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STATA代写-EC421

时间：2021-04-23

EC421: Advanced Econometric Methods - Spring 2021; Professor Vogelsang

Test 2, Monday April 12, 2021.

This test has two parts totaling 100 points. This is a take home test. You must submit your

answers to the D2L dropbox by 11:59PM Eastern Time on Monday April 12, 2021. The test is

OPEN BOOK,OPEN NOTES. Useful formulas and tables of distributions can be found on the

course formula sheet and critical values documents posted to D2L.You MAY NOT share the test

questions with any other individuals. You MUST work on the exam by yourself. The test is open

book/open notes. The internet is NOT to be used. Calculators are permitted. Either print the

answer sheet posted on D2L or use your own blank paper to write up your answers. You may

handwrite your answers, type them, or both. Show all of your work as partial credit will be given.

Please scan your answer sheets and submit using the D2L dropbox using pdf format if possible.

Part I: Short Answer (25 points, 5 points each)

In WORDS, briey describe and discuss the following. Try to limit your answer to no more

than three or four sentences. You may use formulas if they are helpful, but a formula without an

explanation will receive no credit!

a) How is di¤erence-in-di¤erences in pooled independent cross-sections used to estimate policy

e¤ects?

b) Describe the bene ts of using First Di¤erences or Fixed-E¤ects to estimate a panel model

relative to using Pooled-OLS

c) Describe the costs of using First Di¤erences or Fixed-E¤ects to estimate a panel model

relative to using Pooled-OLS

d) What is the interpretation of the coe¢ cient on the time period dummy variable in a panel

model with two time periods?

e) Suppose a panel model has no individual heterogeneity (ai = 0) and uit is NOT correlated

across time. What estimator or estimators would you use among Pooled OLS, First Di¤erencing,

Fixed-E¤ects and Random E¤ects? Why?

Part II: 75 points

This part of the test asks a series of questions about the relationship between dthrte, tra¢ c death

rates (number of tra¢ c deaths per million miles driven), unem, unemployment rates, and admn,

a dummy variable that equals 1 if a State in a given year has administrative laws such as driver

licenses can be suspended for drunk driving. Data was gathered for these variables for the 48

contiguous States of the United States (Hawaii, Alaska and Washington D.C. are not included) for

the years 1980 and 2004. The average death rate across all states was 3.55 in 1980 and was 1.51 in

2004.

Suppose we are interested in the following regression relationship

dthrteit = 0 + 0d2t + 1admnit + 2unemit + ai + uit;

where t = 1 is 1980 and t = 2 is 2004. The variable d2t is a dummy variable that equals 1 if t = 2

(2004). The total error depends on the State speci c heterogeneity, ai, and an idiosyncratic error,

uit. We would expect ai to be correlated with admnit because states with higher than normal

tra¢ c death rates may be under pressure to pass drunk driving laws. You can assume that uit is

not correlated with admnit and unemit.

Consider four options for estimating the parameters 1 and 2. For the rst two options we

estimate separate regressions for 1980 (t = 1) and 2004 (t = 2) using OLS:

dthrtei1 = 0 + 1admni1 + 2unemi1 + ai + ui1;

dthrtei2 = 0 + 1admni2 + 2unemi2 + ai + ui2:

For the third option we can pool the data from both years and estimate the panel model

dthrteit = 0 + 0d2t + 1admnit + 2unemit + ai + uit;

using OLS (i.e. the Pooled-OLS estimators). Finally, we can apply the rst di¤erence transforma-

tion to the panel model and estimate the transformed model

dthrtei = 0 + 1admni + 2unemi + ui:

by OLS (i.e. the First-Di¤erences estimators).

a) What are the interpretations of the 0, 1 and 2 parameters? (6 points) If you used First-

Di¤erences to estimate these parameters, would this change the interpretation? Why or why

not? (2 points)

2

The four estimation methods yielded the following results given in Table 1. Heteroskedasticity

robust standard errors are given in parentheses.

Table 1: Estimates for Death Rate Model Using the Years 1980 and 2004

1980 only 2004 only Pooled OLS First Di¤erencesb1 (admn):::: 1.56 -.0065 .159 -.308

(.833) (.154) (.224) (.238)

b2 (unem) -.070 .028 -.019 .021

(.077) (.062) (.057) (.071)

b0 (d2) NA NA -2.19 -1.75

(.222) (.265)

obs 48 48 96 48

b) Provide an explanation for why the estimates of 1 are so di¤erent across the four estimation

methods. (6 points)

c) Which estimator of 1 do you prefer and why? (4 points) Is your preferred estimator of

