SYSTEMS OF REGRESSION EQUATIONS
The previous chapters discussed estimation of single linear equation models. In practice, it is not uncommon to encounter models that are characterized by several linear or nonlinear equations where the disturbance vectors from the equations are involved in cross-equation correlations. As an example, consider the well-known Grunfeld’s (1958) investment model given by
where Iit is the investment for firm i in time period t, Fit is the market value of the firm, and Cit is the value of capital stock. The original data set was comprised of 10 large US manufacturing firms, which were followed from 1935 to 1954. As discussed by Greene (2003, p. 339), the disturbance vectors in each equation are characterized by shocks that may be common to all the firms. For instance, the general health of the economy may have an impact on the investment behavior of each firm. On the other hand, certain industries exhibit a cyclical nature where they are heavily dependent upon the economy whereas other industries are not cyclical and are not impacted by the economy. Therefore, another component of the disturbance term may be shocks that are specific to the industry the company belongs to.
A naïve approach to analysis may treat the system of equations as unrelated or independent. However, analysis of the residuals from the system of equations may reveal ...