# My fixed effect model and methodology

I'm doing my master thesis on FDI effect on Chinese wage inequality. I am new to quantitative econometrics so I have no idea if my wage equation is correct.

$$W_{it} = β X_{it} + λ_t + η_i + ε_{it}$$

Where the wage paid by firm $i$ in year $t$ is denoted as $W_{it}$. $X_{it}$ contains a set of control variables (including include total sales, total exportations, total labor compensations, firms’ fixed asset, firms’ R&D expenditures, employee’s turn over rate and a dummy variable of foreign ownership). A time effect, $λ_t$, controls for time varying elements that affect all establishments in a given year. An individual effect, $η_i$, captures time invariant element that differ across establishments. An error term, $ε_{it}$. All variables are measured in logarithm units.

Is that correct? If yes, what should I do next? I don't know if I should use pooled OLS or GMM....I have already reshaped and treated my data. I really appreciate your help. Thank you in advance.

• You need to do panel-data econometrics while being "new" to econometrics? Panel-data econometrics is a complicated if not advanced sub-field, and still not consolidated enough. Too many set-ups, too many estimators, too many results and different sets of estimator properties. To what degree your master thesis will be seen as an "educational endeavor" (permitting to make easily all sorts of simplifying assumptions), and to what degree it should try to satisfy the standards of an actual research-level paper (requiring that you properly justify your simplifying assumptions)? Commented Apr 7, 2014 at 11:57
• Hi, thank you for your comments. It's kind of difficult to know even by myself. My professor didn't specify any of these...I did have econometric lessons for the last 2 years , with OLS panel etc, but I have never practical coursework with it. I recently did a paper on financial econometrics with EGARCH and TGARCH model, it was not that complicated as panel-data. I am not a doctorate research so I don't think that my thesis should have the 'real' level of that, thus I think I could simplifying assumptions otherwise I won't understand anything.. What will you advice me? Commented Apr 7, 2014 at 12:37

Two years of econometrics classes is a start. What you need to check in any case, is whether the various series that you will use are 2nd-order ("weakly") stationary or not - you cannot avoid that. If they are not, you cannot overlook their non-stationarity. Hopefully if they are non-stationary, they will be integrated of order 1, and then you should modify your regression specification accordingly to obtain a stationary setup.

Assuming then that you have stationary data in your hands:

1) The first simplifying assumption should be that error terms are stochastically independent cross-sectionally, and in the time dimension also (and are identically distributed). Also, that regressors are independent from the error terms (in some cases independence is more than needed -a way to learn and also show effort is to study and realize how strong your assumptions on stochastic relations need be in your particular model).

2) You have an individual effect, $\eta_i$. Model it as a "fixed effect" and not as a "random effect" to avoid dealing with (and choose among) the different sets of assumptions regarding its relation with the error terms. This is one of the "simplifying assumptions" I was talking about in my comment: as Hsiao(2003, 2nd ed.) "Analysis of Panel Data" p.41 writes,

when $T$(time dimension) is finite and $N$ is large, whether to treat the effects as fixed or random is not an easy question to answer. It can make a surprising amount of difference in the estimates of the parameters.

..and then provides an illustrative example from a research paper by Hausman (1978). But you won't be able to avoid a "random-effects-like" approach, because:

3) You have a common time-varying component, $\lambda_t$. It is difficult to argue that it is not random. Assume then that it is random and stationary, it has a zero-mean, and it is not autocorrelated. And that it is also independent from the error term. This lambda links the cross-sections stochastically and makes the variance-covariance matrix of the stacked model not a scalar matrix.

This implies that Generalized Least Squares on the stacked model is a prospect. If this is what you eventually choose, you are looking at an initial estimation step to obtain consistent estimates of the two variances (of $\lambda_t$ and of $\varepsilon_{it}$), and then apply FeasibleGLS. As for GMM, I understand it is currently in vogue since Hansen received the Nobel prize, but it needs careful steps in order to be sure that you understand what you are doing with it -it can be a complicated business.

• WoooW!!! Thank you very much indeed! This year I do have lessons on stationarity , really helpful what you said. I really appreciate your comment and your time ,now I have a clearer vision of what I should do now ! A big thank you !!! :) Commented Apr 7, 2014 at 20:40
• Dear Papadopolos, I just run my regression and with FE, my dummy and city are omitted because of colinearity (my dummy of foreign ownership is the key of my research), while I don't have the problem when I run with QLS...Is that mean that I should use QLS ? Thank you very much in advance. Commented Apr 8, 2014 at 22:54
• And QLS stands for...? Commented Apr 8, 2014 at 22:56
• Oups sorry for typos, it's GLS Commented Apr 8, 2014 at 22:57
• I would need more detailed information on your sample and your model to help you with that, and a Q&A site is not appropriate for that kind of help. As I said, GLS is needed in order to estimate the variances involved in any case. If the coefficient estimates you obtain using GLS make sense, you could perhaps leave it at that. Commented Apr 8, 2014 at 23:06