# Simultaneous Equations Models

In Chapter 11 of POE4 the authors present a model of supply and demand. The econometric model contains two equations and two dependent variables. The distinguishing factor for models of this type is that the values of two (or more) of the variables are jointly determined. This means that a change in one of the variables causes the other to change and vice versa. The estimation of a simultaneous equations model is demonstrated using the truffle example which is explained below.

11.1 Truffle Example

Consider a supply and demand model for truffles:

qi =ai + a2pi + a3psi + a^dii + ed (11.1)

qi =ві + в Pi + вз pfi + es (11.2)

The first equation (11.1) is demand and q us the quantity of truffles traded in a particular French market, p is the market price of truffles, ps is the market price of a substitute good, and di is per capita disposable income of the local residents. The supply equation (11.2) contains the variable pf, which is the price of a factor of production. Each observation is indexed by i, i = 1,2,…, N.

As explained in the text, prices and quantities in a market are jointly determined; hence, in this

econometric model p and q are both endogenous to the system.