I am performing an univariate regression analysis by basically regressing a default rate on macro economic variables such as

$DR = \alpha + \beta GDP$

I noticed that sometimes the sign of the betas does not correspond to the economic intuition but when I add some other macro variables (unemplyoment, interest rate), then this variable has a economically intuitive sign.

I was wondering if considering such variable can be problematic ? What is the literature saying about this.

Moreover, concerning the p-value, could be also consider variables that are not significant in the univariate analysis?

  • $\begingroup$ Relevant answer. $\endgroup$
    – dimitriy
    Jul 31, 2018 at 23:58

1 Answer 1


Once you add one more regressors, your coefficient $\beta$ will always change if the new variable is correlated with the dependent variable and the other independent variable.

So in your case, the change in sign most likely depend on the omission of very important variables like those you mentioned (unemplyoment, interest rate). This is called the omitted variable bias, and if you imagine that the true model depends for example on both GDP and unemployement:

$$ DR = \alpha + \tilde{\beta} GDP + \gamma Unemp + e $$

then your initial $\beta$ will be:

$$ \newcommand{\Var}{\operatorname{Var}} \newcommand{\Cov}{\operatorname{Cov}} \beta = \tilde{\beta} + \gamma \frac{\Cov(GDP,Unemp)}{Var(Unemp)}. $$

For what concerns the inclusion of new varibles in the regression, you should not decide solely on the basis of the p-value of the univariate regression, because as you can see from the previous equation, they can be nevertheless important.


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