Principale Component Analysis in combination with Panel-Data Fixed Effects Regression

[Maarten Scherjon]

Dear all,

I am currently working on a project related to the sovereign debt crisis related to the Eurozone for the 2000-2017 period with monthly observations
.
Currently, I am trying to detect the existence of a common component in the yields of 12 euro zone countries. Therefore, I used the Principal component analysis, where the first principal component of the twelve yield spreads is used to represent the common euro area risk factor. The first component explains almost 80% of the variance.


However, in related studies, the authors now include the obtained common risk factor in their panel data fixed effects regression. This is in my opinion not possible, as the time fixed effects will capture this variable, as it is constant for all countries over time. However, the authors do find, to my surprise, regression estimates.

My question is, the following:
- Can I include the common euro area risk factor (obtained from the PCA) include in my regression equation (while I include both forms of fixed effects)?
- Alternatively, does any of you have an advice how to distangle the effect of this common euro area risk factor on the sovereign yields?

Thank you in advance.

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

In future, you may find it helpful to try to include the risk factor before asking if it is feasible.

Are they including monthly dummies along with the country fixed effects (one for each of the roughly 17*12 months in the sample with one omitted) or is their time fe at the year level? If it is at the year level, then monthly common risk factors would be estimable. If the risk factor is constant within months across countries, I would think it would not estimate with separate dummies for each month.

There are other estimators (correlated random effects) models that would allow the inclusion of a variable correlated with the random effects - see Shrunk's piece in Stata journal, and look for Mundlak and xthtaylor estimators.

[Maarten Scherjon]

Dear Phil,

Thank your for your helpful response. I will keep the FAQ in mind for further posts.

The authors do seem to include a constant risk factor wit monthly time dummies. This, indeed, seems implausible to estimate.

I will have a look at the recommended alternative estimation techniques. Thank you for pointing this out.