Monetary Policy and Real Interest Rates

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1 Monetary Policy and Real Interest Rates

2 A Simple New Keynesian Model The basic New Keynesian model with Calvo (sticky) price setting simplifies to a system of three equations: 1. The New Keynesian Phillips curve relating inflation to the output gap 2. A "Dynamic IS Equation" linking the evolution of aggregate demand (and the output gap) to the nominal interest rate 3. A monetary-policy rule for setting the nominal interest rate (or, a money-supply rule plus a money-demand specification) These equations determine the nominal and real interest rate, inflation, and the output gap

3 A Simple New Keynesian Model: The New Keynesian Phillips curve The New Keynesian Phillips curve (NKPC) relates current inflation to expected future inflation and the output gap.

4 A Simple New Keynesian Model: The Dynamic IS curve Define the natural real interest rate r tn as the real rate in the flexible-price equilibrium. This interest rate is purely a function of real factors, i.e. productivity, preferences, etc., all of which is beyond the influence of the monetary authority. This Dynamic IS equation relates the current output gap to (expected) future output gaps and the deviation of the current real interest rate from it s natural value.

5 A Simple New Keynesian Model: The Policy Rule We can close the model by specifying an interest-rate rule for monetary policy. The Taylor-rule equation results in a model in which the price level satisfies determinacy when the Taylor principle is applied, i.e. Φ π > 1 and Φ y.

6 A Simple New Keynesian Model Output stabilization policy in the NK model depends on the ability of the central bank to manipulate the real interest rate. This is accomplished, theoretically, by targeting the nominal interest rate at a level that combined with the slow adjustment of inflation results in the desired real interest rate effect. But targeting of the nominal interest rate is achieved through open market operations that will impact the supply of reserves in the banking system and ultimately the broader monetary aggregates, i.e. a liquidity effect.

7 Theoretical Literature: Kydland and Prescott (1982), Econometrica Long and Plosser (1982), JPE Cooley and Hansen (1989), AER Fuerst (1992), JME Christiano and Eichenbaum (1992), AER Cook (1999), JME Edge (2), BOG Federal Reserve Real Economy Monetary Economy- No Liquidity Effect Monetary Models that Generate Liquidity Effects

8 Empirical Literature: Cagan and Gandolfi (1969), AER Melvin (1983), Economic Inquiry Reichenstein (1987), Economic Inquiry Leeper and Gordon (1992), JME Gali (1992), QJE Lastrapes and Selgin (1995), JMacro Strongin (1995), JME Christiano and Eichenbaum (1997), REStat Pagan and Robertson (1998), REStat Finds Liquidity Effects Liquidity Effects Vanish in Late 197s Find Liquidity Effects in a Structural VAR Find Liquidity Effect using Non-Borrowed Reserves as Policy Instrument Finds that Structural VAR Evidence is Weak

9 Long-Run Neutrality and Superneutrality: Lucas (198), AER Geweke (1986), Econometrica Mishkin (1992), JME Crowder and Hoffman (1996), JMCB Crowder (1998), Economic Inquiry King and Watson (1997), FRB Richmond Econ Quarterly Koustas and Serletis (1999), JME Fisher and Seater (1993), AER Find Evidence in Favor of the LRN and/or LRSN Hypothesis Find Evidence Against LRN and/or LRSN Derive Necessary and Sufficient Conditions for LRN and LRSN

10 Liquidity Effect in IS-LM Model i LM LM * i i 1 IS(π) Y Y 1 Y

11 Fisher Effect in IS-LM Model i LM LM * i 2 i i 1 IS(π * ) IS(π) Y Y 1 Y 2 Y

12 Importance of the Orders of Integration of Germane Variables: Fisher and Seater (1993) show that LRN and LRSN can only be tested when variables are integrated. Crowder (1998) finds evidence that monetary base growth and inflation are I(1) and CI(1,1) consistent with LRN. Crowder and Hoffman (1996) find evidence that inflation and nominal interest rates are I(1) and CI(1,1) consistent with LRSN. Granger and Newbold (1977) and Phillips (1986) discuss spurious regression. Phillips (1987) shows that inference in non-standard in regressions with integrated variables.

