1Lecture V Economics 202A Fall 2007Section sign-ups at end of class. Logs: for those of you who feel overworked (which is probably almost everybody)you may submit two, rather than three, logs over the next three weeks. We have now finished Lucas and Sargent.September 11: Taylor modelSeptember 13: 3 questionnaire articles: Kahneman et al, Shafir et al, ShillerSeptember 18: Yellen and Shapiro and Stiglitz on Efficiency WagesSeptember 20: no classSeptember 25: Akerlof and Yellen on Near Rationality.September 27: Fehr and Tyran on experimental general equilibrium & Mankiw on menu costs.October 2: Miller & Orr on Demand for Money October 4: Akerlof on Irving Fisher on Head; Caballero, Engel & Haltiwanger on demand for “durables.”October 9: Dornbusch on exchange rates This takes us to the next starred item on the reading list.I want to start where we ended last time, a bit more hurriedly than expected.I am going to give a very quick summary.There are two ingredients for Sargent’s result:First there are rational expectations.Because of these rational expectations the expected price level at time t,which Sargent calls tp*t-1, mimics pt except for a white-noise error term.As a result the gap between actual inflation and expected inflation is just awhite noise error term, ,t.But then there is another assumption, which is the absence of money illusion.Because there is no money illusion, the Phillips curve depends critically on thedifference between actual and expected inflation, plus another error term.This is equivalent to saying that the deviation from full employment depends onthe gap between actual and expected inflation, plus this extra error term.2As a result we find, robustly, no matter what we do, so long as we have such anaggregate supply equation, that the gap between actual and full employment is ofthe form:(,t + ut.So that is Sargent’s result. Looking at this formula tells us that there is no serial correlation of output.And there is no systematic effect of monetary policy. But there is a critical assumption here.In reality, aggregate supply may depend on the price level because there is someform of money illusion such as sticky money wages.If you believe that money wages may be sticky in some form or other, then youhave probably rejected Sargent’s model and his conclusion of the neutrality ofthe monetary rule.The key assumption in his model then is the absence of money illusion.That is the beginning of today’s lecture. The most standard answer to rational expectations is the model by John Taylor.Taylor’s model is a model of rational expectations, but it also has money illusionof a natural sort. Lucas and Sargent emphasize rational expectations.But in fact their strongest assumption is probably the total absence of moneyillusion. That absence is the most fundamental reason for the neutrality of money and thelack of serial correlation of output in their model.In contrast, in Taylor’s model there is serial correlation of output and alsomonetary policy that is effective in stabilizing output.We shall find three things:1. With RE and with a little bit of money illusion, as in the Taylor model, monetarypolicy will be effective.32. There will also be serial correlation of output (even in the absence of seriallycorrelated supply shocks).3. Also since, the economy is linear, as in Lucas’ and Sargent’s equations, it willbe easy to solve.The simple model by Taylor illustrates all three of these points.I shall describe Taylor’s model:His model has unsynchronized price setting.½ of the firms set their prices in even periods.½ of the firms set their prices in odd periods.Measuring time in 6-month periods we might view½ of the firms as setting their price every January,and ½ of the firms as setting their prices every July.Money illusion is introduced in the following way:nominal prices are constant over the two-period interval.A firm setting a price for time t, sets its price both for time t and for time t+1. Its pricing decision is based on information available at t-1.How could a two-period contract be different?The contract made at t could specify prices at t+1 contingent on information thatonly becomes available at t+1.For example: labor contracts may be indexed by the cost of living. In that case the wages in the second period of the contract are contingent oninformation available only after the contract is made.We are assuming that does not happen here. Good studies have been made of Canadian union contracts. Curiously, most of these contracts are not indexed. Even then they are not fully indexed. Let me continue describing Taylor’s model.I am going to give you the equations of the model and their justification.4The microeconomic basis for the model assumes that there are just two firms.The demand for the product of each firm depends on its own price, on the price ofits competitor’s product, and on aggregate demand.To be simple, assume that these firms have no costs of production—so the firmssetting prices will try to maximize expected discounted revenues.USE RHBB TO LIST VARIABLESWRITE SYMBOLS AS YOU GO – WITH SPACESNow let’s adopt a clever notation. Let xt be the price which is set at time t.We will consider one of these firms that is setting its price at time t.The firm setting its price at time t will see that its demand in the current periodwill depend on the price of its competitor, or xt-1.We have a t-1 subscript because that price was set last period, at t-1.The expected demand for the firm setting its price at t will also depend onexpected aggregate demand. We shall denote this as y$t.$ in Taylor’s notation denotes expectations made on the basis of t-1 information.The firm’s expected demand at t+1 will also depend on the expected value of thecompetitor’s price at t+1, which will be the expected price set next period orx$t+1.The firm’s expected demand will also depend on the expected value of aggregatedemand next period, which will bey$t+1.Let’s not be worried about the functional form.The firm that sets the nominal price over the two periods to maximize profits willthen set:<FAR RHBB; divide in ½ by line>(1) xt = b xt-1 + d y$t + ( (b x$t+1 + d y$t+1) + ,twhere ,t is an additional random variable term in the firm’s prices due tothe mistakes in its pricing behavior.The notation is in logarithms:xt is the log of the price set at time txt-1 is the log of the price