Scaling and Trending Variables

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Scaling and Trending Variables

Postby axiom » Mon Sep 16, 2013 9:45 pm

Let's suppose our Y variable is GDP for some country. Let's say our sample is from 1950 to 2000.

We have X variables like interest rate (X1), unemployment (X2), and disposable income (X3).

If we put these into a standard OLS regression we will get some coefficients for interest rate, unemployment and disposable income.

However, we know that a variable like GDP grows through time where-as interest rate and unemployment do not.

We'll get a coefficient on interest rate, let's say something like -500. This is to suggest that a 1 unit increase in interest rate will result in a reduction in GDP of 500. Whether we are talking about the beginning of the time series (year 1950) or at the end of the time series (year 2000), what the equation is saying is that a 1 unit increase in interest rates will have the same effect all along the entire time series. But we know this can't be true; a 1 unit increase in interest rates will probably have a bigger impact towards the end of the series than at the beginning. So how do we deal with this?

I know that you are supposed-to trend the variable in question, but I still have some confusion as to how best to do this.

I know of one approach where you would take a variable like interest rates, and to trend it you would multiply (interact) it with some other variable that grows through time, like disposable income: interest_rates*disposable_income = X4

I know of another approach where you would take interest rates and multiply it by a time dummy (a dummy that goes 1, 2, 3, 4, etc... increasing by 1 all throughout the series): interest_rates*time_dummy = X5

My question is: which is the better approach?

And as a side, once I have put in my new interaction variable (either X4 or X5 as stated above), do I leave the original non-trended variable (interest rate) in the equation as well, along side the interaction variable? Or do I omit the non-trended variable?

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