Dynamic information asymmetry in micro health insurance: implications for sustainability

Abstract

Micro health insurance is an important channel for financing health expenditure for low-income people, yet the supply of such programmes lags behind demand because many of them become unsustainable. Using individual-level dynamic data from a micro health insurance programme in Pakistan, this study tests for the existence of information asymmetry (adverse selection and moral hazard) using a series of non-parametric tests so that insurers and policymakers can better understand the underlying reasons that lead to dynamic claim patterns before taking appropriate actions to improve the sustainability of these programmes. The study’s contribution lies in constructing an appropriate method and novel test statistics to detect information asymmetry using dynamic claim data in a multivariate recurrent event model framework. The results show that adverse selection exists widely for a variety of disease types and that moral hazard is only significant for chronic diseases. Furthermore, pregnancy-related claims demonstrate an increasing trend of adverse selection that needs to be addressed with priority. The analysis provides insight into the sustainable provision of micro health insurance to low-income people in developing regions.

Appendix

Hypothesis test for the difference in test statistics under homogeneous and heterogeneous claim assumptions

The test statistics designed to test the difference between $\tilde{w}_{R,s} \left( {t_{1}^{*} ,t_{1}^{*} + t_{0} - 12} \right) - \tilde{w}_{R,C} \left( {t_{1}^{*} ,t_{1}^{*} + t_{0} - 12} \right)$ and $\tilde{w}_{s,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{0} } \right) - \tilde{w}_{C,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{0} } \right)$ for various claim types is almost identical to test (10). The formal expression is as follows:

$${\text{Diff}}_{{s,M,{\text{t}},T}} = \mathop \sum \limits_{j = 1}^{M} \left( {\frac{{\tilde{w}_{s,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} } \right) - \tilde{w}_{C,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} } \right)}}{{\sqrt {\hat{\sigma }_{{\tilde{w}_{s,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} } \right)}}^{2} + \hat{\sigma }_{{\tilde{w}_{C,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} } \right)}}^{2} } }}} \right)^{2} ,{ }t_{1}^{*} = 0,12,24; t_{{0,{\text{j}}}} \in \left[ {0,12} \right]$$

(12)

$${\text{Diff}}_{{s,M,{\text{t}},T}} = \mathop \sum \limits_{j = 1}^{M} \left( {\frac{{\tilde{w}_{R,s} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} - 12} \right) - \tilde{w}_{R,C} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} - 12} \right)}}{{\sqrt {\hat{\sigma }_{{\tilde{w}_{R,s} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} - 12} \right)}}^{2} + \hat{\sigma }_{{\tilde{w}_{R,C} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} - 12} \right)}}^{2} } }}} \right)^{2} ,{ }t_{1}^{*} = 12,24; t_{{0,{\text{j}}}} \in \left[ {0,12} \right]$$

(13)

Test statistics (12) and (13) follow the $\chi^{2}$ distribution with degrees of freedom, M, under the null hypothesis, which hypothesises that no difference exists for the estimated coefficient function under the heterogeneous claim assumption versus the homogeneous claim assumption.

(12) is based on the difference $\tilde{w}_{s,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{0} } \right) - \tilde{w}_{C,R} \left( {t_{1}^{*} ,t_{1}^{*} + t_{0} } \right)$ between the coefficients measuring the impact of renewal on later claims under the heterogeneous and homogeneous claim assumptions. (13) is based on the difference $\tilde{w}_{R,s} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} - 12} \right) - \tilde{w}_{R,C} \left( {t_{1}^{*} ,t_{1}^{*} + t_{{0,{\text{j}}}} - 12} \right)$ measuring the impact of previous claims on renewal decisions under the heterogeneous and homogeneous claim assumptions. The test results are reported in Table 10.

We find significant differences in (12) and (13) for all claim types. These results verify the significant difference between homogeneous and heterogeneous claim assumptions, which validates the necessity of performing type-specific tests on adverse selection and moral hazard (Tables 11, 12).

Table 10 Difference in test statistics under heterogeneous and homogeneous claim assumptions

Table 11 Robustness check: Test statistics of moral hazard controlling risk type as another measure of severity (full sample: 12,782 households)

Table 12 Categorisation of all the diagnoses in the sample