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Área 3 – Economia do Trabalho, Economia Social e Demografia

HOME CARE AND HOSPITAL STAYS: A Regression Discontinuity Design Analysis

Fábio NishimuraDoutor em Economia PIMES/UFPEUFMT- Universidade Federal de Mato GrossoPrograma de Pós Graduação em EconomiaEmail: f_nobuo@yahoo.com.brAvenida dos Estudantes, n° 5055Bairro Cidade UniversitáriaRondonópolis/MTCEP: 78736-900

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HOME CARE AND HOSPITAL STAYS: A Regression Discontinuity Design Analysis

RESUMO

A escassez de leitos hospitalares sempre foi uma questão crítica, especialmente para as pessoas mais pobres. Assim, os governos elaboram programas e ações para mitigar esses problemas de saúde e minimizar o sofrimento das pessoas que necessitam de cuidados hospitalares. No caso brasileiro, uma dessas ações é o programa Melhor em Casa (MemC), cujo objetivo é transferir pacientes atendidos na unidade de saúde para completar sua recuperação em domicílio, por meio de atendimento domiciliar, com acompanhamento especializado e a presença de sua família. Nesse contexto, o presente trabalho tem como objetivo verificar se o programa é capaz de reduzir o tempo de internação hospitalar e, consequentemente, aumentar o número de leitos disponíveis nas unidades de saúde. A estratégia empírica empregada foi o modelo de Regressão Descontinua (RDD), uma vez que controla os possíveis problemas de endogeneidade e garante respostas estatisticamente imparciais. Como resultado, confirmamos que o programa conseguiu reduzir o tempo de internação hospitalar.

Palavras-chave: Programa Melhor em Casa; Internações hospitalares; Desenho de Regressão Descontinua.

ABSTRACT

Bed shortage has always been a critical issue, especially for the poorest people. Hence, governments design programs and actions in order to mitigate such health issues and to minimize the suffering of people in need of hospital care. In the Brazilian case, one of these actions is the Melhor em Casa (MemC) program, whose objective is to transfer patients who have been cared for in the health unit to complete their recovery at home via home care services, with specialized monitoring and in the presence of their family. In this context, the present paper aims to verify whether the program is able to reduce the length of hospital stays and, consequently, to increase the number of available beds in health units. The empirical strategy employed was the regression discontinuity design (RDD), since it controls for potential endogeneity problems and ensures statistically unbiased responses. As a result, we confirmed that the program was able to reduce the length of hospital stays.

Keywords: Melhor em Casa program; hospital stays; regression discontinuity design.

Área 3 – Economia do Trabalho, Economia Social e Demografia

JEL Classification: I00; J18; I18

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1. INTRODUCTION

The Brazilian federal government, through it public health system, has always faced difficulties related to providing hospital services, with lack of medicines, shortage and inefficiency of skilled labor and an insufficient and inadequate infrastructure. One of the components of this negative scenario is the bed shortage in health units, which affects negatively the health status of patients. Castro et al. (2005), O’Dwyer et al. (2009) and Bittencourt & Hortale (2009) also addressed such issues in order to observe the effects on health problems.

The bed shortage issue entails a series of consequences that can eventually lead to the death of the patient. According to Ferrero et al. (2001), Amaral et al. (2001), Silva et al. (2014) and Sorensen et al. (2016), bed shortage is closely linked to the high demand for public services, inefficiency of technical management and poor conservation of the existing infrastructure, a situation that ends up generating high maintenance costs to the government.

In this context, the federal government launched the Melhor em Casa (MemC) program in order to increase the number of available beds in hospitals through providing home care services for patients of public hospitals. The program is based on home care (HC), that is, the patient that was already being cared for in the health unit and is able to complete their recovery at home can be transferred. As a result, admission costs decrease as well as hospital mortality rates.

Moreover, HC reduces the chances of infection since it removes the patient from an environment with potentially harmful bacteria and also prevents from medical errors caused by pressure and stress in the team as it has been pointed out by Leite & Farias (2009), De Araújo Madeira et al. (2012) and Triin Pärn et al. (2016).

Another positive implication of HC is the decrease in hospital readmissions. According to Gassaway et al. (2016), Magalhães et al. (2017) and Ryan et al. (2017), recovering at home promotes better and more lasting results in terms of clinical state, avoiding potential relapses in the patient’s health status.

For Shippee et al. (2015) and Hoell et al. (2016), when relatives are involved in the treatment, being more attentive and careful, recovery is positively affected.

In this regard, the objective of this paper is to verify whether the MemC program is able to reduce the length of hospital stays.

