Monetary Policy in a Sto chastic Equilibrium Mo del with Real and Nominal Rigidities Jinill Kim First draft: July 1995 This draft: March 25, 1996 Abstract A dynamic sto chastic general-equilibrium (DSGE) mo del with real and nominal rigidities succeeds in capturing some key nominal features of U.S. business cycles. Monetary p olicy is sp eci ed following the developments in the structural vector autoregression (VAR) literature. Four sho cks, including b oth technology and monetary p olicy sho cks, a ect the economy. Interaction between real and nominal rigidities is essential to repro duce the liquidity e ect of monetary p olicy. The mo del is estimated by maximum likeliho o d on U.S. data. The mo del's t is as go o d as that of an unrestricted rst-order VAR and that the estimated mo del pro duces reasonable impulse resp onses and second moments. An increase of interest rates predicts a decrease of output two to six quarters in the future. This feature of U.S. business cycles has never b een captured by previous research with DSGE mo dels. Lastly, the p olicy implications are discussed. Dept. of Economics, Yale University,Box 208268 Yale Station, New Haven, CT 06520-8268. E-mail: [email protected]. Sp ecial thanks are due to Christopher Sims for his guidance and supp ort. Imp ortant discussions with William Brainard, Giancarlo Corsetti, Jordi Gali, Federico Galizia, Mark Gertler, Rob ert Shiller and T. N. Srinivasan are gratefully acknowledged. I also thank the participants in job market seminars at the Board of Governors of the Federal Reserve System, Federal Reserve Banks of New York and Richmond, the University of Cambridge, Univer- sitat Pomp eu Fabra, SUNY at Stony Bro ok, Washington UniversityinSt. Louis, and the Wharton Scho ol. 1 Contents 1 Intro duction 3 2 The Mo del 8 2.1 The Aggregator : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.2 Households : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2.2.1 Preferences : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2.2.2 Real Rigidities via Capital Adjustment Costs : : : : : : : : : 12 2.2.3 Wage Rigidities via Wage Adjustment Costs : : : : : : : : : : 13 2.2.4 Budget Constraints and First Order Conditions : : : : : : : : 13 2.3 Firms : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 2.3.1 Technology : : : : : : : : : : : : : : : : : : : : : : : : : : : : 16 2.3.2 Price Rigidities via Price Adjustment Costs : : : : : : : : : : 17 2.3.3 Value of Firms and First Order Conditions : : : : : : : : : : : 18 2.4 The Government : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 20 2.5 The Equilibrium : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 22 3 E ects of Monetary Policy 26 3.1 Impulse Resp onses : : : : : : : : : : : : : : : : : : : : : : : : : : : : 26 3.2 Estimation Pro cedure : : : : : : : : : : : : : : : : : : : : : : : : : : : 29 3.3 Estimation Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : 31 3.4 Assessing the Fit : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 35 3.5 Variance Decomp ositions : : : : : : : : : : : : : : : : : : : : : : : : : 39 3.6 Cyclical Implications : : : : : : : : : : : : : : : : : : : : : : : : : : : 42 3.7 Policy Exp eriments : : : : : : : : : : : : : : : : : : : : : : : : : : : : 43 4 Conclusion 46 A App endix 48 A.1 The Data : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 48 A.2 Derivatives and Elasticities : : : : : : : : : : : : : : : : : : : : : : : : 48 A.3 The Equilibrium : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 49 A.4 Steady State : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 50 A.5 Log-linearization : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 51 2 1 Intro duction The comovement of monetary and real aggregates and the inverse relation b etween the movements of money growth and nominal interest rates are two prominent nom- 1 inal features of business cycles in the United States and many other countries. The strong and stable covariation of monetary aggregates and aggregate output has prompted several economists to fo cus on monetary instability as a cause of the Great Depression of the 1930s. The negative correlation of money growth and nominal in- terest rates is also one of the stylized facts in monetary economics. In this pap er, we will try to explain these features through the two channels of monetary p olicy: 2 the output e ect and the liquidity e ect. The output e ect, de ned here as the p ositive resp onse of aggregate output to expansionary monetary p olicy, has b een a key question for economists who have 3 searched for a purely monetary explanation of the business cycle. Explaining the strong relationship b etween money and real activity in a general equilibrium theory faces