ECON20110/30370 Econometrics Semester 1 2016/17 Midterm Examination

1. A data set that consists of a sample of individuals,  households,  firms,  cities,  states, countries, or a variety of other units, taken at a given point in time, is called a(n) ... ?

A. cross-sectional data set

B.  longitudinal data set

C. time series data set

D. experimental data set

E.  none of the above

2.  Find the degrees of freedom in a linear regression model that has  10 observations, 7 independent variables, and a constant.

A.  17

B. 2

C. 3

D. 4

E.  none of the above

3. Which of the following  models  is  not  linear  in  its  parameters  (represented  by  Greek letters)?

A. p = α + βln(q) + γr + u

B. y = γ + δ1 z + δ2 z2 + e

C.  ln(y) = δ + ξ . exp(x) + e

D. w = 1/(β0 + β1 x) + u

E.  none of the above

4. You estimate the following model using Ordinary Least Squares, ln(yi ) = β0 + β1 ln(xi ) + ui

what is the correct interpretation of the estimated coefficient β1 ?

A. an increase of 1 in x will lead to an increase of β1  in y

B. an increase of 1% in x will to to an increase of β1  % in y

C. an increase of 1 in x will lead to an increase of 100 β1 % in y

D. an increase of 1 in x will lead to an increase of 100 β1  in y

E.  none of the above

5.  Consider the following Ordinary Least Squares estimates

yi  =  4.62 + 2.50 zi + ei

(0.049)       (0.128)

where n = 526 and numbers in brackets () are standard errors.  Which of the following represent the 95% confidence interval for the coefficient on zi ?

A.  [1.20,3.80]

B.  [2.37,2.63]

C.  [2.25,2.75]

D.  [2.29,2.71]

E.  [2.17,2.83]

6.  Consider the following Ordinary Least Squares estimates

ln(qi ) = 2.020 + 0.5468pi + ui

(0.036)         (0.345)

where n = 445 and numbers in brackets () are standard errors. You test the null hypothesis H0  : γ1  ● 0 versus the alternative hypothesis H1  : γ1  > 0, where γ1  is the coefficient on pi . Which of the following statements is correct?

A. We reject the null hypothesis at the 1% significance level

B. We reject the null hypothesis at the 5% significance level

C. We fail to reject the null hypothesis at the 5% significance level

D. We fail to reject the null hypothesis at the 10% significance level

E.  none of the above

7. You estimate the parameters of the following regression using the OLS estimator ln(price) = α + β . ln(nox) + ∈

where price are house prices (measured in $’000), and nox is the level of air pollution (measured in parts per million). ∈ is an error term. If you believed that living closer to a motorway (measured in km) decreased the value of housing but increased the amount of air pollution, what problem could this potentially cause?

A. The OLS estimator for β will be biased upwards

B. The OLS estimator for β will be biased downwards

C. The amount of air pollution would be measured with error

D. The sample of house prices and air quality are non-random

E.  none of the above

8.  Consider the following Ordinary Least Squares estimates

log(pricei ) = 10.937 + _0.179log(noxi ) + ei

(0.077)           (0.0135)

n = 506,       SSR = 62.689,       SSE = 21.895

where pricei   is  house selling  price, noxi   is a  measure of air quality,  and  numbers in brackets are standard errors.  Which of the following represents the R-squared for this model?

A. 0.349

B. 0.650

C. 0.259

D. 0.741

E. 0.350

9. You want to estimate the OLS coefficients of the simple linear regression model yi  = γ0 + γ1 xi + ui

and you are given the following values

n

(yi _ y¯)2  = 1700,

i=1

n

(yi _ y¯)xi  = 720,

i=1

n

(xi _ )xi  = 300,

i=1

n

xi(2)  = 1800,

i=1

 = 12,    y¯ = 54

n

yi(2)  = 3000

i=1

Which are the following are the OLS estimates of γ0  and γ1 ?

A. 0  = 25.2, 1  = 0.42

B. 0  = 49, 1  = 2.4

C. 0  = 48.96, 1  = 0.42

D. 0  = 25.2, 1  = 2.4

E.  none of the above

10. A researcher is interested in estimating the effect of living in rural communities on the fertility  rate of women.   They  use a  random sample on the  number of children that n = 1223 women have given birth to and whether they live in rural or urban locations. The model can be written,

y = Xβ + u

where y is a (n × 1) vector containing the number of children, X is a matrix with the first column containing all 1s and the second column is a dummy variable equal to one if the woman lives in a rural location, and zero otherwise. β is a (2 × 1) with β0  in the first element and β1  in the second element. u is a (n × 1) vector of random error terms. The researcher obtains the following values:

Which of the following are the estimates of βˆ1  and s.e.(βˆ1 )?

