Estimating the Causal Effects of Supplemental Health Coverage in Brazil: Evidence from regression kink design

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1 Estimating the Causal Effects of Supplemental Health Coverage in Brazil: Evidence from regression kink design Naercio Menezes-Filho Insper Institute of Education and Research and Universidade de Sao Paulo Ricardo Politi Universidade Federal do ABC Abstract: This paper examines the effects of private health insurance on health care utilization in Brazil. We explore the Brazilian kinked rebate scheme on income tax to tackle the potential endogeneity between private health coverage and the demand for health services, using the fiscal incentive as a source of quasi-experimental variation in a regression kink design. Our results indicate that supplemental coverage has a significant impact on preventive services, notably frequency of visits to doctors and exams for women. We find only limited impacts on non-preventive health utilization, however, such as inpatient services and surgeries. The causal effects on preventive care are higher than those usually found in the literature and are more pronounced in white, women and older individuals. The results as a whole indicate that the fiscal incentives may be cost-effective in the long-run. Keywords: health services utilization, medical insurance, Brazilian health system, regression kink discontinuity JEL codes: J13, H51, C31. 1

2 1. Introduction As several countries in the world (e.g. Australia, Canada, Spain) 1, there exists in Brazil an income tax rebate for health expenses. In the last decade, domestic economic growth and the ageing population have improved the number of individuals eligible for this kind of fiscal subsidy. From 2002 to 2012, the share of population with some kind of supplemental health insurance has increased from 25% to 40% according to Secretary of Health in Brazil (2010). Despite the sharp rise insurance holding among Brazilian population, little is known about the causal effects of tax incentives in deductible health expenses and service utilization. In this paper we address this issue and relate it to empirical literature. Although there is a large literature which addresses health care utilization of the insured, recent research has pointed out that there is still a lack of consistent research design using quasi-experimental studies that estimates the causal effect of insuranced on health services utilization (Anderson, Dobkin and Gross, 2011; Finkelstein et. Al., 2011). 2 Additionally, kinked rebate rules for income tax has posed some econometric challenge on the identification strategy. In this paper, we argue that tax rebate with kinked discontinuity around income cutoffs allow us to estimate the causal effect of supplemental health coverage on the demand for health services. Since the Brazilian income tax scheme is piecewise linear, with progressive tax rates defined at the cutoffs, this kinked policy rules allow us to tackle the potential endogeneity between private health coverage and utilization of services using the fiscal incentive in income tax as a source of quasi-experimental variation (Card et. Al, 2009). This legal framework is explored in a two-stage least squares estimator in a regression kink design, as suggested by Dong (2012) for a binary endogenous treatment variable. The main idea is the same from the standard regression discontinuity approach: however, instead of changes in levels, changes in the slope of the treatment probability are used to identify the average treatment effect of the treated. We explore a large data available over several different health services, including preventive and non-preventive health care, prescribed and non-prescribed drug utilization, and out of pocket expenses. 3 1 See Cameron et. Al. (1988); Smart, M. e Stabile, M. (2005); Rodríguez, M. e Stoyanova, A. (2008),. 2 The seminal research in this field is based on the Rand Health Insurance Experiment (HIE), a randomized experiment which designate individuals across different deductibles and co-payments insurance plans in the seventies, see Maning et. al. (1987) for a summary. 3 Most research on health services presents data limitation on number of health services (as noted by Barros et. Al., 2008) or still, they are concentrated on specific age groups, mostly elderly, due coverage rules of Medicare in U.S.A. (as noted by Anderson, Dobkin and Gross (2011)). 2

