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:
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)
These might change your mind
Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...
Article Fixed and Random effects models: making an informed choice
Article Understanding and misunderstanding Group mean centering: a c...
.Random effects in the within-between formulation can naturally handle autocorrelation and heteroscedasticity and much more.
Extract from Wikipaedia entry https://en.wikipedia.org/wiki/Kelvyn_Jones
"He (with colleagues) has challenged the 'gold standard' that fixed effects should be the standard approach to the analysis of Panel data and that a Hausman test is an appropriate way of choosing between a Fixed effects model and a Random effects model. Somewhat controversially they argue that a particular form of the random effects model (the within-between model or the similar Mundlak model) offers all that fixed effects can provide and more.[16][17][18] They also challenge the Fixed Effects Vector Decomposition (FEVD) model of Plumper and Troeger.[19] One reaction was: "This paper and the instructive controversial over FEVD have shown me that my econometrics training had not - as I once assumed - taught me all that there is to know about fixed effects estimation. In particular, the authors' treatment of 'heterogeneity bias' clarifies the importance of addressing both 'within' and 'between' variation in the data and they make a compelling case for considering both 'individual' and 'ecological' influences".[20] Another was: "Bizarre and often incorrect paper by two political scientists on the virtues of random-effects over fixed-effects".[21] to "You can and should use a well-specified random effects model. Always.".[22]. These models shown algebraically in the table for a two-level panel model
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are discussed and illustrated with snippets of R code by Daniel Lüdecke [23], and there is a R package (panelr) for panel data analysis by Jacob Long that facilitates their implementation.[24][25] An extensive review of the potential of this approach in economics concluded that it has been "unreasonably ignored" due in part to "disciplinary isolation" of the subject.[26] "
In principle, with those data, I would use FE (twoways) with standard errors clustered at the country level in order to control for serial correlation. This applies even miore when the Hausman test favours it. In this way, you control for time-constant unobserved heterogeneity as that elemente is remove with demeaning.
If within-country variation is very small, you can experiment with RE or taking long differences (e.g., 10-year differences) in order to control for time-constant unobserved heterogeneity.
I think a better way to avoid the shortcomings of the methods you have mentioned is to look at Instrumental Variables approach. You can try the 2SLS and dynamic panel GMM. This way, the known problems of endogeneity, heterogeneity and simultaneity bias inherent in panel data modeling can be avoided.
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