# Nominal Values or Real Value & stationary

I'm going to estimate a time series regression which has consumption as a dependent variable. My data source give it in nominal form and unfortunately there are no other sources. It is Question : Can I run a TS model with nominal values ? If not, what should I do ? I think there are 2 possible ways : First: Change variable form to Real form by divide it to CPI(consumer price index). Then change it to a stationary form (e.i Log form) and enter it in the model. Second: Change it suitably and correctly to become a stationary variable. e.i Log form

My question clearly is ; It is possible to use a nominal variable in a time series regression? (regardless of stationary issues)

Please explain which one is right to be done?

My question clearly is ; It is possible to use a nominal variable in a time series regression? (regardless of stationary issues)

Is it possible? Yes.

Should you actually do it? Probably not.

Nominal variables are combination of real variables and prices. For example, nominal consumption $$C_n$$ will be given by:

$$C_n = P C_r$$

where $$C_r$$ is real consumption. If you will run regression (changes are included to get rid of non-stationarity) with

$$y = \beta_1 + \beta_2 \Delta C_n + \epsilon \Longleftrightarrow y = \beta_1 + \beta_2 \Delta P C_r + \epsilon$$

$$\beta_2$$ will not tell you what is the effect of change in consumption on change in dependent variable. This is because you cannot know, without actually examining real consumption, whether variation in $$C_n$$ is due to $$P$$ or also due to $$C_r$$. It is very well possible that all variation in $$C_n$$ is just due to prices where you would be estimating effect of prices on your dependent variable and not consumption. Of course, in reality it is even worse because likely $$C_r$$ and $$P$$ both change at the same time, meaning $$\beta_2$$ will be combined effect of both of those and will not have any stright forward interpretation.

This being said if you are using AR model for forecasting and you just want to forecast nominal consumption based on past nominal consumption where you don't care about above issue it would be fine to use nominal consumption.