3 To avoid taxpayers bunching (endogenous sorting) around the cutoffs, our sample includes only households with wage earner workers. In Brazil, the number of hours weekly worked are rigid and they are typically not workers' choice. Thus, our data in shared in two groups of individuals : those with private insurance coverage and those with public health coverage only (without any supplemental health coverage). The former group faces lower net prices for private health services and therefore are natural candidates to moral hazard behavior. Since insurance holders are expected to use more health services than they would had they faced the true prices for health services, moral hazard arises (Savage and Wright, 2003). 4 The more prices elastic the health services demand is the stronger is the moral hazard effect. As pointed out by Cameron et. Al. (1988), the econometric challenge is to discriminate between lower net price effect (moral hazard) of insurance holders and the higher services demand associated with individuals with poor health status (adverse selection). Our results indicate that supplemental private coverage present a positive and significant impact on preventive services, notably frequency of visits to doctors and exams for women (pap and mammogram). Contrastingly, we do not find strong evidence of a positive impact of supplemental coverage for non preventive health services, as inpatient and outpatient services and surgeries. Additionally, the results suggest that although private insurance has a significant and positive impact over the purchase of prescribed drugs, it does not have a significant effect over non prescribed drugs. Overall, our findings suggest that the main benefit of the income tax rebate is the positive effect on preventive health care demand, which should provoke an impact on health status for the group of individuals with supplemental insurance in the long run, as also reduce future health care expenditure. Moreover, the additional coverage effects on preventive care are more pronounced for women, white and older groups. Casual effects over non preventive care are stronger for men and non-white. Interestingly, we do not find significant different results between individuals with and without chronic disease. The effect of supplemental private care contrastingly to public free care is not trivial in developing economies, in a scenario in which private health expenses are usually above public expenses. 5 Even among the poorest, public service lower quality incentives population to look 4 A positive impact of supplemental coverage over health services utilization could be attributed to other behaviors rather than moral hazard. Meza (1983), for example, provides a model in which optimal insurance leads to a increase in medical demand. Other explanations include supply shocks. 5 According to WHO (2011), meanwhile average health expenditure for rich income countries is around 11% of GDP and 60% of total health expenses are public, in low income and lower middle income countries, the average is around 5% and 42%, respectively. For a review of health background in developing economies see Kremer and Glennerster (2011). 3

4 for private health provision. Because of that, there has been an increasing literature which investigates health utilization in low and medium income countries, mostly to comprehend the effect of the programs targeted for the poor. Recently, Bauhoff et. Al. (2011) investigates the effect of additional insurance publicly financed for the poor in Georgia and finds that, although the program has not affected services utilization, it has decreased out of pocket expenses. Additionally, Wagstaff (2009) studies the effect of a program to finance care to the poor in Vietnam and finds that inpatient care utilization has increased and the risk of catastrophic expenses has decreased although additional health care has not affected out of pocket expenditures. Moreover, Miller et al. (2009) analyze a publicly paid program for supplemental coverage for poor populations in Colombia and find that there is an increase in preventive health care in this group (2009). And Thornton et. Al. (2010) examines the effect of health insurance to informal sector workers in Nicaragua. This paper is organized in six sections. We start with a discussion about the Brazilian Health system and Brazilian tax scheme on the following section. Next, we detail data and sample selection. The methodological approach is explained in Section 4. Results are in section 5. Finally, Section 6 concludes. 2. Health Care and Tax Subsidy in Brazil Health services in Brazil can be characterized as a two tiered health system. Since 1990, the Government has provided universal health care services through Universal Health System (SUS, in Portuguese) 6. SUS is organized in decentralized levels and covers all 5,565 Brazilian municipalities. Public health services are operated directly by municipalities and states. 7 According to Secretary of Health in Brazil (2010), from a total of 8,539 hospitals in Brazil, 3,441 (around 40%) are public. Moreover, under the SUS system, there were in 2010 more than 17 million diagnosis procedures, 1.2 million childbirths, over 70 thousand cardiovascular surgeries and around 85 thousand oncology surgeries (Brazilian Secretary of Health, 2010). Thus, SUS attends a large share of the Brazilian population and provides a significant number of health services. 6 Prior to 1990, free public health services were provided only to workers who were registered at the public retirement system (Instituto Nacional de Seguridade Social - INSS, in Portuguese). 7 This is done by a nominated committee. For a detailed description of Brazilian health system see Alves and Timmins (2001) report for Inter-American Development Bank. 4

