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Lecture Notes in MacroeconomicsJohn C. DriscollBrown University and NBER1December 21, 20031Department of Economics, Brown University, Box B, Providence RI 02912. Phone(401) 863-1584, Fax (401) 863-1970, email:John [email protected], web:http:\\cecon.pstc.brown.edu\ jd. CopyrightJohn C. Driscoll, 1999, 2000, 2001. All rightsreserved. Do not reproduce without permission. Comments welcome. I especiallythank David Weil, on whose notes substantial parts of the chapters on Money andPrices and Investment are based. Kyung Mook Lim and Wataru Miyanaga provideddetailed corrections to typographical errors. Several classes of Brown students haveprovided suggestions and corrections. All remaining errors are mine.

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Contents1 Money and Prices1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . .1.1.1 Prices . . . . . . . . . . . . . . . . . . . . . .1.1.2 Money . . . . . . . . . . . . . . . . . . . . . .1.2 The History of Money . . . . . . . . . . . . . . . . .1.3 The Demand for Money . . . . . . . . . . . . . . . .1.3.1 The Baumol-Tobin Model of Money Demand1.4 Money in Dynamic General Equilibrium . . . . . . .1.4.1 Discrete Time . . . . . . . . . . . . . . . . . .1.4.2 Continuous Time . . . . . . . . . . . . . . . .1.4.3 Solving the Model . . . . . . . . . . . . . . .1.5 The optimum quantity of money . . . . . . . . . . .1.5.1 The Quantity Theory of Money . . . . . . . .1.6 Seigniorage, Hyperinflation and the Cost of Inflation1.7 Problems . . . . . . . . . . . . . . . . . . . . . . . .1222344671013141416212 Nominal Rigidities and Economic Fluctuations2.1 Old Keynesian Economics: The Neoclassical Synthesis .2.1.1 Open Economy . . . . . . . . . . . . . . . . . . .2.1.2 Aggregate Supply . . . . . . . . . . . . . . . . .2.2 Disequilibrium Economics . . . . . . . . . . . . . . . . .2.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . .2.2.2 The Walrasian Benchmark Case . . . . . . . . .2.2.3 Exogenously Fixed Price . . . . . . . . . . . . . .2.2.4 Exogenously Fixed Nominal Wage . . . . . . . .2.2.5 Both prices and wages inflexible . . . . . . . . .2.2.6 Analysis of this model . . . . . . . . . . . . . . .2.3 Imperfect Information Models . . . . . . . . . . . . . . .2.4 New Keynesian Models . . . . . . . . . . . . . . . . . . .2.4.1 Contracting Models . . . . . . . . . . . . . . . .2.4.2 Predetermined Wages . . . . . . . . . . . . . . .2.4.3 Fixed Wages . . . . . . . . . . . . . . . . . . . .2.5 Imperfect Competition and New Keynesian Economics .2.5.1 Macroeconomic Effects of Imperfect i.

