Least Square Dummy Variable Model (LSDV)

                                    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 1^st country as bench mark country meaning the intercept shows slop of 1^st country. In the above model, β1 represent the intercept of 1^st 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