(Near) Zero but significant coefficient

[Helen Chang]

Hi, I was wondering what are some possible reasons to have a near zero but significant coefficient (e.g., 0.00003) in the regression results and if there is any way to improve such results. Thanks for the help in advance.

[Rhys Williams]

Hi Helen,

It depends what the research question is. It could simply be that the true effect is indeed close to zero...

It could also be that the units you are in result in such a seemingly small number but if you adjust the numbers then things become more economically sensible.

Or there might be some omitted variable which is offsetting the result and dragging this to zero (measurement error may also lead to attenuation bias).

In terms of remedies I think it would be difficult to say without knowing more. Obviously, it's always better to have more data, if possible. You could also try reducing your dataset and see if the results still hold across a subset of data (perhaps restrict to a random set of individuals, sort of like a cross-validation approach). You might also try a different econometric methodology if one makes sense and see how that affects the results.

Best,
Rhys

[Hong Il Yoo]

If you divide your independent variable by 1 million, your coefficient estimate will become 1 million times larger. Ok that’s an exaggerated example but what you may want to consider is whether the effect of one unit increase in your independent variable is really an interesting quantity. If not you may want to scale it appropriately e.g. the effect of a 1000 dollar increase in annual income is a lot more interesting than that of a 1 dollar increase so it may make sense to rescale your income variable to be in 1000s of dollars.

[Weiwen Ng]

For completeness, you didn’t state your sample size. If your sample size is very large, essentially anything will have a significant p-value. Here, you will want to make some judgment on the effect size. Sometimes, it’s hard to tell how substantive an effect is. In health services research, there’s a small branch of research on minimally clinically important differences. A related concept is cost effectiveness analysis, which is not specific to health care. Sometimes the effect of a coefficient is obvious, because you can compare it to the intervention cost or some natural unit. It’s usually impossible to say without some context.