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I am dealing with macro-economic data in EVIEWS11:

  • new firms founded per year scaled by population ENT
  • real gdp per capita Y
  • stock market capitalisation scaled by population and in real terms MK
  • control variables X: return, dividend yield and long term return (Government bonds), also ONE LAG of new firms founded per year scaled by population (Log(Ent_t))

The first model (static linear model)I want to estimate with OLS is the following: $$ \log(Ent_{t+1}) = \beta_0 + \beta_1 \log(Y_t) + \beta_2 \log(MK_t) + \beta_3 X_t + \epsilon_{t+1} $$ After performing stationarity tests however, I conclude that all of these variables have unit roots (except for the control variables).. OLS on non-stationary variables is not suitable I thought.

Is taking the first differences of the macro-economic variables a suitable solution for OLS regression? I am using HAC standard errors (NEWEY-WEST) to correct for autocorrelation and heteroscedasticity.

I am also going to perform Granger causality tests & VECM cointegration procedure to see what the direction of the Granger causality is. So both a static model and a dynamic model will be performed.

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You should first test for cointegration and then proceed with first differencing if cointegration is absent or an error correction model if cointegration is present. If some of the variables are actually cointegrated, simply taking first differences of the integrated ones will lead to omitted variable bias because of the missing error correction term.

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  • $\begingroup$ So perform a Johanson cointegration test, check if the independent variables are cointegrated (or also the dependent variable)? And what if there is cointegration and I still do first differencing of the variables, is the OLS output still not correct? Omitted variable bias occurs when other factors still play a role in the model? (I also updated question with more explanation of the variables) $\endgroup$
    – Enjo Faes
    Commented Apr 14, 2020 at 11:10
  • $\begingroup$ is it also better to work with log transformed variables for all variables instead of only a few (I am talking about the return, dividend yield and long term return)? @Richard $\endgroup$
    – Enjo Faes
    Commented Apr 14, 2020 at 11:28
  • $\begingroup$ @EnjoFaes, the most problematic bit is cointegration between the dependent variable and the independent variables. Since we have an equation for the dependent variable, a missing an error correction term would hurt the explanation and/or prediction of it the most (leading to inconsistent estimates of model coefficients). If only the independent variables were cointegrated, it would not be such a big deal. I cannot say much about taking logs of variables, though. $\endgroup$
    – Richard Hardy
    Commented Apr 14, 2020 at 11:39
  • $\begingroup$ Oh okay! thank you! Have you seen my next question about the cointegration test? @Richard do I test cointegration for the whole equation? $\endgroup$
    – Enjo Faes
    Commented Apr 14, 2020 at 11:53

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