5 However, the public system is an alternative mostly to the share of the population which cannot afford a supplemental coverage. Several domestic pools reveal that health services are one of the main concerns of Brazilian citizens. For example, Alves and Timmins (2001) show that the Brazilian system is characterized by long waiting times and questionable quality. Further, IPEA (2010) reveals that although the free disposal of medical drugs is well evaluated in SUS, emergency department and inpatient services are considered bad for 31.4% of the interviewers. There is evidence that public provided health services are under capacity. Among the SUS patients, 37.3% and 34.1% of the interviewers recommend an increase in the number of doctors and a decrease in the waiting time. 8 Supplemental health coverage is available for most companies employees and private insurance is available for wealthier families. Figure 1 shows the share of individuals with any supplemental coverage (considering all kinds of supplemental coverage: private, employer provided and public employees) for different income deciles in a sample of households with at least one wage earner in the year While in the bottom income range, only around 10% of individuals owns any additional health insurance, in the top range this share peaks to 80%. Figure 1: Average and cumulative distribution of supplemental health coverage by household income deciles % % % 60% % % % % % 0.1 0% 0 Average distribution Income deciles % % % % % 0 Cumulative Distribution Income deciles Public and private health expenses have increased in the last decade in Brazil. Total per capita health expenditure increased in the period from US$ 265 to US$ 721 according to World Health Organization (WHO, 2011). Total health expenditures as a percentage of the gross domestic product rose from 7.2 to 8.4 in the same period. The rise in 8 In our sample, 22% of the patients consider SUS services (including visits to a doctor, inpatient and outpatient services ) not satisfactory, contrastingly to only 6% among supplemental insurance holders. Additionally, pool from Brazilian newspaper Folha de São Paulo indicates that from 2008 to 2011 the main concern of Brazilian citizens is health services (around 39%), overpassing public security and unemployment. 5

6 health services demand has been attributed to population ageing and to income gains (IBGE, 2011). Furthermore, the private expenditure share of health was 56% in 2008 (against 44% of public share), similar to the US expenditure pattern, where it is 52%. According to Brazilian Bureau of Economics and Statistics (2009), most private family health expenses are still concentrated on medicines (around 38%) and out of pocket services expenses (around 52%), in contrast to supplemental coverage (around 9%). Figure 2 brings the relative share of each medical service on total health expenses according to income and age deciles in our sample using POF data. It is possible to see that prescribed and non prescribed drugs constitute the major health expenses, with exception to the last two deciles of age. Supplemental health coverage expenses increase with income and, more strongly, with age. Contrastingly, expenses for non prescribed drugs are larger as income and age decrease. Other medical expenses (exams, inpatient and outpatient) increase in income and age, but they never constitute more than 30 per cent of the expenses and they are typically less than 20 per cent. Figure 2: Share on health expenses by income and age deciles 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Income Deciles 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Age Deciles prescribed drugs not prescribed drugs supplemental coverage inpatient and outpatient doctor s visits preventive exams dental care others 2.1 Tax subsidy Due to the great demand for public health services mostly from poor population and the great number of services provided by SUS, the increase of supplemental health coverage should smooth health public costs. Differently from United States, where only the employer 6

7 provided health insurance is exempt from income tax, in Brazil any supplemental health coverage expense is deductible from income tax. 9 This includes both private and corporate provided health coverage. The difference is that, in employer provided plan, only the copayment portion of the employee is tax deductible. The size of tax subsidies depends on income ranges. In 2008, there were three different income tax ranges. 10 The lowest range (cap on approximately US$ 9,750 annual earnings in 2008) was tax free. The intermediary range collected a 15% tax rate. And the higher range (more than US$ 19,350 thousand of annual earnings in 2008) should collect a 27.5% tax rate. The amount of tax subsidy corresponds exactly to the tax fee. For example, if a tax holder has spent R$ 100 in health services and she is in the third income tax range, she should deduct R$ 27.5 from the income tax charge. Although other expenses are also tax deductible, such as educational and private retirement plans, only health expenses are unbounded tax deductible. As a consequence, someone can collect no income tax or can even get a tax refund mostly because of health expenses. Thus, as detailed further in Section 4, our empirical strategy explores the large effect of tax subsidy on supplemental health coverage holding. We should note that not all health expenses are tax deductible. Meanwhile expenses with inpatient and outpatient care, exams, doctors visits and supplemental coverage are eligible for the tax subsidy, some others expenses are not: this is the case of drug expenditure, vaccination, nursery and physiotherapist services. This could cause a potential double effect of income tax rebate over service utilization and insurance holding. Later, in section 5.4, we show that results are maintained whether individuals who pays for health services are excluded or kept in our sample. It is noteworthy to point out that only a small share of individuals with supplemental coverage does not use the insurance and pays occasionally for health service utilization. Official records about total tax rebate are not available, but in our sample, the average tax-deductible health expenses per individual are around R$ 647 for the second income tax range and R$ 140 for the first income tax range in a one year period. This suggests that, at least in our sample, the tax subsidy is around R$ 171 and R$ 21 per individual, in the second and first income tax range, respectively. This quite simple simulation estimates a weighted 9 Income tax is collected over federal level in Brazil. 10 In Brazilian currency ($ Reais), the monthly amount of cutoffs in 2008 were exactly R$ 1, and R$ 2,742.25, after discounted for social security contribution. In Brazil, income tax base deducts social security contribution. We have data on income prior to this discount. In this case, the first and second cutoffs are, respectively, R$ 1,508.5 and R$ 3, Income tax fees and tax base change frequently in annual basis. 7

