I intend to use Pesaran's (2006) common correlated effects pooled (CCEP) estimator. However, I'm not yet very familiar with advanced econometrics and advanced use of eviews. More specifically I want to estimate this model: \begin{equation} y_{it} = \alpha_{i} + \beta_{1}x_{1,it} + \beta_{2}x_{2,it}+\gamma_{i}F_{t}+\epsilon_{it} \end{equation} in which $F_{t}$ is an unobserved common factor and $\gamma_{i}$ is a country-specific factor loading. We were taught that $F_{t}$ can be proxied by: \begin{equation} F_{t}=\frac{(\bar{y_{t}}-\bar{\alpha}-\beta_{1} \bar{x}_{{1,t}} -\beta_{2} \bar{x}_{{2,t}}-\bar{\epsilon}_{{t}})}{\bar{\gamma}}, \end{equation} in which $\bar{y_{t}} = \frac{1}{N}\sum_{i=1}^{N} y_{it}$, and $\bar{\gamma_{}}=\frac{1}{N}\sum_{i=1}^{N} \gamma_{i}$, with $N$ the number of cross-sections.
Substituting the second equation into the first yields: \begin{equation} y_{it} = \alpha_{i}-\frac{\gamma_{i}}{\bar{\gamma}}+\beta_{1} x_{1,it} +\beta_{2} x_{2,it} +\frac{\gamma_{i}}{\bar{\gamma}}\bar{y_{t}} - \beta_{1} \frac{\gamma_{i}}{\bar{\gamma}} \bar{x}_{1,t} -\beta_{2}\frac{\gamma_{i}}{\bar{\gamma}}\bar{x}_{2,t}+\epsilon_{it}-\frac{\gamma_{i}}{\bar{\gamma}}\bar{\epsilon_{t}} \end{equation} or with $\alpha_{i}-\frac{\gamma_{i}}{\bar{\gamma}}=\alpha'_{i}$ and $\frac{\gamma_{i}}{\bar{\gamma}}=\gamma'_{i}$: \begin{equation} y_{it} = \alpha'_{i} +\beta_{1} x_{1,it} +\beta_{2} x_{2,it} +\gamma'_{i}\bar{y_{t}} - \beta_{1} \gamma'_{i} \bar{x}_{1,t} -\beta_{2}\gamma'_{i}\bar{x}_{2,t} +\epsilon_{it}-\gamma'_{i}\bar{\epsilon_{t}}. \end{equation}
To estimate this in eviews, I had the following idea
The cross-sectional averages $\bar{y_{t}}$, $\bar{x}_{{1,t}}$, and $\bar{x}_{{2,t}}$ can be easily calculated from the dataset. I would use cross-sectional fixed effects to estimate all $\alpha'_{i}$. Next, I would need $N$ terms to estimate all $N$ $\gamma'_{i}$. To do this, I would include these $N$ terms: $\gamma'_{A}\bar{y}_{t}dum_{A} + \gamma'_{B}\bar{y}_{t}dum_{B} + ... + \gamma'_{N}\bar{y}_{t}dum_{N}$, in which each capital letter denotes one of the $N$ cross-sections and the dummy variable takes the value of $1$ once for each cross-section. Then, for each averaged explanatory variable, $\bar{x}_{1t}$ and $\bar{x}_{2t}$, I would include these $2 \times N$ terms: $\beta_{1}\gamma'_{A}\bar{x}_{1,t} + \beta_{1}\gamma'_{B}\bar{x}_{1,t}+ ... + \beta_{1}\gamma'_{N}\bar{x}_{1,t}$ and $\beta_{2}\gamma'_{A}\bar{x}_{2,t} + \beta_{2}\gamma'_{B}\bar{x}_{2,t}+ ... + \beta_{2}\gamma'_{N}\bar{x}_{2,t}$.
So, to sum up, my suggested input for eviews (to estimate with cross-sectional fixed effects) is the following:
y = c(1)*x1 + c(2)*x2 + c(3)*y_avg*dumA + c(4)*y_avg*dumB + c(5)*y_avg*dumC + ... + c(1)*c(3)*x1_avg + c(1)*c(4)*x1_avg + c(1)*c(5)*x1_avg + ... + c(2)*c(3)*x2_avg + c(2)*c(4)*x2_avg + c(2)*c(5)*x2_avg + .....
In this equation:
c(1)= $\beta_{1}$;c(2)= $\beta_{2}$;c(3)= $\gamma'_{A}$;c(4)= $\gamma'_{B}$;c(5)= $\gamma'_{C}$.
These are my questions regarding this estimation:
- First of all, confirmation of the correctness of my derivation would be welcome;
- Would the estimation in eviews I suggest do the trick?
- If so, should I include an intercept in the fixed-effects estimation?
- If not, is there an alternative procedure to implement the CCEP estimator in eviews?
- The estimated error terms should be $\epsilon-\gamma'_{i}\bar{\epsilon}$, is this structure automatically obtained? Or should this be imposed one way or another?
- The same question for $\alpha'_{i}$: it should equal $\alpha_{i}-\frac{\gamma_{i}}{\bar{\gamma}}$. Should this condition be imposed, or is it automatically fulfilled when inputting my suggested input in eviews;
- Other suggestions regarding the use of CCEP estimator in eviews are certainly welcome.
Any help, also partial answers, is appreciated!
