men may move with changes in job, income, health status, or health preference. In our estimation sample (Table III, panel b), the general direction of these differences is maintained, though magnitudes do vary mainly due to the elimination of people older than 65, non-earning individuals and those with dependents. Official data on the number of members in the private health system tend to show that there may not be strong loyalty for the bulk of members of private health plans. The majority of individuals have been in their private insurance plan for five years or less, with a fifth of individuals having participated in their plans for two years or less. At the same time, a quarter of individuals have been in the same plan for 10 or more years, (Sanchez, 2005). These data, however, do not include any breakdown by age, sex, or other demographic characteristics. In addition, our estimation sample shows that 92.4% of individuals maintained the same health insurance system between 2002 and 2009, and only 0.83% changed at least twice. Specifically, mirroring the findings of Table III, the percentage of workers that tend to remain at least five years in the public system (private system) is higher (lower) for older individuals. Similarly, the percentage of workers that tend to stay at least five years in the public system (private system) decreases (increases) the greater their number of years of schooling. 3 BRIEF DESCRIPTION OF THE HEALTH SYS- TEM IN CHILE The Chilean health system is mostly an individual health care market in that employers do not provide health insurance, though there are a few private plans for which unions negotiate directly with providers. As mentioned earlier, workers and pensioners by law must spend at 7

8 Table III: Insurance change (percentage change relative to previous wave) Move to Move to Move to Move to Move to Move to public private public private public private in 2004 in 2004 in 2006 in 2006 in 2009 in 2009 a. Full sample Males age <= age age age age > Females age <= age age age age > All b. Estimation sample Males age <= age age Females age <= age age All Source: Authors calculations, EPS 2002, 2004, 2006, least seven percent of their salary on health insurance and individuals can choose between a public provider (FONASA) and one of the private insurers (ISAPREs). The private system, which was created in 1981, currently consists of seven competitive open private insurance companies and five closed insurance companies that are only available to workers in certain industries. ISAPREs are supervised by Chile s Superintendency of Health. The two systems differ structurally in terms of access to health providers, coverage, exclusions, out-of-pocket medical costs and premiums. The premium for public coverage is fixed at seven percent of one s salary and benefits are standard in terms of quality. Depending on the household s income and family structure, public insurance may completely or partially cover the enrollee and his or her family, independent of their risk characteristics. That is, public insurance provides a single fixed benefits package and its premium increases solely 8

9 with income. In addition, public insurance automatically covers low-income individuals. This system, however, relies on public hospitals (and some associated private facilities), and may have longer wait times, higher variance in provider quality, and restrictions on where care may be obtained. In contrast, premiums in the private system are set by the insurer and they reflect their expected medical costs, taking into account the basic health risk of the insured individual and his or her dependents (using publicly available information regarding age, sex, and number of dependents). The premiums consider a table of factors that reflects the relative values for each enrollee as a function of whether the person is the head of the family or a dependent, sex and age (Sanchez and Munoz, 2008), multiplied by the price of the plan, which is a function of the level of coverage. A major consequence of mandating individuals to pay at least seven percent of their salary is that private insurance companies tailor plans according to each individual s exogenously set premium. Therefore, this structure has led to the proliferation of an enormous quantity of plans that differ in terms of benefits, coverage (coinsurance rates and payment caps) and thus premiums. However, a very limited subset of them with similar costs is available to each particular enrollee. For instance, though showing a decreasing trend over the last few years, by January 2014 there were almost 12,000 different plans available for purchase in the private system, whose enormous variety of characteristics are hard to evaluate or compare (Sanchez, 2014), leading to important information costs. In fact, about 47 percent of enrollees in the private system claim to be uninformed about how to access the services provided by their own insurer (Agostini, Saavedra and Willington, 2007). Individuals must report all pre-existing conditions before enrolling in private plans, for which they may be denied partial or complete coverage. Policyholders can terminate the contract with private providers at any time after one year, and then move freely to the public system or to another private insurer. Private insurance tends to be more attractive for outpatient usage, as the cost of care tends to be lower and of higher quality. However, for more serious health conditions requiring expensive treatment, the public system becomes more appealing due to its lower out-of-pocket cost (Henriquez, 2006). Consequently, the structure of this system tends to discriminate against people with higher health risk, such as women of prime childbearing ages and older individuals. Currently, the public system covers 13.5 million people (76.3 percent of population), while private companies insure about 3.2 million individuals, or about 18.2 percent of the population (Ministerio de Salud, 2015). 6 In addition, there is clear evidence of market concentration within the private system. While there were 21 open private providers in 1995, this number has fallen over time to 15 by 2000 and to only seven open providers by Five of these companies covered almost 93 percent of individuals with private insurance in 2015 (Superintendencia de Salud, 2015). 6 About 5.5 percent either belong to the Armed Forces insurance system or are uninsured. 9