8 subsidy around R$ 70 per individual yearly in our sample, considering households in all tax ranges as also income tax exempt. If correct, this amount would represent around 12% of public spending on health in 2008 according to IBGE. According to Internal Revenue Service in Brazil (2010) around 25 million tax statements are filled yearly. We should note that only households with formal wage earners must collect income tax. This includes public employees (as governments and army workers) but exclude self-employed and informal workers. 11 Additionally, income tax in Brazil is based on individual income, but tax statement can be done individually (individual income is considered) or per household (familiar income is considered). For households with only one wage earner, the individual income coincides with the familiar income for tax statement purposes. For cases in which there is more than one wage earner per household, there could be a joint tax statement (family income) or more than one tax statement (individual income) Data and sample selection Data regarding health care utilization is available in the Health Supplementary Questionnaire from National Household Survey (PNAD in Portuguese). PNAD is a yearly crosssectional survey provided by the Brazilian National Bureau of Statistics and Economics (IBGE in Portuguese). PNAD sample follows the Brazilian census methodology in which household selection is randomly assigned and weighted sample should represent the Brazilian total population regarding state and municipality shares. Health Supplementary Questionnaire is realized each five years and because of that data from 2008 is the most recent. Besides demographic and social economics characteristics, survey information includes data about several health care services. We use nine binary responses about services demand, including: visits to a doctor in the last two weeks, visits to a doctor in the last year, use of outpatient hospital services in the last two weeks, use of prescribed medication, treatment 11 Actually, most self-employed are informal workers. According to IBGE, around to 28% of Brazilian workers were not formal in One special characteristic of income tax system is that they are two types of statement: the simplified form and the complete form. In the former, the taxpayer does not fill deductible expenses and can automatically declare that 20% of their total income is tax deductible, without any document. In the latter, the taxpayer has to declare exactly her deductible expenses and has to keep the records for potential auditing. Thus, anyone with tax deductible expenses higher than 20% of total income should collect income tax through completed form. According to IRS in Brazil, one third of all income tax forms are on the complete form. In our data we are not able to identify if income tax contributors have filled complete or simplified form. Despite this drawback, our data suggest that potential tax subsidy is closed associated to health expenses, since supplemental health coverage holding is strongly related to income tax cutoffs. 8

9 services (it includes both inpatient and outpatient hospital stay), surgery in the last year, in home emergency service in the last year, and women having a mammogram and a pap smear in the last year. In order to obtain an adequate sample for our analysis we exclude individuals with nonstandard health coverage status. This includes public employees which receive exclusive free supplemental health coverage. Additionally, we exclude employees with employer provided health insurance. For these two groups, only the coparticipation expenses are eligible for health deduction on their income tax. However, we do not observe the coparticipation share. They typically tend to be low. Additionally, most public employees can use hospital not available for public service. Also, in accordance with our discussion in Section 2, we exclude households with no wage-earning employees, as households with only self-employed or other labor status are not supposed to declare income tax. Due these reasons, we drop respectively, 13,889 and 5,513 and 120,733 cases from our sample. We also drop individuals under 18 years old (120,191 cases) and information supplied by non-family members (1,294 cases), as housemaid, to mitigate potential measurement errors. Although, we do not have data about pregnancy status, we exclude 2,301 women which have attended any medical service related to pregnancy in the last year. Finally, our sample includes 110,841 individuals and 53,588 households, in which 104,106 individuals are beneficiary only of SUS and 6,735 individuals own private supplemental coverage. They all correspond to households with at least one wage earner employee. Besides PNAD, we collect data on the Household Budget Survey (Pesquisa de Orçamento Familiar, POF in Portuguese). This cross sectional survey is also provided by IBGE and has household and individual expenses on supplemental health coverage, hospital services, visits to doctors, medical exams and prescribed drugs. We use POF data to analyze supplemental coverage effect over out of pocket expenses and non prescribed drugs usage. Moreover, we use the same exclusion criteria used for PNAD data as detailed in the previous paragraph. Because of that, we are left with 75,816 cases, after excluding 121,476 cases. 9

