In the example provided, a model is built with the aim of explain certain behaviours of individuals who pertain for a classroom, let's assume we are speaking about a high school scenario and a class of teenagers. Data is gathered only from the male students.
When including age as an explanatory variable in a regression equation, it is very likely that it produces a causal effect on the dependent variable, but also on many of the other regressors, and hence it will be 'contaminating' the effects quantified for those.
A possible solution to avoid this inconvenience could be to gather again the same data 10 years later, and to build a new regression function. In the end, it is necessary to use an estimation method which compares the old and new regressions, to conclude in which extent has time (=age) affected each of the regressors, in order to isolate the effect of time on the regressors, from the pure effect that each regressor causes on the dependent variable. Like this, we are able to know the real effect of each regressor on the dependent variable, that is the ultimate goal of the model.
A possible estimator to use in this scenario is the so-called 'difference in differences' model.