To do so, a regression discontinuity (RD) model was used as statistical instrument where, through a cutoff point existing in the program (minimum population of 20,000 inhabitants), a counterfactual could be constructed to help answer our question. Thus, using this method, the results guarantee a defense against endogeneity problems. Seeking causality, we were concerned with a potential selection bias and with the existence of some type of manipulation in our cutoff point, which is a key factor for the empirical strategy; hence, we performed tests to verify the possibility of rejecting such hypotheses. Finally, to ensure the estimated results statistically, robustness tests were performed.

The paper is split into five sections besides this introduction. The second section presents the MemC program, its basic operational characteristics, objectives and coverage. In the third section, we present the data, linking variables of interest, descriptive statistics and the behavior of covariates in the model. Fourth section details the empirical strategy and also some robustness tests to check the estimators. Finally, the last section presents the results and the final considerations.

2. THE MELHOR EM CASA (MemC) PROGRAM

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Universal access to quality public health is desired by every society; however, the actual available supply presents great difficulties in delivering such principles. Attempting to overcome these obstacles, public managers design and execute actions and programs that reach most of the society and, thus, provide more access to the health network.

Hence, the Brazilian federal government, in 24 August 2011, launched the Melhor em Casa (MemC) program to improve and expand the assistance in the Unified Health System (SUS) to patients that can receive humanized care at home and close to their family (Ministério da Saúde, 2011).

The main idea of the program is home care (HC) which, according to the Ministry of Health (2011), consists of a modality of health care either substitutive or complementary to the already existing ones, characterized by a set of actions to promote health, prevention and treatment of diseases and rehabilitation provided at home, with the continuity of care guaranteed and integrated to health care networks.

The great advantage of this program is that care received at home, with the affectivity of relatives, result in a more positive and effective recovery in comparison with hospitalization. This is due to the humanized care provided by the health team specific to home care and, especially, to the family affection received. According to Feuerwerker & Merhy (2008), being at home enables a new “care space” that can “refer to an identification and proximity to the caretaker that goes beyond the technical function and the hospital institution”.

Thus, the home environment and the family relationships established there, which differ from the relationship established between the health team and the patient, tend to humanize care, reinserting the user more in the position of subject to the process and less in the position of object of intervention (Brasil, 2011). The other part of the program seeks to reduce the length of hospital stays, which promotes a better use of hospital beds (Brasil, 2011).

MemC represents an improvement in the management of the entire public health system since it helps vacate hospital beds, providing better care and regulation of hospital urgency services. It is estimated that, with the implementation of home care, up to 80% of the costs with patients are saved when compared to the costs incurred if they were hospitalized (Brasil, 2011).

According to the Brazilian Ministry of Health (Ministério da Saúde, 2011), Home Care must follow the following guidelines:

I – Be structured in the perspective of health care networks, with basic care being the beacon for care and territorial action;

II – Seek integration with other levels of health care, with back-up services and incorporated to the regulation system;

III – Be structured following the principles of expanding access, reception, equity, humanization and integrality of care;

IV – Be inserted in the lines of care through clinical care practices based on the user’s needs, reducing the fragmentation of care;

V – Adopt a care model centered in the work of multiprofessional and interdisciplinary teams; and

VI – Stimulate the active participation of the health professionals involved, the user, the family and the caregiver.

As a criterion of implementation, the municipality must have at least 20,000 inhabitants according to data from the Brazilian Institute of Geography and Statistics (IBGE), have a reference hospital in the municipality itself or in the region where it is located and a SAMU (Mobile Urgency Service Care) unit (Brasil, 2011).

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According to Brasil (2011), home care (HC) in the context of the Unified Health System (SUS) should be organized into three modalities, established from the characterization of the patient and the type of care and procedures:

HC1: is intended for users whose health problems are either controlled or compensated and with physical difficulty or impossibility to get to a health unit, who need care with less frequency and less health resources. Basic care teams are in charge of the provision of care in the modality HC1, including Family Health teams and Family Health Support Centers through regular home visits at least once a month.

HC2: is intended for users with health problems and difficulty or impossibility to get to a health unit who need care with more frequency, health resources and continuous monitoring that can be from different services provided by the care network. The Home Care Multiprofessional Team (EMAD) and the Multiprofessional Support Team (EMAP), both designated for this purpose, are in charge of the health care provision in modality HC2.

HC3: this modality is intended for users with health problems and difficulty or impossibility to get to a health unit who need care with more frequency, health resources and continuous monitoring that can be from different services provided by the care network. The Home Care Multiprofessional Team (EMAD) and the Multiprofessional Support Team (EMAP), both designated for this purpose, are in charge of the health care provision in modality HC3.