10 TABLE 1 : Descriptive Statistics Health Insurance Group SUS Private Variable mean s.d. mean s.d. Health services Visits to a doctor (last 2 weeks) Visits to a doctor (last Number of visits to a doctor (last Pap smear (last Mammogram (last Outpatient stay (last 2 weeks) In home emergency service (last Inpatient stay (last Surgery (last Use of prescription medication Socioeconomic Lives in urban area Gender (if male, D=1) Age Ethnic group (if non white, D=1) Years of schooling Nº of household members Married with children Married without children Household income 1,869 2,420 4,524 5,436 Chronic diseases Cancers Diabetes Heart disease Hypertension Kidney disease Rheumatism Some chronic disease (binary variable=1) Others Involved in some accident (last Mobility difficult Smoker Self reported health status (% very good or good) Notes: PNAD data. Number of cases 110,

11 Table 1 brings summary statistics on PNAD data for our dependent variables, independent variables and other variables of interest in our sample. As expected, individuals with supplemental health coverage present higher services utilization. The main exception is emergency department services, the only case that individuals with only access to the public system use more the service. 13 On most services, private insurance holders present higher services utilization, mostly on visits to the doctor in the last two weeks, inpatient services, surgery and prescribed drug usage. These results probably reflect some adverse selection, in the sense that wealthier individuals with worse health status hold more private insurance. Regarding socioeconomic characteristics, individuals without supplemental coverage (SUS users) are less urbanized, present fewer years of schooling, have a greater proportion of non-whites and earn less income. Additionally, private insurance holders have the highest income average and compose the elderly group. Furthermore, analysis of health status reveals that occurrence of all chronic disease is more pronounced in individuals with private coverage is in all illness in the list. This last information, as also age average, reinforces the occurrence of adverse selection over private holders. Nevertheless, the percentage of smokers is larger on SUS and self-reported health status is a little worse for individuals without supplemental coverage. Finally, around 80% of individuals with private coverage in our sample consider the supplemental coverage very good or good. In section 5.2 we explore some data regarding individuals behavior and socioeconomic characteristics to obtain some robustness checks. Next we address the methodological framework. 4. Methodological Framework 4.1 Identification Strategy The identification strategy is based on the idea that the kinked rebate rules of the Brazilian income tax system provide exogenous variation on supplemental insurance relative prices. Individuals just above kink points face different relative prices compared to individuals just below these kink points. Larger supplemental health coverage holding could occur due to higher price elasticity for individuals with income around the cutoff point (medium and low 13 One possible explanation to this is that poorer individuals tend to make less use of preventive health care services. Also, in emergency departments entrance is unexpected and in rural areas public center can be closer than private hospitals. 11

12 ,000 1,083 1,167 1,250 1,333 1,417 1,583 1,750 1,917 2,083 2,250 2,417 2,583 2,742 2,833 3,000 3,167 3, ,000 1,083 1,167 1,250 1,333 1,417 1,583 1,750 1,917 2,083 2,250 2,417 2,583 2,742 2,833 3,000 3,167 3,333 income socioeconomic group). The magnitude and mechanism of the relative fall in price in supplemental health coverage are depicted in Figure 3. Figure 3 simulates the fiscal subsidy for a supplemental coverage plan with cost of R$ 100 monthly. Figure 3: Tax rebate kinked scheme for a suplemental coverage of R$ 100 per month 120 Insurance price ($100/monthly) Income Cumulated Discount % Income It is noteworthy that relative price changes because deductible health expenditures (as it is the case for prepaid health plan) decreases the income tax base, since eligible individuals around cutoff points move from a higher tax rate range to a lower one. For example, individuals with a R$ 100 deductible health expenditure and a monthly income just above the 12