10 4 THE MODEL This section presents the dynamic choice model on health insurance selection that we use to examine the impact of the health care reform in Chile. We solve the dynamic optimization problem recursively and, due to the models nonlinearity, we estimate its parameters numerically using maximum likelihood. We assume that individuals start making health insurance decisions at the age of 25, when most have completed schooling, as the data do not distinguish between unemployment and being out of the labor force. If employed, workers choose the type of health insurance that maximizes their expected lifetime utility. Therefore, every period an individual chooses the type of health insurance they want to buy (l t ), private (ISAPREs) or public (FONASA): l = { 0 if Public 1 if Private We assume that once individuals make health insurance, they cannot switch to a different type until the period between the surveys have passed, as the data log only the current choice of health insurance type, not from previous years. The sources of uncertainty in this model are given by shocks to individuals health and income. In terms of the evolution of health over time, we consider two kinds of shocks. A regular health shock (H) and a GES health shock (H G ). For simplicity, we classify health status (h) into two categories: H = { 0 if good to excellent 1 if fair to very poor The GES health shock is a more restrictive measure of health status. Given that the data do not identifies whether or not an individual suffers from a condition that classifies as a GES illness, for simplicity we assume that H G takes the value of 1 when the individuals health status falls into the categories poor to very poor and zero otherwise. We model the probability of falling into a state of health for an individual of age t (π t ) as an exogenous logistic stochastic process that depends on the individuals health status in the previous year, age (t), sex (f) and education (S) 7, for instance, consistent with the higher morbidity rates observed for women, females are expected to be more likely to move to low health statuses than males, all else equal. (1) (2) π k = P r(h t = k) = exp{γ k=1 γ 2,kD(H t 1 = k) + γ 3 t + γ 4 f + γ 5 S t } 1 + exp{γ k=1 γ 2,kD(H t 1 = k) + γ 3 t + γ 4 f + γ 5 S t } (3) 7 As in Verbrugge (1985). 10

11 Health care utilization and, in particular, preventive care, may be major determinants of the probability of becoming ill, all else equal. For computational tractability, however, we do not explicitly model health care utilization, but consider variables such as education, as important determinants of preventive care, and thus critical in determining the evolution of health status over time. Ross and Wu (1995), Cutler and Lleras-Muney (2006) and others have shown that education significantly explain the evolution of health over time. In our model, the link between education and health status can be direct (individuals with more education people tend to make better and more informed about their health care) and/or indirectly (income tends to rise with education, implying more preventive medical care). Earnings vary over time and across individuals due to differences in human capital accumulation as in a standard Mincer (1958) earnings function: log Y t = η 1 + η 2 S + η 3 t + η 4 t 2 + ξ t = W t + ξ t (4) where ξ t is a serially uncorrelated income shock parameter that presents a log-normal distribution with a zero mean and a finite σ 2 ξ variance. The utility level that an individual who has chosen a health insurance of type l receives every period is captured by the function: 8 U l (C l t ) = α 1 l t + α 2 H t + C l t (5) where C t is a bundle of goods for household consumption purchased by an individual of age t. The coefficient α 1 would capture the direct utility that private insurance amenities provide the individual, including the quality of health care, shorter waiting time, the access to new technologies, etc. The parameter α 2 would reflect the direct utility due to the individuals health, such as physical and mental discomfort, etc. 9 In addition, the model incorporates unobservable heterogeneity among individuals. Namely, those who do not expect certain illnesses or who do not receive a sufficiently high nonpecuniary benefit from pricier private insurance plans will not chose that option. Therefore, individuals from poorer backgrounds are less likely to choose the more expensive private insurance option. The budget constraint is: C l t = Y t I l t H t m l t G t H G t m l,g t (6) 8 As in Eckstein and Wolpin (1989), for simplicity we assume a linear utility function, as it allows us to solve the model analytically. We can justify this assumption given the mandatory nature of the health insurance system in Chile in that workers main decision is not whether to purchase insurance (like in the U.S.), but what type of insurance to buy: one that is more expensive but of better quality or one of lower quality but potentially more affordable. 9 Note that both health status and the choice of health insurance also enter into the utility function indirectly through the individuals budget constraint. 11