ivCONTENTS2.62.72.5.2 Imperfect competition and costs of changing prices2.5.3 Dynamic Models . . . . . . . . . . . . . . . . . . .Evidence and New Directions . . . . . . . . . . . . . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .515657583 Macroeconomic Policy3.1 Rules v. Discretion . . . . . . . . . . . . . . . . . . . . . . . . . .3.1.1 The Traditional Case For Rules . . . . . . . . . . . . . . .3.2 The Modern Case For Rules: Time Consistency . . . . . . . . . .3.2.1 Fischer’s Model of the Benevolent, Dissembling Government3.2.2 Monetary Policy and Time Inconsistency . . . . . . . . .3.2.3 Reputation . . . . . . . . . . . . . . . . . . . . . . . . . .3.3 The Lucas Critique . . . . . . . . . . . . . . . . . . . . . . . . . .3.4 Monetarist Arithmetic: Links Between Monetary and Fiscal Policy3.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .656666686973757779804 Investment874.1 The Classical Approach . . . . . . . . . . . . . . . . . . . . . . . 874.2 Adjustment Costs and Investment: q Theory . . . . . . . . . . . 884.2.1 The Housing Market: After Mankiw and Weil and Poterba 914.3 Credit Rationing . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.4 Investment and Financial Markets . . . . . . . . . . . . . . . . . 954.4.1 The Effects of Changing Cashflow . . . . . . . . . . . . . 984.4.2 The Modigliani-Miller Theorem . . . . . . . . . . . . . . . 994.5 Banking Issues: Bank Runs, Deposit Insurance and Moral Hazard 1004.6 Investment Under Uncertainty and Irreversible Investment . . . . 1034.6.1 Investment Under Uncertainty . . . . . . . . . . . . . . . 1074.7 Problems: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105 Unemployment and Coordination Failure5.1 Efficiency wages, or why the real wage is too high . . . . .5.1.1 Solow model . . . . . . . . . . . . . . . . . . . . .5.1.2 The Shapiro-Stiglitz shirking model . . . . . . . .5.1.3 Other models of wage rigidity . . . . . . . . . . . .5.2 Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2 Steady State Equilibrium . . . . . . . . . . . . . .5.3 Coordination Failure and Aggregate Demand Externalities5.3.1 Model set-up . . . . . . . . . . . . . . . . . . . . .5.3.2 Assumptions . . . . . . . . . . . . . . . . . . . . .5.3.3 Definitions . . . . . . . . . . . . . . . . . . . . . .5.3.4 Propositions . . . . . . . . . . . . . . . . . . . . .5.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .Continuous-Time Dynamic 26127131

CONTENTSStochastic Calculusv133IntroductionCourse Mechanics Requirements: Two exams, each 50% of grade, each covers half of materialin class. First exam: on Tuesday, March 12th. Second and final exam: onTuesday, April 30th. Problem sets: will be several, which will be handed in and corrected, butnot graded. Good way to learn macro, good practice for exams and core. On the reading list: It is very ambitious. We may well not cover everything. That is fine, as not everything is essential. I may cut material as Igo along, and will try to give you fair warning when that happens. The lectures will very closely follow my lecture notes. There are twoother general textbooks available: Romer, which should be familiar andBlanchard and Fischer. The latter is harder but covers more material.The lecture notes combine the approaches of and adapt materials in bothbooks. References in the notes refer to articles given on the reading list. Withfew exceptions, the articles are also summarized in Romer or Blanchardand Fischer. It is thus not necessary to read all or even most of the articles on the list. Since articles are the primary means through whicheconomists communicate, you should read at least one. Some of the articles are in the two recommended volumes by Mankiw and Romer, NewKeynesian Economics, both of which will eventually be in the bookstore.Just about all articles prior to 1989 are available via the internet at thesite www.jstor.org, provided one connects through a computer connectedto Brown’s network. I would ask that everyone not individually print outevery article, since that would take a lot of paper, energy and computingpower. Students considering macroeconomics as a field are strongly encouragedto attend the Macroeconomics Workshop, on Wednesdays from 4:00-5:30in Robinson 301.MotivationConsider the handout labeled “The First Measured Century.” It presents graphsfor the U.S. of the three most important macroeconomic statistics, output, unemployment and inflation, since 1900. Essentially, Ec 207 tried to explain whythe graph of real GDP sloped upwards. It also tried to explain why there werefluctuations around the trend, via real business cycle theory, but was much less

