# rates vs. level

For my thesis I will run some regression (OLS and ML: Probit). I like to distingish between variables in growth rates and variables in level form, if there is any important issue that I have to consider.

I will regress the cyclical component of the GDP on a business survey variable in order to have some short term forecasts. A feature of the cyclical component of the GDP is that it is already stationary.

The question is: What form is recommended for the GDP? Level, log of Level, growth rate, difference.

The reason I am asking is that I would like to limit the number of regressions so that I do not have to regress with both rate and level form. This is not an issue of saving work but rather of deciding for the best (or appropriate) procedure before the analysis. That is just to make sure that the theoretical and logical thoughts on the right variable form match the analysis.

Also, I will need a literature linked that explains that problem.

Thanks so far.

It doesn't much matter as far as the mechanics/results of the regression. However, your interpretation will change depending on which dependent variable you use.

Note that your interpretation of the coefficient(s) of interest will be in the units of your dependent variable. For example, if you use levels, your interpretation is something like: "A 1 unit increase in X results in a \\beta_1\$ increase in GDP".

Think about the context of your research question an ask yourself what kind of interpretation makes the most sense.

• Thanks for your reply. As I explained, it is the detrended GDP. It is said, detrending causes some problems. Especially at turning points, the trend is not the same as elsewhere. Hence detrending will not work fine for turning points (turning points are my research project, I detrended with Baxter-King if that is of interest). So I was thinking wether it is correct to assume that the growth rate does not have these problems, since detrending is not neccessary. Am I correct with this assumption?
– Econ
Mar 19 '18 at 22:11
• Well I still say it depends on the context. Do you believe your independent variable will cause the growth rate of GDP to change (e.g. economic growth speeds up) or do you think it will cause GDP to increase but continue growing at a similar rate? Ultimately the answer to that question will determine if you want to use rates VS. levels.
– JKK
Mar 20 '18 at 22:43
• I expect an influence of my independent variable on the GDP. Otherwise, I had a coefficient of the independent variable (btw it's a survey variable) of zero, if I am not mistaken. So yes, I expect an influence. Right now I am not sure wether the growth rate of GDP and the survey variable reach their maximum at the same time. It is possible, that the survey variable reaches it's local maximum when the growth rate changes from positive to negative growth (a turning point). Since I need to cite what you said for my project, could you provide some literatur that explains that?
– Econ
Mar 22 '18 at 7:56
• Hi: deciding whether to use levels or differences ( differences are really rates if one uses log(GDP) ) is not a trivial issue. In fact, this issue is what eventually led to engle and granger getting the nobel prize for their cointegration paper. ( I think it's 1987-econometrica). There is obviously a large literature on cointegration. If you don't want to deal with the cointegrating issue, then just test log(GDP) for I(1) using DF or ADF. If it is I(1), difference it and use the difference as the dependent var. If it's I(0), use it directly. No experience on the turning point issue. Jun 18 '18 at 5:59
• hi: one other thing that I should have mentioned. if you skip the cointegration step-issue, the LHS and the RHS still have to have to be of same order. So, if you use say levels and therefore log(GDP) because it's I(0), then your RHS needs to be I(0) also. If the order on the RHS and LHS are different, then a regression model is ill specified. good luck with project. Jun 18 '18 at 16:08