12 where It l represents the premium paid for a health insurance plan of type l, G t is a dummy variable that takes the value one when the GES plan is in place and zero otherwise and m l t and m l,g t capture the out-of-pocket medical costs incurred by an individual who gets sick with a condition that does not and does qualify as GES illness, respectively. Note that the model does not incorporate saving decisions, both for reasons of computational simplification and, as in Bravo, Mukhopadhyay and Todd (2010), because few individuals report significant levels of voluntary savings. Although individuals cannot borrow or save, the utility specification described below is essentially linear in consumption, meaning that individuals are indifferent to consuming across different periods. As introduced earlier, variables such as education, age and gender may affect the probabilities of sickness(π t and πt G ). Once in bad health, we assume that individuals would face an amount of out-of-pocket medical costs that are determined for the most part by the severity of the illness and the plans coverage at each point in time: and m l t = ρ 1 l t + ρ 2 l t (1 l t 1 )H t 1 (7) m l,g t = ρ G 1 l t + ρ G 2 l t (1 l t 1 )H t 1 (8) where coefficients ρ 1 and ρ G 1 reflect the contribution to out-of-pocket medical costs of the private systems relative to the public system (ρ 0 ). As mentioned earlier, at the time of joining an ISAPRE, each member must declare any illness and the ISAPRE decides whether or not to accept them. If an affiliate becomes ill after signing the contract, the ISAPRE cannot limit coverage. However, if the condition was not declared, the ISAPRE will not pay. Therefore, an individual will be considered affected by pre-existing condition restrictions when he or she is either denied private coverage or is impeded from switching to the private system due to his or her current health conditions. The variable l t (1 l t 1 )H t 1 captures the described pre-existing condition situation. Namely, an individual that is not currently covered by a private plan (l t 1 = 0) and considers purchasing one (l t = 1) but had previously moved to a low state of health (H t 1 = 1), the corresponding out-of-pocket medical costs that this person would face would be much higher than if he or she had been in the private system when the adverse health shock took place. In such a case, the person would be required to either face all medical costs out-of-pocket or stay in FONASA. Consequently, we expect positive values for the coefficients ρ 2 and ρ G 2. While workers pay seven percent of their salary for public insurance regardless of expected utilization (It 0 ), premiums in the private system (It 1 ) are set by each ISAPRE. Specifically, private the premium paid by a subscriber results from the plans basic price adjusted by the households expected medical costs. The basic price of the plan reflects the insurers loading factor, or the amount added in order to finance other operating costs such as administrative and/or overhead expenses, and the plans coverage. 12

13 By law, ISAPREs cannot base their premiums on the current members health status. Instead, they can only calculate expected medical costs using basic health risk information of the insured and his or her dependents, such as sex and age, for which they use a table of factors that adjusts the plans price due to each members health risk. Private insurers offer a wide variety of plans that differ in terms of benefits, coverage and thus premiums, and in equilibrium the premium paid for a private plan, and thus the level of coverage received, is closely linked to the households income. We assume for simplicity that the loading factor remains unchanged over time. Therefore, fluctuations in the amount of coverage included per each peso of insurance purchased reflects the medical costs expected by the insurer. Consequently, we assume for simplicity that private premiums (I 1 t ) are a deterministic function of the individuals age and sex: I 0 t = 0.07Y t I 1 t = δ 1 ft t + δ 1 G t (9) where parameters δ 1 and δ 2 capture the impact on the private insurance premium of both the members age and gender, and the value of the GES plan, respectively. Let Ω t = (l t 1, H t 1, S, t, ft t, G t ) represent the vector of state variables. 4.1 Solution This section briefly presents the model s solution method. An individual of age t chooses the health insurance of type l that maximizes the present discounted value of utility over a time horizon until reaching an age T. Every period, individuals choose their health insurance of type l = {0, 1}, given the state space Ω t (including the realization of the earnings shock parameter, ξ t ) and the discount factor β. V (Ω t ) = max E t l τ { T β [ τ t l τ Uτ 1 (Cτ 1 ) + (1 l τ )Uτ 0 (Cτ 0 ) ]} (10) τ=t The value function above can be expressed as the maximum of the value functions that are specific to each health insurance type V l (Ω t ), { } V (Ω t ) = max V 0 (Ω t ), V 1 (Ω t ) (11) where l T = { U l (Ct l ) + βe t V (Ω t+1 l t ) if t < T U l (CT l ) + βe T V (Ω T l T ) if t = T (12) For computational tractability, we set a maximum age T = 65 until which individuals actively make health insurance choices. That is, at age T individuals choose the insurance 13

