110年 - 110 國立臺灣大學_碩士班招生考試_國際企業研究所乙組:統計學(K)#105685

2. Is G an unbiased estimator of γ? Explain.

4. Suppose that our primary interest is inβ₁,, the partial eflect of x₁ on y. We thus estimate the equation excluding x₂:

Note that the variable x₂ may or may not be correlated with x₁ . What is the effect, if any, of excluding x2 from the model on the estimatedβ₁Explain.

5. Suppose we specify the model as

However, x₃ has no effect on y after x₁ and x₂ have been controlled for. Because we do not know thatβ₃ = 0 in practice, we still estimate the equation including x₃:
 Notc that the variable x₃ may or may not be correlated with x₁ or x₂. What is the effect, if any, of including x₃ in the model on the estimated β₁? Explain.

Question IV (48 points, 6 points each)
 A problem of interest to health officials is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various ilinesses. Our data sct contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in grams (bwght), and qan explanatory variable, average numbet of cigarettes the motber smoked per day during pregnancy (cigs). We also take other factors into accoun unt and specify the model as where The estimates of this equation, obtained using the method of ordinary least squares (OLS), are given in column (1) of Table 1. Standard errors are listed in parentheses. 6. Interpret the coefficient on cigs. In particular, what is the effect on bught from smoking 10 more cigarettes per day?