# Determinants of economic growth in ARDL model - nominal or real variables?

I'm investigating the determinants of economic growth of my country. Some of them are of long term other are of short term. For that I'm trying to construct an ARDL model, but I'm confused about the right variables to choose and whether I implement them in difference in level or difference in logarithm.

I found out that we use the logarithm of real GDP in differences which tend to represent the growth rate. The explicative variables are foreign direct investment credits to private sector education spending health spending.

My question is: if I'm using real GDP as a response variable, do I have to use deflated explicative variables? Or it's better to use nominal GDP and nominal explicative variables?

My experience is that most of the papers estimating these sort of regressions use real variables, all of them deflected with the same index. As Roy says, you not want to confound an effect by inflation.

For example, assume the "true" model is that with variables in real terms:

$$Y_t = \beta_0 + \beta_1 X_t$$

Converting into nominal variables, you get:

$$Y_tp_t = \beta_0 p_t + \beta_1 X_tp_t$$

Then, a correct estimation of the "true" model when using nominal variables would require you to add prices as a regressor (or inflation if using log of differences). Thus, you have a further robustness check of your model by estimating it in nominal terms and adding inflations as a regressor.

Someone could rightly ask, what if the "true" model is in nominal terms? That is slightly odd though. Such model would be something like

$$Y_tp_t = \alpha_0 + \alpha_1 X_tp_t$$

But say that there is a change in $p_t$ and in $X_t$ such that $X_tp_t$ remains unchanged. And yet, $Y_tp_t$ would change because of the change in $p_t$, withouth any right-hand side variable changing - a clear inconsistency.

The growth rate of the economy should be calculated in the real term, so I would say you definitely should use real variables. For instance, the price went up 20% from last year, do you say that this economy grew by 20%? Maybe no. Thus, in this case you should use real variable for every variable you include.

FYI, the growth rate of the real GDP can be well approximated by the 1st log difference in real GDP provided that the growth rate is close to zero. If this is the case for you, you can use the first log difference.