1 Question 1 Briefly explain after you decide if the statement is True or False. Stating only if it is True or False is not enough to get points. • a. (5 points) The interpretation of the slope...

1 Question 1

Briefly explain after you decide if the statement is True or False. Stating only if it is True or False is not enough to get points.

• a. (5 points) The interpretation of the slope coefficient in the model Yi = β0+β1 ln (Xi)+ ui is as follows: a change in X by one unit is associated with a β1 change in Y .

• b. (5points)TodecidewhetherYi =β0+β1X+ui orln(Yi)=β0+β1X+ui fitsthe 2

data better, you should not consult the regression R .
• c. (5 points) E (Y | X1,...,Xk) = Pr(Y = 1 | X1,...,Xk) means that: the exponential

of Y is the same as the probability of Y happening.

• d. (5 points) The LPM model always forces the predicted values to lie between 0 and 1

• e. (5 points) Probit coefficients are typically estimated using the method of maximum likelihood.

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2 Question 2

Information:

The expected change in Y,∆Y, associated with the change in X1,∆X1, holding X2,...,Xk constant, is the difference between the value of the population regression function before and after changing X1, holding X2, . . . , Xk constant. That is, the expected change in Y is the difference:

∆Y =f(X1 +∆X1,X2,...,Xk)−f(X1,X2,...,Xk)
The estimator of this unknown population difference is the difference between the predicted

ˆ
values for these two cases. Let f (X1, X2, . . . , Xk) be the predicted value of Y based on the

ˆ
estimator f of the population regression function. Then the predicted change in Y is

ˆˆˆ
∆Y =f(X1 +∆X1,X2,...,Xk)−f(X1,X2,...,Xk)

Question Starts here:

Consider the regression model Yi = β0 + β1X1i + β2X2i + β3 (X1i × X2i) + ui. Using the given information above, show:

• a. (8 points)∆Y/∆X1 = β1 + β3X2 ( effect of change in X1, holding X2 constant). • b. (8 points) ∆Y/∆X2 = β2 + β3X1 ( effect of change in X2, holding X1 constant). • c. (9 points) If X1 changes by ∆X1 and X2 changes by ∆X2, then

∆Y = (β1 + β3X2) ∆X1 + (β2 + β3X1) ∆X2 + β3∆X1∆X2 Write down everything clearly, show your work in detail.

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3 Question 3 Empirical

Believe it or not, workers used to be able to smoke inside office buildings. Smoking bans were introduced in several areas during the 1990s. In addition to eliminating the externality of sec- ondhand smoke, supporters of these bans argued that they would encourage smokers to quit by reducing their opportunities to smoke. In this question you will estimate the effect of workplace smoking bans on smoking, using data on a sample of 10,000 U.S. indoor workers from 1991 to 1993 (Smoking data in your Final Exam folder).

The data set contains information on whether individuals were or were not subject to a workplace smoking ban, whether the individuals smoked, and other individual characteristics. A detailed description is given in Smoking- Description, available in your Final Exam folder.

• a. Estimate a linear probability model with smoker as the dependent variable and the following regressors: smkban, female, age, age2, hsdrop, hsgrad, colsome, colgrad, black, and hispanic.

• b.

– i. Mr. A is White, non-Hispanic, 20 years old, and a high school dropout. Using the probit regression and assuming that Mr. A is not subject to a workplace smoking ban, calculate the probability that Mr. A smokes. Carry out the calculation again, assuming that he is subject to a workplace smoking ban. What is the effect of the smoking ban on the probability of smoking?

• – ii. Repeat (i) using the linear probability model.

• – iii. Based on your answers to (i)–(ii), do the probit, and linear probability models differ? If they do, which results make most sense? Are the estimated effects large in a real work sense?

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4 Question 4 Empirical

Use cps12.dta for this question, which contains data for full-time, full-year workers, ages 25–34, with a high school diploma or B.A./B.S. as their highest degree. A detailed description is given in CPS12-Description file (in folder).

In this question, you will investigate the relationship between a worker’s age and earnings. (Generally, older workers have more job experience, leading to higher productivity and higher earnings.)

• a. Run a regression of ln(AHE) (you have to create this variable it is not in the data set) on Age, Age2 (square of age: you have to create this variable it is not in the data set), Female, Bachelor, and the interaction term Female * Bachelor (you have to create this variable it is not in the data set). What does the coefficient on the interaction term measure?

– i. Alexis is a 30-year-old female with a bachelor’s degree. What does the regression predict for her value of ln(AHE)?

– ii.Jane is a 30-year-old female with a high school degree. What does the regression predict for her value of ln(AHE)? What is the predicted difference between Alexis’s and Jane’s earnings?

– iii.Bob is a 30-year-old male with a bachelor’s degree. What does the regression predict for his value of ln(AHE)?

– iv.Jim is a 30-year-old male with a high school degree. What does the regression predict for his value of ln(AHE)? What is the predicted difference between Bob’s and Jim’s earnings?

• b. After running the regressions from (i)-(iv), do you think if the effect of degree (HS or BA) on earnings is different for men and for women?