Should I relocate for a job that pays less?

Typically, companies take geographic differences in living costs
into account when determining construction salary levels for their employees.
Although exceptions exist, companies in lower-cost areas often pay
lower salaries than those in higher-cost regions.
It's rare for companies to reduce an employee's construction salary, particularly
if they are being asked to relocate. What happens is that the employee might see lower pay growth for the next couple of years, but they are benefiting from the lower cost of living.
You'd have to weigh the equity or other incentives you'd receive and
your future construction career opportunities when making your decision.