1 statistically signi cant at the 10% level? Why or why not? (2 points) Is it practically

signi cant? Why or why not? (2 points)

d) Using the First Di¤erences estimator, test the null hypothesis that mean tra¢ c death rates

did NOT fall from 1980 to 2004 (holding admn and unemp constant) against the hypothesis

that mean tra¢ c death rates did fall. Write down the null and alternative hypotheses in

terms of the relevant parameter and carry out your test at the 5% level. (6 points) What

do you conclude? (1 point)

e) From the Table we see that First Di¤erences is based on only one years worth of data

(obs = 48). Someone suggests that Fixed-E¤ects is a better estimation option than First

Di¤erences because there is unlikely to be much, if any, correlation between uit at years 1980

and 2004 because shocks to tra¢ c death do not last for 25 years. Suppose it is true that ui1

(1980) is uncorrelated with ui2 (2004). Can Fixed-E¤ects be better than First Di¤erences?

Why or why not? (6 points)

3

An intern was hired to collect data for all the years between 1980 and 2004 increasing the sample

size of the panel from 96 to 1,200 observations. We now have T = 25 rather than T = 2. The model

of interest is the same except that dummy variables are included for the additional time periods:

dthrteit = 0 + 2d2t + 3d3t + :::+ 25d25t + 1admnit + 2unemit + ai + uit; (1)

Model (1) was estimated using Pooled-OLS, First Di¤erences, Fixed-E¤ects and Random E¤ects.

The results are in given in the following table. Time dummy parameter estimates are only reported

for every 5th year. The estimated value of used for the random e¤ects transformation wasb = :749. All standard errors are robust to heteroskedasticity and correlation across time (serial

correlation).

Table 2: Estimates for Death Rate Model Using the Years 1980 through 2004

Pooled OLS First Di¤erences Fixed E¤ects Random E¤ectsb1 (admn)::: .031 -.115 -.140 -.136

(.114) (.039) (.058) (.056)

b2 (unem) .080 -.023 -.043 -.039

(.030) (.010) (.015) (.015)

b5 (d5; 1984) -1.03 -.864 -.848 -.851

(.092) (.068) (.066) (.069)

b10 (d10; 1989) -1.22 -1.33 -1.35 -1.35

(.110) (.085) (.086) (.086)

b15 (d15; 1994) -1.70 -1.73 -1.74 -1.74

(.130) (.089) (.092) (.088)

b20 (d20; 1999) -1.72 -1.88 -1.92 -1.92

(.149) (.093) (.101) (.100)

b25 (d25; 2004) -1.91 -1.98 -2.00 -2.00

(.140) (.093) (.102) (.101)

obs 1200 1152 1200 1200

4

f) Assuming that cov(admnit; ai) 6= 0, which estimation methods of model (1) could be LUE?

Why? (3 points) Which estimation methods are biased? Why? (3 points)

g) For each of the potentially LUE estimators, under what assumptions will that estimator be

BLUE? (4 points)

h) The Pooled-OLS estimator of 1 has the opposite sign as the First-Di¤erence and Fixed-

E¤ects estimators. Provide a theoretical explanation for this fact. (4 points) The Random

E¤ects estimator of 1 is very similar to Fixed-E¤ects. Are you surprised by this? Why or

why not? (2 points)

i) Calculate 95% con dence intervals for 1 using the First Di¤erence and Fixed-E¤ects esti-

mators. (4 points) Can you reject the null hypothesis that 1 = 0 with either con dence

interval? (2 points) Which estimator would you use for measuring the impact of adminis-

trative laws on tra¢ c death rates? Why? (2 points)

j) Go back to Table 1 that only uses the 1980 and 2004 data and compute a 95% con dence

interval for 1 using the First Di¤erence estimator. (2 points) You should nd that this

con dence interval is substantially wider than the con dence intervals using all the data from

1980 to 2004. What accounts for this di¤erence in con dence interval widths? (2 points)

What do you conclude about using just the 1980 and 2004 data compared to using all the

years from 1980 to 2004? (2 points)

k) Using the First Di¤erences estimator from Table 2 (all years from 1980 to 2004), test the null

hypothesis that mean tra¢ c death rates did NOT fall from 1980 to 2004 (holding admn and

unemp constant) against the hypothesis that mean tra¢ c death rates did fall. Write down

the null and alternative hypotheses in terms of the relevant parameter and carry out your

test at the 5% level. (2 points) How do your results compare to what you found in part (d)?

(2 points) Provide an explanation for any di¤erences you see. (2 points)

l) Using the Fixed-E¤ects estimated parameters, holding admn and unem constant, over what

5 year period did tra¢ c death rates fall more: 1984 to 1989, 1989 to 1994, 1994 to 1999, or

1999 to 2004? Provide details on your calculations. (4 points)

5

学霸联盟

Test 2, Monday April 12, 2021.

