I want to include both parent's education variables as control variables in my estimation about the effects of maternal bargaining power to child's educational attainments. They are stated as categorical variables ranging 0 for "not receiving educ" and 4 for "tertiary-level educ". Many previous papers in my topic have also included these as controls, and most of them yield significant results in the main independent variable (maternal bargaining power). But when I did the same, my independent variable would lose significance greatly, and turns out they're highly correlated with each other. Is there any way to get around this and still include these variables in the model without sacrificing significance?
Four considerations come to mind.
Does your variable of interest ("maternal bargaining power") have a high variance inflation factor? (There are generalizations of variance inflation factor if you are not using OLS linear regression.) I will leave vague what I mean by "high", but people often take five or ten to be high and to indicate problems with the standard errors being inflated far too much. If you have a modest variance inflation factor on your "maternal bargaining power" variable, then the correlation between the two education features is not important for your study. Sure, you might get funky behavior with those, but those are not the variables of interest, so there is a sense in which you need not care. Further, the fact that the two education variables are correlated is not much of a consideration for this kind of variance inflation factor analysis. If they are independent yet the variance inflation factor on "maternal bargaining power" is high, then you might have an issue, and if the correlation is high yet the variance inflation factor on "maternal bargaining power" is low, then there probably is no problem.
What kind of effect do you observe in your data, and how does this compare to other studies? If you observe a smaller effect size than other studies have found (which might be a result of publication bias that leads to only the large magnitudes being published), then of course you are having a hard time rejecting a null hypothesis of zero effect.
What other control variables do other studies use that might be able to cut down on some of the error variance that is used for calculating standard errors? The point of including control variables is to account for variability in the outcome and to reduce the variance of the error term that is used for calculating coefficient standard errors. If you do not include controls that other studies include, you might not be shrinking the error variance as much as they are, so you wind up with larger standard errors and a study with less power.
What kind of sample size do you have compared to other studies? If they have billions compared to your hundreds, they have a considerable edge when it comes to power to reject a null hypothesis of zero effect, even if your observed effect magnitude is larger. The larger sample size, all else equal, leads to smaller standard errors and higher power.