Ex-ante moral hazard: empirical evidence for private health insurance in Brazil

Maia, Ana Carolina; Andrade, Mônica Viegas; Chein, Flávia

doi:10.1590/0103-6351/4886

Ana Carolina Maia

Faculdade de Economia, Administração e Atuária da Universidade de São Paulo, São Paulo, SP, Brasil.

Ana Carolina Maia - anacmaia@usp.br Faculdade de Economia, Administração e Atuária da Universidade de São Paulo, São Paulo, SP, Brasil. ORCID: https://orcid.org/0000-0002-4956-5948.

https://orcid.org/0000-0002-4956-5948

Mônica Viegas Andrade

Centro de Desenvolvimento e Planejamento Regional, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brasil.

Mônica Viegas Andrade - mviegas@cedeplar.ufmg.br Centro de Desenvolvimento e Planejamento Regional, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brasil. ORCID: https://orcid.org/0000-0003-4606-2795.

https://orcid.org/0000-0003-4606-2795

Flávia Chein

Departamento de Economia, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brasil.

Flávia Chein - ﬂavia.chein@ufjf.edu.br Departamento de Economia, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brasil. ORCID: https://orcid.org/0000-0003-4002-2522.

https://orcid.org/0000-0003-4002-2522

Ana Carolina Maia - anacmaia@usp.br Faculdade de Economia, Administração e Atuária da Universidade de São Paulo, São Paulo, SP, Brasil. ORCID: https://orcid.org/0000-0002-4956-5948.

Mônica Viegas Andrade - mviegas@cedeplar.ufmg.br Centro de Desenvolvimento e Planejamento Regional, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brasil. ORCID: https://orcid.org/0000-0003-4606-2795.

Flávia Chein - ﬂavia.chein@ufjf.edu.br Departamento de Economia, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brasil. ORCID: https://orcid.org/0000-0003-4002-2522.

Variable	Description
Time before leaving the pool	Number of months until leaving the pool specified by a set of six dummy variables. Each dummy variable d_itj assumes a value equal to one if individual iduring ttime is jmonths away from leaving the portfolio, and zero other- wise; jvaries from 1 to 6 while t varies from 1 to 60. These are our interest variables that measure for each indicator the average increase observed in the health care utilization j months before exiting the risk pool.
Age	Age variable built by considering a set of 17 dummy variables A_itj regarding 5-year age groups: 0-4, 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, and over 80 years. Each dummy variable a_itj assumes a value equal to one if individual iduring t time belongs to jage group, and zero otherwise; jvaries from 1 to 17 while t varies from 1 to 60. The reference category is 0-4 years. Age is a proxy variable for individual risk.
Family size	Number of beneficiaries in each family enrolled in the Sabesprev pool. Family size can affect opportunity costs to use health care services.
Relationship with the policyholder	Set of three dummy variables R_itj regarding the beneficiary’s relationship with the policyholder. Three types of household membership are available: proper policyholder, aggregate, or dependent. Each dummy variable r_jtj assumes a value equal to one if individual iduring time t has j relationship with the policyholder, and zero otherwise. Reference category: policyholder.
Sex	Dummy variable S that assumes a value equal to 1 if the beneficiary is a man, and zero otherwise. Sex is a proxy for individual risk.
Type of contract	Set of three dummy variables C_itj regarding each type of contract: full, basic, and special plan. The reference category is full plan.
Time	Set of 60 dummy T_t variables for each year. This allows controlling for aggregate shocks that can affect health care utilization. The reference category is January 2004.

Active benefi ciaries during the whole period		Benefi ciaries who lost health insurance coverage in 2005	Difference
	(1)	(2)	(2) – (1)
Age	34,30	35,13	-0,82
Age	(0,089)	(0,823)	(0,814)
Sex (1 if male)	0,49	0,50	0,00
Sex (1 if male)	(0,002)	(0,020)	(0,021)
Relationship to policyholder
Policyholder	0,36	0,33	0,03
Policyholder	(0,002)	(0,019)	(0,020)
Aggregate	0,03	0,04	0,009
Aggregate	(0,001)	(0,008)	(0,008)
Dependent	0,58	0,63	-0.04**
Dependent	(0,002)	(0,020)	(0,020)
Type of health insurance plan
Full	0,89	0,92	-0.03**
Full	(0,001)	(0,011)	(0,013)
Basic	0,019	0,012	0,01
Basic	(0,001)	(0,005)	(0,006)
Special	0,089	0,066	0.022*
Special	(0,001)	(0,010)	(0,011)
Family size	3,71	3,52	0.18***
Family size	(0,006)	(0,068)	(0,058)
Observations	46,927	573,00

