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We apply several estimators to Indonesian household data to estimate the relationship between health insurance and the number of outpatient visits to public and private providers. Once endogeneity of insurance is taken into account, there is a 63 percent increase in the average number of public visits by the beneficiaries of mandatory insurance for civil servants. Individuals’ decisions to make first contact with private providers is affected by private insurance membership. However, insurance status does not make any difference for the number of future outpatient visits.

Count data models have been widely used to estimate the predictors of health care demand [

In estimating health care demand, complexities arise because the underlying behaviors driving health care utilization may have implications for the choice of the most appropriate model [

In practice we will estimate the relationship between health insurance and the number of outpatient visits to public and private health care providers in Indonesia. There are previously published studies on health insurance and health care demand [

This study also confronts directly the statistical tradeoffs associated with correcting for endogenous regressors (

In 1992, the government passed a Social Security Act (SSA) mandating enrolment of private employees in either privately-provided insurance schemes or the government-provided

The government also enacted the Insurance Act in 1992 which allows private insurance firms to sell health insurance products. These schemes usually offer both public and private health providers in their provider networks. The consensus estimate of the number of people with private health insurance is 5 million [

Even given public policy and this menu of insurance opportunities, in 2004 only a small fraction of the Indonesian population (<15 percent) was covered by any health insurance. Motivated largely by the expectation that health insurance improves access to health care, the president signed a National Social Security Law in 2004 which will used as a basis for introducing an NHIP in the country.

This study estimates the relationship between insurance status and the demand for health care. The variable capturing demand is the number of outpatient visits during the four weeks prior to a household interview. The discreteness and non-negativity of this variable call for count data modeling [

The number of outpatient visits for an individual (_{i}_{i}_{i}_{1}_{i}_{i}_{i}_{i}_{1}_{i}

Maximum likelihood (ML) estimation of _{i}_{i}_{i}_{1}); _{i}_{2i}_{i}

_{i}_{1}) of the demand equation. For example, those who are less healthy may have a higher than average propensity to seek insurance as well as a higher than average propensity to seek care given illness. It is likely that unobservable factors influencing demand are positively correlated with the error term _{1} which would mean _{1} and _{2} are correlated. This would imply correlation between insurance status _{1}. In maximum likelihood estimation, correlation between _{1} (E(_{1}|

The dependent variable takes only non-negative integer values, and thus the family of count data models provides appropriate estimation techniques [

A variant of the Poisson is the negative binomial (NB) model [

Following Deb and Trivedi [_{i}_{i}_{i}_{i}β

The second part of the hurdle model is assumed to follow the density for a truncated negative binomial [_{i}

We use the above count data models to estimate

However, maximum likelihood yields consistent estimates only if regressors are exogenous. Here we suspect the regressors to be endogenous, so we consider both linear instrumental variables (IV) and generalized method of moments (GMM) estimators for both

We carry out several tests in order to evaluate the overall specification of the model.

The first step is testing endogeneity assumptions. To test the endogeneity of insurance status, Hausman specification tests (Wu-Hausman and Durbin-Wu-Hausman, or DWH) were carried out for each regression. In our case, this test can be interpreted as summarizing the consequences of employing different estimation methods on the same equation, not as a test for the endogeneity of regressors per se. If there is significant difference between coefficients from ML and GMM or IV, the null hypothesis of exogeneity can be rejected, suggesting either IV or GMM is necessary. Given that IV-estimated standard errors are inconsistent in the presence of unknown heteroskedasticity, we carry out various flavors of Pagan and Hall's test for heteroskedasticity [

Unfortunately, the consistency of the endogeneity test as well as coefficient estimates of IV and GMM depend on the validity of the instruments

To evaluate whether potential instruments are weak and whether the instruments are orthogonal to the error process, several tests were employed. First, the relevance of the instruments (to suspected endogenous variables) was assessed by evaluating the ^{2} value and the ^{2} and ^{2} measure, which takes into account correlations among the instruments [^{2}, the more inconsistent the IV estimates will be whenever the instruments are not perfectly exogenous. Even when the instruments are exogenous, a small value of the partial ^{2} will mean increased asymptotic standard errors and therefore reduction in the power of the

Second, the validity of the instruments was tested by an over-identification test [^{2} in the number of overidentifying restrictions. The Sargan statistic is distributed as χ^{2} with the degrees of freedom calculated as N*^{2} from a regression of IV residuals on the full set of instruments. The joint null hypothesis of both Hansen and Sargan tests are that the excluded instruments are valid instruments (

Finally, to satisfy an orthogonal requirement of the instruments, ^{2} with degrees of freedom equal to the loss of overidentifying restrictions, has the null hypothesis that the specified variables are proper instruments.