In summary, the MemC program seeks to reduce hospital stays, increasing the availability of beds for more severe cases and, in addition, enables the patient to recover together with their relatives, improving their health.

The next section presents the data used to verify the effect of MemC on hospital admissions.3. MATERIALS AND METHODS

3.1 Data

The dependent variable, length of hospital stays, was collected from the Department of Informatics of the Unified Health System (DATASUS), an organ of the Ministry of Health, through the set of micro data of the System of Hospital Admissions for the 2010-2013 period.

Within this period, we observed an average hospital stay of 5.32 days in municipalities where the program existed, against 4.99 days where it did not. This indicates there should be some type of incentive for the program to be implemented where hospital stays are longer.

To analyze the effect of MemC, data were collected from DATASUS and CNES (National Registry of Health Facilities) – both organs of the Ministry of Health.

To identify the municipalities where MemC works, we used a dummy where municipalities where the program works are defined as treated (and take value 1) and the rest is defined as controls (and take value 0).

Analyzing the data set we observe that in 2011 the program contemplated 23 out of the 5,570 Brazilian municipalities. In 2012, this number grew to 90 and, in 2013, to 1804. This represents a leap from 0.4% to 3.3% in the coverage of the program in two years even without considering its indirect effect due to coverage, very usual in the health environment.

The covariates or control variables employed were GDP per capita and public health services. The GDP per capita was used to control for potential income inequalities across municipalities, with data from IPEADATA (the database of the Brazilian Institute for Applied Economic Research) for the 2010-2013 period. This

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control has been used since households with higher incomes can hire private home care services that are usually offered at high prices; thus, we attempted to capture such effect through this covariate.

The health services variable is composed of the number of teams related to health care that do not participate in the group that works for the program; in addition, it has also been considered the number of equipaments existing in the municipality. These grouped statistics were used to control for people’s health conditions, since the clinical wellbeing makes the contingent of health services, coming from forms other than the program, to cause changes in the length of hospital stays. Hence, the data were collected from DATASUS through information generated by the Hospital Information System (SIH/SUS).

It is noteworthy that these control variables are used to enhance the accuracy to the estimated values, according to Imbens & Lemieux (2008), though they should neither interfere nor cause any bias in the results of the model.

Once the variables have been presented, the next section details the empirical strategy.

3.2 Empirical Strategy

3.2.1 Test for the manipulation of the cutoff point by municipalities

A crucial point of the empirical strategy of this paper is to analyze the criterion imposed by the program, under which the municipalities contemplated must have at least 20,000 inhabitants (the cutoff point). This numerical imposition of the cutoff creates room for discussion on the counting the population of municipalities (Monastério, 2004). Municipal managers interested in receiving MemC can somehow attempt to manipulate the population information so as to be covered by the program. To test this hypothesis, we followed the strategy of Cattaneo, Jansson & Ma (2017)1, named "Manipulation Test”, which is based on the density of the discontinuity functions at the cutoff.

According to CJM (2017), we have a random sample formed by a random variable x, a probability density function f(x) and a cumulative distribution function F(x), and a cutoff x where, depending on whether the random variable is above or below x, we have the treatment or the control group. The hypothesis of this manipulation test is to verify if f(x) is continuous in x, that is, if there is continuity at the cutoff.

Formally, the interest lies in testing the following problem

H 0 : limx↑ x

f (x)=limx ↓ x

f (x )vs H1 : limx ↑ x

f (x)≠ limx ↓ x

f (x)

CJM (2017) constructed this statistical tests using the local polynomial density estimator based on the c.d.f. of the observed sample.

3.3.2 Sample selection bias: the Heckman correction model

Another factor potentially harmful to the chosen statistical model would be the lack of randomness in the sample, what would cause selection bias. This problem may come from the quality, the quantity and the availability of pre-existing health

1 From now on, CJM (2017).

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infrastructure in the municipality, or even from the condition of genetic improvement by the population, where both would cause a reduction in the length of hospital stays. Hence, we used in this paper a strategy known as “Heckit”, elaborated by Heckman (1979), to correct the problem of sample selectivity. It is noteworthy that this strategy was used only when the hypothesis of sample selectivity was identified, mitigating the selection bias in the results of the paper.

Thus, we present below the form of Heckman’s two-stage selection bias correction method (Heckit) to identify potential causes of selection bias, where2:

Y 2=αZ+δ (1)

Y 1=β0+β1 X+σ ρϵδ λ (T−αZ )+σ ´ ϵ ´ (2)

In the selection equation (1), estimated with a Probit, Y 2 is the dichotomic dependent variable, Z is the independent variable, α is the coefficient of Z and δ is the normally distributed error term. In the regression equation (2), the value of Y 1 is observed when Y 2 is above a limit T and is censored if Y 2 ≥ T. The estimate of (2) is a simple regression of Y against X and will be biased due to the term σ, which represents the omitted variable.