13 second cutoff (as R$ 2,800, for example) change from a 27.5% income tax rate range to a 15% income tax rate range. The relative discount increases (decreases) as far as the difference between the individual income to the income tax cutoff approaches (strays) the maximum amount of deductible health expenditure (the tax rate value), and after this cap the discount is constant. Due the rebate mechanism, meanwhile there is no price variation in supplemental health coverage for points far from the cutoff, around the cutoff there is a kink variation in the relative insurance price. The change of slope instead of a change in levels (jump) around cutoffs points summarizes the main idea of the regression discontinuity design with a kink or regression kink design (RKD) (Card et. Al, 2009; Dong 2012; Simonsen et. Al., 2011). While income impacts personal decision of purchase supplemental health coverage, we expect that an insignificant share of health service utilization is explained by income around tax cutoffs. We argue that if income tax cutoffs (our instrument to supplemental health coverage holding) are smoothly related to other explanatory variables used in the model, changes in the slopes of supplemental coverage holding can be attributed to health expense rebate found on income tax cut offs. Our main assumption is that income tax cutoffs are not related to individual's health status, including unobservable characteristics. Thus, adverse selection bias is ruled out and we should get a valid estimate of the effects of additional health coverage on health care demand. In recent years, the number of studies which applies regression discontinuity as an identification tool in health services demand has increased. 14 Card, Dobkin and Maestas (2008) use the threshold at age 65 for Medicare eligibility to estimate the impact of supplemental insurance coverage on health care demand in the U.S.. The authors notice that Medicare eligibility causes an increase in health care utilization and most interesting, this rise varies with the type of services and across groups. Likewise Card, Dobkin and Maestas (2008), Anderson, Dobkin and Gross (2011) use the discontinuous change in coverage status in young dependants of their parents' insurance plans to estimate how uninsured young adults behave differently of their insured counterpart. They identify a fall in the use of some health care services as emergency department visits and nonurgent hospital admissions. Finally, similar to our identification strategy, Simonsen et. Al. (2011) explores a kink reimbursement scheme of prescribed drugs in Denmark to investigate drugs price elasticity of demand. 14 To the best of our knowledge, Card and Shore-Sheppard (2004) were the first to apply regression discontinuous framework to evaluate health care programs effects. 13

14 4.2 Regression Kink Design (RKD) As described by Van der Klaauw (2002), the main idea behind RDD method is that in the case of lack of treatment, individuals in a small distance around the cutoff point should present similar results in the dependent variable. Likewise the standard regression discontinuity approach, RKD is considered a quasi-experimental method, similar to randomized experiments, in which individuals just below the kink cutoff compose the control group and individuals above the kink cutoff compose the treatment group. Dong (2012) proposes a general estimator in which the identification is based on changes in level, or slope, or both, of the treatment probability at the cutoffs of the assignment variable. In the case of a kink policy, comparison (difference) of slopes change between the groups provides the local average treatment effect. As demonstrated first by Hahn, Todd and Van der Klaauw (2001), under a two stage least square model (2SLS) the causal effect is obtained by instrumenting the treatment dummy. Dong (2012) extends this result for RKD and proves that, over some non very restrictive conditions, regression estimate of causal effects of a change in level or slope are numerically equivalent to IV regressors. Thus, we use selected cutoffs and their respective slopes as excluded instruments to obtain consistent estimates of the causal effect of supplemental health coverage (T i ) on services utilization (Y i ). 15 More formally, suppose that the treatment effect, in our case access to supplemental health care coverage, take the functional form: Y i = α +βt i + Ɛ i (1) in which Y i is a binary dependent variable that indicates health service utilization, T i represents a binary treatment effect, and Ɛ i stands for others unobserved determinants of the dependent variable. We should note that ordinary least squares (OLS) estimate of equation 1 are biased because self-selection into treatment is not random, as the decision to purchase additional coverage is associated with health status. In fact, we should expect E[(Ɛ T)] 0. Consider that both the treatment effect (T) and the outcome of interest (Y) are a function of the assignment (or forcing) variable X (household income). In a standard RD approach, a change in level of the treatment probability at a threshold value of X (X=c, the 15 This follows Dong (2012) pp. 8 to

15 cutoff) is explored to identify the average treatment effect of the treated τ(c) on the outcome of interest (Y). In this framework, Y(1) and Y(0) designate potential outcomes for treated and not treated. It follows: Y=TY(1)+(1-T)Y(0). The conditional means functions are defined as: E(T X)=f(X) and E(Y X)=g(X) A complier is defined as D* = I (T=T*), where T*=I(X>=c) ;and the compliance rate at the threshold (X=c) is defined as E(D* X=c). The main difference between the standard RD approach and the RKD approach is that meanwhile the first looks at the the limits of means around the right and the left cutoff sides, the latter looks at the respective derivatives (slopes). Thus meanwhile the jump estimator follows (2), the kink estimator follows (3): ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) if ( ) ( ) (2) if ( ) ( ) (3) The two are valid estimators and in the special case of both (2) and (3) exists, they identify the same treatment effect (τ). To achieve these properties, the model assumes that: E(Y(t) X=x, D*=1) for t=0,1 E(Y X=x, D*=0) E(T X=x, D*=0) (i) (ii) (iii) are all continuously differentiable for all x around cutoff x=c. Smoothness of (i), (ii) and (iii), assures, respectively, that outcomes are not affected by sorting behavior, the change in the outcome is due to compliers and that the treatment change is due to compliers. Rewriting the changes of level and slope as: ( ) ( ) and ( ) ( ) ( ) ( ) and ( ) ( ) Someone can define the treatment equation as: T=r+s(X-c)+pT*+q(X-c)T*+V (4) And someone can write the reduced-form for Y as: Y=A 1 +A 2 (X-c)+BT*+C(X-c)T*+U (5) 15

