tailieunhanh - Lecture Introductory econometrics for finance – Chapter 7: Multivariate models

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;. | Chapter 7 Multivariate Models ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 1 Simultaneous Equations Models • All the models we have looked at thus far have been single equations models of the form y = Xβ + u • All of the variables contained in the X matrix are assumed to be EXOGENOUS. • y is an ENDOGENOUS variable. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 2 Simultaneous Equations Models (Cont’d) • An example from economics to illustrate - the demand and supply of a good: Qdt = α + βPt + γSt + ut (1) Qst = λ + µPt + κTt + vt (2) Qdt = Qst (3) where Qdt = quantity of new houses demanded at time t Qst = quantity of new houses supplied (built) at time t Pt = (average) price of new houses prevailing at time t St = price of a substitute (. older houses) Tt = some variable embodying the state of housebuilding technology, ut and vt are error terms. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Simultaneous Equations Models: The Structural Form • Assuming that the market always clears, and dropping the time subscripts for simplicity Q = α + βP + γS + u (4) Q = λ + µP + κT + v (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). ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 4 Obtaining the Reduced Form • Solving for Q, Solving for Q α + βP + γS + u = λ + µP + κT + v (6) • Solving for P, Q α γS u Q λ κT v − − − = − − − β β β β µ µ µ µ ‘Introductory Econometrics for Finance’ c Chris Brooks .

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