viCONTENTSsuccessful. This course will explain the trend in and growth rates of inflationand unemployment, and fluctuations in real GDP. It will also explain why thesevariables move together- that is, unemployment tends to be low when outputgrowth is high, and inflation is often (but not always) low when output growthis low.[Omitted in Spring 2002: An important distinction that I have made implicitly above is the separation of variables into a trend component and a cyclicalcomponent. The trend component can be thought of informally as the long-runaverage behavior of the variable, and the cyclical component deviations fromthat trend. For inflation and unemployment, the trend components appear tobe horizontal lines (with possible shifts in the level of the line for both overtime). When one assumes that a model like the Solow growth model explainsthe long-run growth rate of output, but not the short run, one is already doingsuch a division. There has been a debate in recent years over whether it isappropriate to do such a division; some claim that variables like output, ratherthan having a deterministic trend, as is claimed in the Solow model (where thetrend component, in log terms, is just proportional to time), instead have astochastic trend. Algebraically, the two cases are:yt α βt ²t(1)for the deterministic trend case, andyt β yt 1 ²t(2)in the stochastic trend case (a random walk with drift).1 yt ln(GDP ) measured at time t. In the first case, βt is the trend component or GDP and ²tis the deviation around the trend. Changes in ²t cause temporary variationsin GDP, but do not affect the long-run level of yt , which is only determinedby α βt, trend growth. In contrast, in the second specification changes in ²tpermanently affect the level of yt .In the stochastic-trend case, it may be more appropriate in some instances tostudy the long-run and the short-run together. This was one of the motivationsof the RBC literature. For the purposes of this course, I am going to sidestepthis debate, partly because it requires some heavy-duty econometrics to fullyunderstand, but primarily because many macroeconomists have concluded thateven if output does have a stochastic trend, analyzes assuming it has a deterministic trend will give many of the right answers. This is because computing yt yt yt 1 gives the same answer in both cases, so that any finite-sampletime series with average growth rate of β can be represented by both processes.For more information, see the first chapter of Blanchard and Fischer.]We will cover the following topics in this course: Money and Prices: In Ec 207, although you may have occasionally referredto variables denominated in dollars, the fact that transactions required a1 This is a special case of what is known as a unit root process. See any time series textbookfor further discussion.

CONTENTSviimedium of exchange wasn’t mentioned, and played no role in any of theanalyses you went through. This section will define what money is (whichturns out to be less obvious a question than one might immediately think),describe theories of money demand, and describe the long-run behavior ofmoney and the price level. Nominal Rigidities and Economic Fluctuations. The previous section wasmerely a prelude to this section, in a way. In the RBC section of 207,you saw some explanations for why output and unemployment fluctuatedaround their trend values (loosely speaking): variations in technology andin tastes for leisure. In this section of the course you will see other explanations. They all center around the notion that prices and wages maybe inflexible, and thus do not move rapidly enough to clear the marketsfor goods or labor. This is an idea which dates back to the foundations ofmacroeconomics, with the writings of Keynes. Over the years, in responseto problems fitting the model to empirical data and theoretical challenges,people have made Keynes’ thinking more mathematically precise. Manyof the same conclusions remain. This section will essentially present thesemodels as they developed historically. Along the way, we will need tothink about how firms set prices and wages and about the macroeconomicimplications of imperfect competition. Macroeconomic Policy: Given an understanding of what causes economicfluctuations, here we consider what policy can and should do about them.We focus on whether policy should consist of adherence to (simple, butpossibly contingent) rules or should be permitted to vary at the policymaker’s discretion. Investment: Investment is the most volatile components of real GDP, andis an important part to any serious theory of business cycles, as well asgrowth. We will consider various theories of investment and also howimperfections in financial markets may affect real economic outcomes Unemployment and Coordination Failure: We will conclude with a consideration of several important kinds of macroeconomic models. We firstconsider several reasons why the labor market fails to clear fully. We willthen think about models in which agents are searching for something- ajob, the best price, etc. These turn out to be important for determiningthe average rate of unemployment. Next, we turn to models involving coordination failure- that is, models in which all individuals would be betteroff if they were allowed to coordinate among themselves. These modelsare important for some theories of economic fluctuations.

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Chapter 1Money and PricesIn Ec 207, there was scant reference to the fact that transactions needed amedium of exchange to be carried out. The only references to money camein the few cases where you were presented economic data denominated in somecurrency. In this part of the course, we will see why it may have been acceptableto ignore money, and look at the long-run relationship between money andprices.For some of this section, with an important exception, real output will beexogenous with respect to money- that is, changes in the supply of money haveno effect on the level of real GDP (which is determined, for example, by theneoclassical growth model). Later in the course, you will see models in whichchanges in the nominal stock of money have real effects. Economists who believesuch models are sometimes referred to as K