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lecture4

# lecture4 - Lecture IV Economics 202A Fall 2007 At the end...

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1 Lecture IV Economics 202A Fall 2007 At the end of this morning&s class I promised you that I would go over Sargent&s model of the Lucas Critique. That will be the topic of this class. Before I begin the Sargent model, I must go over an important technical detail. Sargent has terms in his equations, such as p t - p t-1 where lower case p t is the log of the price level at t and lower case p t-1 is the log of the price level at t-1. In fact, such a term is almost equal to the percentage change in the price level. It is almost equal to the rate of inflation. Let me show you why. Let upper case P t be the Price Level. p t - p t-1 = ln P t - ln P t-1 = ln P t / P t-1 . Let me make an assertion. My assertion is that ln P t /P t-1 is approximately equal to or, which is the percentage change in the price level. How do I know that

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2 Consider any number close to one. I will show you that ln x x - 1. I know by Taylor series expansion that: ln 1 = 0, POINT AND ALSO So ln x (x - 1). Using this approximation If you do not follow what I have said here now I want you to be able to accept my interpretation of Sargent&s formulas, and then you can later come back and verify that in fact this formula follows. ERASE BB I am now going to present to you Sargent&s 3 equations. I will use his notation, which will make it easier for you to read it.
3 David Romer explains in detail how they arise out of microfoundations. I am going to just write them down and explain why these correspond to standard macroeconomics from your intermediate course. Equation (1) is an aggregate supply equation. (1) y t = k t + ( ( p t - t p* t-1 ) + u t where y t is real income k t is potential GDP p t is the actual price level at time t t p* is the expected price level at time t, with the expectations made at time t-1, and u t is an uncorrelated random variable. All of these variables are in logarithms , so I should have been more careful and said y t is the log of real income k t is the log of potential GDP p t is the log of the actual price level at time t, and t p* is the log of the expected price level at time t, with the expectations made at time t-1. Equation (2) is an IS curve. Again the variables are in logs with the exception of the nominal rate of interest r t . (2) y t = k t + c ( r t - ( t+1 p* t - p t )) + d z t + e t where r t is the nominal rate of interest, z t is a vector of exogenous variables, including government spending and tax rates, and

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4 e t is a random error term. Equation (3) is an LM curve (3) m t = p t + y t + br t + 0 t , where m t is the log of the money supply, p t , y t , and r t are as before and 0 t is a random error term. While this notation is slightly hard to read, it turns out that this is exactly the standard Keynesian model with the standard Phillips Curve describing labor supply. Let me now review the equations in reverse order.
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lecture4 - Lecture IV Economics 202A Fall 2007 At the end...

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