This problem can be solved in two stages. First, equation (1) is estimated using a Probit and the predicted values are retained as estimates of (T − αZ). The, the inverse Mills proportion is estimated for each case, where we have the ratio between the normal density function evaluated at (T − αZ) and the denominator stipulated in one minus the normal distribution function estimated at (T − αZ), related to equation (3).

λ (T−αZ )= φ (T−αZ )1−ϕ (T−αZ )

(3)

The second stage is an ordinary least squares regression (2) with X and the inverse Mills production included as regressors. The estimator is consistent when the assumptions are met.

3.3.3 Regression Discontinuity Design

The paper aims to analyze the effect of home care on the length of hospital stays – in this case, the effect of the MemC program. Thus, as an empirical strategy, the regression discontinuity design (RDD)3 will be considered following Thistlewaite & Campbell (1960). The choice for this empirical strategy is due to the point of probability jump where it is denominated cutoff point and which is part of the criterion for the municipality’s adhesion to the program. This cutoff point is possible, exactly, in municipalities with more than 20,000 inhabitants.

According to Rocha & Belluzzo (2010), the discontinuity assumption formalizes the idea that individuals slightly above and below the cut need to be comparable, requiring that they have a similar average of potential outcomes when receiving or not the treatment. Thus, we estimated the following equation:

Y ip=β0+β1 MemC ip+β2T ip+εip (4)

2 The proof can be found in Bushway, Johnson & Slocum (2007). 3 This work follows the same strategy of discontinuous regression adopted by Fujiwara (2015), Smith (2016) e Toro et al. (2015).

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Where Y ip is the variable of interest of the model, in municipality i for year p; MemC is the Melhor em Casa program which takes value 1 if the program works in the municipality and value 0 if not, for municipality i and year p. T ip is the value that indicates whether the municipality is above or below the aforementioned cutoff point, for municipality i and year p and, finally, ε ip is the error term.

However, observing the data, there are municipalities that, over time, have their population increased due to the natural socioeconomic dynamics, promoting variations in their number of inhabitants, that is, in some years they are above the cut and, in others, they are below the cut, what generates correlation between the error term and the variable of interest. Thus, the fuzzy regression discontinuity (FRD) model was chosen, which, according to Trochim (1984), has the sensitivity of considering an increase in the probability, though not from 0 to 1 since treatment assignment may depend on additional factors. Hence, to estimate the effects of MemC in an FRD model, we used the instrumental variables (IV) approach proposed by Angrist & Pischke (2008) through a two-stage least squares (2SLS) model:

Y ip=β0+β1 MemC ip+ f ( Popip ,Cut ip )+ X ip Θ+η1i (5)

MemCip=δ0+δ1Cut ip+ f ( P o p i ,Cut i )+¿ X i Ω+η2 i (6)

Where Cut ip is a dummy variable that takes value 1 if municipality i’s population is above the cutoff point in the year p. f ( Popi , Cut i ) is a polynomial of degree 2 that interacts with Cut ip. X ip is a vector of covariates4 with municipal characteristics of health services and socioeconomic conditions.

According to the adopted strategy, the estimation is in its nonparametric form. For this purpose, it is determined that the kernel function will be triangular, following the same strategy adopted by Smith (2014). Also, the model was calculated in its linear and quadratic forms5.

3.3.4 Robustness Tests

To test the specification of our model, five robustness tests were performed. The first one was a placebo test were previous trends were tested; hence, the results of the estimated parameters for the year immediately prior to the MemC program, cannot display statistical significance.

The second test verified the bandwidth, using the bandwidths developed by Calonico, Cattaneo & Farrel (2016), namely MSERD - Mean Square Error; MSETWO - Two different MSE-optimal bandwidth selectors, and MSESUM - MSE-optimal bandwidth selector for the sum of regression estimates for RDD. As a result of this test, there should be statistical significance in all bands.

For the third test, the cutoff point was arbitrarily changed for 15,000 and 25,000 inhabitants. As a result, the estimated parameters cannot be statistically significant, what would cause a weakening of the argumentative strategy of the paper.

4 In this paper, covariates are included in the model because, according to Imbens & Lemieux (2008), inserting covariates enhances the accuracy of the model.5 The specification of the polynomial of the model follows Gelman & Imbens (2014).

