Panel Data Models Analysis

A general model that pools time series and cross section data is

                              k

Yit =  Yit =αi +βt ∑γi,k  Xk,i, t + ℰi, t

                                        k=0

where i=1,…, N (number of cross sections, e.g., countries); t=1,…, T (number of time periods, e.g., years); and K = number of explanatory variables. Note that this model gives each state its own intercept. Let suppose Pakistan have high growth rate holding other thing constant so this model allow each year have its own effect (βt).

Different models are derived by making various assumptions concerning the parameters of this model. If we assume that  α1 = α2 = = αN,  β1 = β2 = βt … , and  γ1,k = γ2,k = = γN,k … then we have the OLS model.

If we assume that the  αi and  βt not all equal but are fixed numbers (and that the coefficients i,k  are constant across countries, i) then we have the fixed effects (FE) model. This model is also called the least squares dummy variable (LSDV) model, the covariance model, and the within estimator. If we assume that the αi and  βt are random variables, still assuming that the γi are all equal, then we have the random effects (RE) model also known as the variance components model or the error components model. Finally, if we assume the coefficients are constant across time, but allow the k, αi and k, γi to vary across countries and assume that  βt = = βt = 0… , then we have the random coefficients model.

The Fixed Effects Model

Let’s assume that the coefficients on the explanatory variables k,i,t x are constant across countries and across time. The model therefore reduces to

                    k

Yit =αi +βt ∑  γk  Xk,i, t + ℰi, t

                           k=0             

i will explain fixed effect model with dummy variables in next blog.....nshallah