# 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:
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).