14 type that they will maintain for the rest of their lives. 10 Consequently, an individual of age T solves a static decision problem that affects their contemporaneous and future utility. In particular, he or she would prefer public health insurance for ages t T if the implied present discounted value of lifetime utility associated with that choice is greater than that for private health insurance. That is, if where V 0 (Ω T ) V 1 (Ω T ) (13) (14) V 0 (Ω T ) = α 2 π T + exp{w T + ξ T } 0.07 exp{w T + ξ T } + β V 0 V 1 (Ω T ) = α 1 δ 1 ft T δ 2 G T + [α 2 ρ 1 ρ 2 (1 l T 1 )H T 1 ]π T [ρ G 1 + ρ G 2 (1 l T 1 )H T 1 ]G T πt G + exp{w T + ξ T } + β V 1 and V l = V (Ω T l T ) captures future utility, which we assume is a function of the state space for age T, and whose parameters are jointly estimated with the other parameters of the model. 11 Note that since health status is unknown at the beginning of each year, the expected out-of-pocket cost of treatment is given by its expected value (i.e., E t H t m l t = π t m l t and E t Ht G m l t = πt G m l t). Given that increases in earnings (Y t ) raise the public insurance premium (It 0 ) without corresponding increases in benefits, then, holding everything else constant, people with earning levels sufficiently low will prefer public insurance; otherwise they would choose private health insurance. Defining ξi (Ω T ) as the cutoff value for the earnings s error term, ξ t, that would make the health insurance options equally attractive for an individual, then he or she would prefer public health insurance if the realization of the earnings shock parameter (ξ T ) is lower than the aforementioned cutoff. Consequently, the health insurance decision rule at age T is given by the binomial logit form: where and c 1 = α 1 + βθ 1. l T = { 0 if ξ T ξi (Ω T ) 1 if ξ T > ξi (Ω T ) ξi (Ω T ) = log{ c 1 + δ 1 ft T + δ 2 G T + (ρ 1 + ρ 2 (1 l T 1 )H T 1 )π T +(ρ G 1 + ρ G 2 (1 l T 1 )H T 1 )G t πt G} log(0.07) W T 10 This assumption is plausible, since, after retirement, pension earnings tends to be rather predictable and premium rates for private insurance do not change. 11 That is, V (Ω T l T ) = θ 0 l T + θ 1 H T. (15) (16) 14

15 The expected discounted value function at age T is: E T 1 V (Ω T ) = (α 2 + βθ 1 )π T Pr(ξ T ξ I (Ω T )) + [α 1 + βθ 1 δ 1 ft T δ 2 G T +(α 2 ρ 1 ρ 2 (1 l T 1 )H T 1 + βθ 2 )π T (ρ G 1 ρ G 2 (1 l T 1 )H T 1 )π G T ] Pr(ξ T > ξ I (Ω T )) +(1 0.07) exp{w T }E T 1 { e ξ T ξ T ξ I (Ω T ) } Pr(ξ T ξ I (Ω T )) + exp{w T }E T 1 { e ξ T ξ T > ξ I (Ω T ) } Pr(ξ T > ξ I (Ω T )) which, given the assumption of normal distribution for ξ, implies E T 1 V (Ω T ) = [ ( ξ c 2 π T + exp{w T }e 0.5σ2 )] ξ Φ I (Ω T ) σξ 2 σ ξ +[c 1 δ 1 ft T δ 2 G T (ρ 1 + ρ 2 (1 [ l T 1 )H ( T 1 )π )] T (ρ G 1 + ρ G 2 (1 l T 1 )HT G 1 )G ξ T π T ] 1 Φ I (Ω T ) σ ξ (17) where c 2 = α 2 + βθ 2 and Φ ( ) is the cumulative distribution function for the normal distribution. Solving backwards, individuals of age T 1 make health insurance decisions in a similar fashion. That is, they compare the value functions specific to each insurance type: V (Ω T 1 ) = max {V 0 (Ω T 1 ), V 1 (Ω T 1 )} (18) Unlike for the terminal age T, individuals of age T 1 now consider the expected impact of current decisions on decisions for age T, which is given by the second term of the right-hand side of each insurance-specific value functions: V l (Ω T 1 ) = E t U l (C l T 1) + βe T 1 V (Ω T l T 1 ) (19) Notice that the term βe T 1 V (Ω T l T 1 ), which captures the expected discounted value function for age T with information as of age T 1, equals the weighted average of the insurance-specific value functions, E T 1 V (Ω T l T 1 ) = V 0 (Ω T ξ T ξi (Ω T l T 1 )) Pr(ξ T ξi (Ω T l T 1 ))+ V 1 (Ω T ξ T > ξi (Ω T l T 1 )) Pr(ξ T > ξi (Ω T l T 1 )) where the weights are the probabilities of choosing either options that arise from the decision rules found for individuals of age T (equation (15)). Following the methodology described above, the value functions for each age t < T as a function of the relevant state space are: V 0 (Ω t ) = α 0 + π t (α 2 ρ 0 ) + exp{w t + ξ t } 0.07 exp{w t + ξ t } +βe t V (Ω t+1 l t = 0) V 1 (Ω t ) = α 0 + α 1 δ 0 δ 1 ft t + π t (α 2 ρ 0 ρ 1 ρ 2 (1 l t 1 )H t 1 ) + exp{w t + ξ t } + βe t V (Ω t+1 l t = 1) (20) 15

