代做Econ7810: Econometrics for Economic Analysis, Fall 2024 Homework #3代写C/C++程序
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Homework #3
Due date: 30 Nov. 2024; 1pm.
Do not copy and paste the answers from your classmates. Two identical homework will be treated as cheating. Do not copy and paste the entire output of your statistical package's. Report only the relevant part of the output. Please also submit your R-script. for the empirical part. Please put all your work in one single file and upload via Moodle.
Part I
Multiple Choice (3 points each, 24 points in total)
Please choose the answer that you think is appropriate.
1.1 The interpretation of the slope coe cient in the model Yi = β0 + β1 ln(Xi ) = ui is as follows:
a. 1% change in X is associated with a β1 % change in Y.
b. 1% change in X is associated with a change in Y of 0.01β1.
c. change in X by one unit is associated with a 100β1 % change in Y.
d. change in X by one unit is associated with a β1 change in Y.
1.2 In the regression model Yi = β0 +β1Xi +β2 Di +β3 (Xi ×Di )+ui , where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the
a. t-statistic separately for β2 = 0, β3 = 0.
b. F-statistic for the joint hypothesis that β0 = 0, β1 = 0.
c. t-statistic separately for β3 = 0.
d. F-statistic for the joint hypothesis that β2 = 0, β3 = 0 .
1.3 If you reject a joint null hypothesis using the F-test in a multiple hypothesis setting, then
a. a series of t-tests may or may not give you the same conclusion.
b. the regression is always signi cant.
c. all of the hypotheses are always simultaneously rejected.
d. the F-statistic must be negative.
1.4 You have estimated the following equation:
TestScore = 607.3 + 3.85Income - 0.0423Income2
where TestScore is the average of the reading and math scores on the Stanford 9 stan- dardized test administered to 5th grade students in 420 California school districts in 1998 and 1999. Income is the average annual per capita income in the school district, measured in thousands of 1998 dollars. The equation
a. suggests a positive relationship between test scores and income for most of the sample.
b. is positive until a value of Income of 610.81.
c. does not make much sense since the square of income is entered.
d. suggests a positive relationship between test scores and income for all of the sample.
1.5 The linear probability model is
a. the application of the multiple regression model with a continuous left-hand side variable and a binary variable as at least one of the regressors.
b. an example of probit estimation.
c. another word for logit estimation.
d. the application of the linear multiple regression model to a binary dependent variable.
1.6 The probit model
a. is the same as the logit model.
b. always gives the same fit for the predicted values as the linear probability model for values between 0.1 and 0.9.
c. forces the predicted values to lie between 0 and 1.
d. should not be used since it is too complicated.
1.7 In the logit model Pr(Y = 1jX1 , X2, ...Xk ) = F (β0 + β1X1 + β2X2 + ... + βkXk ),
a. the β 's do not have a simple interpretation.
b. the slopes tell you the e ect of a unit increase in X on the probability of Y.
c. β0 cannot be negative since probabilities have to lie between 0 and 1.
d. β0 is the probability of observing Y when all X's are 0.
1.8 Your textbook plots the estimated regression function produced by the probit regression of deny on P/I ratio. The estimated probit regression function has a stretched S shape given that the coe cient on the P/I ratio is positive. Consider a probit regression function with a negative coe cient. The shape would
a. resemble an inverted S shape (for low values of X, the predicted probability of Y would approach 1)
b. not exist since probabilities cannot be negative
c. remain the S shape as with a positive slope coe cient
d. would have to be estimated with a logit function
Part II
Short Questions (36 points in total)
Please limit your answer to less than or equal to 5 lines per sub-question.
(8 points) 2.1 Dr. Qin would like to analyze the Return to Education and the Gender Gap . The equation below shows the regression result using the 2005 Current Population Survey. lnEearnings refer to the logarithem of the monthly earnings; educ refers to the year of education; DFemme is a dummy variable, if the individual is female, =1; exper is the working experience, measured by year; Midwest, South and West are dummy variables indicating the residence regions, while Northeast is the ommited region. Interpret the major results(discuss the estimates for all variables and also address the question that Dr. Qin wants to analyze.
LnEar(^)nings = 1.215 + 0.0899 × educ — 0.521 × DFemme + 0.0180 × (DFemme × educ)
(0.018) (0.0011) (0.022) (0.0016)
+0.0232 × exper — 0.000368 × exper2 — 0.058 × Midwest — 0.0078 × South (0.0008) (0.000018) (0.006) (0.006)
—0.030 × West (0.006)
-
n = 57, 863 R2 = 0.242
(15 points) 2.2 Sports economics typically looks at winning percentages of sports teams as one of various outputs, and estimates production functions by analyzing the relationship be- tween the winning percentage and inputs. In Major League Baseball (MLB),the determinants of winning are quality pitching and batting. All 100 MLB teams for the 1999 season. Pitching quality is approximated by Team Earned Run Average (teamera), and hitting quality by On Base Plus Slugging Percentage (ops). Your regression output is:
Winpct = —0.19 — 0.099 × teamera + 1.49 × ops, R2 = 0.92 (0.08) (0.008) (0.126)
(a) (5 points) Interpret the regression. Are the results statistically signi cant and impor- tant?
(b) (8 points) There are two leagues in MLB, the American League(AL) and the National League (NL). One major di erence is that the pitcher in the AL does not have to bat.
