Department of Economics
Economics UN3412
Midterm Exam
Question 1 (25 points):
Allcott and Gentzkow (2017) conducted an online survey of US adults regarding fake news after the 2016 presidential election. In their survey, they showed survey respondents news headlines about the 2016 election and asked about whether the news headlines were true or false. Some of the news headlines were fake and others were true. Their dependent variable Yi takes value 1 if survey respondent i correctly identifies whether the headline is true or false, value 0.5 if respondent is “not sure”, and value 0 otherwise. Suppose that one conducts a similar survey and obtains the following regression result:
Y(̂)i = 0.62 + 0.011college + 0.013Ln(Daily media time) + 0.002Age, R2 = 0.12, n = 752
(0.02) (0.003) (0.004) (0.001)
where College is a binary indicator that equals 1 if a survey respondent is college graduate and 0 otherwise, ln(Daily media time) is the logarithm of daily time consuming media, and Age is age in years.
(a) (6p) Suppose that you would like to test that people with higher education have more accurate beliefs about news at the 1% level. State your null hypothesis precisely and report your test result.
(b) (6p) The estimated coefficient for ln(Daily media time) is significantly positive. Interpret this result. Explain why this is plausible.
(c) (6p) Even if Age is omitted, there will be little concern about the omitted variable bias problem. Do you agree? Explain briefly.
(d) (7p) Suppose that you now conjecture that Republicans may have different beliefs about news than Democrats. Assume that there are three groups in the data: Democrats, Republicans and Independents. How would you change the specification of the linear regression model by adding or subtracting regressors? Explain briefly.
Question 2 (30 points):
Consider the following results, note that the dependent variable is log of hourly earnings, regressors are self-explanatory.
(a) [5 pt] What is the estimated economic return to education in regression (4) for each year of education for men and for women?
(b) [5 pt] What is the gender gap for 12 years of education? for 16 years of education?
(c) [5 pt] What is the estimated wage difference between Northeast and West? Which region has higher estimated wages? Is the difference statistically significant?
(d) [5 pt] Potential experience of the worker is measured by years since the completion of schooling. Interpret the estimated coefficient. (that is, what is the effect of experience on log hourly earnings?)
(e) [5 pt] Is the slope and the intercept of the regression for females different than those of the regression for males. Explain (be careful about which regressions are needed to answer this question.)
(f) [5 pt] Does the wage gap between genders widen or narrow as the level of education increases? Explain your answer in detail.
Question 3 (25 points):
Suppose that we are interested in estimating the effect of maternal education on child performance in math tests. Math test scores are likely to be a function of both maternal education (because, for example, mothers with higher levels of education provide richer and more stimulating environments to their children) and of maternal cognitive ability (because, for example, of genetic transmission of ability, or because more able mothers are better equipped with helping their children learn math). In particular, suppose the true model is:
yi = α0 + α1x1i + α2x2i + vi
where yi is the child’s test score, x1i is the maternal education, x2i is the maternal cognitive ability, and vi is the regression error that satisfies E(vi|x1i, x2i) = 0.
(a) (8 p) In most datasets, maternal cognitive ability (x2i) is unobserved, and so we are forced to estimate the following model:
yi = β0 + β1x1i + ui
Suppose you estimate β0 and β1 by ordinary least squares. Under what conditions is β1 a consistent estimator for α1 ? Explain briefly.
(b) (8 p) It is likely that maternal education and maternal cognitive ability are positively correlated. Suppose that your estimated β1 to be 1.5. Can you conjecture the true value of α1 based on this estimate? Justify your answer.
(c) (9 p) Suppose there are two components to maternal ability, X3i (math ability) and X4i (reading ability), so that X2i = X3i + X4i. Imagine we have a dataset where we can measure X3i but not X4i so you can run the following regression:
yi = δ0 + δ1X1i + δ2X3i + εi .
Is it plausible to conclude that the OLS estimator of δ1 is consistent for α1 ? Justify your answer.