# Determining a variable from empirical results obtained from regression analysis

For context, I am trying to estimate the excess supply and demand in the Commercial Real Estate market and the rental price adjustment mechanism following the change in vacancy.

I found a paper titled "The Price Adjustment process and natural vacancy rate" that explores this rental price adjustment process for the housing market. Basically, the author estimates the demand, level of vacancy and supply stock in the market to construct an regression equation that attempts to explain the determinants of change in rental price (R).

Demand D, may be assumed to be a function of the rent per unit of housing services, R; the user cost of home- ownership, U; real income per household, Y; the price level, P; and demographic variables, Z, as set out in D=d(R,U,Y,P,Z).

Vacancy V = Vacant units / Total Supply stock (Vacant units = Occupancy - Supply).

Then, the rate of change in rents (R) is a function of excess demand or supply in the market. This excess is the difference between long-run equilibrium vacancy (Vn) - V.

The results are obtained by assuming constant Vn and fitting regression equation R = b0 + b1.E - b2.V

From the results obtained, they estimate the long run equilibrium vacancy or the natural vacancy rate (Vn).

This is the part that I am not following. How is Vn calculated? Here's an excerpt from the paper:

"An estimate of the natural vacancy rate for each city can be determined from the empirical results in Table 1. If we assume the appropriate estimating specification of equation (4) would exclude an intercept, and that V' is constant over the estimating period for each city, then the intercept in estimating equation (5) for each city can be interpreted as bo = b2Vn, and the natural vacancy rate for each city is bo/b2. Assuming this specification, the last column in Table 1 sets out the estimated natural vacancy rate for each city. 1 "