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Which regression for country panel data?

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Asked 13th Aug, 2020
Mazlum S.
Carl von Ossietzky Universität Oldenburg
Which regression for country panel data?
Hello, everyone,
I have a country panel data: 160 countries x 25 years.
I want to analyze the influence of several metric and quasi-metric variables on a dependent variable. The paper deals with a political science question. To be more precise, determinants of democracy.
First, I use a pooled OLS model: Since this model does not consider the panel structure, the results are inconsistent. Especially for country data autocorrelation and heteroskedasticity are present. Also, robust standard errors do not really help.
One way is to use the fixed-effects model (within transformation/demeaning) and random-effects model (quasi-demeaning). The RE model also assumes that the individual error term a_i has an expected value of 0. (Hausman test confirms the endogeneity)
Actually, the supposedly "best" model of the three, is the FE model, right? I'm not sure. Because this demeaning of all variables also means that variables that change only minimally over time (e.g. population shares) are determined and therefore even flatter than they already are.
My questions:
Which model is common for country panel data (with 160i and 25t)?
2. Can I analyze country data with the methods mentioned above? (Country data is never a random sample. Even if I can handle autocorrelation, all other OLS assumptions are violated)
3. If I use the "twoways" method in the fixed effects model (i.e. both country fixed-effects and year fixed-effects), is Lambda_t part of the composite error v_it? So v_it = a_i + Lambda_t + e_it?
4. If I use the "twoways" method in the RE model, is Lambda_t treated exactly like a_i? (i.e. both country random-effects and year random-effects) Does this mean no correlation with X_it?
5. It is always said that unobserved heterogeneity within the units of investigation (here countries) is eliminated by the FE model and is therefore advantageous for the exogeneity assumption of the independent variable. Is this true? How can a simple demeaning achieve such a result? Only variables that are included in the model can be determined. And the idiosyncratic error can also include unobserved properties.
You would help me a lot if you could give me an answer or some advice. Thank you very much & Best regards
Mazlum
P.S.
For the methodology I use the textbook by Jeffrey M. Wooldridge, Introductory Econometrics: A Modern Approach. 2012.
For the application I use the Software R with the plm package. (Yves Croissant & Giovanni Millo, Panel Data Econometrics with R, 2019​

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