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Table 7 Summary of tests for choice of model, endogeneity of insurance and instrumental variables for OOPE

From: Can health insurance protect against out-of-pocket and catastrophic expenditures and also support poverty reduction? Evidence from Ghana’s National Health Insurance Scheme

Test Explanation Results Comment
Durbin-Wu-Hausman test for choice of model H0: Random effects is preferred Chi-sq (15) = 14.70 p-value = 0.4733 Did not reject null hypothesis hence random effects is preferred.
Endogeneity test: Wu-Hausnam F test Durbin-Wu-Hausman chi sq-test H0: variable is exogenous. Rejection of H0 means that the variable is endogenous and instruments are needed 12.58 F (1,2283) Insurance is endogenous. IV estimates appropriate.
p-value = 0.00040
12.61 Chi-sq (1)
p-value 0.00038
Kleiberg-Paap test for under-identification (Anderson canon. correlation LM statistic) H0: model is under-identified. Rejection of H0 implies that the model is well identified. LM statistic 225.565 Instruments well identified.
Chi-sq (4) p-value = 0.000
Weak instrument test (Cragg-Donald Wald F statistic) H0: weakly identified. Rejection of H0 & t statistic >10 (=rule of the thumb) implies that the model is not weak. F statistic 61.976 5 % maximal IV relative bias = 16.85 Instruments not weak.
Sargan-Hansen J statistic Test if instruments are uncorrelated with error term. Rejection of H0: instruments are invalid. No problem Statistic = 2.548 Null hypothesis is not rejected implying that the instruments are valid
Chi-sq = (3)
P-value = 0.4667