13 Overview of my results: Using data for five developed economies we find: 1. The data are well characterized by unit root processes which satisfy the cointegration restrictions implied by the Fisher equation and long-run money super-neutrality (LRSN). 2. The impulse responses from the structural model are consistent with a strong and persistent liquidity effect for all economies considered.

14 Econometric Model The structural dynamic model is given by, is 3x1 vector of endogenous variables, is a matrix polynomial in the lag operator and is an innovation sequence. (1) The unrestricted reduced form VAR is given by, (2) where is related to the structural coefficient matrix lag polynomial by such that is the 3x3 identity matrix. The reduced form errors and structural innovations are similarly related, i.e..

15 One final relationship is derived by adopting the conventional assumption that the variances of the three structural innovations are equal to unity. Thus or equivalently. In general has p 2 elements but the relationships between the (directly estimable) reduced form parameters and those of the structural model imply only different pieces of information (remember that a covariance matrix is symmetric). That leaves more restrictions that must be imposed on the reduced form model to id the structural model. Q- Where do these restrictions come from? A- Economic theory.

16 If the variables are cointegrated then use the ECM in equation (3), where and. (3) The ECM implies extra restrictions on the model parameters that help to id. Once structural model has been identified, i.e. we can get an estimate of, we can use this estimate to calculate impulse response functions from the moving average (MA) representation of the model.

17 The MA form is arrived at by inverting (1) to yield, (4) where or. Empirical Results Data from five economies, the U.S., the U.K., Canada, Japan and the E.U. For each, we use an aggregate measure of money, i.e. base, M1, M2, etc., a measure of the price level, i.e. CPI, GDP deflator, etc., and a short-term market interest rate, such that where money growth and inflation are the annualized monthly changes in the log-levels.

18 Figure 1 Canada Money Growth 1973 to Inflation 1973 to Interest Rate 1973 to

19 Figure 2 E.U. 8 Money Growth 1973 to Inflation 1973 to Interest Rate 1973 to

20 Figure 3 Japan 12 Money Growth 1973 to Inflation 1973 to Interest Rate 1973 to

21 Figure 4 United Kingdom Money Growth 1973 to Inflation 1973 to Nominal Interest Rate 1973 to

22 Figure 5 U.S. 3 Money Growth 1973 to Inflation 1973 to Interest Rate 1973 to

23 Table 1: Horvath-Watson Test for Known Cointegration Country VAR lag LR Test Canada E.U Japan U.K U.S % C.V The optimal VAR lag was determined by minimizing the Schwarz-Bayesian information criterion. 5% critical values come from table 1 Case 3 of Horvath and Watson (1995). The LR Test statistic is distributed as a.

24 Figure 6 Canada 1 Response of Monetary Base Growth Rate 7 Response of Monetary Base Growth Rate 4 Response of Monetary Base Growth Rate

25 Figure 7 European Union Response of Monetary Base Growth Rate Response of Monetary Base Growth Rate Response of Monetary Base Growth Rate

26 Figure 8 Japan Response of Monetary Base Growth Rate Response of Monetary Base Growth Rate Response of Monetary Base Growth Rate

27 Figure 9 United Kingdom Response of Money Growth Permanent Money Growth Shock Response of Money Growth Money Supply Shock Response of Money Growth Money Demand Shock Permanent Money Growth Shock Money Supply Shock Money Demand Shock Permanent Money Growth Shock.5 Money Supply Shock 5 Money Demand Shock Permanent Money Growth Shock Money Supply Shock Money Demand Shock

28 Figure 1 United States Response of Monetary Base Growth Rate Response of Monetary Base Growth Rate Response of Monetary Base Growth Rate

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