I would like to estimate a translog production frontier function. For that I want to normalize my variables relative to the mean ( i suppose that means subtracting the mean from the variable itself? i understand there are other ways to normalize as well like z=X-Xbar/sd or X-Xmin/Xmax-Xmin as well). When i do so, it creates very small and negative values in both dependent and independent variables. Also after normalization when i log transform, there are even more zero and negative values. My question is, can i still run a multiple regression with negative and zero values (particularly in dependent variable), and does the interpretation of the coefficients change? Can someone please assist. Thanks
My first question is that, why you need to normalize your variables? Why don't you use the original data? Since in my opinion, it is more prudent to use the original dataset instead of its transformation. Before we go to the regressions method, we can try to 'guess' the relationship between dependent and independent(s) variables (linear, nonlinear, etc) by using scatterplot. Then we can use any appropriate regression method based on this scatterplot afterward.
The main reason is that If i use transformed data where inputs are measured relative to their means, then Translog elasticities at means would simply be the estimated coefficient..
Why not use the original variables in your Johansen then multiply by minus 1 to normalize the vector. After, obtaining the elasticities, then multiply the obtained estimates by the ratio of the mean of the regressor divided by the regressand. This can then be interpreted as elasticity.
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