Help on interpreting the results when significane level change, but not the coefficient

Question

I am studying the effect of employment on population growth using barroregressions. The dependent variable is thus the average log population growth in Norwegian regions between 1995 and 2013. The controls are log population in 1995 (initial population to see if there were divergence in Norwegian regions in the period 1995-2013), share of the workforce with a higher education degree and employment in a sector (where a sector is either the production sector, the business sector or the service sector).

In the next regression I change the employment variable to be a so called "shift-share" variable after Bartik (1991). This variable removes the idiosyncratic "shocks" in the employment growth variable, and is constructed from a period before our study period. The variable is constructed for the period 1970-1990.

When we use the employment in the production variable as a control, the coefficient is 0.16 and significant at a 5%-significance level. When we use the Bartik variable instead, the coefficient is still 0.16, but more significant (at 1%).

What does the higher significance level imply, and why doesn't the coefficient change you think?

Answer 1

Possibly, by removing shocks in the employment growth, you remove variation in the independent variable's ability to predict the outcome. The overall fitted model might give the same line with the same slope (and therefore the same coefficient), but the extent to which the model fits is improved by removing noise in the predictive ability of the independent variable. Therefore, the p-value would decrease: the independent variable is more informative for the outcome.