ECON4003 Econometrics 1 Mock Exam
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Mock Exam
Econometrics 1, ECON4003
QUESTION 1
A researcher runs an experiment to measure the impact of a short nap on memory. There are 200 participants and they can take a short nap of either 60 minutes or 75 minutes. After waking up, each participant takes a short test for short-term recall. Each participant is randomly assigned one of the examination times, based on the flip of a coin.
Consider the following regression model:
where 
is the test score by the student 
, 
is the amount of time for which the student slept prior to taking the test (
= 60 or 75) and 
is the error term.
(a) Explain what the term 
represents. Why will different students have different values of 
? [Maximum 150 words]
(b) With reference to relevant OLS assumption(s), explain if the OLS estimators (
0, 
1) are unbiased. [Maximum 350 words]
(c) The researcher wants to test if that nap has no effect on test score at 1% significance level. Write down and explain all Stata codes required for this hypothesis test including the appropriate critical value . No calculation is needed. [Maximum 100 words]
(d) Suppose 
|
~
(0, 
2). Explain the factors that affect the variance of 
1 . How can this variance be estimated? [Maximum 200 words]
(Total 50%)
QUESTION 2
A researcher collected a random sample of 100 individuals in the US who report their household income and savings . They estimate the following model:
where ln(
) is the natural log of annual savings of household 
. ln (
) is the natural log of annual income of household 
, 
is the annual interest rate faced by household 
, and 
= 
.2
is the error term of household 
.
Assume that 
|
~
(0, 
); 
and 
are independent.
(a) Find 
(
|
) and 
(
|
) . Show all your calculation steps clearly. (Maximum 150
words)
(b) Explain whether the OLS estimator for 
1 is the Best Linear Unbiased Estimator (BLUE).
[Maximum 350 words]
(c) The researcher wants to estimate model (1). Write down and explain all Stata codes required for regression. No calculation is needed. [Maximum 100 words]
(d) The researcher constructs a scatterplot of annual savings on annual income. They find that the household with maximum annual savings looks like an outlier (see diagram below) .
How would the inclusion of this household in the regression affect the OLS estimate for 
1? [Maximum 200 words]
(Total 50%)
QUESTION 3
Consider a sample of 2,231 individuals who report their wages, tenure and occupation (blue collar, white collar or managerial). A researcher estimates a simple regression model 
where 
is the log of wages; 
is the years of tenure 
is a dummy variable which equals to 1 if the individual is a blue-collar worker and 0 otherwise; 
ℎ
is a dummy variable which equals to 1 if the individual is a white-collar worker and 0 otherwise . Standard errors are in parenthesis below the coefficients.
(a) Interpret the coefficient estimate for 
1 and the 
2 in equation (2). [Maximum 100
words]
(b) Suppose you estimate equation (2) using Stata. What would happen to the estimates for
1 , 
2 and 
3 if you included a dummy variable 
which equals to 1 if the individual is a manager and 0 otherwise? [Maximum 200 words]
(c) Suggest one reason why the coefficient estimates for 
are similar in equations (1) and (2). [Maximum 100 words]
(d) Using the results in equation (2), test the hypothesis that 
1 equals to 0.04 at 5% level of significance. State your conclusion. [Maximum 150 words]
(e) Assuming that the error term is homoskedastic, test the hypothesis 
2 = 
3 = 0 at 5%
level of significance . Explain the test procedure in detail and state your conclusion. [Maximum 250 words]
(Total 50%)
QUESTION 4
Using a sample of 200 students and the following model, we want to analyse the effect of class size on the students’ academic success.
The academic success variable (
) is measured using a test score ranging from 0 (i.e. the poorest score) to 100 (highest score) and the class size (
) variable is a dummy variable
equal to 1 for classes with more than 15 students and 0 otherwise.
We obtain the following estimation output:
(a) Provide an interpretation for the parameters 
0 and 
1 . Are the signs of these coefficients
in line with your expectations? [Maximum 100 words]
(b) Calculate the 90 and 95 percent confidence intervals for 
0 and 
1 . [Maximum 200
words]
(c) Is the estimated effect of class size on test scores statistically significant? Test this hypothesis at 5 percent significance level. [Maximum 200 words]
(d) Suppose that the true model should also include a binary variable which is equal to 1 if families show high effort for their children’s academic success and 0 if they show low effort. If this variable is negatively correlated with the class size, would omission of family effort variable lead to downward or upward bias for the estimate for 
1? Show you calculations explicitly. [Maximum 300 words]
(Total 50%)
2021-12-20