Use the health expenditure data of Section 16.6. The model is a probit regression of DMED, an indicator variable for positive health expenditures, against the 17 regressors listed in the second paragraph of Section 16.6. You should obtain the estimates given in the first column of Table 16.1. Consider joint test of the statistical significance of the self-rated health indicators HLTHG, HLTHF, and HLTHP at level 0.05 .

(a) Perform a Wald test.

(b) Perform a likelihood ratio test.

(c) Perform an auxiliary regression to implement an \(L M\) test. [This will require some additional coding.]

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Table 16.1. Health Expenditure Data: Estimates from Two-Part and Selection Models" Two-Part Model Equation Selection Two-Step Selection MLE DMED LNMED DMED LNMED DMED LNMED LC -0.119 -0.016 -0.119 -0.028 -0.107 -0.076 (-4.41) (-0.52) (-4.41) (-0.70) (-4.03) (2.25) IDP -0.128 -0.079 -0.128 -0.028 -0.109 -0.150 (-2.45) (-1.28) (-2.45) (-0.70) (-2.13) (-2.26) LPI 0.028 0.003 0.028 0.005 0.029 0.015 (3.19) (0.28) (3.19) (0.47) (3.42) (1.42) FMDE 0.008 -0.031 0.008 -0.030 0.001 -0.024 (0.47) (-1.69) (0.47) (-1.62) (0.05) (1.21) PHYSLIM 0.273 0.262 0.273 0.281 0.285 0.355 (3.67) (3.81) (3.67) (3.50) (3.94) (4.70) NDISEASE 0.022 0.020 0.022 0.022 0.021 0.029 (6.25) (5.78) (6.25) (4.29) (6.03) (7.54) HLTHG 0.039 0.144 0.039 0.147 0.058 0.156 (0.88) (2.97) (0.88) (3.01) (1.35) (2.99) HLTHF 0.192 0.364 0.192 0.382 0.224 0.445 (2.29) (4.13) (2.29) (3.98) (2.75) (4.66) HLTHP 0.640 0.787 0.640 0.833 0.798 0.999 (3.01) (4.63) (3.01) (4.22) (3.90) (5.32) P 0.000 0.168 0.736 02 1.401 1.570 012 = p2 0.000 0.236 1.155 (0.47) (16.43) -In L 10184.1 10170.1 a The t-statistics are in parentheses. Regressors also include eight socioeconomic characteristics. DMED is an indicator for whether or not medical expenditures are positive and LNMED is the natural logarithm of expen- ditures if positive. The 1-statistics for the second step of the two-step selection model are based on errors that correct for the first-step estimation used to obtain the fitted inverse Mills ratio term.