程序代寫案例-EFIM20011

時間：2021-01-25

DO NOT REMOVE THIS PAPER FROM THE EXAMINATION ROOM

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January 2019

EFIM20011

ECONOMETRICS

Time allowed: TWO hours and THIRTY minutes

Answer ALL questions

30 marks are allocated to Section A. 35 marks are allocated to Section B. 35 marks are

allocated to Section C.

Justify all your answers. Non programmable calculators may be used, but candidates

must show the basis of all calculations.

TURN OVER

Section A. [30 marks]

Answer all of the following 6 questions. Each question is worth 5 marks. Give concise

justifications for all your answers.

1. We throw a cubic die n times and compute the average of the n results. If n = 5 the

average is 4.6. If n = 10 the average is 3.1. If n = 50 the average is 3.3 and if n = 100

it is equal to 3.4. Explain this result pattern. What average would we observe if we

threw the die 10,000 times?

2. Let W denote the wage and M be a dummy variable equal to 1 if the individual is

male and equal to 0 if the individual is female. We regressW onM (and a constant)

by OLS using a large iid sample and denote the estimated coefficient of M as bb.

What is the interpretation of bb?

3. Consider the linear model Y = a+ b ·X1 + c ·X2 + d ·X3 + U where X1, X2, X3 are

observed exogenous regressors, a, b, c, d are parameters and U is an unobserved

error term. We estimate the parameters using an OLS regression on an iid sample

with 1,000 observations and we want to test whether the three regressors jointly

have no effect on the outcome Y . Which test should we use and what would be the

distribution of the test statistic under the null assumption?

4. Consider the linear model Y = a + b · X + c · W + U where W is an exogenous

regressor and U is an unobserved error term. Let Z be an observed variable. Write

down the conditions required for Z to be a valid instrument for X in this linear model.

5. We want to know the effect of a training program (for unemployed workers) on unem-

ployment duration. Write down a potential outcome model for this evaluation problem.

6. What are the conditions under which an Instrumental Variable estimator only cap-

tures a Local Average Treatment Effect (LATE)?

Section B. [35 marks]

We study the gender wage gap in a population. We have one large iid sample of male and

female workers. We consider the following variables:

? W is the (monthly) wage of an individual (in US dollars),

? M is a male gender dummy, equal to 1 for men and to 0 for women,

? A is the individual’s age (in years),

? S is the individual’s education, measured as years spent in education.

We define the linear model: W = a+ b ·M + c ·A+ d · S + U , where U is an error term.

1. What is the interpretation of the parameters b, c and d? [3 marks]

We regress W on M , A and S (and a constant) by OLS using our data sample. The

estimates of a, b, c and d (and their estimated variances) are:ba = 550, bb = 950, bc = 42, bd = 29.5bV (ba) = 184, bV ?bb? = 1.2, bV (bc) = 0.4, bV ?bd? = 0.1

2. Write down the first-order conditions characterising these OLS estimates. You are

not asked to solve this system of equations. [4 marks]

3. What is the interpretation of bb? What is the interpretation of bd? [3 marks]

4. Write down the exogeneity assumption in the linear model and interpret this assump-

tion. If exogeneity holds, how can you interpret the estimates bb, bc and bd? [4 marks]

From now on, we assume that exogeneity holds.

5. Test whether there is no wage difference between men and women at the 5% signif-

icance level, even when controlling for age and education. [3 marks]

6. Is there evidence of a positive wage difference between men and women at the 5%

level, even when controlling for age and education? [3 marks]

7. How would you test for the equality of wage returns to age and wage returns to

education? You are not asked to conduct this test. [3 marks]

8. Suggest a model specification that would allow for the effect of education and the

effect of age to be different across genders. How would you then test whether wage

returns to age are different between men and women? You are not asked to conduct

this test. [7 marks]

9. Explain how an omitted variable could lead to the exogeneity assumption being vio-

lated in the linear model. How could selection also affect the credibility of the exo-

geneity assumption? [5 marks]

TURN OVER

Section C. [35 marks]

This exercise is based on an article published in 2004 in the Journal of Labor Economics.

