Health insurance enrollment and vision health in rural China: an epidemiological survey

Table. 3 Tests of instrumental variables

	Value of statistic	P-value
1. Overidentification test of all instruments
Sargan statistic	0.0000	0.9999
2. F-value test
F statistic	64.0900	0.0000
3. Underidentification test
Kleibergen-Paap rk LM statistic	188.1150	0.0000
4. Weak identification test
Cragg-Donald Wald F statistic	96.7100
Kleibergen-Paap Wald rk F statistic	64.0900
Stock-Yogo weak ID test critical values for K1 = 1 and L1 = 3:
10 % maximal IV size	22.3000
15 % maximal IV size	12.8300
20 % maximal IV size	9.5400
25 % maximal IV size	7.8000
5. IV redundancy test
IV tested: Inscover	25.4870	0.0000
IV tested: Insfund	168.3660	0.0000
IV tested: Insyear	122.8600	0.0000
6. IV heteroscedasticity test
Pagan-Hall general test statistic	743.0980	0.0000
7. Endogeneity test
Wu-Hausman F test	6.4473	0.0111
Durbin-Wu-Hausman chi-sq test	6.4488	0.0111

Note: Column 2 and 3 show the values and p-values of the statistics of each test respectively
Abbreviations: IV instrumental variables; Inscover the respondent’s county’s health insurance participation rate; Insfund the county’s per capita funding of health insurance; Insyear the county’s duration of health insurance implementation

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