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In this chapter, you will learn how to: Compare and contrast single equation and systems-based approaches to building models; discuss the cause, consequence and solution to simultaneous equations bias; derive the reduced form equations from a structural model; describe several methods for estimating simultaneous equations models; explain the relative advantages and disadvantages of VAR modelling;. | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 7 Multivariate models ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Simultaneous Equations Models All the models we have looked at thus far have been single equations models of the form y = X + u All of the variables contained in the X matrix are assumed to be EXOGENOUS. y is an ENDOGENOUS variable. An example from economics to illustrate - the demand and supply of a good: (1) (2) (3) where = quantity of the good demanded = quantity of the good supplied St = price of a substitute good Tt = some variable embodying the state of technology ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Assuming that the market always clears, and dropping the time subscripts for simplicity (4) (5) This is a simultaneous STRUCTURAL FORM of the model. The point is that price and quantity are determined simultaneously (price affects quantity and quantity affects price). P and Q are . | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 7 Multivariate models ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Simultaneous Equations Models All the models we have looked at thus far have been single equations models of the form y = X + u All of the variables contained in the X matrix are assumed to be EXOGENOUS. y is an ENDOGENOUS variable. An example from economics to illustrate - the demand and supply of a good: (1) (2) (3) where = quantity of the good demanded = quantity of the good supplied St = price of a substitute good Tt = some variable embodying the state of technology ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Assuming that the market always clears, and dropping the time subscripts for simplicity (4) (5) This is a simultaneous STRUCTURAL FORM of the model. The point is that price and quantity are determined simultaneously (price affects quantity and quantity affects price). P and Q are endogenous variables, while S and T are exogenous. We can obtain REDUCED FORM equations corresponding to (4) and (5) by solving equations (4) and (5) for P and for Q (separately). Simultaneous Equations Models: The Structural Form ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Solving for Q, (6) Solving for P, (7) Rearranging (6), (8) Obtaining the Reduced Form ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Multiplying (7) through by , (9) (8) and (9) are the reduced form equations for P and Q. Obtaining the Reduced Form (cont’d) ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 But what would happen if we had estimated equations (4) and (5), i.e. the structural form equations, separately using OLS? Both equations depend on P. One of the CLRM assumptions was that E(X u) = 0, where X is a matrix containing all the variables on the RHS of the equation. It is clear from (8) that P is related to the errors in (4) .