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In the fourth test, the kernel functions of the estimations were changed from triangular to Epanechnikov and Uniform. As a result, even changing the kernel function, the statistical significance should be maintained.

In the fifth test, a placebo test, we used the covariates that are not related to the program or cannot undergo changes in case they become related. In this case, we used as placebos: the amount spent at the Intensive Care Unit (ICU), the reduction in the length of hospital stays of people who died and, finally, people who died exclusively due to neoplasms. As a result, the estimated parameters cannot be statistically significant.

The next section covers the empirical results and the analyses of the effect of MemC on the length of hospital stays.

4. RESULTS

Prior to analyzing the regressions, we present the results of the sample selection bias tests (Heckit) and the manipulation tests (Cattaneo, Jansson & Ma, 2017) for a potential manipulation of the cutoff point. As a result of the first tests, we can statistically reject the hypothesis of sample selection bias according to Table 1. Thus, we used the regression discontinuity model to estimate the parameters. For the second test, as it can be seen on Table 1, we verify that the hypothesis of manipulation of the cutoff point by the municipalities can also be rejected.

To start the analysis of our estimations, in order to verify the effect of MemC on the length of hospital stays, we observe Figure 1. This figure evaluates the relation between the municipalities’ population density and MemC. It can be noticed that there is a discontinuity with regard to municipalities with more than 20,000 inhabitants when compared to municipalities with less than 20,000 inhabitants, and the difference of population density between these two groups separated by the discontinuity reaches 0.103. This shows that the selection criterion for adopting MemC in municipalities exists and works exactly as described in the pre-established conditions of the program.

In Figure 2, a discontinuity related to the length of hospital stays is highlighted in the chart, which shows that the program causes a variation close to the cutoff point and such variation is related to a reduction in the length of hospital stays.

Table 1 refers to the magnitude of the effect of MemC on the length of hospital stays without the inclusion of the control variables in the model. Eight columns can be observed in this Table, where the first three are related to linear regressions and the columns 5 to 7 are related to quadratic regressions. Columns 4 and 8 are regressions that test years prior to the implementation of the program, used, in this case, as robustness tests. This Table also has two Panels, A and B. Panel A shows results for the year when the program is implemented and Panel B shows the effects of the following two years.

Hence, with the results of Panel A, it is verified that MemC was able to reduce the length of hospital stays, being statistically significant in all the bandwidths used (Msetwo, Msesum and Mserd), as well as in its linear and quadratic forms. The program can reduce the length of hospital stays by 14.6% to 16.9%, helping vacate beds for new users. With regard to Panel B, we also observed a reduction in the length of hospital stays of 14.8%-17.1% in the second year and of 12.7%-16.4% in the third year.

In Table 2 we have the same format as Table 1; however, the regressions now include control variables. With the inclusion of these variables, more accuracy is expected in the estimators. In Panel A, the results indicated a reduction of 16.7%-21.7% in the length of hospital stays, whereas in Panel B we observe a reduction of 19.7%-23.9% in the second year after the implementation of the program in the municipality

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and 11%-19.2% in the third year. All the results presented in Panels A and B display statistical significance and are, thus, empirically coherent with the hypothesis that the program reduces the length of hospital stays.

4.1 Analysis of Robustness Tests

To validate the estimated parameters of the adopted model, five robustness tests were performed. The first one refers to the results of the estimated parameters for the year immediately prior to the MemC program, and statistical significance is not expected. In the second test, a change in the bandwidth in relation to the cutoff point occurs; thus, if one band increases, the model should remain statistically significant. In the third tests, the cutoff point was changed for 15,000 and 25,000 inhabitants and, as a result, it is expected that the estimated parameters are not statistically significant, showing that the cutoff point is unique. In the fourth robustness test, the kernel functions of the estimations were changed and, after this substitution, the statistical significance should be maintained. The fifth and last test performs regressions with variables that are not related to MemC, that is, cannot change or display significance because of the existence of the program.

For the first test, we observe in Tables 1 and 2, more specifically in columns 4 and 8, that the results did not display statistical significance and, thus, it is verified that no other program or activity in a period prior to MemC may have caused some influence that can change the length of hospital stays.

The second test was employed in all the estimations in Tables 1 and 2 and allowed us to notice that, even changing the bandwidth, the model’s parameters remained statistically significant, strengthening the idea of this paper.

The third tests, represented by the results in Table 3, reveals that when the cutoff point is changed, for both 15,000 and 25,000 inhabitants, the results are not statistically significant, giving evidence that the cutoff point exists and is necessary for the construction of the quality counterfactual addressed in this paper.