When null hypotheses of exogenous regressors were not rejected, we used count data models that ignore endogeneity. A number of approaches were employed to select a specification that could appropriately accommodate overdispersion and excess zeros. First, to discriminate between Poisson and NB, we used a regression based approach [_{logit} + ln_{truncNB} − ln_{NB}). Both AIC and BIC measures were again utilized; models yielding the smallest values of the AIC and BIC are preferred [

The data for this study come from the second round of the Indonesian Family Life Survey (IFLS2) carried out by the RAND Corporation. The first round of survey (IFLS1) included interviews with 22,347 individuals from 7,224 households. The IFLS2 re-contacted the same households and succeeded in re-interviewing 93.5percent of IFLS1 households (6751 households with over 33,000 individuals). An overview of the survey is described in [

This study considers two mutually exclusive measures of OP visits: public and private providers. Not all insurance schemes offer health care services from both public and private providers and sample distributions of these variables (presented in

Two insurance variables,

In demand

The endogeneity test as well as IV and GMM estimators can only be applied if one finds appropriate instruments. We propose candidate instrumental variables z that may satisfy two requirements [

We estimated reduced form regressions of the endogenous variables on the full set of instruments (^{2} reveals that the covariates in the

For public OP visits, the endogeneity test was rejected at 1 percent level (^{2}(40) = 1140.59) and in IV-estimate (χ^{2}(40) = 1147.01) rejected the null hypothesis of homoskedasticity at 1 percent level. This result suggests that GMM estimator is preferable to model the number of public OP visits.

An appropriate set of instruments are prerequisites to employ the endogeneity test as well as to estimate a model using IV and GMM estimators. A number of tests were therefore employed to test the relevancy, validity and orthogonality requirements of the instruments. ^{2} shows that the models explained a high proportion of the variation for ^{2} and a small value of the Shea measure, one may conclude that the instruments lack sufficient relevance to explain all the endogenous regressors and the model may be essentially unidentified [^{2} and Shea partial ^{2} were similar for both

The relevance of the instruments was also investigated using the

The validity of the instruments was performed by applying a standard test for the over-identifying restrictions. We could not reject the null hypothesis of correct specification in public outpatient visits. The value of the Hansen's

The orthogonality condition of the instruments was assessed using the

For private OP visits, we could not reject the exogeneity hypothesis (

In order to select whether NB or ZINB could be used, the Vuong test was employed. The result shows that the test was highly significant in favor of the ZINB. However, there were very large standard errors of the coefficients in the ‘inflation’ equation. This implied a definite lack of fit in case of the ZINB (results from the inflated equation are not presented here but are available from the first author).

Another option to model excess-zeros is to apply HNB. We based the comparison of this specification on the LR test and AIC values. The resulting LR test statistic χ^{2}(29) for the NB model against the HNB model was 70.18 {2 × [1,047.57 − (866.94 + 145.54)]}, and was significant at 1 percent level, indicating that the HNB model could be justified well. This was also supported by the AIC, ^{2}(1) was 8966.5 and was significant at 1 percent level, indicating that the truncated Poisson model must be rejected against the truncated NB model. The LR test does not appear in

Putting together all of the above evidence, we concluded that the HNB specification is preferable to estimate the number of private OP visits. We describe below the results obtained from GMM estimation for public OP visits and HNB for private OP visits.

The first column of _{i}_{i}α_{i}β_{i}_{ik}_{k}

Coefficients on insurance dummies (

Women are 11 percent more likely to have more visits to public OP than men. Being married increased the average number of visits by five percent. With the exception of elementary school, the estimated effect of education is significantly negative. This indicates that higher levels of education lead to a reduction in the number of visits to public OP care (holding health status and all other covariates constant). Income elasticity for public visits was 0.03 (

The results from HNB estimation of private OP visits are presented in the second column of

With regard to health status, gender, household size, income, electricity, travel cost and time, and age, coefficients are similar to those in the public OP demand regressions described above. For example, the estimated effects of all health status measures were significantly positive in the first-part (contact decision) suggesting that individuals with a lower health status have a higher probability of visiting private OP providers.

