Problem of Mixing Real and Nominal Variables – A Query

One of my colleague asked me a question,

Whether mixing real and nominal variable in the model can create a problem or not?

So in this blog I will try to see through specification of the model if this mixing of variables can create a problem or not.

Consider following specification of the model, with none of the variable are in log form.

A = a0 + a1B*P + a2C*P + a3ΔP

Where A is a real variable and other variable include nominal variables and Inflation

A = a0 + a1B*P + a2C*P + a3(Pt – Pt-1)

we can extract Pt from here

A = Pt (a0/Pt + a1B + a2C + a3 – a3(Pt-1/Pt))

A/Pt =  a3 + a1B + a2C – a3(Pt-1/Pt) +a0 (1/Pt)

Analyzing the following equation, following problems can be pointed out from this.

  1. The intercept is biased, it is completely different.
  2. The dependent variable is different, so model is different.
  3. Running intercept less equation will not insure the removal of problem.
  4. It was assumed that they are stationary otherwise the problem would have been more complex

This is just my perception about this problem, certainly it could be wrong. Please share your views about this issue.

One thought on “Problem of Mixing Real and Nominal Variables – A Query

  1. Noman Arshed says:

    I have received several responses for this query,
    Mathematically or statistically there is no prominent issue visible but theoretically as nominal variables to not effect real variables in long run, and most of our econometric models are based on long run relationship, so to avoid criticism these variables should not be mixed.

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