We study the effect of firm-sponsored training programs on workers’ wage in the Nether-

lands.

We have a large iid sample of Dutch workers and observe their wage W , their age A,

genderM (1 for men, 0 for women), education S (years of schooling) and a dummy variable

T equal to 1 if the worker received training in the past year and equal to 0 otherwise.

We consider the following linear model: (referred to as model 1)

W = ?+ ·M + · S + ·A+ · T + U,

where U is an unobserved error term and ?, , , and are parameters.

1. Explain why not controlling for the worker’s skill level may lead an OLS estimation of

model (1) to produce a biased estimate of the effect of training on wages. [4 marks]

2. If firms offer more training opportunities to low-skill workers, would the OLS estimate

of be biased upwards or downwards? [4 marks]

To overcome identification issues, we can use the following tax policy: in the Netherlands,

employers get an extra tax deduction for training their employers who are at least 40 years

old (this does not apply to workers below 40). We then create a dummy variable D equal

to 1 if the worker is at least 40 years old and equal to 0 if the worker is younger than 40.

3. Explain why this policy motivates a fuzzy regression discontinuity design. [5 marks]

4. Present the two conditions for D to be a valid instrument for T in model (1). Discuss

these assumptions. [6 marks]

5. Present the two stages of the 2SLS estimation of model (1) usingD as an instrument

for T . You need to mention precisely which regressors and outcomes are used in

each stage. [5 marks]

6. Which statistic should we use to assess the strength/weakness of the instrument? If

this statistic is equal to 5.14 in the data, what should we conclude? [4 marks]

7. The 2SLS estimator of is equal to -1150 with an estimated standard error of 960.

Give a 95% confidence interval for the effect of training on wages. [4 marks]

8. Can we conclude that is significantly different from 0 at the 1% level? [3 marks]

END OF EXAM

學霸聯盟:"http://aessay.org"

UNIVERSITYOFBRISTOL

&9".*/"5*0/0'5)&%&(3&&4*/5)&4$)000-0'&$0/0.*$4

'*/"/$&"/%."/"(&.&/5

January 2019

EFIM20011

ECONOMETRICS

Time allowed: TWO hours and THIRTY minutes

Answer ALL questions

30 marks are allocated to Section A. 35 marks are allocated to Section B. 35 marks are

allocated to Section C.

Justify all your answers. Non programmable calculators may be used, but candidates

must show the basis of all calculations.

TURN OVER

Section A. [30 marks]

Answer all of the following 6 questions. Each question is worth 5 marks. Give concise

justifications for all your answers.

1. We throw a cubic die n times and compute the average of the n results. If n = 5 the

average is 4.6. If n = 10 the average is 3.1. If n = 50 the average is 3.3 and if n = 100

it is equal to 3.4. Explain this result pattern. What average would we observe if we

threw the die 10,000 times?

2. Let W denote the wage and M be a dummy variable equal to 1 if the individual is

male and equal to 0 if the individual is female. We regressW onM (and a constant)

by OLS using a large iid sample and denote the estimated coefficient of M as bb.

What is the interpretation of bb?

3. Consider the linear model Y = a+ b ·X1 + c ·X2 + d ·X3 + U where X1, X2, X3 are

observed exogenous regressors, a, b, c, d are parameters and U is an unobserved

error term. We estimate the parameters using an OLS regression on an iid sample

with 1,000 observations and we want to test whether the three regressors jointly

have no effect on the outcome Y . Which test should we use and what would be the

distribution of the test statistic under the null assumption?

4. Consider the linear model Y = a + b · X + c · W + U where W is an exogenous

regressor and U is an unobserved error term. Let Z be an observed variable. Write

down the conditions required for Z to be a valid instrument for X in this linear model.

5. We want to know the effect of a training program (for unemployed workers) on unem-

ployment duration. Write down a potential outcome model for this evaluation problem.

