# Correlation over time, panel data variable

I think my question seems to be quite simple, but I cannot figure out a solution. I have panel data with about 1000 different people over 10 years. Standard panel regression is not the problem, but I am searching for a method to measure the correlation or effect of the independent variable on itself over time for the whole dataset (not for every single year). Is the answer a time-series method?

Thanks! Best Tom

The answer (if I understand your question correctly) is a dynamic panel data model. In such models, one expresses the DGP as follows: $$y_{it}=\rho y_{it-1}+x_{it}'\beta+\alpha_{i}+u_{it}$$ This has been studied extensively for the past 20 years. Some classic estimators are:

a) Arellano-Bond estimator b) Anderson-Hsiao estimator and c) Arellano-Bover systems GMM estimator.

I would suggest that you go with the 3rd option. I think this one is the latest+most robust estimator. You can verify the statement. Each of these methods deals with an alternative way of consistently estimating $\rho$ by using instruments (or systems of instruments).

thanks for this fast answer. I already used the Arellano/Bond estimator, but I think my problem is, that I want the correlation of the variable with itself over all periods in one measure. The AB-method only has one lag, or is it possible to include more lagged variables?

Thanks! Tom

• Yes you can..you will have to exploit moment conditions just like in the Arellano Bond estimator..they use the AR(1) nature of the DGP to exploit orthogonality conditions. You will have to manipulate orthogonality conditions in the same way that they do. – ChinG Nov 24 '15 at 14:15
• It can be generalized to an AR(p) process – ChinG Nov 24 '15 at 14:15