The estimated effects of the four education dummies (elementary, junior, senior and high) were all positive and significant at 1 percent level in the contact decision. Living in an urban area increased the probability to visit a private OP by 25 percent and the frequency of private OP visits by 28 percent. East Java residents were more likely to contact private OP (36 percent) and make more subsequent visits (55 percent) compared to Jakarta inhabitants.

This study has estimated the relationship between health insurance and the number of public and private outpatient visits in Indonesia. We have explored two econometric classes of count data models: a specification that ignores endogeneity of insurance choice and a specification that considers endogeneity of insurance choice. Although both IV and GMM estimators allow for controlling endogeneity of the insurance in the estimation [

We observed evidence for endogeneity (of insurance status) in the number of public OP visits. This led us to conclude that the GMM estimator is the best to model the number of public outpatient visits. Comparison of estimation results obtained from all econometric techniques explored in the study (complete results available upon request) reveals that the parameter estimates for the

In the case of private visits, several statistical tests suggested that the HNB hurdle specification is superior to the standard one-part specification. The use of HNB is justified by the fact that health care use in this study is measured by number of contacts instead of the total cost of all contacts [

The HNB estimates confirm that

Another way to look into the evidence of supply induced demand (SID) for health care is to examine how the doctors’ density affects demand. Physician density in Indonesia is higher in urban areas. Physicians practicing in urban areas facing negative income shocks could use their dual role—both as evaluator and supplier—to induce demand [

The finding that insurance increases individuals’ propensity for health care utilization is important for policy makers, particularly in Indonesia where current debate is dominated by discussions regarding improving access to care and the introduction of national health insurance scheme. Although such findings have been reported elsewhere [

Another finding from this analysis bears more discussion. A negative (and statistically significant) relationship to health care demand of

The authors are grateful to the RAND Corporation for providing us with the IFLS data. We would also like to thank the guest editor, Ulf-G. Gerdtham, and to two anonymous referees for helpful comments that improve this paper substantially. Finally, we thank Jon Jellema for correcting English errors. All views expressed and errors encountered are the sole responsibility of the authors.

Framework to select econometric techniques for modeling the relationships between health insurance and the number of outpatient visits.

Characteristics of health insurance schemes in Indonesia.

Regulation | Gov’t Regulation 69/91 | Social Security Act #3/1992 | Insurance Act #2/1992 |

Insurer | Private insurance firms | ||

Membership | Mandatory | Optional-mandatory | Voluntary |

Eligibility | Civil servants, pensioners of civil servants and armed force | Private sector employee | Varies, depend on the contract |

Beneficiaries | Spouse and 2 oldest children (<21 years if unemployed & unmarried, or <25 years if a student) | Spouse and 3 oldest children <21 years of age | Varies |

Premium rate | 4% payroll deduction (regardless of marital status) | Payroll deduction (single 3%; married 6%) | Varies, depend on the risk and the benefits |

Premium policy | Contributory | Non-contributory | Full Contributory |

Benefits, providers network | OP and IP at public providers | OP at both public and private providers; IP at public providers only | Usually OP and IP, and mostly in the private providers networks |

Note: OP = outpatient health care services; IP = Inpatient health care services.

Sample frequency distribution of the number of public and private outpatient visits (number of observations = 13639).

0 | 11,589 | 84.97 | 12,573 | 92.18 |

1 | 1,061 | 7.78 | 562 | 4.12 |

2 | 544 | 3.99 | 269 | 1.97 |

3 | 246 | 1.80 | 118 | 0.87 |

4 | 150 | 1.10 | 81 | 0.59 |

5 | 15 | 0.11 | 5 | 0.04 |

6 | 17 | 0.12 | 6 | 0.04 |

7 | 7 | 0.05 | 7 | 0.05 |

8 | - | 8 | 0.06 | |

9 | - | - | ||

10 | 10 | 0.07 | 10 | 0.07 |

0.28 | 0.15 | |||

^{2} |
0.67 | 0.43 | ||

^{2} |
2.39 | 2.87 |

Summary statistics of the variables used in the demand equation.

