Understanding Gorman Polar Form I've been reviewing my microeconomics notes and have found a point that I still don't quite understand. this being Gorman Polar Form

Gorman form of the indirect utility function is  as defined by Varian is:

$$v(p,m)=a_i(p)+b(p)m$$

where $a_i(p)$ differs from each consumer and $b(p)m$ is the same for every consumer. 

How does one estimate $b(p)m$?
After doing some reading on the topic, it appears we would estimate this equation as we would with any other demand estimation. 

the reason why the term $b(p)m$ is written this way is due to the assumption of homothetic preferences (or homogeneous of degree 1, this dosen't matter in demand analysis). Since Gorman polar form is a homothetic form this implies that:

$$v(p,m)=a_i(p)+b(p)m \equiv a_i(p)+b(p,m)$$ 

more specifically $$b(p,m) \Rightarrow b(p)m$$ 

if preferences are homothetic or homogeneous of degree 1.