Method		Generalized estimation equations			Random effect model
		Correlation structure
		AR1	Exchangeable	Non-structured
last month on the portfolio (1 month to go)		0.072 ^* * signifi cant at 10%,	0.038	0.036	0.029
last month on the portfolio (1 month to go)		(0.037)	(0.037)	(0.037)	(0.033)
2 months to go		0.173 ^* ***** signifi cant at 1%.	0.140 ^* ***** signifi cant at 1%.	0.141 ^* ***** signifi cant at 1%.	0.142 ^* ***** signifi cant at 1%.
2 months to go		(0.034)	(0.034)	(0.033)	(0.031)
3 months to go		0.102 ^* ***** signifi cant at 1%.	0.084 ^ signifi cant at 5%,	0.083 ^ signifi cant at 5%,	0.073 ^ signifi cant at 5%,
3 months to go		(0.034)	(0.033)	(0.033)	(0.030)
4 months to go		0.116 ^* ***** signifi cant at 1%.	0.103 ^* ***** signifi cant at 1%.	0.108 ^* ***** signifi cant at 1%.	0.097 ^* ***** signifi cant at 1%.
4 months to go		(0.031)	(0.030)	(0.029)	(0.027)
5 months to go		0.056 ^* * signifi cant at 10%,	0.044	0.048 ^* * signifi cant at 10%,	0.046 ^* * signifi cant at 10%,
5 months to go		(0.029)	(0.028)	(0.028)	(0.027)
6 months to go		0.045	0.042	0.046	0.035
6 months to go		(0.029)	(0.028)	(0.028)	(0.026)
5 to 9 years		-0.435 ^* ***** signifi cant at 1%.	-0321 ^* ***** signifi cant at 1%.	-0.298 ^* ***** signifi cant at 1%.	-0.333 ^* ***** signifi cant at 1%.
5 to 9 years		(0.014)	(0.011)	(0.011)	(0.008)
10 to 14 years		-0.761 ^* ***** signifi cant at 1%.	-0.522 ^* ***** signifi cant at 1%.	-0.510 ^* ***** signifi cant at 1%.	-0.579 ^* ***** signifi cant at 1%.
10 to 14 years		(0.016)	(0.013)	(0.013)	(0.010)
15 to 19 years		-0.634 ^* ***** signifi cant at 1%.	-0.417 ^* ***** signifi cant at 1%.	-0.424 ^* ***** signifi cant at 1%.	-0.493 ^* ***** signifi cant at 1%.
15 to 19 years		(0.016)	(0.014)	(0.014)	(0.012)
20 to 24 years		-0.414 ^* ***** signifi cant at 1%.	-0.307 ^* ***** signifi cant at 1%.	-0.298 ^* ***** signifi cant at 1%.	-0.384 ^* ***** signifi cant at 1%.
20 to 24 years		(0.019)	(0.018)	(0.017)	(0.014)
25 to 29 years		-0.347 ^* ***** signifi cant at 1%.	-0.248 ^* ***** signifi cant at 1%.	-0.221 ^* ***** signifi cant at 1%.	-0.319 ^* ***** signifi cant at 1%.
25 to 29 years		(0.018)	(0.017)	(0.016)	(0.013)
30 to 34 years		-0.343 ^* ***** signifi cant at 1%.	-0.233 ^* ***** signifi cant at 1%.	-0.206 ^* ***** signifi cant at 1%.	-0.297 ^* ***** signifi cant at 1%.
30 to 34 years		(0.016)	(0.015)	(0.015)	(0.013)
35 to 39 years		-0.348 ^* ***** signifi cant at 1%.	-0212 ^* ***** signifi cant at 1%.	-0186 ^* ***** signifi cant at 1%.	-0.272 ^* ***** signifi cant at 1%.
35 to 39 years		(0.016)	(0.015)	(0.014)	(0.012)
40 to 44 years		-0.295 ^* ***** signifi cant at 1%.	-0.164 ^* ***** signifi cant at 1%.	-0.142 ^* ***** signifi cant at 1%.	–0.220 ^* ***** signifi cant at 1%.
40 to 44 years		(0.016)	(0.014)	(0.014)	(0.012)
