Demeaning Models over Two Time Periods

Basic Concepts

Another way of handling the unobserved time-invariant variable u_i (see Panel Data over Two Periods) when we have two time periods is to use demeaning. For each unit, we calculate the mean of each variable in the model across both time periods and then subtract this value. Thus, for each i and t, the data element x_it is replaced by x_it – x̄_i. Here, x̄_i = (x_i0 + x_i1)/2.

Notice that this results in the elimination of any time-invariant variables, such as u_i, since in this case x_i – x̄_i = 0.

Equivalence with Differencing Model

Since x_i1– x̄_i = x_i1 – (x_i0 + x_i1)/2 = x_i1– x_i1, we see that this model is equivalent to the model using differencing. This equivalence won’t hold for models with more than two time periods.

Examples Workbook

Click here to download the Excel workbook for the use of demeaning instead of differencing to address Example 1 of Differencing Models over Two Time Periods.

See Demeaning for Panel Data for further information and examples.

References

Gujarati, D. & Porter, D. (2009) Basic econometrics. 5th Ed. McGraw Hill
http://www.uop.edu.pk/ocontents/gujarati_book.pdf

Hill, R. C., Griffiths, W. E., Lim, G. C. (2018) The principles of econometrics. 5^th edition. Wiley.