# Anderson 5 example cont both h and w are endogenous

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Economics 20 - Prof. Anderson 5 Example (cont) Both h and w are endogenous because they are both determined by the equilibrium of supply and demand z is exogenous, and it’s the availability of this exogenous supply shifter that allows us to identify the structural demand equation With no observed demand shifters, supply is not identified and cannot be estimated

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Economics 20 - Prof. Anderson 6 Identification of Demand Equation w h D S (z=z1) S (z=z2) S (z=z3)
Economics 20 - Prof. Anderson 7 Using IV to Estimate Demand So, we can estimate the structural demand equation, using z as an instrument for w First stage equation is w = π 0 + π 1 z + v 2 Second stage equation is h = α 2 ŵ + u 2 Thus, 2SLS provides a consistent estimator of α 2 , the slope of the demand curve We cannot estimate α 1 , the slope of the supply curve

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Economics 20 - Prof. Anderson 8 The General SEM Suppose you want to estimate the structural equation: y 1 = α 1 y 2 + β 1 z 1 + u 1 where, y 2 = α 2 y 1 + β 2 z 2 + u 2 Thus, y 2 = α 2 ( α 1 y 2 + β 1 z 1 + u 1 ) + β 2 z 2 + u 2 So, (1 – α 2 α 1 ) y 2 = α 2 β 1 z 1 + β 2 z 2 + α 2 u 1 + u 2 , which can be rewritten as y 2 = π 1 z 1 + π 2 z 2 + v 2
Economics 20 - Prof. Anderson 9 The General SEM (continued) By substituting this reduced form in for y 2 , we can see that since v 2 is a linear function of u 1 , y 2 is correlated with the error term and α 1 is biased – call it simultaneity bias The sign of the bias is complicated, but can

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