The General Linear Case
Let y be a column vector of M endogenous variables. In the case above with Q and P, we have M = 2. Let x be a column vector of exogenous variables; in the case above x consists only of Z. The structural linear model (without error terms, as above) is:
where A and B are matrices; A is a square M × M matrix. The reduced form of the system is:
Again, each endogenous variable depends on each exogenous variable. It is easily verified that:
Without restrictions on the A and B, the coefficients of A and B can not be identified from data on y and x: each row of the structural model is just a linear relation between y and z with unknown coefficients. (Again the parameter identification problem.) The M reduced form equations (the rows of the matrix equation y = Π x above) can be identified from the data because each of them contains only one endogenous variable.
Read more about this topic: Reduced Form
Famous quotes containing the words general and/or case:
“The nearest the modern general or admiral comes to a small-arms encounter of any sort is at a duck hunt in the company of corporation executives at the retreat of Continental Motors, Inc.”
—C. Wright Mills (1916–1962)
“The case of Andrews is really a very bad one, as appears by the record already before me. Yet before receiving this I had ordered his punishment commuted to imprisonment ... and had so telegraphed. I did this, not on any merit in the case, but because I am trying to evade the butchering business lately.”
—Abraham Lincoln (1809–1865)