16 To obtain the 2SLS estimator of τ, define y as Y, t as T, t* as T* and z as (X-c)T*. The Y, T and reduced-form Y equation are rewritten as: y=τt+e t=pt*+qz+v y=bt*+cz+u It is possible to write τ as : τ= cov(y,pt*+qz )= cov(t,t*)b + cov(t,z)c = w 1 B + w 2 C cov(t,pt*+qz )= cov(t,t*)p + cov(t,z)q = w 1 p + w 2 q Dong (2012) proves that 2SLS is a special case of the general RD with kink and jump. Either T* or (X-c)T*, or both can be used as excluded IV s for the causal effect in a jump, kink or jump and kink regression discontinuity. To obtain the unconditional average treatment effect covariates are not necessary for consistency, but they may increase efficiency. The main limitation of any RD design is that it estimates the treatment effect for the individuals around the threshold. In the case of varying treatment effects, as discussed in Van Der Klaauw (2001), extrapolation of the results depends on additional assumptions about the average outcome, and the assignment variable. Our estimates should represent more accurately the effect of private insurance for wage earners, since this group is the one which benefits most from the income tax deduction scheme. Indeed, since the income tax rebate represents a fall in the relative price of private insurance independent from health status, extrapolation of estimates should not be driven by adverse selection mechanisms, and could be extended for similar socioeconomic groups as workers with employer provided health coverage. 5. Results 5.1 First stage results Table 2 presents the first stage results. On column I we estimate the coefficient of the standard (jump) RD as suggested in Lee and Lemieux (2010). We report the coefficient of the cutoffs, smoothness and interacted parameters of a first order polynomial function. 16

17 Specification of column II and III follows the RKD approach as suggested by Dong (2012). 16 We do not model the jump (we discard the dummy variables), but we estimate the slopes and the assigned variable coefficients, this last in level and squared. Finally, column IV follows function (3) with the full set of covariates. We expect significant coefficients for the slopes (kink) parameters. In function (3), our estimates suggest a change of slope of and at the first and second cutoff, respectively. Those coefficients are significant at the 1% level and can be considered high, since in our sample the average of private insurance holding is 6.1%. When reported (on column A), the jump parameters are weakly significant in the first cutoff but are significant at the second cutoff, although both jump parameters present a small magnitude when compared to the slope parameter coefficients. Our first stage coefficients are also similar in both data sets (PNAD and POF). Moreover, to illustrate how a piecewise linear income tax rule can be used to estimate health services utilization, we provide some graphical evidence of the effect of income on supplemental coverage holding. As suggested in Lee and Lemieux (2010), we split the forcing variable into a number of bins on each side of the first and the second cutoff point. Figure 4 plots for each bin, the fraction of individuals with supplemental health coverage against income tax cutoffs. The solid line brings the fitted values of ordinary least square regression of private health coverage against the level and slope dummies (actually, first stage fitted values). Inspection of Figure 4 reveals that insurance holding is positively associated with income level. There is some evidence of change of levels, but more importantly for our approach, there is a change of slope in the fitted values of insurance holding around both cutoffs. This policy (tax rebate) induced kink around cutoffs of the assigned variable is what makes our identification strategy feasible. This visual evidence does not allow us to rule out a jump on the supplemental coverage average holding, although it suggests that the change of slope is more significant than the change in level, mainly in the first cutoff, as confirmed by our first-stage estimates reported in Table 2. First stage results and graphical representation of fitted values suggest that cutoff slopes provide an appropriate instrument for applying the TSLS-RKD approach. Based on this evidence, we generate several regressions over health service utilization in preventive and non preventive health utilization. This should provide a large scenario of supplemental health 16 As noted by Dong (pp and footnote 10, 2012), someone does not need to include higher order terms to avoid misspecification. We discuss results with the quadratic term on section 5.4. So far, we note that quadratic term on both smooth parameters cutoffs are collinear, and because of that we include only the squared income as covariate. As described in Table 2 (colum III) this term is not significant in the first stage regresion. 17