Instead there is a designatedhitter in the hitting line-up. You are concerned that, as a result, there is a di erent e ect of pitching and hitting in the AL from the NL. To test this Hypothesis, you allow the AL regression to have a di erent intercept and di erent slopes
from the NL regression. You therefore create a binary variable for the American League (DAL) and estiamte the following speci cation:
Winpct = —0.29 + 0.10 × DAL — 0.100 × teamera + 0.008 × (DAL × teamera) (0.12) (0.24) (0.008) (0.018)
+1.622 * ops — 0.187 * (DAL × ops) (0.163) (0.160) R2 = 0.92
How should you interpret the winning percentage for AL and NL? Can you tell the di erent e ect of pitching and hitting between AL and NL? If so, how much?
(2 points) (c) You remember that sequentially testing the signi cance of slope coe cients is not the same as testing for their signi cance simultaneously. Hence you ask your regression package to calculate the F-statistic that all three coe cients involving the binary variable for the AL are zero. Your regression package gives a value of 0.35. Looking at the critical value from the F-table, can you reject the null hypothesis at the 1% level?
(13 points) 2.3 A study analyzed the probability of Major League Baseball (MLB) players to survive for another season, or, in other words, to play one more season. The researchers had a sample of 4,728 hitters and 3,803 pitchers for the years 1901-1999. All explanatory variables are standardized. The probit estimation yielded the results as shown in the table:
|
Regression |
(1) Hitters |
(2) Pitchers |
|
Regression model |
probit |
probit |
|
constant |
2.010 (0.030) |
1.625 (0.031) |
|
number of seasons played |
-0.058 (0.004) |
-0.031 (0.005) |
|
performance |
0.794 (0.025) |
0.677 (0.026) |
|
average performance |
0.022 (0.033) |
0.100 (0.036) |
where the limited dependent variable takes on a value of one if the player had one more season (being survival) (a minimum of 50 at bats or 25 innings pitched), number of seasons played is measured in years, performance is the batting average for hitters and the earned run average for pitchers, and average performance refers to performance over the career. (Note that all variables are standardized, so that the mean is zero, and the variance is 1 )
( 4 points) (a) Interpret the two probit equations and calculate survival probabilities for hitters and pitchers at the sample mean.
( 4 points) (b) Calculate the change in the survival probability for a player who has a very bad year by performing two standard deviations below the average (assume also that this player has been in the majors for many years so that his average performance is hardly a ected). How does this change the survival probability when compared to the answer in (a)?
(5 points) (c) Since the results seem similar, the researcher could consider combining the two samples. Explain in some detail how this could be done and how you could test the hypothesis that the coe cients are the same.
Part III
Empirical part (40 points in total)
Please limit your answer to less than or equal to 10 lines per sub-question. PLEASE REPORT YOUR REGRESSION OUTCOMES IN TABLES, NOT SCREENSHORTS.
(20 points) 3.1 Please use VOTE2016.dta to answer the following questions. The following model can be used to study whether campaign expenditures a ect election outcomes:
voteA = β0 + β1 log(expendA) + β2 log(expendB) + u_(1)
voteA = β0 + β1 log(expendA) + β2 log(expendB) + β3prtystrA + u (2)
where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign expenditures (in 1000 dollars) by Candidates A and B, and prtystrA is a measure of party strength for Candidate A (the percentage of the most recent presidential vote that went to A's party).
(6 points)(a) Please run the regression (1) and report your result in a table. Do A's expenditure a ect the outcome and how? What about B's expenditure? (Hint: you need to
rst creat the variables ln(expendA) and ln(expendB)
(8 points)(b) Please run the regression (2) and report your result in the same table. Do A's expenditure a ect the outcome and how? What about B's expenditure? Compare result
from (a) and (b), explain whether we should include prtystrA in the regression or not. If we exclude it, to which direction the coe cient of interest tend to be biased towards?
(6 points) (c) Can you tell whether a 1% increase in A's expenditures is o set by a 1% increase in B's expenditure? How? Please suggest a regression or test and then answer the question according to your result.
(20 points) 3.2 Please download the data jtrain2.dta from Moodle and answer the following questions. There is a job training experiment for a group of men. Men could enter the program starting in January 1976 through about mid-1977. The program ended in December 1977. A study tried to test whether participation in the job training program had an e ect
on unemployment probabilities and earnings in 1978. (Note: for each sub-question ((a), (b), (c), (d)), the answer should not be longer than 8 lines.) Here is the description of the related variables:
unem78: =1, if unemployed in 1978; 0, otherwise.
train: the job training indicator. =1, trained; 0, otherwise. unem74: =1, if unemployed in 1974; 0, otherwise.
unem75: =1, if unemployed in 1975; 0, otherwise. age : age in 1977
educ: years of education
white: =1, the individual is white; 0, otherwise. married; =1, if married; 0, otherwise.
( 3 points) (a) Please run a linear probability model of unem78 on train, unem74, unem75, age, educ, white, and married. Interpret the results.
(8 points) (b) Run a probit and a logit regression of unem78 on train, unem74, unem75, age, educ, white, and married. Report the results. Can you compare the coe cients of train in the two models to conclude which model gives out bigger e ect of train? Explain.
(6 points) (c) What is the probability for a single white, aged 25, with 12 year education, being unemployed in both year 1974 and 1975 to be unemployed in 1978 if she/he attended the training program? What is the probability if this individual did not attend the training program?
(3 points) (d) Does the training program seem to help a 30 year old individual who has 16 year education? If so, what's the e ect? Explain.