45 to 49 years		-0.229 ^* ***** signifi cant at 1%.	-0.110 ^* ***** signifi cant at 1%.	-0.087 ^* ***** signifi cant at 1%.	-0165 ^* ***** signifi cant at 1%.
45 to 49 years		(0.016)	(0.014)	(0.014)	(0.012)
50 to 54 years		-0164 ^* ***** signifi cant at 1%.	-0.041 ^* ***** signifi cant at 1%.	-0.023	-0101 ^* ***** signifi cant at 1%.
50 to 54 years		(0.016)	(0.014)	(0.014)	(0.013)
55 to 59 years		-0.125 ^* ***** signifi cant at 1%.	0,023	0.030 ^* * signifi cant at 10%,	-0.036 ^* ***** signifi cant at 1%.
55 to 59 years		(0.018)	(0.016)	(0.015)	(0.013)
60 to 64 years		-0.103 ^* ***** signifi cant at 1%.	0.074 ^* ***** signifi cant at 1%.	0.078 ^* ***** signifi cant at 1%.	0.025 ^* * signifi cant at 10%,
60 to 64 years		(0.021)	(0.018)	(0.017)	(0.015)
65 to 69 years		-0.022	0.135 ^* ***** signifi cant at 1%.	0.137 ^* ***** signifi cant at 1%.	0.090 ^* ***** signifi cant at 1%.
65 to 69 years		(0.024)	(0.020)	(0.020)	(0.016)
70 to 74 years		0.025	0.163 ^* ***** signifi cant at 1%.	0171 ^* ***** signifi cant at 1%.	0.122 ^* ***** signifi cant at 1%.
70 to 74 years		(0.025)	(0.021)	(0.021)	(0.018)
75 to 79 years		0.004	0.160 ^* ***** signifi cant at 1%.	0.154 ^* ***** signifi cant at 1%.	0.122 ^* ***** signifi cant at 1%.
75 to 79 years		(0.027)	(0.024)	(0.023)	(0.020)
ewer 80 years		-0.182 ^* ***** signifi cant at 1%.	0.076 ^* ***** signifi cant at 1%.	0.047 ^* * signifi cant at 10%,	0.034
ewer 80 years		(0.033)	(0.027)	(0.027)	(0.023)
male		- ^0.345* ***** signifi cant at 1%.	-0.352 ^* ***** signifi cant at 1%.	-0.350 ^* ***** signifi cant at 1%.	-0.393 ^* ***** signifi cant at 1%.
male		(0,007)	(0,008)	(0,008)	(0,007)
aggregate		-0,026	0.002 ^* ***** signifi cant at 1%.	-0,004	-0,005
aggregate		(0,022)	(0,020)	(0,019)	(0,016)
dependent		-0.101 ^* ***** signifi cant at 1%.	-0.122 ^* ***** signifi cant at 1%.	-0.116 ^* ***** signifi cant at 1%.	-0.104 ^* ***** signifi cant at 1%.
dependent		(0,009)	(0,010)	(0,009)	(0,009)
basic plan		0.043 ^* ***** signifi cant at 1%.	-0.093 ^* ***** signifi cant at 1%.	-0.044 ^* * signifi cant at 10%,	-0.105 ^* ***** signifi cant at 1%.
basic plan		(0,023)	(0,027)	(0,023)	(0,017)
special plan		–0.080 ^* ***** signifi cant at 1%.	-0.133 ^* ***** signifi cant at 1%.	-0.111 ^* ***** signifi cant at 1%.	-0.125 ^* ***** signifi cant at 1%.
special plan		(0,016)	(0,016)	(0,015)	(0,012)
tamily size		-0.031 ^* ***** signifi cant at 1%.	-0.031 ^* ***** signifi cant at 1%.	-0.032 ^* ***** signifi cant at 1%.	-0.034 ^* ***** signifi cant at 1%.
tamily size		(0,002)	(0,002)	(0,002)	(0,002)
time dummies		yes	yes	yes	yes
number of observations		2,888,257	2,889,284	2,889,284	2,889,284
number of individuals		49,087	49,106	49,106	49,106
number of obs. per individual	min.	13	13	13	13
	avg.	580.8	580.8	580.8	580.8
	max.	60	60	60	60
link function		log	log	log
family		binomial	binomial	binomial
family		(k = 1.3043)	(k = 1.3043)	(k = 1.3043)

