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I am trying to run a regression that has the (logged) values of GDP per capita (PPP) for the past 15 years in a given country (in my case Sudan and Rwanda, separatley of course) as dependent variable and an index that measures political stability (WGI) as independent variable. It seems to me that it would make sense to include lags of the independent variable as change in political stability does not have an immediate effect on GDP.

Taking the case of Rwanda if I run the regression without lags I get very good R squared (around 70%), if I include up to 5 lags the R squared goes up but the null hypothesis cannot be rejected for any of the variables except for the constant, however if I run a regression with the dependent variable and the lags taken separatley ex. GDP per capita and political stability (t-3) the R squared is very high and the variable is significant (the null can be rejected), I find that the lag for which I get the highest $R^2$ is t-5 (more than 80%) for both Sudan and Rwanda.

My question is: does it make sense to run a regression with the dependent variable and only the t-5 lag as dependent variable? Does any of this make sense? Am I doing something wrong?

P.S. please leave aside for now stationarity and cointegration

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Concerning the significance of your model: I think the problem lays in your number of observations. If I understood you correctly you have a time series of 15 data points. If you now include five lags you end up with six predictors. This reduces your degrees of freedom to nine. From your statistic class you should know that decreasing the number of degrees of freedom the "harder" it gets to reject the null-hypothesis.

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  • $\begingroup$ Fair point. However, I only have political stability data for the past 15 years therefore I can't go any further back than that. What would you suggest me to do? It is a time series and I am trying to prove that a change in the degree of political stability has an effect (either positive or negative) on the GDP per capita. Thanks. $\endgroup$
    – frankie96
    Commented Jul 19, 2018 at 12:37
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    $\begingroup$ First of all I would question which way is the influence. I am not a politician. But I could imagine that an economic crisis could also lead to political instability. So I think the question is more about correlation of both numbers than of causality? However, maybe there is clear proof in the literature. However, what about simply reporting that t5 showed the strongest correlation? But keep in my mind that for time series there are some "pitfalls" concerning correlation (both variables have a positive trend etc.). $\endgroup$
    – burton030
    Commented Jul 19, 2018 at 12:57

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