This test has two parts totaling 100 points. This is a take home test. You must submit your

answers to the D2L dropbox by 11:59PM Eastern Time on Monday April 12, 2021. The test is

OPEN BOOK,OPEN NOTES. Useful formulas and tables of distributions can be found on the

course formula sheet and critical values documents posted to D2L.You MAY NOT share the test

questions with any other individuals. You MUST work on the exam by yourself. The test is open

book/open notes. The internet is NOT to be used. Calculators are permitted. Either print the

answer sheet posted on D2L or use your own blank paper to write up your answers. You may

handwrite your answers, type them, or both. Show all of your work as partial credit will be given.

Please scan your answer sheets and submit using the D2L dropbox using pdf format if possible.

Part I: Short Answer (25 points, 5 points each)

In WORDS, briey describe and discuss the following. Try to limit your answer to no more

than three or four sentences. You may use formulas if they are helpful, but a formula without an

explanation will receive no credit!

a) How is di¤erence-in-di¤erences in pooled independent cross-sections used to estimate policy

e¤ects?

b) Describe the bene ts of using First Di¤erences or Fixed-E¤ects to estimate a panel model

relative to using Pooled-OLS

c) Describe the costs of using First Di¤erences or Fixed-E¤ects to estimate a panel model

relative to using Pooled-OLS

d) What is the interpretation of the coe¢ cient on the time period dummy variable in a panel

model with two time periods?

e) Suppose a panel model has no individual heterogeneity (ai = 0) and uit is NOT correlated

across time. What estimator or estimators would you use among Pooled OLS, First Di¤erencing,

Fixed-E¤ects and Random E¤ects? Why?

Part II: 75 points

This part of the test asks a series of questions about the relationship between dthrte, tra¢ c death

rates (number of tra¢ c deaths per million miles driven), unem, unemployment rates, and admn,

a dummy variable that equals 1 if a State in a given year has administrative laws such as driver

licenses can be suspended for drunk driving. Data was gathered for these variables for the 48

contiguous States of the United States (Hawaii, Alaska and Washington D.C. are not included) for

the years 1980 and 2004. The average death rate across all states was 3.55 in 1980 and was 1.51 in

2004.

Suppose we are interested in the following regression relationship

dthrteit = 0 + 0d2t + 1admnit + 2unemit + ai + uit;

where t = 1 is 1980 and t = 2 is 2004. The variable d2t is a dummy variable that equals 1 if t = 2

(2004). The total error depends on the State speci c heterogeneity, ai, and an idiosyncratic error,

uit. We would expect ai to be correlated with admnit because states with higher than normal

tra¢ c death rates may be under pressure to pass drunk driving laws. You can assume that uit is

not correlated with admnit and unemit.

Consider four options for estimating the parameters 1 and 2. For the rst two options we

estimate separate regressions for 1980 (t = 1) and 2004 (t = 2) using OLS:

dthrtei1 = 0 + 1admni1 + 2unemi1 + ai + ui1;

dthrtei2 = 0 + 1admni2 + 2unemi2 + ai + ui2:

For the third option we can pool the data from both years and estimate the panel model

dthrteit = 0 + 0d2t + 1admnit + 2unemit + ai + uit;

using OLS (i.e. the Pooled-OLS estimators). Finally, we can apply the rst di¤erence transforma-

tion to the panel model and estimate the transformed model

dthrtei = 0 + 1admni + 2unemi + ui:

by OLS (i.e. the First-Di¤erences estimators).

a) What are the interpretations of the 0, 1 and 2 parameters? (6 points) If you used First-

Di¤erences to estimate these parameters, would this change the interpretation? Why or why

not? (2 points)

2

The four estimation methods yielded the following results given in Table 1. Heteroskedasticity

robust standard errors are given in parentheses.

Table 1: Estimates for Death Rate Model Using the Years 1980 and 2004

1980 only 2004 only Pooled OLS First Di¤erencesb1 (admn):::: 1.56 -.0065 .159 -.308

(.833) (.154) (.224) (.238)

b2 (unem) -.070 .028 -.019 .021

(.077) (.062) (.057) (.071)

b0 (d2) NA NA -2.19 -1.75

(.222) (.265)

obs 48 48 96 48

b) Provide an explanation for why the estimates of 1 are so di¤erent across the four estimation

methods. (6 points)

c) Which estimator of 1 do you prefer and why? (4 points) Is your preferred estimator of