The results in Table 4 refer to the fourth test. It is understood that, even promoting changes in the kernel functions from triangular to Epanechnikov or Uniform, the results remain statistically significant, confirming their statistical robustness.

Finally, in Table 5, we verify that when we replace the dependent variables of the model with others that are not related to the program, the results are not statistically significant, which reveals that the parameters are robust and the empirical strategy is correct in determining the effects of MemC.

In summary, the MemC program is the causal factor of reducing the length of hospital stays and, thus, increases considerably the number of available hospital beds in the municipalities through a higher efficiency and effectiveness in both the management and the use of public health services and would cover the poorest classes of society.

5. CONCLUSION

The objective of the present paper was to analyze the effect of home care, here represented by the Melhor em Casa (MemC) program, on the length of hospital stays, with the purpose of verifying whether the program allows a reduction in the length of hospital stays and, thus, increases the availability of hospital beds.

For such analysis, the empirical strategy was the regression discontinuity design. This approach was possible because the program has a criterion that only municipalities with at least 20,000 inhabitants can receive the benefits of home care. This cutoff point

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established by the program serves as a counterfactual for analyzing the effect of MemC. However, we were careful with problems such as sample selection bias and the manipulation of information regarding this criterion, since they could cause severe errors to our estimation. For the first case, the Heckman correction model (Heckit) was used and, for the second one, the Manipulation Test of Cattaneo, Jansson & Ma (2017) was performed.

In addition to the methodological care regarding the regression instrument used, we were also concerned with potentially inconsistent results of the model due to endogeneity problems. Thus, we performed robustness tests to ensure our estimated parameters and to guarantee a causal analysis of the shock that occurred in the treated.

From the results of the regressions, it was found that MemC can reduce by 14.6%-16.95 the length of hospital stays, helping vacate beds to new users. Another relevant factor is that the reduction caused by the program lasts for the subsequent years, causing a reduction of 14.8%-17.1% in the length of hospital stays in the second year and of 12.7%-16.4% in the third year. We emphasize that these results were all statistically significant and without control variables.

With the purpose of enhancing the accuracy of estimators, we inserted controls in the model, which also revealed a reduction of 16.7%-21.7% in the length of hospital stays in the year of implementation of MemC. In the second and third years this reduction lasts, showing that the program is effective in improving the management of hospital beds, besides enabling patients to recover at home.

In summary, all the robustness tests performed corroborated the expectations, since they guaranteed that the calculated estimators reflected, in fact, that the effects of the housing financings that occurred in the municipalities treated are indeed consistent.

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14

Figure 1- Discontinuity: Population x MemC.Source: The authors (2017).

Figure 2- Discontinuity: Hospital Stays x MemC.Source: The authors (2017).

15

Table 1 - The effect of the “Melhor em Casa” program on the length of stay in hospitals - without Covariates.Variables (1) (2) (3) (4) (5) (6) (7) (8)

Panel A: MemC on the length of stay in hospitals

-0.169 *** -0.157*** -0.146*** -0.712 -0.150*** -0.168*** -0.159*** 0.045(0.016) (0.016) (0.017) (0.626) (0.015) (0.016) (0.019) (1.106)

Panel B: MemC on the length of stay in hospitals - Years Later

-0.171*** -0.158*** -0.140*** - -0.148*** -0.167*** -0.158*** -(0.016) (0.016) (0.017) - (0.015) (0.016) (0.017) -

-0.145*** -0.154*** -0.163*** - -0.128*** -0.127*** -0.135*** -(0.013) (0.013) (0.013) - (0.014) (0.013) (0.014) -

Specification Linear Linear Linear Linear Quad Quad Quad QuadBandwidth Msetwo Msesum Mserd Msetwo Msetwo Msesum Mserd Msetwoλ Mills (Heckit) No No No No No No No NoManipulation Teste - P>|T| 0.4813Obs. 277,021 277,021 277,021 277,021 277,021 277,021 277,021 277,021

Note: Var. Dependent: log the length of stay in hospital. All specifications use Kernel Triangular. O MemC (Melhor em Casa) estimates the discontinuity of municipalities just above 20,000 inhabitants. MSERD - Mean Square Error; MSETWO - two different MSE-optimal bandwidth selectors e MSESUM - MSE-optimal bandwidth selector for the sum of regression estimates for RDD refer to the optimum bandwidth selectors of Calonico; Cattaneo e Farrel (2016). Columns 4 and 8 refers to a one-year placebo test prior to the initiation of MemC. Robust Standard Error in parentheses. *** p<0.01, ** p<0.05 e * p<0.1.

