k
Yit = β1+ ∑
βj Xijt + gt + αi + ℰi
j=2
k
n
Yit = ∑
βj Xijt + gt +∑ αiDi + ℰi
j=2
i=1
The above model called
least square dummy variable model which is extension of fixed effect model,
this also include explicity of unobserved effect we can conclude from above
equation that Di is a dummy variable, if Di is equals to 1 that means that
these observation belong to country one (in this example our entity is
countries) so the final model would be that unobserved effect is converted into
co-efficient of the countries dummy variables, αiDi is shows a fined effect on
dependent variable Yi for country i (which is fixed effect approach), it
can be uses through OLS approach.
Note: if it is included
dummy for each country along with intercept than we would face dummy variable
trap or perfect multicollinearity. To avoid perfect multicolinearity, we
normally put 1st country as bench mark
country meaning the intercept shows slop of 1st country. In the above model, β1 represent the intercept of 1st country and ai represent the intercept of
remaining countries. we have also option to drop intercept meaning β1 and put dummy for all countries then there
will be no issue of perfect multicollinearity because ai shows the
intercept for each country.
Cross section-wise intercept
MXPit
= β1 + β2POP1t + β3CTP1t + δ2D2i + δ3 D3t + δ4 D4it + δ5 D5i + ℰi
As
Gujrathi says in his book basics economitrics in chapter 17, to find country
wise coefficient we have to multiplying coefficient of country dummy with
parameters of that model to find country wise intrepation or coefficients.
Though its consume degree of freedom
Country
wise coefficients
MXPit
= β1 + β2POP1t + β3CTP1t + δ2 (D2*POP2t) + δ2 (D2*CTP2t) + δ3 (D3*POP3t) + δ3 (D3*CTP3t) + δ4 (D4*POP4t) + δ4 (D4*CTP4t) + δ5 (D5*POP5t) + δ5 (D5*CTP5t) + ℰi
