I have the following question, any hint would be really welcome:
I am trying to conduct a two-country comparison by running two separate regressions, one for each country, and testing $H_0:\,b_1=b_2$ (using Wald tests), where $b_1$ is the coefficient of an explanatory variable in regression group 1 and $b_2$ is the coefficient of the same explanatory variable in regression group 2 (the two groups have unequal size). However, I have came up with the following outcome: $b_1$ is statistically significant, $b_2$ is statistically insignicant, and $H_0$ cannot be rejected, i.e. the difference between the two coefficients is statistically insignificant.
I know that this outcome is possible in terms of statistics, but it sounds a bit "problematic" in terms of logic. How could someone sensibly justify it?