Can I include gdp growth and dummy for recession in the same regression?

Question

I am analysing business cycle effects on health behaviour (smoking, alcohol abuse etc. and want to see whether the size of the recession or the fact there is a recession is more important.

Hence I am using gdp growth and recession in my regression.

$cigarettes smoket_{it} = β_1 * employment_{it} + β_2 * earnings_{it} + β_3 gdpgrowth_{ it} + β_4 recession_{it} + control variables + u_{it}$

For some reason I get the feeling I shouldn't use these both in the same regression.

Answer 1

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $y_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

1. (Informal) Two consecutive quarters of GDP decline.
2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear. A problem in all of macro though is that you have limited data relative to everything you'd like to estimate. If you have a twenty year sample, you only have TWO recessions! It would be like you have two subjects that got treatment.

Answer 2

You are doing a regression with very dependant variables. It's a good instinct to worry about this! There are some good suggestions about how to deal with this in the answers to a similar question: Regression with multiple dependent variables?.

Practically speaking, in your case, these variables are probably so dependant on each other that you should remove one unless you have reason to believe that they contain meaningfully different information. This is especially true since I imagine that you don't have very many data points to do the regression on.