Solved – What kind of assumptions do I need to test when running a fixed effects panel model

assumptionsfixed-effects-modelmultiple regressionpanel dataregression

I am running a regression analysis on a panel data set.
The Hausman test and the logical setup of the research question indicate that a fixed effects model would be best for running the regression.

But I am unsure now what kind of assumptions I need to test for ?
The "normal" assumptions of heteroscedasticity, autocorrelation, exogeneity, …?
Or is it enough to run the Hausman test as it tells me the most important assumption for fixed effects is fulfilled (namely: the individual specific effect is correlated with the independent variables)?

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Correlation of individual-specific effects with the regressors is not assumption of FE, FE merely is robust to this, unlike RE.

The fixed-effects transformation will wipe out any variable without time-variation (think gender), so if such a variable is the focus of your analysis, FE will not be suitable.

Also, exogeneity is indeed a major concern, as things like reverse causality or measurement error do not cease to be a concern once you employ panel data. (Indeed, measurement error is argued to have more serious consequences when using panel data.)

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Solved – Panel regression: what to do when Hausman test fails and want to keep time invariant regressors

The following not-yet-published paper is, in my opinion, an excellent introduction and answer to the problem you bring up:

http://polmeth.wustl.edu/media/Paper/FixedversusRandom_1_2.pdf

To summarize, you can still proceed with the random effects approach, but you must first modify the model to account for the fact that the within-cluster and between-cluster effects differ (i.e., what the Hausman test indicates). You can do this by adding the cluster means of your predictor as a separate predictor in the model, and then optionally also applying within-cluster centering to the original predictor. The details of this procedure and the resulting interpretations are discussed at some length in the paper linked above.

Panel Data Regression – Correct Way to Deal with Multiple Fixed Effects

When you use time dummies, you don't need a time dummy for every individual separately but for every year. So this leaves you with 28 time dummies and 997 individual dummies (always omitting the first year and first individual to avoid the dummy variable trap).

The solution to your problem is much simpler than what the other answer suggested here. If you read any introductory text on panel data (you can start with these lecture notes), you should acquaint yourself with the fixed effects estimator which is sometimes referred to as the within estimator as well.

The procedure is as follows:

average each variable over time for each individual, e.g. $\overline{y}_i = \frac{1}{T}\sum_{t=1}^{29}y_{it}$ and $\overline{x}_i = \frac{1}{T}\sum_{t=1}^{29}x_{it}$
subtract this individual mean from each observation, $\tilde{y}_{it} = y_{it} - \overline{y}_{i}$ and $\tilde{x}_{it} = x_{it} - \overline{x}_i$
regress $\tilde{y}_{it}$ on $\tilde{x}_{it}$ and you year dummies, and cluster the standard errors on the individual's ID to account for serial correlation

Even though it is not very apparent, Mundlak (1978) has shown that this procedure is equivalent to including a dummy for every individual minus 1 (again omitting the first individual) as you propose it. The advantage is obvious: you don't need all those dummies when you use this three step procedure which is called the "within transformation".

Most statistical software have ready canned packages/routines for this type of estimation as it is fairly standard. In Stata you would simply declare your data to be a panel data set which allows you to use the corresponding panel data regression and data analysis commands. For example:

webuse nlswork
tsset idcode year
xtreg ln_wage age union i.year, cluster(idcode)

Where i.year automatically inserts your year dummies for the regression. So with 29 years you lose 28 degrees of freedom which isn't awful. A nice introduction to the topic is

Wooldridge, J. (2008) "Introductory Econometrics", 4th Edition, South Western College
Baltagi, B.H. (2013) "Econometric Analysis of Panel Data", 5th Edition, John Wiley & Sons
Wooldridge, J. (2010) "Econometric Analysis of Cross Section and Panel Data", 2nd Edition, MIT Press

The last reference is for advanced students.

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Solved – Panel regression: what to do when Hausman test fails and want to keep time invariant regressors

Panel Data Regression – Correct Way to Deal with Multiple Fixed Effects

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