6. What are the conditions under which an Instrumental Variable estimator only cap-

tures a Local Average Treatment Effect (LATE)?

Section B. [35 marks]

We study the gender wage gap in a population. We have one large iid sample of male and

female workers. We consider the following variables:

? W is the (monthly) wage of an individual (in US dollars),

? M is a male gender dummy, equal to 1 for men and to 0 for women,

? A is the individual’s age (in years),

? S is the individual’s education, measured as years spent in education.

We define the linear model: W = a+ b ·M + c ·A+ d · S + U , where U is an error term.

1. What is the interpretation of the parameters b, c and d? [3 marks]

We regress W on M , A and S (and a constant) by OLS using our data sample. The

estimates of a, b, c and d (and their estimated variances) are:ba = 550, bb = 950, bc = 42, bd = 29.5bV (ba) = 184, bV ?bb? = 1.2, bV (bc) = 0.4, bV ?bd? = 0.1

2. Write down the first-order conditions characterising these OLS estimates. You are

not asked to solve this system of equations. [4 marks]

3. What is the interpretation of bb? What is the interpretation of bd? [3 marks]

4. Write down the exogeneity assumption in the linear model and interpret this assump-

tion. If exogeneity holds, how can you interpret the estimates bb, bc and bd? [4 marks]

From now on, we assume that exogeneity holds.

5. Test whether there is no wage difference between men and women at the 5% signif-

icance level, even when controlling for age and education. [3 marks]

6. Is there evidence of a positive wage difference between men and women at the 5%

level, even when controlling for age and education? [3 marks]

7. How would you test for the equality of wage returns to age and wage returns to

education? You are not asked to conduct this test. [3 marks]

8. Suggest a model specification that would allow for the effect of education and the

effect of age to be different across genders. How would you then test whether wage

returns to age are different between men and women? You are not asked to conduct

this test. [7 marks]

9. Explain how an omitted variable could lead to the exogeneity assumption being vio-

lated in the linear model. How could selection also affect the credibility of the exo-

geneity assumption? [5 marks]

TURN OVER

Section C. [35 marks]

This exercise is based on an article published in 2004 in the Journal of Labor Economics.

We study the effect of firm-sponsored training programs on workers’ wage in the Nether-

lands.

We have a large iid sample of Dutch workers and observe their wage W , their age A,

genderM (1 for men, 0 for women), education S (years of schooling) and a dummy variable

T equal to 1 if the worker received training in the past year and equal to 0 otherwise.

We consider the following linear model: (referred to as model 1)

W = ?+ ·M + · S + ·A+ · T + U,

where U is an unobserved error term and ?, , , and are parameters.

1. Explain why not controlling for the worker’s skill level may lead an OLS estimation of

model (1) to produce a biased estimate of the effect of training on wages. [4 marks]

2. If firms offer more training opportunities to low-skill workers, would the OLS estimate

of be biased upwards or downwards? [4 marks]

To overcome identification issues, we can use the following tax policy: in the Netherlands,

employers get an extra tax deduction for training their employers who are at least 40 years

old (this does not apply to workers below 40). We then create a dummy variable D equal

to 1 if the worker is at least 40 years old and equal to 0 if the worker is younger than 40.

3. Explain why this policy motivates a fuzzy regression discontinuity design. [5 marks]

4. Present the two conditions for D to be a valid instrument for T in model (1). Discuss

these assumptions. [6 marks]

5. Present the two stages of the 2SLS estimation of model (1) usingD as an instrument

for T . You need to mention precisely which regressors and outcomes are used in

each stage. [5 marks]

6. Which statistic should we use to assess the strength/weakness of the instrument? If

this statistic is equal to 5.14 in the data, what should we conclude? [4 marks]

7. The 2SLS estimator of is equal to -1150 with an estimated standard error of 960.

Give a 95% confidence interval for the effect of training on wages. [4 marks]

8. Can we conclude that is significantly different from 0 at the 1% level? [3 marks]

END OF EXAM

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