16 which implies the following decision rule at age t < T : { 0 if ξ t log α 1 δ 1 ft t δ 2 G t + (ρ 1 + ρ 2 (1 l t 1 )H t 1 )π t l t = = ξi (Ω t) 1 if ξ t > ξi (Ω t) +(ρ G 1 + ρ G 2 (1 l t 1 )H t 1 )πt G } β[e t V (Ω t+1 l t = 1) E t V (Ω t+1 l t = 0)] log(0.07) W t and expected discounted value function as of the beginning of age t: E t 1 V (Ω t ) = [ ( ξ α 2 π t + exp{w t } e 0.5σ2 )] ξ Φ I (Ω t) σξ 2 σ ( ) ξ ξ +βev (Ω t+1 l t = 0)Φ I (Ω t) σ ξ + [α 1 δ 1 ft t δ 2 G t (ρ 1 + ρ 2 (1 l t 1 )H [ t 1 )π t ( (ρ G 1 + )] ρ G 2 (1 l t 1 )H t 1 )G t πt G ξ +βev (Ω t+1 l t = 1)] 1 Φ I (Ω t) σ ξ (21) (22) With respect to the earnings function, as in Eckstein and Wolpin (1989), we assume that the salaries are reported with error, which helps alleviate the impact of outlier observations in the likelihood function. log Y r t = log Y t + ψ t (23) where Y r t is the reported income, Y t is the true income, ψ t N(0, σ 2 ψ ) and E(ξ tψ t ) = 0. The probabilities of choosing either system provided by the solution of the optimization problem through the cutoffs (ξ I (Ω t)), define the corresponding likelihood function: L = N T Pr ( ξ τ > ξi (Ω τ ) ) l τ ( Pr ξτ ξi (Ω τ ) ) 1 l τ (24) n τ=t where for each individual τ ( ξ Pr(ξ t ξi (Ω τ ), Yτ r I (Ω τ ) κ σ ξ σ ) = Φ ξ u τ σ ξ 1 κ 2 ) ( ) 1 uτ φ σ u σ u (25) and Φ( ) is the cumulative normal distribution function, φ( ) is the normal probability density function, u τ = ξ τ + ψ τ, κ = σ ξ /σ ψ and σ u = σξ 2 + σ2 ψ (1 κ2 ). We follow a standard estimation algorithm. Given an initial set of parameter values, the computer calculates all predicted decisions (as given by the cutoffs, ξi (Ω t)), and computes the likelihood function value using the actual decisions (l t s). The optimization program finds a new set of parameters and the iterative process is repeated until the improvement in the likelihood function falls below a certain convergence criteria. The resulting set of parameters provides predicted responses that best match the actual responses. 16

17 The initial condition problem, as described in Heckman (1981), implies that the use of predetermined state variables as initial conditions normally generates inconsistent parameter estimates, as they contain information from previous choices. When the shocks are not serially correlated, however, these estimations problems need not occur. Consequently, as in Eckstein and Wolpin (1999) and Todd and Wolpin (2006), we assume serial independence of the error term (ξ t ). This assumption allows us to use observed values of the state variables, including age (26 years old), sex, education, health status and health insurance, in the likelihood function, without implying inconsistent estimates. 4.2 Identification Though the variables of a structural model are identified by construction, the solution of the model and the functional form of some of its equations may imply that some variables cannot be uniquely identified. In this model, the functional form of the earnings function and data on health status, earnings, age and health insurance participation allow the direct identification of the following parameters: the cutoff values (ξ I (Ω t)), the probability of change in health status parameters (γ k 1, γ k 2,H k 1, γ k 3, γ k 4, γ k 5 ), the utility function parameters (α 1 and α 2 ), the earnings function parameters (η 1, η 2, η 3. η 4 ), the medical cost of sickness in the private sector (ρ 1 and ρ G 1 ), the medical cost of sickness under potential pre-existing condition exclusions (ρ 2 and ρ G 2 ), the joint impact of the affiliates age and gender on the private insurance premium (δ 1 ), the impact of the GES plan on the private insurance premium (δ 2 ), the volatility of true earnings (σξ 2) and the volatility of reported earnings (σ2 ψ ). In addition to the aforementioned parameters, the following sum of parameters can be also identified: c 1 = α 1 + βθ 1 and c 2 = α 2 + βθ 2. These group of paramenters allow the identification of the terminal value function parameters (θ 1 and θ 2 ). 5 RESULTS Table IV presents the estimation results. First, there seems to be persistence in health status (γ 2 5 > 0) as the probability of a certain health status occurring tends to be the highest when the individual had that same health status in the previous period. In addition, as expected the probability of transiting to a lower health status increases with age and if the individual is female (γ 6 > 0 and γ 7 > 0). Several international studies have found that females, all else equal, tend to present higher observed morbidity than men (though, lower mortality rates). For instance, Case and Paxson (2005), find that differences in self-rated health in women relative to man can be fully explained by gender differences in the distribution of health conditions. In addition, as explained earlier, the probability of moving to a lower health status decreases the more educated the person is γ 8 < 0, mainly due to the impact of education on more informed preventive care decisions and/or on income, as preventive 17

