ECS4863 ASSIGNMENT 3 2024
QUESTION 1
a) Reasons to prefer Random Effects over Pooled OLS
Accounts for unobserved heterogeneity that is correlated with explanatory variables
More efficient by utilizing both cross-sectional and time-series variation
Allows estimation of time-invariant variables
b) Choosing between Random Effects and Pooled OLS
To choose between the Random Effects and Pooled OLS approaches, the Breusch-Pagan
Lagrange Multiplier (LM) test can be used. The null hypothesis of the LM test is that the
variance of the individual-specific error component is zero, which implies that the pooled OLS
model is appropriate. If the null hypothesis is rejected, it suggests that the Random Effects model
is preferred over the Pooled OLS approach.
Weakness of the LM test
The main weakness of the LM test is that it assumes the individual-specific error component is
uncorrelated with the explanatory variables. If this assumption is violated, the LM test may not
be valid, and the choice between Random Effects and Pooled OLS should be made based on
other considerations, such as the presence of unobserved heterogeneity, the need for time-
invariant variable estimation, and the efficiency of the estimates.
c) Implications of not considering correlation structure in panel data
Biased and inconsistent parameter estimates
Inefficient estimation
Remedied by using appropriate panel data methods (fixed effects, random effects, GLS,
robust standard errors)
QUESTION 2
2.1 Logarithmic Form.
, ln(Yit)=ln(A)+β1ln(Kit)+β2ln(Lit)+β3ln(Eit)+β4ln(Iit)+β5ln(Pit)+uit
Expected Signs
β1\beta_1β1 (Capital)- Positive
Economic Explanation- Increased capital formation generally enhances a country's productive
capacity. More capital enables higher production and, consequently, a higher GDP.
β2\beta_2β2 (Labor)- Positive
Economic Explanation- Higher employment levels typically lead to increased production, as
more workers contribute to the production process. Thus, greater total employment usually
correlates with higher GDP.
2.2 pooled OLS regression gives
ln(Yit)=1.2+0.5ln(Kit)+0.4ln(Lit)+0.2ln(Eit)−0.1ln(Iit)+0.05ln(Pit)+uit
β1+β2=0.5+0.4=0.9
Since 0.9 ≠ 1, constant returns to scale are not present.
Log GDP Model
ln(Yit)=1.2+0.5ln(Kit)+0.4ln(Lit)+0.2ln(Eit)−0.1ln(Iit)+0.05ln(Pit)+uit\ln(Y_{it}) =
1.2 + 0.5 \ln(K_{it}) + 0.4 \ln(L_{it}) + 0.2 \ln(E_{it}) - 0.1 \ln(I_{it}) + 0.05 \ln(P_{it}) +
u_{it}ln(Yit)=1.2+0.5ln(Kit)+0.4ln(Lit)+0.2ln(Eit)−0.1ln(Iit)+0.05ln(Pit)+uit
Pooled OLS Results:
Capital= 0.5
Labor=0.4
Exports= 0.2
Imports=-0.1
CPI= 0.05
QUESTION 1
a) Reasons to prefer Random Effects over Pooled OLS
Accounts for unobserved heterogeneity that is correlated with explanatory variables
More efficient by utilizing both cross-sectional and time-series variation
Allows estimation of time-invariant variables
b) Choosing between Random Effects and Pooled OLS
To choose between the Random Effects and Pooled OLS approaches, the Breusch-Pagan
Lagrange Multiplier (LM) test can be used. The null hypothesis of the LM test is that the
variance of the individual-specific error component is zero, which implies that the pooled OLS
model is appropriate. If the null hypothesis is rejected, it suggests that the Random Effects model
is preferred over the Pooled OLS approach.
Weakness of the LM test
The main weakness of the LM test is that it assumes the individual-specific error component is
uncorrelated with the explanatory variables. If this assumption is violated, the LM test may not
be valid, and the choice between Random Effects and Pooled OLS should be made based on
other considerations, such as the presence of unobserved heterogeneity, the need for time-
invariant variable estimation, and the efficiency of the estimates.
c) Implications of not considering correlation structure in panel data
Biased and inconsistent parameter estimates
Inefficient estimation
Remedied by using appropriate panel data methods (fixed effects, random effects, GLS,
robust standard errors)
QUESTION 2
2.1 Logarithmic Form.
, ln(Yit)=ln(A)+β1ln(Kit)+β2ln(Lit)+β3ln(Eit)+β4ln(Iit)+β5ln(Pit)+uit
Expected Signs
β1\beta_1β1 (Capital)- Positive
Economic Explanation- Increased capital formation generally enhances a country's productive
capacity. More capital enables higher production and, consequently, a higher GDP.
β2\beta_2β2 (Labor)- Positive
Economic Explanation- Higher employment levels typically lead to increased production, as
more workers contribute to the production process. Thus, greater total employment usually
correlates with higher GDP.
2.2 pooled OLS regression gives
ln(Yit)=1.2+0.5ln(Kit)+0.4ln(Lit)+0.2ln(Eit)−0.1ln(Iit)+0.05ln(Pit)+uit
β1+β2=0.5+0.4=0.9
Since 0.9 ≠ 1, constant returns to scale are not present.
Log GDP Model
ln(Yit)=1.2+0.5ln(Kit)+0.4ln(Lit)+0.2ln(Eit)−0.1ln(Iit)+0.05ln(Pit)+uit\ln(Y_{it}) =
1.2 + 0.5 \ln(K_{it}) + 0.4 \ln(L_{it}) + 0.2 \ln(E_{it}) - 0.1 \ln(I_{it}) + 0.05 \ln(P_{it}) +
u_{it}ln(Yit)=1.2+0.5ln(Kit)+0.4ln(Lit)+0.2ln(Eit)−0.1ln(Iit)+0.05ln(Pit)+uit
Pooled OLS Results:
Capital= 0.5
Labor=0.4
Exports= 0.2
Imports=-0.1
CPI= 0.05
