题目
单项选择题
When we regress y on x1, we obtain the following simple regression line: 𝑦 ~ = 𝛽 ~ 0 + 𝛽 ~ 1 𝑥 1 (1). When we regress y on x1 and x2, we obtain the following multiple regression line: 𝑦 ^ = 𝛽 ^ 0 + 𝛽 ^ 1 𝑥 1 + 𝛽 ^ 2 𝑥 2 (2). The relationship between 𝛽 ~ 1 and 𝛽 ^ 1 is: 𝛽 ~ 1 = 𝛽 ^ 1 + 𝛽 ^ 2 𝛿 1 ~ (3), where 𝛿 1 ~ is the slope coefficient of the regression of x2 on x1, 𝑥 ~ 2 = 𝛿 ~ 0 + 𝛿 ~ 1 𝑥 1 (4). Let y = ln(wage), x1 = educ, and x2 = exper, where wage is hourly wage (measured in dollars), educ is years of formal education, and exper is years of labor market experience. Assuming 𝛽 ^ 1 , 𝛽 ^ 2 > 0, which of the following statements is correct?
选项
A.If
𝛿
~
1
> 0, that is, if years of formal education and years of labor market experience are negatively correlated, then the effect of education on wage in the simple regression line (1) will be overestimated.
B.If
𝛿
~
1
> 0, that is, if years of formal education and years of labor market experience are positively correlated, then the effect of education on wage in the simple regression line (1) will be overestimated.
C.If
𝛿
~
1
> 0, that is, if years of formal education and years of labor market experience are positively correlated, then the effect of education on wage in the simple regression line (1) will be underestimated.
D.If
𝛿
~
1
< 0, that is, if years of formal education and years of labor market experience are negatively correlated, then the effect of education on wage in the simple regression line (1) will be overestimated.
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思路分析
The question examines omitted variable bias in the context of regressing wage on education when experience is also an important predictor. It defines δ1 as the slope in the regression of x2 on x1, and notes that β1_hat and β2_hat in the simple and multiple regressions relate through δ1.
Option 1: 'If δ1 > 0, that is, if years of formal education and years of labor market experience are negatively correlated, then the effect of education on wage in the simple regression line (1) will be overestimated.' Here δ1 > 0 is explicitly contra......Login to view full explanation登录即可查看完整答案
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