18 medical care is a normal good. Table IV: Estimation Results a. Multinomial logit estimates Variable Coefficient Probability of change in health π k=2 π k=3 π k=4 π k=5 Constant: γ * * * * (0.179) (0.223) (0.418) (0.929) Dummy(H t 1 = 2): γ * 0.840* 0.995* (0.071) (0.104) (0.263) (0.571) Dummy(H t 1 = 3): γ * 2.532* 3.069* 2.247* (0.105) (0.126) (0.264) (0.547) Dummy(H t 1 = 4): γ * 3.112* 5.050* 4.871* (0.317) (0.315) (0.388) (0.610) Dummy(H t 1 = 5): γ * 4.301* 5.047* (0.682) (0.635) (0.669) (0.828) Age: γ * 0.046* 0.074* 0.074* (0.003) (0.004) (0.006) (0.013) Sex: γ * 0.461* 0.752* 1.171* (0.061) (0.073) (0.109) (0.249) Schooling: γ * * * * (0.008) (0.010) (0.014) (0.028) b. Maximum likelihood estimates Variable Coefficient Variable Coefficient Utility for private system: α * Constant: η * (654.5) (0.160) Disutility for being sick: α Schooling: η * (418426) (0.002) Out-of-pocket medical costs Age: η For private: ρ * (0.007) (2686) Age 2 : η Pre-existing condition: ρ * ( ) (2085) Constants For private (GES): ρ G * C (7283) (1325) Pre-existing condition (GES): ρ G * C * (2303) (7.3E+08) Private insurance premium Variances Gender-age index: δ * Earnings: σξ * (228.7) (0.013) GES plan: δ * Reported earnings: σψ * (491.7) (0.011) Log-likelihood function Notes: Standard errors are in parentheses. * means significant at 95 percent confidence. Relative to state k = 1 (excellent). Second, as one might expect, in the baseline scenario (no GES plan in place), the potential cost of presenting pre-existing conditions reduces the marginal utility of switching to the private system (that is, ρ 2 > 0). We can interpret this parameter as the value of relaxing the 18

19 pre-existing conditions restriction to an individual who has transited to a poor health status while outside of the private system. In particular, individuals in such a situation would be willing to pay on average roughly 8,000 Chilean pesos extra every month in addition to the premium, or almost 6 percent of the sample s median monthly wage, in order to gain access to private insurance. 12 This result suggests that the existence of pre-existing conditions restrictions may lead to more individuals involuntary choosing public insurance. Third, the parameters relative to the GES plan when it is in place and applies (ρ G 1 and ρ G 2 ), which represent the additional impact of the plan on out-of-pocket medical costs, have the expected negative sign. That is, relative to the baseline scenario, the GES plan seems to have a significant impact in reducing these costs to people affected by the illnesses covered by the GES plan. Interestingly, even though the GES plan does not specifically eliminate preexisting condition clauses in the private system, by guaranteeing the treatment of several illnesses, the GES plan effectively reduces the out-of-pocket costs of some conditions even if they were contracted outside the private system. Fourth, as observed in the raw data, the marginal utility of participating in the private system falls for females and is decreasing with age due to their impact on the health insurance premium in the private system (that is, δ 1 > 0). In addition, as mentioned earlier, the GES plan also increases the premium in the private system, but not in the public system, as captured by a positive parameter δ 2. Finally, since wages increase with education (η 2 > 0), an individual is less likely to choose public insurance as income increases, since the public premium increases with income, but with no accompanying increase in benefits. However, the marginal utility of choosing private insurance through its earnings channel is not significantly affected by the individuals age (η 3 and η 4 ). Table V shows the actual participation rates in the public system and those predicted by the model for the overall estimation sample, as well as by age category, education, sex and health status. Results show that the model does a very good job at predicting true participation, as judged by the 95-percent confidence chi-square test of goodness of fit (χ 2 ), there are no statistical significant differences between the two measures. As expected, panel a in table V shows that both actual and predicted participation in the public system increases with age. That is, the impact of age on expected medical costs and therefore on private insurance premiums tends to more than compensate for any impact of age on salary, which would increase public premium without additional benefits. Likewise, panel b shows participation in public insurance by both age and education. Also as expected, higher levels of education are correlated with lower levels of participation in the public system, mainly due to the positive impact of education on wages, and thus, on the public premium. We see this pattern for all age categories. However, the observed increasing public participation as people age becomes much more erratic when observed 12 Given that people affected by pre-existing conditions would remain uncovered by the private system and thus would not switch, ρ 2 captures a monthly cost instead of a lump sum payment. 19