18 coverage influence over services demand in Brazil. Next, on section 5.2, we argue that our empirical approach presents internal validity. Table 2: First-stage results - OLS regression Dataset PNAD POF I II III IV I II III IV D 1 (=1 if Income > 1,508.5) 0.004* 0.004* 0.005* 0.006** (1.909) (1.722) (1.921) (2.218) D 2 (=1 if Income > 3,082.3) 0.018*** 0.018*** 0.012*** 0.010** (3.857) (3.930) (2.676) (2.419) Ln( income i - 1,508.5) 0.047*** 0.047*** *** 0.037*** 0.038*** *** (18.354) (19.227) (-1.025) ( ) (13.465) (14.551) (1.379) (-7.524) Ln( income i - 3,082.3) *** *** *** *** *** *** ( ) ( ) (1.263) (14.820) ( ) ( ) (-1.353) (8.917) Ln( income i - 1,508.5) * D *** 0.073*** 0.052*** 0.064*** 0.033*** 0.048*** 0.041*** 0.046*** (8.356) (16.046) (7.154) (14.462) (5.286) (10.561) (4.511) (10.187) Ln( income i - 3,082.3) * D *** 0.043*** 0.053*** 0.045*** 0.049*** 0.037*** 0.057*** 0.035*** (6.357) (5.628) (6.041) (5.973) (6.015) (5.130) (5.674) (4.844) Ln( income i ) (0.345) (-1.224) Lives in urban area 0.006*** 0.012*** (4.100) (8.118) Gender (if male, D=1) (1.609) (1.561) Age 0.003*** 0.003*** (13.670) (11.269) Age *** *** (-2.597) (-5.697) Ethnic group (if non white, D=1) *** *** ( ) (-4.472) Ln years of schooling 0.029*** 0.020*** (30.285) (18.713) Ln nº of household members *** *** ( ) ( ) Married with children *** (-4.729) (-1.332) Married without children *** ** (-7.522) (-2.448) Notes: In parentheses are robust t statistics. Significant at 10%; significant at 5%; significant at 1%. Number of cases is 75,816 for POF data. For PNAD data, number of cases is 110,841 and 110,429 for the regression with the full set of covariates. 18

19 Figure 4: Private coverage holding per household income (1st and 2nd cutoff) Notes: Solid lines represent fitted values of first stage regression. 5.2 RDK internal validity The main issue about RD is whether other variables, including observable and unobservable, could also be discontinuous at each threshold. As suggested by Dong (2012) and Van der Klaaw (2002), we select some variables related to health condition and test whether the continuity assumption holds for this set of observable variables. We run first stage 19

20 regression with the full set of covariates over these health characteristics (as described in Table 1) as the dependent variable. Table 3 presents the estimated coefficients for smoothness and interacted at the cutoffs for six different chronic diseases, if the individual presents some mobility difficult and, or if she or he is a smoker. Auspiciously, there is no systematic discontinuity found around the cutoff. It is noteworthy to point out that all interacted coefficients are quite close to zero and the majority is not significant. Only the interacted term for mobility difficulty is significant in the first and second cutoff, although the estimated coefficients present different signal (the first is negative and the second positive) and much less magnitude than in private insurance regression. Additionally, in Appendix in Figure A.1, we depict eights plots with the average of individuals with chronic disease, mobility difficulty, share of smokers and age average in the two income cutoff points likewise Figure 4. There is no evidence of significant adverse selection around the thresholds. Although we cannot investigate unobservable variables, those results reinforce the idea that continuity assumption holds over most variables. Another concern is the possibility that individuals would manipulate income near the threshold to collect less or avoid income tax and this manipulation around thresholds would invalidate RD design. First, we argue that this hypothesis is less likely in the case of wage earners employees. Second, we apply the McCrary (2008) test of discontinuity in the density of the assigned variable and do not find any discontinuity in the density around the first and second cutoffs. 17 Figure 5 depicts the raw density of average household income over bins and inspection of them reveals peaks of cases around whole number multiples of 100 and of 500. Similarly, we compute a density histogram of the total household income distribution (Figure A.3 on appendix) and observe the same peaks of cases around whole numbers as also around the minimum wage in 2008 (minimum wage was at that time R$ 415). Thus, we do not identify any other pattern that could cast doubt about self-selection around thresholds. 17 The local linear estimated parameters for discontinuity in the density (and standard errors) are for the first and the second cut-off, respectively, (-0.092) and (-0.098). 20

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