I am interested in studying the intercept of a multivariate linear regression model such as:
$y_t = a + b_1x_{1,t} + b_2x_{2,t} + ... + b_mx_{m,t} + u_t$ with $t = 1, 2, ..., n$
Under two possible scenarios that depend on the value of a variable $z$, which is not included in the above model:
- Scenario "High": includes all periods $t$ such that $z_t > \bar{z}$
- Scenario "Low": includes all periods $t$ such that $z_t \leqq \bar{z} $
I have thought of simply performing two regressions, one for each scenario, on two subsets of the full sample selected based on $t$.
I would like to know whether the above methodology would be acceptable or there are some better alternatives.