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SimultaneousEquation

# SimultaneousEquation - ECON3300/7360 SIMULTANEOUS EQUATION...

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ECON3300/7360 SIMULTANEOUS EQUATION MODELS Readings: Chapter titles (3 of them) of Simultaneous Equations Models, The Identification Problem, and Simultaneous Equation Methods. Simultaneous Equation Models - is a regression model involving a number of equations in which endogenous variables may appear on both the left and right-hand side. Y t = f(X 1 , X 2 , Y t-1 ) predetermined variable X 1 = f(X 2 , Y t , Y t-1 ) DD & SS Models DD : 0 1 1 1 0 < + + = α αα t t d t U P Q SS : 0 U P Q 1 t 2 t 1 0 s t > β + β + β = Eq m condition : s t d t Q Q = P P* SS DD Q* Q P and Q are jointly determined 1

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DD : 0 1 1 1 0 < + + = α αα t t d t P Q U contains other variables that affect Q d e.g. income, taste SS : t 2 t 1 0 s t U P Q + β + β = contains other variables that affect Q s e.g. weather, strikes P SS DD 1 DD Q P There is simultaneous dependence between Q and P, U 1t and P t , and U 2t and P t Recall : For OLS, E(Xe) = 0 i .e. no correlation between an explanatory variable and the error term. Another example of Simultaneity Bias C t = α 0 + α 1 y t + U t y t = C t + I t Solve simultaneous equations using ILS, IV, 2SLS, 3SLS identification problem to decide on which technique to use. SS DD Q If U 1t changes (say y ± ) DD ± both P & Q change If U 2t changes (say strike) SS ² both P & Q change SS 1 2
Instrumental Variable Estimation DD : t 1 t 1 0 d t U P Q + α + α = Since P t and U 1t are correlated, find an exogenous variable that is correlated or a proxy for P t but uncorrelated with U 1t e.g. Income used as instrument If y ± DD ± P ± - Regress P t on constant and y to obtain t P ˆ - Regress Q d on α 0 and to obtain t P ˆ 1 0 ˆ , ˆ α α Note : If more than 1 instrument is available, then use 2SLS and don’t choose between instruments. Indirect Least Squares Consider the following equations Equation 1 : C t = β 0 + β 1 Y t + U t 0 < β 1 < 1 Y t = C t + I t In the above model, C and Y are endogenous I is exogenous These equations are structural (or behavioural

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SimultaneousEquation - ECON3300/7360 SIMULTANEOUS EQUATION...

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