# HW

Let’s suppose that each year a large university admits exactly 3,000 students into its incoming class. In the year 2000, 60 students were economics majors. In the year 2020, 187 students were economics majors.

a. Calculate the proportional change of economics majors from 2000 to 2020.

b. Calculate the percentage change of economics majors from 2000 to 2020.

C. Calculate the percentage point change of economics majors from 2000 to 2020.

Recall the simple linear regression model: Vi = Bo + B1x + U; Suppose the covariance of x and y = 50, the variance of x = 10, the variance of y = 5, the mean of x is 600, and the mean of y is 800.

a. Given the covariance of x and y, how strong is the relationship between x and y?

b. Calculate the estimated B1 slope parameter.

c. Calculated the estimated B1 slope parameter.

d. Write the sample regression model.

8.

Formulate a case for omitted variable bias in a model that regresses blood alcohol content (dependent variable, y) on accidents at the scene (independent variable, X1), but omits an important variable, x2.

Give an example of what this variable might be

Explain the direction of the bias on the ß coefficient.

Explain whether the By coefficient is over- or under estimated.

Use the following table to formulate your answer:

Corr(x1, X2) =

Corr(X1, X2) < 0
(B2 = 0
(B2 < 0
7.
QUESTION 7
10 points
Consider the following sample regression model: wagei = 6.25 + 3.2educ; + 8.8privatei + Ui where wage is the hourly wage received, education is the number of years of schooling received, and private is a binary indicator that =1 if the person attended private school and 0 otherwise. The standard error for the
coeficient on education is 1.5 and the standard error for the coefficient on private school is 2.6
Say we want to test the hypothesis that education increases hourly wage by 4.00
Formulate the appropriate test statistic to test this hypothesis. Do you reject or fail to reject this hypothesis, given a 95% confidence level? 99% confidence level?

b calculate the 95% conidence interval for this edualon. What does in mean I his confidence inerval inciudes zero?

Note that vour critical values are +/- 1.96 and +/-2.56. respectively

Suppose that you estimate a model with an unnecessary variable. X2, added to the regression. What happens with this overspecification of the model? Specifically, under what circumstance does the f1 estimator remain unbiased? What happens to the variance of this estimator?

Suppose a wage model is estimated, where vacationdays = 3.27 + 1.6tenure -.003tenure^2 where vacation days equal the number of vacation days accrued, and experience is the number of years the individual has worked. a Can vou directly interpret the coefficient on tenure? Why or why not?Calculate the marginal change in vacation days for someone who has worked for 8 years vs. 9 years. c. Calculate the marginal change in vacation days for someone who has worked 13 years vs. 14 years.

Given a model In(y) = Bo + B1x + U, a. In words, explain the interpretation of the ß1 coefficient. b. How would this change if the x variable were replaced with its logarithmic form, In(x)? c What is the economic term for what the log-log model in part b estimates?

A researcher is interested in understanding the relationship between wages (dependent variable), gender, and education. She has reason to believe that the level of education may change the wages received, given the person’s gender. How can she test for this effect? Write the full model.

How does a linear probability model vary from the standard OLS regression? Name one advantage and one disadvantage to using this approach

If vou are trvina to understand the effect of a policy, program, or some other intervention or treatment. the potential outcome is the outcome for the individual under a notential treatment. The treatment effect for an individual is the difference between the potential outcome if treatment had been received and the potential outcome if it is not. Why can’t we direct measure the treatment effect?

Suppose you regress employment status (==1 if employed, 0 otherwise) on the independent variables age and age^2 a. Why might it make sense to include age^2 in this regression? b. What sign would you expect to see on age^2 What is the economic term for this effect?

Suppose you estimated the following difference-in-differences model that estimates the impact of marijuana legalization introduced in Washington (WA) on traffic tickets against the outcomes in nearby states that did not legalize marijuana. Specifically, assume the following model is being estimated Yi1 = 16.4 – 3.9(WA;) + 6.7 (LEGALIZE; ) + ß3(WAit * LEGALIZE;) + Ui + Vt + Eit Where WAit is a dummy variable indicating the state, LEGALIZE; is a dummy variable indicating if the time period was when the treatment occurred or not, and (WAit × LEGALIZE;) is an interaction term indicating the treatment state after the legalization occurred. Given that the difference in outcome Yit for the treated state after the change occurred is 8.6, calculate the difference-in-differences estimator B3

A research proposes the use of an instrumental variable to test if weekly drinking has an effect on an individual’s body weight. Why might he suggest this method? What assumptions would the instrument need to satisfy in order to justify its use?

Suppose that you are interested in estimating the average impact a job training program has on wages. After controlling for observed factors that influence wages, participation in the training program, you find that the coefficient for the training is 0.55 and the standard error is 1.06. What can you infer about the effect of the job training program on wages:

In the following equation, gdp refers to gross domestic product, and FDI refers to foreign direct investment.

log(gdp) = 2.65 + 0.527l0g (bankcredit) + 0.222FDI

(0.13) (0.022)

(0.017)

Standard erros are in darenthese underneath the vanables. Given this

a. Interpret the coefficient on log (bankcredit).

b. Calculate the appropriate test statistic to test the null hypothesis that log (bankcredit) has no effect on log(GDP). Is this coefficient is statistically significant?

c. Interoret the coefficient on FDI.

d. Calculate the appropriate test statistic to test the null hypothesis that FDI has no effect on log(GDP). Is this coefficient statistically significant? Show your work for all answers

Consider the following regression equation: graduate = Bo + Bi female + B2score + u where graduate is a dummy variable (1 if the person graduated from college, and 0 otherwise), female is a dummy variable (1 if the person is female, and 0 otherwise), and score is the college admission test score. What does b1 measure? Now let’s say we switch the dependent variable to female and make graduate the independent variable in this model. How does the interpretation of this model change?

OK

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