two challenges. The rst is to provide a theory in which money is valued in 4 equilibrium. The second and more dicult one is to showhow monetary p olicy has real e ects in a world where economic agents are b ehaving rationally without simply asserting some ad hoc form of money illusion. In this pap er, the nonneutrality of money stems from menu costs. The liquidity e ect, de ned as the decrease in interest rates in resp onse to mon- 5 etary expansion, has b een an imp ortant issue in empirical macro economics. Re- cently, pursuing alternative assumptions for identifying monetary p olicy sho cks, re- searchers provide strong empirical evidence in supp ort of the liquidity e ect. They argue that innovations in monetary aggregates re ect sho cks to money demand rather than to money supply, or p olicy. This pap er intro duces this recent develop- 1 Even if the rst feature is universally accepted, the presence of the second feature is somewhat controversial. It dep ends on the choice of monetary aggregates and trending mechanisms. See Chari, Christiano and Eichenbaum (1995) as an example. Co oley and Hansen (1995) summarize additional stylized facts of the nominal features. 2 In a static IS-LM framework, an increase in money supply moves interest rates down to induce larger money demand. The decrease of interest rates moves investment and output up. Interpreting the two features as the e ects of monetary p olicy is, of course, not unanimous. Plosser (1990), following King and Plosser (1984), interprets the two features as a consequence of endogenous inside money. 3 Friedman and Schwartz (1963) do cumented a strong asso ciation between p erio ds of severe economic decline and sharp declines in the sto ck of money. 4 Three frameworks have b een develop ed: money in the utility function, transaction cost tech- nology, and cash-in-advance constraints. 5 This de nition of the liquidity e ect as a causal relation is, of course, not universal. For example, Ohanian and Sto ckman (1995) use the term to refer to the statistical correlation. 3 mentinto a general equilibrium mo deling. Stimulated by Kydland and Prescott (1982) and Long and Plosser (1983), dy- namic sto chastic general-equilibrium (DSGE) mo dels have b ecome a useful to ol for 6 macro economic analysis, esp ecially for business cycle analysis. Previous work using a exible-price, comp etitive DSGE mo del has provided a reasonable description of the data on real variables. Recently, the prototyp e DSGE mo dels have b een en- riched by the intro duction of non-newclassical features and sources of uctuations other than technology sho cks. Furthermore, many recent mo dels are characterized by sub optimal equilibria, which generally provide a rationale for activegovernment intervention. One stream of recentwork incorp orates outside money in a exible-price comp et- 7 itive DSGE mo del. Money is intro duced in a cash-in-advance economy by Co oley and Hansen (1989) to study the e ects of in ation. Sims (1989, 1994) intro duces 8 money through a transaction-cost framework. Using a simple money-in-the-utility- function mo del, Benassy (1995) shows analytically that the dynamics of the real variables are exactly the same as those in the mo del without money. Such mo dels do not provide a good description of the money-output correlation and cannot re- pro duce reasonable impulse resp onses to the sho cks in monetary p olicy, b ecause of the following generic implication. If money growth displays a p ositive p ersistence, then sho cks to the growth rate of money drive output down and nominal interest rate up through an anticipated in ation e ect. To generate the output e ect, nominal rigidities are intro duced into DSGE 9 mo dels. There are two alternative ways of intro ducing nominal rigidities. The 6 DSGE mo dels broadly refer to real business cycle (RBC) mo dels, equilibrium business cycle mo dels, and neo classical growth mo dels. They are regarded as a paradigm for macro analysis. Prescott (1986) compares a DSGE mo del to the supply and demand construct of micro economics. 7 Despite the e ort to analyze monetary phenomenon to b e describ ed b elow, DSGE mo deling has not b een used so frequently to analyze the e ects of monetary p olicy. Friedman (1995) categorize the empirical metho dologies for monetary p olicy into three: partial equilibrium structural mo dels, VARs based on observed prices and quantities, and VARs based incorp orating non-quantitative information. DSGE mo deling is not included. 8 The two pap ers fo cus on rather di erent p oints. Sims (1989) shows by simulation that a purely classical equilibrium mo del with monetary p olicy misses certain asp ects of the actual b ehavior of the data. Meanwhile, Sims (1994)