A. βˆ1  = 0.460, s.e.(βˆ1 ) = 0.013

B. βˆ1  = 2.278, s.e.(βˆ1 ) = 0.002

C. βˆ1  = 0.460, s.e.(βˆ1 ) = 0.112

D. βˆ1  = 2.278, s.e.(βˆ1 ) = 0.083

E.  none of the above

11. You estimate the simple linear regression model

h = α + βa + u

where h is a measure of health of an individual and a is the age. Which of the following Gauss-Markov assumptions is not needed to show that the OLS estimator βˆ is an unbiased estimator for β?

A. The mean of the error term, conditional on age, is zero; E[u}a] = 0

B.  oh,a{ are randomly sampled from the population of interest

C. the model is linear in α and β

D. The data contain individuals of different ages

E.  none of the above

12. The true population model is given by

yi  = β0 + β1 xi + ei

yˆ = βˆ0 + βˆ1 xi + βˆ2 zi

What are the consequences of including zi  in the model on the estimates of β1 , β2 ?

A.  E[βˆ1] < β1

B.  E[βˆ1] > β1

C.  E[βˆ1] = 0

D.  E[βˆ2] > β2

E.  none of the above

13. A researcher is interested in the effect of education on wages and obtains a random sample of data on n = 5093 individuals and obtains the following OLS estimates,

wagei  = 0.320 + 0.565 educi

The researcher then obtains information on the years of labour market experience for

these individuals and adds them to the regression to obtain the following OLS estimates, wagei  = _3.905 + 0.826 educi + 0.201 experiencei

Which of the following statements is not true?

A.  Education and experience are negatively correlated

B.  Holding years of experience fixed, an individual with 1 additional year of edu- cation would earn on average 0.565 wages

C. An individual with 1 additional year of education would earn on average 0.826 higher wages, condition on their experience

D. An individual with 1 year additional education and 1 year additional experience would earn on average 1.027 higher wages

E.  none of the above

14.  Heteroskedasticity ...

A.  is when the variance of the error term, conditional on explanatory variables, is constant.

B.  is required for the OLS estimator to be BLUE.

C. will result in incorrect inference using the usual t-statistics.

D.  is required for the F-statistic to follow a F distribution

E.  none of the above

15.  Consider the following Ordinary Least Squares estimates

w一age =  3.73 + 1.89male + 0.287experience

(0.356)       (0.26)                     (0.078)

n = 526,        R2  = 0.087

(standard errors in brackets). Which of the following represents the value of the t-statistic for the null hypothesis H0  : βmale  ● 2 versus the alternative hypothesis H1  : βmale  > 2?

A. 7.269

B. -0.423

C. -14.962

D.  14.962

E. 0.423

16.  Consider the following Ordinary Least Squares estimate for the hourly wage rate (measured in ($’s) of a population of workers

w一age = 8.163 _ 0.283female + 2.616married _ 2.565female * married

(0.568)        (0.844)                           (0.734)                              (1.053)

where female = 1 if the individual is a women and zero otherwise, married = 1 if the individual is married and zero otherwise, and the numbers in brackets () are standard errors. What is the average predicted wage for a married woman?

A. $8.16 / hr

B. $7.88 / hr

C. $5.60 /hr

D. $7.93 /hr

E.  none of the above

19.  Consider the population regression model

yi  = β0 + β1 xi + ui .

The model is estimated using Ordinary Least Squares. Which of the following is not true?

A. The point  ,y¯ always lies on the regression line.

B. There are always as many points above the fitted line as there are below it.

C. The mean of the fitted values of y is the same as the mean of the observed values of y

D. The sum of the residuals is always zero

E.  none of the above

20.  Consider the following model used to determine annual savings of an individual on the basis of their annual income and education,

savingsi  = β0 + δ0 educi + β1inci + u

where the variable educ takes a value of 1 if the person has at least completed college and zero otherwise, and the variable inc measures the income of the individual.    The inclusion of another binary variable in this model that takes a value of 1 if the person has not completed college will give rise to the problem of which of the following?

A. omitted variable bias

B. self-selection

C.  heteroskedasticity

D. dummy variable trap

E.  none of the above