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ECN225 Econometrics 2 – 2019
Questions and Answers
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Question 1
(a)
The sign of the coefficient on grant should be negative. This is because we would expect that if a
firm receives a job training grant, their workers will be more productive and will therefore have to
scrap items less often.
(b)
The estimated coefficient 𝛽 is the average ln(scrap) for firms which did not receive a grant.
Therefore, it represents the average proportion of items which needed to be scrapped after it has
been logged.
The estimated coefficient 𝛽 is the average difference in ln(scrap) between firms who did receive a
grant and those that did not receive a grant. It therefore reflects the predicted effect that getting a
grant has on worker productivity.
(c)
The regression does not provide statistically significant evidence that job training grants increase
firm productivity on average. This can be observed by noting that the estimated effect of grant on
ln(scrap) is positive. This means that for the following hypothesis test:
H0: 𝛽 < 0
H1: 𝛽 > 0
We can reject the null hypothesis at any level of statistical significance, as the associated test
statistic will be positive.
(d)
The hypothesis test that the coefficient on the variable grant in regression (2) is statistically
significant is:
H0: 𝛽 = 0
HA: 𝛽 ≠ 0
The associated test statistic is:
−0.254 − 0
𝑡= = −1.728
0.147
We then must choose an appropriate significance level, which in this case we will choose to be 5%.
The critical value of this test, using the normal distribution, is 1.96. Comparing the test statistic with
the critical value of 1.728 does not allow us to reject the null hypothesis with 95% confidence.
Therefore, the regression does not indicate that the coefficient on the variable grant is statistically
significant. It does, however, have the expected negative sign which would indicate that a grant
decreases the proportion of produced items which have to be scrapped.
(e)
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The 95% confidence interval for the coefficient on variable grant can be calculated using the critical
values of the normal distribution, using the formula:
[𝛽 ± 1.95 ∗ 𝑆𝐸(𝛽 )]
[−0.254 ± 1.96 ∗ 0.147]
[−0.073, 0.034]
(f)
One method of comparing between regression specifications is to compare the R2, which is the ratio
of the explained variation compared to the total variation. Using this method of comparison,
regression (2) is significantly better as the R2 is 0.873, as compared to the R2 of regression (1) which
is 0.0004.
(g)
Based on regression (2), my conclusion would be that job training grants have no effect on firm
productivity. This is because, once accounting for the past productivity of a firm, the coefficient for
grant had no effect on the proportion of items which were scrapped.
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
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ECN225 Econometrics 2 – 2019
Questions and Answers
, FOR MORE HIGH-QUALITY PAST PAPER MODEL ANSWERS, ONLINE TUTORING AND
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
Question 1
(a)
The sign of the coefficient on grant should be negative. This is because we would expect that if a
firm receives a job training grant, their workers will be more productive and will therefore have to
scrap items less often.
(b)
The estimated coefficient 𝛽 is the average ln(scrap) for firms which did not receive a grant.
Therefore, it represents the average proportion of items which needed to be scrapped after it has
been logged.
The estimated coefficient 𝛽 is the average difference in ln(scrap) between firms who did receive a
grant and those that did not receive a grant. It therefore reflects the predicted effect that getting a
grant has on worker productivity.
(c)
The regression does not provide statistically significant evidence that job training grants increase
firm productivity on average. This can be observed by noting that the estimated effect of grant on
ln(scrap) is positive. This means that for the following hypothesis test:
H0: 𝛽 < 0
H1: 𝛽 > 0
We can reject the null hypothesis at any level of statistical significance, as the associated test
statistic will be positive.
(d)
The hypothesis test that the coefficient on the variable grant in regression (2) is statistically
significant is:
H0: 𝛽 = 0
HA: 𝛽 ≠ 0
The associated test statistic is:
−0.254 − 0
𝑡= = −1.728
0.147
We then must choose an appropriate significance level, which in this case we will choose to be 5%.
The critical value of this test, using the normal distribution, is 1.96. Comparing the test statistic with
the critical value of 1.728 does not allow us to reject the null hypothesis with 95% confidence.
Therefore, the regression does not indicate that the coefficient on the variable grant is statistically
significant. It does, however, have the expected negative sign which would indicate that a grant
decreases the proportion of produced items which have to be scrapped.
(e)
, FOR MORE HIGH-QUALITY PAST PAPER MODEL ANSWERS, ONLINE TUTORING AND
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
The 95% confidence interval for the coefficient on variable grant can be calculated using the critical
values of the normal distribution, using the formula:
[𝛽 ± 1.95 ∗ 𝑆𝐸(𝛽 )]
[−0.254 ± 1.96 ∗ 0.147]
[−0.073, 0.034]
(f)
One method of comparing between regression specifications is to compare the R2, which is the ratio
of the explained variation compared to the total variation. Using this method of comparison,
regression (2) is significantly better as the R2 is 0.873, as compared to the R2 of regression (1) which
is 0.0004.
(g)
Based on regression (2), my conclusion would be that job training grants have no effect on firm
productivity. This is because, once accounting for the past productivity of a firm, the coefficient for
grant had no effect on the proportion of items which were scrapped.
