# 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. – kjetil b halvorsen Jul 1 '14 at 16:23
• @kjetil I am so desperate for answers that I didnt explain my problem clearly. Sorry for that. Question is edited. – Ali-Jena Jul 1 '14 at 17:09

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.