# Is there any standard measure of economic significance?

One measure is to look at standard deviations. If a one standard deviation increase in X leads to a more than a 0.5 (or 1, or ⅓, or whatever) standard deviation increase in Y, then we say that X has a economically significant effect on Y.

Is this standard? And if not, what other measures are there to formalize the notion of "economic significance"?

$Y_i = \alpha + X_i \beta + \epsilon, \epsilon \sim N(0,\sigma^2)$
Holding everything else fixed, increasing $\sigma$ will increase the standard deviation of $Y$ and therefore, for a fixed relationship between $X$ and $Y$, eventually move the relationship between them to economic insignificance by the standard you present. But the relationship might still be quite economically important. It might be better to instead ask about the standard deviation effects on $\sigma_\hat{Y}$, the standard deviation of the fitted values of $Y$, to ask if the effect is large relative to the total variation that can be explained by the model.