Askes insurance | 1 if govt-employ insurance; 0 otherwise | 0.098 | 0.298 |

Private insurance | 1 if priv-employ insurance; 0 otherwise | 0.052 | 0.223 |

Askes*income | Interaction |
0.165 | 0.775 |

Private*income | Interaction |
0.073 | 0.419 |

Symptoms | 1 if had ≥ 1 symptom; 0 otherwise | 0.963 | 0.189 |

Score ADLs | Physical ability to perform daily activity | 0.295 | 0.456 |

Very good GHS |
Very good health status | ||

GHS is good | General health status was good | 0.788 | 0.409 |

GHS is poor | General health was bad & very bad | 0.135 | 0.342 |

Serious illness | 1 if had serious ill; 0 otherwise | 0.127 | 0.333 |

Female | 1 if female; 0 otherwise | 0.574 | 0.495 |

Household size | Number of household members | 5.878 | 2.594 |

Married | 1 if married; 0 otherwise | 0.842 | 0.365 |

No-schooling |
Had no education | ||

Elementary | Had some primary education | 0.475 | 0.499 |

Junior | Had some secondary education | 0.136 | 0.343 |

Senior | Had some senior education | 0.196 | 0.397 |

High | Had some higher education | 0.069 | 0.254 |

Age (years) | Individual age in years | 36.988 | 11.654 |

Ln. Income | Log natural per-capita income (Rp) | 11.099 | 0.855 |

Electricity | 1 if had electricity; 0 otherwise | 0.870 | 0.336 |

TravCost public | Log one way travel-costs to public health post | 6.688 | 5.868 |

TravCost private | Log one way travel-costs to private health post | 3.278 | 4.792 |

TravTime public | Log one way travel-time to public post | 8.053 | 1.769 |

TravTime private | Log one way travel-time to private post | 6.975 | 2.353 |

Urban | 1 if urban; 0 otherwise | 0.488 | 0.500 |

Jakarta Region |
Jakarta residence | ||

Sumatra | Lived in Sumatra | 0.195 | 0.396 |

West Java | Lived in West Java | 0.178 | 0.383 |

Central Java | Lived in Central Java | 0.188 | 0.391 |

East Java | Lived in East Java | 0.121 | 0.326 |

Bali & WNT | Lived in Bali and WNT | 0.112 | 0.316 |

Kalimantan | Lived in Kalimantan | 0.049 | 0.216 |

Sulawesi | Lived in Sulawesi | 0.056 | 0.229 |

is the reference group.

Endogeneity tests.

Hausman | F(2,13607) = 10.283 | 0.00003 | F(2) = 0.537 | 0.585 |

Durbin Wu Hausman | χ^{2}(2) = 20.584 |
0.00003 | χ^{2}(2)=1.076 |
0.584 |

Tests for the relevance of instruments.

Pseudo ^{2} | ||

Unadjusted ^{2} |
0.4973 | 0.5697 |

Adjusted ^{2} |
0.4962 | 0.5688 |

Partial ^{2} |
0.0561 | 0.0213 |

Shea Partial ^{2} |
0.0518 | 0.0197 |

Wald test |
434.24 |
581.22 |

Wald test |
202.26 |
74.17 |

F-test all instruments F(31,13607);

F-test excluded instruments F(4,13607);

significant 1%.

Selection criteria of the standard count data models: private outpatient visits.

^{st} part: Logit |
^{nd} part: Truncated NB | ||||
---|---|---|---|---|---|

Observation (n) | 13,639 | 13,639 | 13,639 | 13,639 | 1,066 |

LR test (29) |
1,203.21 |
1,047.57 |
779.22 |
866.94 |
145.54 |

−Log- |
5,829.72 | 4,735.27 | 4,712.28 | 3,271.52 | 1,346.48 |

Overdispersion test |
12.48 |
||||

Vuong test |
3.3 |
||||

Alpha |
7.07 | 4.17 | 0.53 | ||

AIC | 11,719.45 | 9,532.55 | 9,504.56 | 6,603.05 | 2,752.95 |

BIC | 1,970.47 | 588.42 | 533.08 | 661.79 | |

LR |
8,966.49 |

Log ratio test of the joint significance of the regressors (in ZINB, number of regressors are 38);

Overdispersion test for Poisson

Vuong test for standard NB

An ancillary parameter alpha (α) is an estimate of the degree of overdispersion in the data;

Log ratio test for truncated NB

significant at 1%.

