# The between estimator in panel data

When you model the between estimator of you panel data, you regress the averages of the explanatory variables of the subjects against the averages of the outcome variables of the subjects.

But in this regression model, do you have to include an intercept?

Out of our textbook:

The between estimator exploits the cross-sectional dimension (differences between units) of the data by regressing the individual averages of y on the individual averages of x and a constant using OLS

I have played around with the example data of the book of Gujarati: Basic in econometrics, chapter 16. You can find the data here: http://shazam.econ.ubc.ca/student/gujarati/table15.4

This is the plot I made (the colors represent 3 different companies):

On the plot you can see the Pooled OLS regression data and the fixed effects (aka within estimator) regression data. How would the between estimator look like? Does it have one intercept or three? And what if all the data points of the companies lie exactly above each other, so they have the same average x?

• Not sure what you mean by the "between estimator". Do you mean you have two groups? Jan 27, 2014 at 11:20
• Post edited to give a better understanding... Jan 27, 2014 at 11:42

As you said correctly, the between estimator takes the individual effects model $$y_{it} = \alpha_i + x'_{it}\beta + \epsilon_{it}$$ and averages out the time component resulting in the regression $$\overline{y}_{i.} = \alpha + \overline{x}'_{i.} + (\alpha_i - \alpha + \overline{\epsilon}_{i.})$$ where bars indicate average variables and . signifies that time has been averaged out. You still need an intercept in this model to consistently estimate it.

Note though that this estimator only uses the cross-sectional information and completely discards the time variation in your data. The estimator is only consistent if $\alpha_i$ are random effects (though in this case you may opt for the random effects estimator which is more efficient and also uses the time variation in the data).

You can easily implement the between estimator in your statistical software by averaging the data for each panel unit to average out the time component and then regress the averaged variables on each other. For more information on this topic see for instance Cameron and Trivedi (2009) "Microeconometrics using Stata" or Wooldridge (2010) "Econometric Analysis of Cross-Section and Panel Data".

• What exactly are you plotting when you say you "plot an estimator"? Do you mean the predicted values? Sorry that my answer doesn't fully address your question now after the edit but if you could clarify the plotting issue I'll be happy to edit it.
– Andy
Jan 27, 2014 at 12:17
• I mean plotting the estimated regression lines. And a more specific question is what happens when all the subjects have the same average x for a particular predictor. Thanks in advance! Jan 27, 2014 at 12:25
• If all companies have the same average, then there is no cross-sectional variation in the data and hence the estimator would not be identified. So in that case you wouldn't have anything to plot. Otherwise you will get again three lines for each company as in the above graphs but with only one data point per company.
– Andy
Jan 27, 2014 at 12:31
• I mean the same average x, but not the same average y. For example wages against working years, and all subjects have working years going from 1 to 10, but their wages are very different. You would have three lines above eachother. In that case it is clair what fixed effects does, but I can't understand how the in between estimate works in that case Jan 27, 2014 at 12:37
• And this is why it it important probably to first describe the "in between" and "within" variation of your predictors, exactely as she does: m.youtube.com/watch?v=aUVZWnVnjxs Thx a lot for your help! Jan 27, 2014 at 12:54