# Regression in different regimes

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.