ABSTRACT
Many of the traditional econometric applications involve the estimation of linear equations or systems of equations to describe the behavior of individuals or groups of individuals. For example, we can specify that the quantity of an input demanded by a firm is a linear function of the firm’s output price, the price of the input, and the price of other inputs
xDt = α0 + α1pt + α2w1t + α2w2t + α3w3t + t (10.1)
where xDt is the quantity of the input demanded at time t, pt is the price of the firm’s output, w1t is the price of the input, w2t and w3t are the prices of other inputs used by the firm, and t is a random error. Under a variety of assumptions such as those discussed in Chapter 6 or by assuming that t ∼ N
( 0, σ2
) , Equation 10.1 can be estimated using matrix methods. For
example, assume that we have a simple linear specification
yi = α0 + α1xi + i. (10.2)
Section 7.6 depicts the derivation of two sets of normal equations.
