Var var wald var x x r 0 i q 0 rb q d r b b r d d d d

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= ;     [Var( , )] = Var[ ] Wald Var[ ] 0 X X 0 R 0 I q 0 Rb - q d R b b R'  d d d d ε β ε
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Part 9: Hypothesis Testing - 2 Application – Health and Income German Health Care Usage Data, 7,293 Individuals, Varying Numbers of Periods Variables in the file are Data downloaded from Journal of Applied Econometrics Archive. This is an unbalanced panel with 7,293 individuals. There are altogether 27,326 observations. The number of observations ranges from 1 to 7 per family. (Frequencies are: 1=1525, 2=2158, 3=825, 4=926, 5=1051, 6=1000, 7=987). The dependent variable of interest is DOCVIS = number of visits to the doctor in the observation period HHNINC = household nominal monthly net income in German marks / 10000. (4 observations with income=0 were dropped) HHKIDS = children under age 16 in the household = 1; otherwise = 0 EDUC = years of schooling AGE = age in years MARRIED=marital status WHITEC = 1 if has “white collar” job ™    7/27
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Part 9: Hypothesis Testing - 2 Men +----------------------------------------------------+ | Ordinary least squares regression | | LHS=HHNINC Mean = .3590541 | | Standard deviation = .1735639 | | Number of observs. = 14243 | | Model size Parameters = 5 | | Degrees of freedom = 14238 | | Residuals Sum of squares = 379.8470 | | Standard error of e = .1633352 | | Fit R-squared = .1146423 | | Adjusted R-squared = .1143936 | +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ |Constant| .04169*** .00894 4.662 .0000 | |AGE | .00086*** .00013 6.654 .0000 42.6528| |EDUC | .02044*** .00058 35.528 .0000 11.7287| |MARRIED | .03825*** .00341 11.203 .0000 .76515| |WHITEC | .03969*** .00305 13.002 .0000 .29994| +--------+------------------------------------------------------------+ ™    8/27
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Part 9: Hypothesis Testing - 2 Women +----------------------------------------------------+ | Ordinary least squares regression | | LHS=HHNINC Mean = .3444951 | | Standard deviation = .1801790 | | Number of observs. = 13083 | | Model size Parameters = 5 | | Degrees of freedom = 13078 | | Residuals Sum of squares = 363.8789 | | Standard error of e = .1668045 | | Fit R-squared = .1432098 | | Adjusted R-squared = .1429477 | +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ |Constant| .01191 .01158 1.029 .3036 | |AGE | .00026* .00014 1.875 .0608 44.4760| |EDUC | .01941*** .00072 26.803 .0000 10.8764| |MARRIED | .12081*** .00343 35.227 .0000 .75151| |WHITEC | .06445*** .00334 19.310 .0000 .29924| +--------+------------------------------------------------------------+ ™    9/27
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Part 9: Hypothesis Testing - 2 All +----------------------------------------------------+ | Ordinary least squares regression | | LHS=HHNINC Mean = .3520836 | | Standard deviation = .1769083 | | Number of observs. = 27326 | | Model size Parameters = 5 | | Degrees of freedom = 27321 | | Residuals Sum of squares = 752.4767 | All | Residuals Sum of squares = 379.8470 | Men | Residuals Sum of squares = 363.8789 | Women +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
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