Method		Generalized estimation equations			Random
		Correlation structure			effect
		AR1	Permutable	Non-structured	model
last month on the portfolio (1 month to go)		0.148 ^ signifi cant at 5%,	0.172 ^ signifi cant at 5%,	0.171 ^ signifi cant at 5%,	0.110 ^ signifi cant at 5%,
last month on the portfolio (1 month to go)		(0.072)	(0.069)	(0.068)	(0.044)
2 months to go		0.190 ^* ***** signifi cant at 1%.	0.203 ^* ***** signifi cant at 1%.	0.208 ^* ***** signifi cant at 1%.	0.227 ^* ***** signifi cant at 1%.
2 months to go		(0.063)	(0.062)	(0.062)	(0.041)
3 months to go		-0.013	0.013	0.011	0.069 ^* * signifi cant at 10%,
3 months to go		(0.065)	(0.063)	(0.063)	(0.041)
4 months to go		0.046	0.085	0.094	0.017
4 months to go		(0.063)	(0.061)	(0.061)	(0.038)
5 months to go		–0.075	–0.034	–0.031	–0.025
5 months to go		(0.060)	(0.057)	(0.057)	(0.038)
6 months to go		0.041	0.074	0.072	–0.005
6 months to go		(0.057)	(0.055)	(0.055)	(0.036)
5 to 9 years		–0.153 ^* ***** signifi cant at 1%.	–0.123 ^* ***** signifi cant at 1%.	–0.121 ^* ***** signifi cant at 1%.	–0.261 ^* ***** signifi cant at 1%.
5 to 9 years		(0,021)	(0,019)	(0,019)	(0,012)
10 to 14 years		–0.245 ^* ***** signifi cant at 1%.	–0.159 ^* ***** signifi cant at 1%.	–0.163 ^* ***** signifi cant at 1%.	–0.422 ^* ***** signifi cant at 1%.
10 to 14 years		(0.024)	(0.022)	(0.021)	(0.012)
15 to 19 years		–0.011 ^* ***** signifi cant at 1%.	0.058 ^* ***** signifi cant at 1%.	0.047 ^ signifi cant at 5%,	–0.281 ^* ***** signifi cant at 1%.
15 to 19 years		(0.025)	(0.023)	(0.023)	(0.012)
20 to 24 years		0.357 ^* ***** signifi cant at 1%.	0.371 ^* ***** signifi cant at 1%.	0.369 ^* ***** signifi cant at 1%.	0.014
20 to 24 years		(0.028)	(0.027)	(0.027)	(0.014)
25 to 29 years		0.526 ^* ***** signifi cant at 1%.	0.544 ^* ***** signifi cant at 1%.	0.545 ^* ***** signifi cant at 1%.	0.157 ^* ***** signifi cant at 1%.
25 to 29 years		(0.026)	(0.024)	(0.024)	(0.013)
30 to 34 years		0.639 ^* ***** signifi cant at 1%.	0.664 ^* ***** signifi cant at 1%.	0.663 ^* ***** signifi cant at 1%.	0.198 ^* ***** signifi cant at 1%.
30 to 34 years		(0.023)	(0.022)	(0.021)	(0.012)
35 to 39 years		0.706 ^* ***** signifi cant at 1%.	0.754 ^* ***** signifi cant at 1%.	0.751 ^* ***** signifi cant at 1%.	0.223 ^* ***** signifi cant at 1%.
35 to 39 years		(0.023)	(0.021)	(0.021)	(0.011)
40 to 44 years		0850 ^* ***** signifi cant at 1%.	0.890 ^* ***** signifi cant at 1%.	0.887 ^* ***** signifi cant at 1%.	0.298 ^* ***** signifi cant at 1%.
40 to 44 years		(0,022)	(0,020)	(0,020)	(0,011)
45 to 49 years		0.977 ^* ***** signifi cant at 1%.	1.006 ^* ***** signifi cant at 1%.	1.003 ^* ***** signifi cant at 1%.	0.386 ^* ***** signifi cant at 1%.
45 to 49 years		(0,022)	(0,020)	(0,020)	(0,011)
50 to 54 years		1.098 ^* ***** signifi cant at 1%.	1.111 ^* ***** signifi cant at 1%.	1.107 ^* ***** signifi cant at 1%.	0.466 ^* ***** signifi cant at 1%.
50 to 54 years		(0.022)	(0.020)	(0.020)	(0.011)
55 to 59 years		1.177 ^* ***** signifi cant at 1%.	1.200 ^* ***** signifi cant at 1%.	1.192 ^* ***** signifi cant at 1%.	0.534 ^* ***** signifi cant at 1%.
