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finalexamsoln - PADP 8120 Fertig Final Exam Solution 1...

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1 PADP 8120 Spring 2011 Fertig UGA Final Exam Solution 1. Estimate the effect of the head’s health status categories (make separate dummy variables) on family income. Interpret the coefficients on the health status categories and on the constant term. Discuss sign, significance, and magnitude. Source | SS df MS Number of obs = 5943 -------------+------------------------------ F( 4, 5938) = 57.88 Model | 3.4000e+11 4 8.4999e+10 Prob > F = 0.0000 Residual | 8.7205e+12 5938 1.4686e+09 R-squared = 0.0375 -------------+------------------------------ Adj R-squared = 0.0369 Total | 9.0605e+12 5942 1.5248e+09 Root MSE = 38322 ------------------------------------------------------------------------------ fincome | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hstat_1 | 8545.915 1409.836 6.06 0.000 5782.124 11309.71 hstat_2 | 5364.753 1236.235 4.34 0.000 2941.284 7788.223 hstat_4 | -13127.81 1817.489 -7.22 0.000 -16690.75 -9564.876 hstat_5 | -24453.08 3105.058 -7.88 0.000 -30540.12 -18366.03 _cons | 55255.16 920.558 60.02 0.000 53450.53 57059.79 ------------------------------------------------------------------------------ The coefficients indicate that excellent and very good health status is correlated with a significantly higher family income compared to heads who report their health to be good (the middle category, which I have chosen to be the reference category). Head’s who rate their health as fair or poor have significantly lower family incomes on average compared to the reference category. The higher you rank your health, the richer you are. The effect appears to be non-­૒ linear, or not evenly spaced. That is, the effect of moving from good to very good health is small relative to the effect of moving from good to fair health. *The average family income among those who rated their health as good is $55,255. *The average family income among those who rated their health as very good is $61,220=$55,255+$5,365. *The average family income among those who rated their health as excellent is $64,401=$55,255+$8,546. *The average family income among those who rated their health as fair is $42,107=$55,255-­૒ $13,128. *The average family income among those who rated their health as very good is $30,802=$55,255-­૒$24,453.
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2 2. Suppose you believe that the effect of head’s age on IRA retirement savings amount will be greater for married couples than for singles. a. How would you test this empirically? What are the null and alternative hypotheses? I would test this by estimating an interaction effect between head’s age and marital status. The null hypothesis is that the coefficient on the interaction is 0. The alternative hypothesis is that the coefficient will be significantly different from 0 (two-­૒sided). A one-­૒sided alterative hypothesis is that the coefficient will be significantly greater than 0. b. Run the test and interpret the results with respect to your hypotheses. Source | SS df MS Number of obs = 1386 -------------+------------------------------ F( 3, 1382) = 45.48 Model | 6.4584e+11 3 2.1528e+11 Prob > F = 0.0000 Residual | 6.5421e+12 1382 4.7338e+09 R-squared = 0.0899 -------------+------------------------------ Adj R-squared = 0.0879 Total | 7.1879e+12 1385 5.1898e+09 Root MSE = 68802 ------------------------------------------------------------------------------ iraval | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ageh | 901.5629 185.5771 4.86 0.000 537.5197 1265.606 married | -17969.93 12788.21 -1.41 0.160 -43056.33 7116.477 agemarr | 721.6754 247.5896 2.91 0.004 235.9833 1207.367 _cons | -1209.808 9812.234 -0.12 0.902 -20458.29 18038.67 ------------------------------------------------------------------------------ The coefficient on the interaction between head’s age and married is positive and significant such that we can reject the null hypothesis that the effect is 0. Thus, it does appear that the effect of head’s age on IRA retirement savings amount is greater for married couples than for singles.
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