1 We will continue with a variation on the basic model. We will now hypothesize that p is a function...

1

We will continue with a variation on the basic model. We will now hypothesize that p is a function of m, the rate of growth of the money supply, as well as w.

INSTRUMENTAL VARIABLES ESTIMATION: VARIATION

structuralequations pumwp 321 wuUpw 321

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An increase in the money supply is likely to increase price inflation and hence we would anticipate 3> 0.



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The reduced form equations are now as shown. Again, we see that we would obtain inconsistent estimates if we used OLS to fit the structural equations.


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reduced form equation

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The equation for p remains identified. It contains the endogenous variable w as an explanatory variable, but we can use U as an instrument for it. U satisfies the three conditions of being correlated with w, independent of up, and not already in the equation.



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As an exogenous variable, m was also a potential instrument but, since it appeared in the equation in its own right, it could not be used.



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Note that, since this is now a multiple regression, the mathematical expression for the IV estimator of the slope coefficient will now be different from that in the simple regression model.



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The equation for w is now identified. p is an endogenous variable correlated with uw, so we need to find an instrument to act for it. U is ruled out, as before, because it appears in the equation in its own right.



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However, m is now available as an instrument.



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m is correlated with p, by virtue of the reduced form equation for p, it is exogenous and therefore distributed independently of uw, and it is not already in the equation in its own right.



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Both equations are now exactly identified. An equation is said to be exactly identified if the number of exogenous variables available as instruments is equal to the number of endogenous variables that require instruments.



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In each case there was one endogenous variable on the right side and one exogenous variable was available to act as an instrument.

11



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Copyright Christopher Dougherty 2012.

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Introduction to Econometrics, fourth edition 2011, Oxford University Press.

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2012.11.21

1 We will continue with a variation on the basic model. We will now hypothesize that p is a function...

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