55 to 59 years		(0.023)	(0.022)	(0.021)	(0.012)
60 to 64 years		1.213 ^* ***** signifi cant at 1%.	1271 ^* ***** signifi cant at 1%.	1.261 ^* ***** signifi cant at 1%.	0.589 ^* ***** signifi cant at 1%.
60 to 64 years		(0.027)	(0.024)	(0.024)	(0.013)
65 to 69 years		1.311 ^* ***** signifi cant at 1%.	L354 ^* ***** signifi cant at 1%.	1344 ^* ***** signifi cant at 1%.	0.695 ^* ***** signifi cant at 1%.
65 to 69 years		(0.029)	(0.027)	(0.026)	(0.014)
70 to 74 years		1.378 ^* ***** signifi cant at 1%.	L420 ^* ***** signifi cant at 1%.	1.412 ^* ***** signifi cant at 1%.	0.749 ^* ***** signifi cant at 1%.
70 to 74 years		(0.031)	(0.029)	(0.028)	(0.014)
75 to 79 years		L368 ^* ***** signifi cant at 1%.	1.407 ^* ***** signifi cant at 1%.	1.397 ^* ***** signifi cant at 1%.	0.733 ^* ***** signifi cant at 1%.
75 to 79 years		(0.033)	(0.029)	(0.029)	(0.015)
over 80 years		1230 ^* ***** signifi cant at 1%.	L323 ^* ***** signifi cant at 1%.	1.309 ^* ***** signifi cant at 1%.	0.617 ^* ***** signifi cant at 1%.
over 80 years		(0,036)	(0,032)	(0,032)	(0,016)
male		-0.367 ^* ***** signifi cant at 1%.	-0374 ^* ***** signifi cant at 1%.	-0.372 ^* ***** signifi cant at 1%.	-0.344 ^* ***** signifi cant at 1%.
male		(0,009)	(0,010)	(0,010)	(0,004)
aggregate		-0.129 ^* ***** signifi cant at 1%.	-0.122 ^* ***** signifi cant at 1%.	-0.119 ^* ***** signifi cant at 1%.	-0.096 ^* ***** signifi cant at 1%.
aggregate		(0,026)	(0,025)	(0,025)	(0,010)
dependent		-0.221 ^* ***** signifi cant at 1%.	-0.234 ^* ***** signifi cant at 1%.	-0.231 ^* ***** signifi cant at 1%.	-0.172 ^* ***** signifi cant at 1%.
dependent		(0,011)	(0,011)	(0,011)	(0,005)
basic plan		0.087 ^* ***** signifi cant at 1%.	0,044	0,048	-0.024 ^ signifi cant at 5%,
basic plan		(0,030)	(0,030)	(0,030)	(0,010)
special plan		0.152 ^* ***** signifi cant at 1%.	0.103 ^* ***** signifi cant at 1%.	0.111 ^* ***** signifi cant at 1%.	-0.040 ^* ***** signifi cant at 1%.
special plan		(0,018)	(0,018)	(0,018)	(0,007)
family size		-0.033 ^* ***** signifi cant at 1%.	-0.035 ^* ***** signifi cant at 1%.	-0.036 ^* ***** signifi cant at 1%.	-0.022 ^* ***** signifi cant at 1%.
family size		(0,002)	(0,003)	(0,003)	(0,001)
time dummies		yes	yes	yes	yes
number of observations		2,888,257	2,889,284	2,889,284	2,889,284
number of individuals		49,087	49,106	49,106	49,106
number of obs. per individual	min.	13	13	13	13
	avg.	580.8	580.8	580.8	580.8
	max.	60	60	60	60
link function		log	log	log
family		binomial	binomial	binomial
family		(k =0.0921)	(k = 0.0921)	(k = 0.0921)

[1] Ana Carolina Maia - anacmaia@usp.br Faculdade de Economia, Administração e Atuária da Universidade de São Paulo, São Paulo, SP, Brasil. ORCID: https://orcid.org/0000-0002-4956-5948.

Brasil

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Ex-ante moral hazard: empirical evidence for private health insurance in Brazil

Risco Moral Ex-ante: uma evidência empírica para o setor de seguro saúde privado no Brasil

Abstract