# Using first differenced variables in fixed effects model

It might be a basic question but since fixed effects estimator either mean centers the data or uses first differences, is it entirely wrong to take first differences of the data and then run fixed effects regression in Stata?

Here is the explanation of the problem. So my model is the following

$$\Delta LP = \alpha+\beta_1 \Delta HC+\beta_2 \Delta FDI+\beta_3 \Delta HC*\Delta FDI$$

Where LP is labor productivity, HC is human capital and FDI is foreign direct investment.

Since I have panel of 21 countries for 16 years, I need to control for country specific effects and for that Hausman test suggested fixed effects model. However, when we use fixed effects model, it automatically uses first differences of the data. So my question was, is it ok to use first differenced data in fixed effects model? wouldn't it be double first differencing? thank you.

• There is, I think, no specific reason this should be a problem, but, as I said elsewhere , you really must post your real problem, with your applied context, and the model you want to analyse, and the questions you want to answer. Commented Jul 1, 2014 at 16:23
• @kjetil I am so desperate for answers that I didnt explain my problem clearly. Sorry for that. Question is edited. Commented Jul 1, 2014 at 17:09

As kjetil said in his comment it should not be a problem to use a differenced variable in a fixed effects regression. The question is: why would you want to do it? First differencing removes information from your variables and you lose one observation per panel. If the sole purpose is to remove the country specific fixed effects you might be throwing out the baby with the bath water.

I also think there is some misconception with respect the statistical programing part of your problem. What do you mean by "when we use fixed effects model, it automatically uses first differences of the data". I don't know what statistical package you use, but for instance in Stata the command xtreg lp hc fdi hc_fdi, fe uses the within transformation and not first differences. Conversely, when you first difference your data and then use the regress command, this will give you a first difference regression. Both are ways to eliminate the unobserved country specific effects and do not need to be done together as they are distinct concepts.
It's probably worthwhile to review these two concepts (for instance in the lecture here).

• thank you Andy. The need for first differencing arises with the possible spurious correlation problem since I have relatively long time dimension. Also for economics interpretation, in my case, explanation in differences make more sense. I am also getting fairly nice economically useful results with first differences but not without it. Thank you for the link. I will go through it. Commented Jul 1, 2014 at 17:37
• If you are worried about the time dimension and you want to use a dynamic panel estimator have a look at the Arellano-Bond estimator. You'll easily find useful lecture notes on this estimator with your preferred internet search engine :-)
– Andy
Commented Jul 1, 2014 at 17:39
• Yes I am aware of the Arellano-Bond estimator. Thank you. So basically what I learned from these answers is that I can use first differenced variables in fixed effects model. Thank you.. Commented Jul 1, 2014 at 17:58
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– Andy
Commented Jul 1, 2014 at 18:03