We use a land rent model along the lines of Chomitz and Gray (1996) and Nelson and Hellerstein (1996). Land rent Rik for land use k at any given point i is defined as the difference between the value of outputs and inputs, Qik and Xik, at their respective location-specific prices Pik and Cik:
Assuming a Cobb-Douglas production function with a technology-shift parameter Sik and prices to be affected by a vector (Zik) of variables that location-specific include distance to infrastructure,
This enables us to express land rent Rik as a function of Sik and the Zik’s as follows
which, by taking logs and collecting coefficients, can be transformed into an expression of the form
where u is a stochastic parameter.
Empirically, we distinguish between two forms of land use, agriculture (k = 1) and forestry (k = 0) and note that point i will be devoted to agriculture if Ri1 > Ri0. Defining the potential difference between agricultural and forest uses R* = Ri1 - Ri0 , a plot will be used for agriculture if R*> 0. Then, observed land use can be written as:
Together with the assumption that u is normally distributed, this allows us to use a standard probit model that expresses observed land use as a function of the Sik and Zik variables. This requires to relate the latter to R* and to variables in our data set to establish their potential effect and the predicted signs of individual coefficients in this regression. Before doing so, we briefly discuss the available data used in the analysis and relate them to R*.