MemC t

MemC t+1

MemC t+2

16

Table 2 - The effect of the “Melhor em Casa” program on the length of stay in hospitals - with Covariates.Variables (1) (2) (3) (4) (5) (6) (7) (8)

Panel A: MemC on the length of stay in hospitals

-0.217 *** -0.205*** -0.173*** -0.034 -0.167*** -0.199*** -0.170*** -0.249(0.015) (0.016) (0.014) (0.680) (0.016) (0.016) (0.019) (0.695)

Panel B: MemC on the length of stay in hospitals - Years Later

-0.239*** -0.198*** -0.201*** - -0.217*** -0.197*** -0.206*** -(0.016) (0.017) (0.017) - (0.016) (0.019) (0.019) -

-0.192*** -0.110*** -0.163*** - -0.136*** -0.121*** -0.121*** -(0.014) (0.012) (0.013) - (0.013) (0.013) (0.013) -

Specification Linear Linear Linear Linear Quad Quad Quad QuadBandwidth Msetwo Msesum Mserd Msetwo Msetwo Msesum Mserd Msetwoλ Mills (Heckit) No No No No No No No NoManipulation Teste - P>|T| 0.4813Obs. 272,554 272,554 272,554 272,554 272,554 272,554 272,554 272,554

Note: Var. Dependent: log the length of stay in hospital. All specifications use Kernel Triangular. O MemC (Melhor em Casa) estimates the discontinuity of municipalities just above 20,000 inhabitants. MSERD - Mean Square Error; MSETWO - two different MSE-optimal bandwidth selectors e MSESUM - MSE-optimal bandwidth selector for the sum of regression estimates for RDD refer to the optimum bandwidth selectors of Calonico; Cattaneo e Farrel (2016). Columns 4 and 8 refers to a one-year placebo test prior to the initiation of MemC. Robust Standard Error in parentheses. *** p<0.01, ** p<0.05 e * p<0.1.

MemC t

MemC t+1

MemC t+2

17

Table 3 - Robustness test of the effect of the “Melhor em Casa” program on the length of stay in hospitals – False CutoffVariables (1) (2) (3) (4) (5) (6)

Panel A: False Cutoff in 15,000 inhabitants

0.024 0.025 0.025 0.029 0.024 0.027(0.020) (0.019) (0.020) (0.028) (0.028) (0.028)

-0.035 -0.025 -0.009 -0.037 -0.036 -0.105(0.040) (0.039) (0.038) (0.089) (0.089) (0.065)

-0.069 -0.069 -0.060 0.011 -0.081 -0.074(0.056) (0.056) (0.055) (0.043) (0.065) (0.047)

Panel B: False Cutoff in 25,000 inhabitants

0.015 0.100 0.009 0.118 0.132 0.007(0.069) (0.065) (0.052) (0.087) (0.083) (0.055)

-0.034 -0.047 0.023 -0.055 0.069 -0.010(0.028) (0.032) (0.020) (0.040) (0.046) (0.025)

-0.308 -0.313 -0.158 -0.389 -0.571 -0.389(0.290) (0.268) (0.301) (0.388) (0.389) (0.388)

Specification Linear Linear Linear Quad Quad QuadBandwidth Msetwo Msesum Mserd Msetwo Msesum MserdControls Yes Yes Yes Yes Yes YesObs. 28,848 28,848 28,848 28,848 28,848 28,848Note: Var. Dependent: log the length of stay in hospital. All specifications use Kernel Triangular. O MemC (Melhor em Casa) estimates the discontinuity of municipalities just above 20,000 inhabitants. MSERD - Mean Square Error; MSETWO - two different MSE-optimal bandwidth selectors e MSESUM - MSE-optimal bandwidth selector for the sum of regression estimates for RDD refer to the optimum bandwidth selectors of Calonico; Cattaneo e Farrel (2016). Robust Standard Error in parentheses. *** p<0.01, ** p<0.05 e * p<0.1.

MemC t

MemC t+2

MemC t+1

MemC t

MemC t+2

MemC t+1

18

Table 4 - Robustness test of the effect of the “Melhor em Casa” program on the length of stay in hospitals – Change of Kernel function

VariablesKernel Epanechnikov Kernel Uniform

(1) (2) (3) (4) (5) (6)   (7) (8) (9) (10) (11) (12)

Panel A: MemC on the length of stay in hospitals

-0.216*** -0.210*** -0.140*** -0.167*** -0.187*** -0.165*** -0.102*** -0.226*** -0.207*** -0.154*** -0.165*** -0.206***(0.015) (0.014) (0.012) (0.016) (0.015) (0.019) (0.015) (0.014) (0.015) (0.016) (0.018) (0.019)