Estimation results of the GMM and HNB models.

^{st} part: Logit |
^{nd} part: NB | |||||
---|---|---|---|---|---|---|

Askes insurance | 0.631^{‡} |
(0.154) | −0.017 | (0.135) | −0.298 | (0.219) |

Private insurance | 0.197 | (0.281) | 1.274^{‡} |
(0.184) | 0.272 | (0.210) |

Askes*income | 0.003 | (0.040) | −0.023 | (0.044) | 0.033 | (0.064) |

Private*income | −0.145 | (0.114) | −0.319^{‡} |
(0.107) | 0.075 | (0.153) |

Symptoms | 0.287^{‡} |
(0.024) | 3.174^{‡} |
(0.717) | 16.314 | (0.000) |

Score ADLs | 0.098^{‡} |
(0.021) | 0.345^{‡} |
(0.079) | 0.077 | (0.100) |

GHS very good | ||||||

GHS is good | 0.050^{†} |
(0.021) | 0.414^{‡} |
(0.149) | 0.471^{‡} |
(0.174) |

GHS is poor | 0.355^{‡} |
(0.032) | 1.390^{‡} |
(0.164) | 0.738^{‡} |
(0.216) |

Serious illness | 0.086^{‡} |
(0.024) | 0.721^{‡} |
(0.083) | 0.493^{‡} |
(0.170) |

Female | 0.118^{‡} |
(0.015) | 0.147^{†} |
(0.074) | 0.289^{‡} |
(0.086) |

Household size | 0.006^{†} |
(0.003) | 0.046^{‡} |
(0.013) | 0.029 | (0.020) |

Married | 0.055^{†} |
(0.022) | −0.286^{‡} |
(0.102) | −0.117 | (0.155) |

No | ||||||

Elementary | −0.019 | (0.024) | 0.362^{†} |
(0.142) | 0.357^{†} |
(0.160) |

Junior | −0.091^{‡} |
(0.033) | 0.455^{‡} |
(0.169) | 0.117 | (0.186) |

Senior | −0.083* | (0.046) | 0.505^{‡} |
(0.164) | −0.246 | (0.193) |

High | −0.262^{‡} |
(0.056) | 0.756^{‡} |
(0.185) | 0.175 | (0.234) |

Age (years) | −0.001 | (0.001) | 0.003 | (0.004) | −0.001 | (0.004) |

Ln income | 0.031^{‡} |
(0.012) | 0.383^{‡} |
(0.051) | −0.034 | (0.062) |

Electricity | 0.106^{‡} |
(0.022) | 1.003^{‡} |
(0.198) | 0.107 | (0.263) |

TravCost(ln) | 0.002 | (0.001) | 0.015^{†} |
(0.007) | −0.004 | (0.007) |

TravTime (ln) | 0.009^{†} |
(0.004) | 0.029* | (0.018) | 0.065^{†} |
(0.026) |

Urban | −0.109^{‡} |
(0.021) | 0.228^{‡} |
(0.083) | 0.276^{†} |
(0.112) |

Jakarta Region | ||||||

Sumatra | 0.027 | (0.034) | −0.327^{†} |
(0.127) | 0.077 | (0.204) |

West Java | −0.047 | (0.034) | −0.112 | (0.116) | 0.302^{†} |
(0.132) |

Central Java | −0.034 | (0.032) | 0.089 | (0.122) | 0.141 | (0.152) |

East Java | 0.052 | (0.037) | 0.509^{‡} |
(0.135) | 0.554^{‡} |
(0.157) |

Bali & WNT | 0.076^{†} |
(0.036) | 0.150 | (0.143) | 0.015 | (0.170) |

Kalimantan | 0.136^{†} |
(0.054) | −1.080^{‡} |
(0.257) | 0.360 | (0.425) |

Sulawesi | 0.042 | (0.042) | −0.648^{‡} |
(0.242) | 0.092 | (0.289) |

Constant | −0.730^{‡} |
(0.129) | −12.743^{‡} |
(1.002) | −17.923^{‡} |
(1.097) |

Number observations | 13639 | 13639 | 1066 |

The estimated parameters; superscript ^{‡},^{†}, and ^{*} indicate significance at 1%, 5%, and 10% level, respectively;

Robust standard errors in (parentheses);

is the reference group.