My data set consists of time series of consumption of 4 countries, and the average temperature of each country during the time period. I know that consumption is largely dependent on temperature, so for each country I have a linear model with consumption as the dependent, and temperature as the independent variable. I haven't been able to test it yet, but I heavily suspect some other, unobserved factor to influence consumption in all countries, causing the errors to be correlated. I want to use Pesaran's common correlated effects (CCE) approach to circumvent this and obtain estimators for my model.

Is this possible with N=4?

The idea:

So for each country i, with i=1,...,N and N=4, I have a linear model:


As you can see, I allow for heterogeneous coefficients. Since there is cross-sectional dependence in the error terms, I remodel them as


where $\gamma$ is the factor loading, $f$ the unobserved common factor and $\epsilon$ the individual error. As I understand, the trick here is to find an estimator for the unobserved common factor, and to show that it asymptotically converges to this estimator for $N,T\rightarrow\infty$.

I skipped a few steps here, but Pesaran basically proposes the cross-sectional average as an estimator. Now I read somewhere that for the approach to make sense, you need to have a sample/factor ratio of N/f~5. So 5 observations per factor.

Of course I only have 4, so I wonder to what extent this is only a rule of thumb. But apart from that, I don't see how an average of only 4 (or 5) observations per time step could be representative. Should I worry about this? Should I try to collect data for one more country, or should I abandon this approach?



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