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 esteem of good men is the reward of our worth, but the reputation of the world in general is the gift of our fate.”
—François, Duc De La Rochefoucauld (1613–1680)
“I’m a very smart guy. I haven’t a feeling or a scruple in the world. All I have the itch for is money. I am so money greedy that for twenty-five bucks a day and expenses, mostly gasoline and whisky, I do my thinking myself, what there is of it; I risk my whole future, the hatred of the cops ... I dodge bullets and eat saps, and say thank you very much, if you have any more trouble, I hope you’ll think of me, I’ll just leave one of my cards in case anything comes up.”
—Raymond Chandler (1888–1959)