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I'm running a TSCS analysis with the plm library in R with which I want to explain students' performances. The data consist of approximately 1100 units and has 25 points of measurement - panel data with ~27,000 units. I lagged my main independent variable by two years. Now, my results show a negative coefficient for the two years lagged independent variable. However, when I add a higher lag of that IV - let's say a three or 4 years lag - the coefficient of the two years lagged IV becomes positive while the higher lags are negative.

Is that normal? How do I interpret these results?

Could it be that my highest lag (in this case lag2) also represents higher lags?

Sorry for any wordiness and thank you very much for your help.

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  • $\begingroup$ Could you please add some more information to this question. What software are you using? What are the outputs? What is your data? $\endgroup$
    – Patrick
    Commented Oct 17, 2019 at 15:05
  • $\begingroup$ Hi Patrick. I'm running a TSCS analysis with the plm library in R. The data consist of approxiamtely 1100 units and has 25 points of measurement - panle data with +-27,000 units. I'm not quite sure what you mean by output, but I want to interpret the coeeficients from the TSCS analysis. $\endgroup$
    – Lennart
    Commented Oct 18, 2019 at 7:24
  • $\begingroup$ What are the variables that you are lagging? $\endgroup$
    – Peter Flom
    Commented Oct 18, 2019 at 12:51
  • $\begingroup$ Hi Peter, it is the representativeness of the teaching body and it is bulit through a concetration index ranging from -0.42 to 1. This is the only variable I lag. But in one model I lag it by 2 and in the other by 4 years with the result that the coeffcient for the two years lagged variable changes dramatically - including the sign. $\endgroup$
    – Lennart
    Commented Oct 21, 2019 at 14:44

1 Answer 1

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Since the predictor series might be inter-dependent due to auto-correlation the estimated coefficients are correlated thus a change to the "mix of the predictors" will yield a change in the estimated coefficients. See https://web.stanford.edu/~mrosenfe/soc_meth_proj3/soc_180B_regression_whatchanges.htm particularly point 3 ..

"All the coefficients are jointly estimated, so every new variable changes all the other coefficients already in the model. This is one reason we do multiple regression, to estimate coefficient B1 net of the effect of variable Xm."

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