1. Pooled Regression: If z contains only a constant term, then there is no individual specific characteristics in this model. All we need is pooling the data yit=xtB+a+t,i=1,2,,N;t=1,2,…,!T and OlS provides consistent and efficient estimate of the common B and a 2. Fixed Effects: If za=ai, then it is the fixed effect approach to take ai as a group-specific constant term in the regression model vit=xaB+a1+et,i=1,2,…,N;t=1,2,…,T 3. Random effects: If the unobserved individual heterogeneity can be assumed to be uncorrelated with the included variables, then the model may be formulated yit= xitB+E(zia)+Zia-e(zia)+Eit xtB+a+u1+et,i=1,2,…,N;t=1,2,,T The random effect approach specifies that ui is a group specific random element similar to Eit except that for each group, there is but a single draw that enters the regression identically in each period 1 Fixed effects This formulation of the model assume that differences across units can be cap- tured in difference in the constant term. each a is treated as an unknown parameter to be estimated. Let yi and Xi be the T observations the ith unit, i be atx 1 column of ones and let e be associated tx 1 vector of disturbance Then yi=Xi B+ia; +Ei, i=1, 2, It is also assumed that the disturbance terms are well behaved. that is E(E)=0 E(EE= 0I E(e;)=0fi≠1. Pooled Regression: If z 0 i contains only a constant term, then there is no individual specific characteristics in this model. All we need is pooling the data, yit = x 0 itβ + α + εit, i = 1, 2, ..., N; t = 1, 2, ..., T. and OLS provides consistent and efficient estimate of the common β and α. 2. Fixed Effects: If z 0 iα = αi , then it is the fixed effect approach to take αi as a group-specific constant term in the regression model. yit = x 0 itβ + αi + εit, i = 1, 2, ..., N; t = 1, 2, ..., T. 3. Random effects: If the unobserved individual heterogeneity can be assumed to be uncorrelated with the included variables, then the model may be formulated as yit = x 0 itβ + E(z 0 iα) + [z 0 iα − E(z 0 iα)] + εit = x 0 itβ + α + ui + εit, i = 1, 2, ..., N; t = 1, 2, ..., T. The random effect approach specifies that ui is a group specific random element, similar to εit except that for each group, there is but a single draw that enters the regression identically in each period. 1 Fixed Effects This formulation of the model assume that differences across units can be cap￾tured in difference in the constant term. Each αi is treated as an unknown parameter to be estimated. Let yi and Xi be the T observations the ith unit, i be a T × 1 column of ones, and let εi be associated T × 1 vector of disturbance. Then yi = Xiβ + iαi + εi , i = 1, 2, ..., N. It is also assumed that the disturbance terms are well behaved, that is E(εi) = 0; E(εiε 0 i ) = σ 2 IT; and E(εiε 0 j ) = 0 if i 6= j. 2