Panel B: MemC on the length of stay in hospitals - Years Later

-0.241*** -0.242*** -0.165*** -0.210*** -0.235*** -0.210*** -0.254*** -0152*** -0.122*** -0.200*** -0.205*** -0.227***(0.016) (0.015) (0.013) (0.016) (0.017) (0.019) (0.016) (0.020) (0.011) (0.020) (0.019) (0.020)

-0.215*** -0.1056*** -0.180*** -0.196*** -0.286*** -0.121*** -0.285*** -0.181*** -0.187*** -0.270*** -0.304*** -0.304***(0.014) (0.012) (0.014) (0.014) (0.021) (0.012) (0.018) (0.014) (0.014) (0.024) (0.023) (0.023)

Specification Linear Linear Linear Quad Quad Quad Linear Linear Linear Quad Quad QuadBandwidth Msetwo Msesum Mserd Msetwo Msesum Mserd Msetwo Msesum Mserd Msetwo Msesum MserdControls Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes YesObs. 277,021 277,021 277,021 277,021 277,021 277,021   277,021 277,021 277,021 277,021 277,021 277,021

Note: Var. Dependent: log the length of stay in hospital. Columns 1 through 6 refer to the Kernel Epanechnikov Function. The columns from 7 to 12 are related to Uniform Kernel Function. O MemC (Melhor em Casa) estimates the discontinuity of municipalities just above 20,000 inhabitants. MSERD - Mean Square Error; MSETWO - two different MSE-optimal bandwidth selectors e MSESUM - MSE-optimal bandwidth selector for the sum of regression estimates for RDD refer to the optimum bandwidth selectors of Calonico; Cattaneo e Farrel (2016). Robust Standard Error in parentheses. *** p<0.01, ** p<0.05 e * p<0.1.

MemC t+2

MemC t+1

MemC t

19

Table 5: Robustness test of the effect of the “Melhor em Casa” program on the length of stay in hospitals – change in the endogenous variables

 VariablesLength of stay in hospitals of deceased people Intensive Care Unit expenditure Death by Cancer

(1) (2) (3) (4) (5) (6)   (7) (8) (9) (10) (11) (12)   (13) (14) (15) (16) (17) (18)

-0.04 -0.088 -0.087 -0.204 -0.152 -0.174 0.049 0.043 0.053 0.175 0.147 0.118 -0.0006 -0.0001 -0.001 -0.0004 -0.0004 -0.0005

(0.083) (0.084)(0.084

) (0.122) (0.132) (0.139) (0.085) (0.095) (0.099) (0.121) (0.121) (0.127) (0.002) (0.001) (0.001) (0.001) (0.001) (0.001)

-0.09 -0.036 -0.06 -0.107 -0.092 -0.107 0.05 0.075 0.079 0.057 0.067 0.059 -0.001 -0.001 -0.0013 -0.0015 -0.0013 -0.0012

(0.084) (0.083)(0.079

) (0.107) (0.117) (0.119) (0.070) (0.072) (0.072) (0.076) (0.075) (0.078) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

0.071 0.089 0.073 0.01 -0.02 -0.023 0.058 0.081 0.053 0.107 0.122 0.123 -0.0002 -0.0005 -0.0006 -0.0004 -0.0002 -0.0003

(0.106) (0.108)(0.101

) (0.141) (0.157) (0.158) (0.079) (0.083) (0.078) (0.118) (0.122) (0.119) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

Specification Linear Linear Linear Quad Quad Quad Linear Linear Linear Quad Quad Quad Linear Linear Linear Quad Quad Quad

BandwidthMsetw

o Msesum Mserd Msetwo Msesum Mserd Msetwo Msesum Mserd Msetwo Msesum Mserd Msetwo Msesum Mserd Msetwo Msesum MserdControls Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

     

N. Obs. 12,715 12,715 12,715 12,715 12,715 12,715   13,869 13,869 13,869 13,869 13,869 13,869   288,539 288,539288,53

9 288,539 288,539 288,539

Note: The MemC (Melhor em Casa) estimates the discontinuity of municipalities just above 20,000 inhabitants. All specifications use Kernel Triangular. MSERD - Mean Square Error; MSETWO - two different

MemC t

MemC t+1

MemC t+2

20

MSE-optimal bandwidth selectors e MSESUM - MSE-optimal bandwidth selector for the sum of regression estimates for RDD refer to the optimum bandwidth selectors of Calonico; Cattaneo e Farrel (2016). Robust Standard Error in parentheses. *** p<0.01, ** p<0.05 e * p<0.1.