1 statistically signi cant at the 10% level? Why or why not? (2 points) Is it practically

signi cant? Why or why not? (2 points)

d) Using the First Di¤erences estimator, test the null hypothesis that mean tra¢ c death rates

did NOT fall from 1980 to 2004 (holding admn and unemp constant) against the hypothesis

that mean tra¢ c death rates did fall. Write down the null and alternative hypotheses in

terms of the relevant parameter and carry out your test at the 5% level. (6 points) What

do you conclude? (1 point)

e) From the Table we see that First Di¤erences is based on only one years worth of data

(obs = 48). Someone suggests that Fixed-E¤ects is a better estimation option than First

Di¤erences because there is unlikely to be much, if any, correlation between uit at years 1980

and 2004 because shocks to tra¢ c death do not last for 25 years. Suppose it is true that ui1

(1980) is uncorrelated with ui2 (2004). Can Fixed-E¤ects be better than First Di¤erences?

Why or why not? (6 points)

3

An intern was hired to collect data for all the years between 1980 and 2004 increasing the sample

size of the panel from 96 to 1,200 observations. We now have T = 25 rather than T = 2. The model

of interest is the same except that dummy variables are included for the additional time periods:

dthrteit = 0 + 2d2t + 3d3t + :::+ 25d25t + 1admnit + 2unemit + ai + uit; (1)

Model (1) was estimated using Pooled-OLS, First Di¤erences, Fixed-E¤ects and Random E¤ects.

The results are in given in the following table. Time dummy parameter estimates are only reported

for every 5th year. The estimated value of used for the random e¤ects transformation wasb = :749. All standard errors are robust to heteroskedasticity and correlation across time (serial

correlation).

Table 2: Estimates for Death Rate Model Using the Years 1980 through 2004

Pooled OLS First Di¤erences Fixed E¤ects Random E¤ectsb1 (admn)::: .031 -.115 -.140 -.136

(.114) (.039) (.058) (.056)

b2 (unem) .080 -.023 -.043 -.039

(.030) (.010) (.015) (.015)

b5 (d5; 1984) -1.03 -.864 -.848 -.851

(.092) (.068) (.066) (.069)

b10 (d10; 1989) -1.22 -1.33 -1.35 -1.35

(.110) (.085) (.086) (.086)

b15 (d15; 1994) -1.70 -1.73 -1.74 -1.74

(.130) (.089) (.092) (.088)

b20 (d20; 1999) -1.72 -1.88 -1.92 -1.92

(.149) (.093) (.101) (.100)

b25 (d25; 2004) -1.91 -1.98 -2.00 -2.00

(.140) (.093) (.102) (.101)

obs 1200 1152 1200 1200

4

f) Assuming that cov(admnit; ai) 6= 0, which estimation methods of model (1) could be LUE?

Why? (3 points) Which estimation methods are biased? Why? (3 points)

g) For each of the potentially LUE estimators, under what assumptions will that estimator be

BLUE? (4 points)

h) The Pooled-OLS estimator of 1 has the opposite sign as the First-Di¤erence and Fixed-

E¤ects estimators. Provide a theoretical explanation for this fact. (4 points) The Random

E¤ects estimator of 1 is very similar to Fixed-E¤ects. Are you surprised by this? Why or

why not? (2 points)

i) Calculate 95% con dence intervals for 1 using the First Di¤erence and Fixed-E¤ects esti-

mators. (4 points) Can you reject the null hypothesis that 1 = 0 with either con dence

interval? (2 points) Which estimator would you use for measuring the impact of adminis-

trative laws on tra¢ c death rates? Why? (2 points)

j) Go back to Table 1 that only uses the 1980 and 2004 data and compute a 95% con dence

interval for 1 using the First Di¤erence estimator. (2 points) You should nd that this

con dence interval is substantially wider than the con dence intervals using all the data from

1980 to 2004. What accounts for this di¤erence in con dence interval widths? (2 points)

What do you conclude about using just the 1980 and 2004 data compared to using all the

years from 1980 to 2004? (2 points)

k) Using the First Di¤erences estimator from Table 2 (all years from 1980 to 2004), test the null

hypothesis that mean tra¢ c death rates did NOT fall from 1980 to 2004 (holding admn and

unemp constant) against the hypothesis that mean tra¢ c death rates did fall. Write down

the null and alternative hypotheses in terms of the relevant parameter and carry out your

test at the 5% level. (2 points) How do your results compare to what you found in part (d)?

(2 points) Provide an explanation for any di¤erences you see. (2 points)

l) Using the Fixed-E¤ects estimated parameters, holding admn and unem constant, over what

5 year period did tra¢ c death rates fall more: 1984 to 1989, 1989 to 1994, 1994 to 1999, or

1999 to 2004? Provide details on your calculations. (4 points)

5

学霸联盟