# Econometrics Problem Set 4 Solution School of Business

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Submitted By pege1989
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Problem 1:

i) All the coefficients are significant, because t (crit) = 1,96 is smaller than the absolute values of these three coefficients β1, β2 and β3.
Estimated equation is:
Log (wage) = 0.128 + 0.0904educ + 0.041exper – 0.000714exper2 (0.106) (0.0075) (0.0052) (0.000116) n = 526, R2 = 0.30

ii) Yes, the coefficient is significant because t-statistics absolute value 6,16 is greater than t (critical value) at 1 % significance level which is 2,586 in this case.

iii)

100 * [0.041-2*(0.000714)*4] = 3,53%
100 * [0.041-2*(0.000714)*19] = 1,39% iv) x* = 0.0410089/(2*(-0.0007136)) = -28.7338 28.7338

There are 121 people in the sample with at least 29 years of experience.

Problem 2:

a) SSE + SSR = SST SST – SSE = SSR SSR = 7160,41429–10.6243285= 7149,79 b) n =524 c) R2 = SSE/SST = 10.62/7160.41 = 0,001484 d) t = (-0,4682478/0,5306473) = -0,88241 e) t = coefficient/ std. error coefficient / t = (5,944174/34,96) = 0,170028 f) F = t^2 = (-0,88241)^2 = 0,778645

Problem 3:

Model 1:

a) Coefficient on variable cigs indicates that one cigarette smoked per day reduces birth weight by
0,44 %. Therefore, the effect on birth weight from smoking 10 more cigarettes will be that it reduces birth weight by 4,4 %.

b) In model 1, a white child is predicted to weight 5,5 % more than a non-white child on average, holding other factors fixed. Since t-stat (for zero null hypothesis) value is 4,20, which is greater than critical value for t= 1,960 we can make a conclusion that this difference is statistically significant.

c) Model 2:

Increase in mother’s education reduces expected birth weight according to coefficient estimate of motheduc. Coefficient indicates that an extra year of

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