Hi everyone,

I'm trying to do something which I'm not sure is possible with Stata.

Basically, I'm trying to replicate a paper on rent control (Caudill 1993) which compared prices of controlled rental units to the inefficient output of a production function (where inputs are the hedonic characteristics of the units) and prices of uncontrolled units as the inefficient output of a cost function; the "frontier" level would be the equilibrium price in absence of controls. The comparison stems from the fact that controlled rents should be lower than the hypothetical equilibrium price in absence of controls (lower than the "frontier") while uncontrolled rents should be higher.

My dataset contains rent and housing characteristics on a sample of housing units, and contains both controlled and uncontrolled units.
So I need to estimate a stochastic frontier production function and a stochastic frontier cost function simultaneously on different groups of my dataset (but the Y variable and the X variables are the same!), imposing coefficients of the two models to be equal. The dependent variable Y is the rent and the independent variables X1 X2 X3 X4 are characteristics of the units. Units are controlled if C=1 and uncontrolled if C=0.
So to estimate the separate frontiers for the two groups (the production SF for controlled units and cost SF for uncontrolled) I'd do:

Code:
sfcross Y X1 X2 X3 X4 if c==1

sfcross Y X1 X2 X3 X4 if c==0, cost
Is there a way to estimate the two frontiers simultaneously, imposing the beta coefficients for the two models to be equal?

Or, as a second-best option, is there a way to estimate the first model first, and then estimate the second imposing the coefficients of the first one?

Hope it is clear enough.
Aurora