20 Table V: Participation in the public system, actual and predicted values, overall and by Age, Schooling, Sex and Health Status Age Category All Ages χ 2 (row) A P A P A P A P A P a. Overall (9873) (2551) (2535) (2562) (2225) χ 2 (column) b. Schooling (2767) (2399) (2646) (2061) χ 2 (column) c. Sex Males (4829) Females (5044) χ 2 (column) d. Health Good (6415) Poor (3458) χ 2 (column) e. Health Good (9082) Poor (791) χ 2 (column) Notes: A is actual value, P is predicted value; * signifies the actual and predicted to be statistically different; sample sizes are in parentheses; χ 2 = chi-square statistic with critical values χ 2 3(0.05) = 7.82 and χ 2 1(0.05) =

21 within different categories of education. For instance, participation in the public system increases between the age categories and only for those who have between 8 and 12 years of schooling. Panel c shows that the model predicts slightly higher female public participation. As mentioned earlier, though females present higher rates of longevity, they tend to also have higher rates of morbidity (for instance, due to higher prevalence of chronic conditions), in addition to the costs linked to child-bearing. When analyzing participation by sex and age category, we see that both males and females are more likely to increase their participation in public insurance as they age. The results by both measures of health status (panels d and e) reveal that, indeed, individuals with a lower health status are more likely to choose public insurance, as out-ofpocket medical costs tend to be more predictable and, in some cases, lower (in particular for low income individuals). However, it could also be a consequence of pre-existing condition clauses for private insurance as leaving the public system may not even be an option for those who have transited to low health status. Examining these choices by age and health status, both the model predictions and the actual data show higher public participation for people with poor health, regardless of age category. At young ages (26-36 years of age), however, participation in the private system is substantially higher for those with good health than for those with poorer health. 6 SIMULATION Having estimated the structural parameters for the model, we can now conduct a simulation exercise in order to examine the impact of a policy change on health insurance selection. In particular, I look at the introduction of the GES plan in It is worth recalling that the GES plan provides enrollees from both systems with guarantees in coverage and access to benefits for several medical conditions. This plan involves no extra cost to enrollees in the public system, while ISAPREs charge an additional price to all their subscribers, regardless of their health status. In exchange, however, ISAPRE users have now access to many conditions that have been traditionally considered catastrophic and that were in many cases limited to FONASA subscriber. For those reasons, some have used FONASA as catastrophic insurance. Since the GES plan was introduced gradually starting in 2005, our data set allows us to have observations for the periods before and after the reform. In order to assess the impact of the said reform, I simulate health insurance choices from individuals that have been exposed to the reform under a hypothetical pre-reform scenario. Specifically, I conduct the simulation without the GES plan by adjusting the budget constraint so that it reflects (i) medical costs without the explicit guarantees provided by the GES plan, and (ii) a private insurance premium that does not include the extra mandatory price charged to private subscribers. 21

