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I do some empirical research. I typically use regression analysis and panel data econometrics (with fixed effects).

Usually, when I include more variables, the initial variables of the model become less significant.

But, in a few cases, I see that one variable becomes even more significant when I include more variables.

Why is this happening? What is the interpretation of that? I suppose it has something with the correlation between the covariates and the residuals?

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  • $\begingroup$ This is probably more appropriate for stats.stackexchange.com $\endgroup$ – John Oct 20 '15 at 15:59
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A Change in the statistical significance of a variable when more variables are included can come from two sources.

One is the fact that the estimate of the coefficient becomes larger when new variables are included. This can happen when the newly included variables are negatively correlated with the variable of interest and contribute positively to the depend variable. So essentially, you have an omitted variable bias that bias upwards your original estimates. You are wrongly contributing the negative effect of the omitted variable on the dependent variable to the variable included. Provided that the variance of the model doesn't increase much, your t-stat, $\frac{\beta}{std err}$, will increase, and thus you see a change in your statistical significance.

Another possible reason is that the newly included variables don't correlate with the variable of interest, but it reduces the model variance (an imporvement of Rsquare). This will help reduce your estimation uncertainty and thus lower the standard error of your estimate. Again, provided that the estimate doesn't change much, you will see an improvement in your t-stat.

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