22 Each individuals decision is replicated 1000 times. Table VI describes simulations results, which suggest a noteworthy change in participation towards the public system (about 5 percentage points). Given that this exercise examines what the average health insurance decision would look like had the program not been in place, a predicted drop in public participation in the scenario of no policy change tends to indicate that the introduction of the GES plan has made the public system relatively more attractive. Put differently, the increase in relative attractiveness for the private system due to the added coverage (formerly limited to FONASA as catastrophic insurance) and greater transparency in due to ISAPREs lower ability to discriminate or increase plan prices, tend to be insufficient to compensate for the extra cost due to the price charged for the GES plan by ISAPREs, or the fact that ISAPREs are no longer allowed to offer cheap outpatient-only health plans, mostly preferred by the young and the healthy. In fact, simulations results suggest that, in fact, the migration towards the public system tends to be stronger for the young and the healthy, as seen in panels (a), (d) and (e) in Table VI. The less strong migration to the public system predicted for women could arise from the fact that the GES plan provides coverage at a cost that is independent of the persons health risks. That is, as ISAPREs consider womens health risk to be higher than mens, ISAPREs limited ability to discriminate against women makes the private system relatively more attractive for them. Likewise, the predicted migration towards the public system seems to be stronger for the more educated. The model links higher education to lower health risk and higher labor earnings. As mentioned earlier, low-risk individuals have been more strongly affected by the elimination of cheap outpatient-only plans formerly offered by ISAPREs. Higher earnings, on the other hand, are also associated with the fact that the GES plans price represents a smaller fraction of a private plans total cost, which all else equal would predict a weaker migration to the public system. In the overall, the first effect seems to be stronger that the second, hence the observed greater migration to the public system as education increases. This trend is particularly true for the young (low health-risk due to both age and higher education) and the old (higher health-risk but lower income due to retirement). The move towards the public system is weaker for those between the ages of 37 and 59 with college education, possibly as a consequence of a more important income effect due to greater labor experience. To sum up, the introduction of the GES plan seems to have favored a transition towards the public system, possibly due to the additional cost faced by ISAPRE users, both in terms of the added mandatory price of the GES plan and because of the fact that the reform has forced ISAPREs to discontinue many inexpensive, low health-risk plans. In fact, the movement towards the public system is predicted to be stronger for the young and the healthy, as wells as for males and the higher educated. In that sense, one could say that the reform may have eased somewhat adverse selection problem in Chiles health care system as 22

23 Table VI: Predicted public system participation with and without policy change, overall and by age, education, sex and health Status Age Category All Ages χ 2 (row) A PC A PC A PC A PC A PC a. Overall χ 2 (column) b. Schooling χ 2 (column) c. Sex Males Females χ 2 (column) d. Health Good or better Fair or worse χ 2 (column) e. Health Fair or better Poor or worse χ 2 (column) Notes: A is actual value, PC is predicted value under the policy change scenario; * signifies the actual and predicted to be statistically different; χ 2 = chi-square statistic with critical values χ 2 3(0.05) = 7.82 and χ 2 1(0.05) =

24 it has drawn low-risk individuals towards the public system. 7 CONCLUSIONS This paper takes advantage of Chiles mature health insurance system where public and private health insurers co-exist in order to extract some policy lessons for countries considering reform in their health care systems. Differences in the structure of insurance premiums, benefits and out-of-pocket medical costs between the two systems imply that adverse selection may arise. Namely, riskier individuals are more likely to choose FONASA since premiums do not vary with health risk, and people with higher income are more likely to select an ISAPRE, as they receive more for their money. Mobility restrictions due to pre-existing condition clauses in the private system suggest that insurance selection is essentially a dynamic process as current insurance choices may affect future health insurance selections. The GES plan, which provides guarantees in coverage and benefits to several conditions, is a major component of Chile s health care reform of the 2000s. The introduction of this plan may also have some repercussions on the selection of health insurance due to differences in its costs and benefits across insurance systems. This paper builds and estimates a simple structural, dynamic choice model using panel data from Chile and examines the impact of the GES plan on health insurance selection. Estimation results suggest that (i) individuals affected by pre-existing condition restrictions would be willing to pay on average almost 6 percent of the sample s median monthly wage in order to gain access to private insurance; (ii) the GES plan seems to have significantly reduced out-of-pocket medical costs to people affected by the illnesses covered by the GES plan, even if they were contracted outside the private system; (iii) females and older individuals are in fact less likely to choose private insurance due to higher premiums; (iv) the link between education and both income and preventive care cause individuals with higher number of years of schooling to be less likely to choose public insurance; and (v) tests of goodness of fit show that the model does a very good job at predicting true participation. The simulation exercise on the impact of the introduction of the GES plan on health insurance selection suggest an overall change in participation towards the public system of about 5 percentage points. Additional costs faced by ISAPRE users, both in terms of the added mandatory price of the GES plan and the discontinuation of many inexpensive, low health-risk plans, seem to have favored this transition towards the public system. The fact that the movement towards the public system is predicted to be stronger for the young and the healthy, as wells as for males and the higher educated, signals that the reform may have eased somewhat adverse selection problems in Chiles health care system as it has drawn low-risk individuals from the private system towards the public system. 24

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