Working Paper Series Department of Economics Alfred Lerner College of Business & Economics University of Delaware Working Paper No. 2003-09 Do Fixed Exchange Rates Fetter Monetary Policy? A Credit View Burton A. Abrams and Russell F. Settle October 2003 http://www.be.udel.edu/economics/workingpaper.htm c 2003 by author(s). All rights reserved.
Do Fixed Exchange Rates Fetter Monetary Policy? A Credit View Burton A. Abrams And Russell F. Settle Department of Economics University of Delaware Newark, DE. 19716 October, 2003 Submitted to the AER on 10/14/03 File name: credit_model
Abstract Do Fixed Exchange Rates Fetter Monetary Policy? A Credit View The Bernanke-Blinder credit-view model is expanded to encompass a small, open economy with fixed exchange rates. In contrast to conventional wisdom and traditional models, monetary policy is resurrected as a stabilization tool. Further, various financial sector shocks are shown to have real aggregate demand effects. We show that independent monetary policy actions can have substantive impacts on aggregate demand despite perfect capital mobility and adherence to a fixed exchange rate regime. (JEL: E51 (Money Supply; Credit; Money Multipliers); F41 (Open Economy Macroeconomics)) 2
The problem [with fixed exchange rates or exchange-rate targeting] is that with capital mobility the targeting country no longer can pursue its own independent monetary policy and so loses its ability to use monetary policy to respond to domestic shocks that are independent of those hitting the anchor country. Frederic S. Mishkin 1 Introduction. The quote above reflects the widely accepted proposition in economics that monetary authorities in small open economies cannot engage in independent monetary policy actions while simultaneously adhering to a fixed exchange rate regime. Fixed exchange rates, such as found under a gold standard or exchange-rate targeting, impede the ability of the monetary authorities to stabilize the macro economy. 2 Expansionary monetary policy actions, for example, produce balance of payments deficits that require equal and offsetting contractionary monetary policy actions in order to maintain the fixed exchange rate. This proposition is perhaps most clearly illustrated in the standard Mundell-Fleming model. The elimination of monetary policy as a stabilization tool under fixed exchange rates is a primary factor leading many economists to support flexible exchange rate regimes. Support for this view comes from the improved economic performance of those countries that abandoned the gold standard during the Great Depression and were thus able to engage in independent monetary stabilization actions. 3 In this paper we combine the Mundell-Fleming model with a credit channel model developed by Bernanke and Blinder (1988) to show that monetary policy is not entirely fettered under a fixed exchange rate regime. Monetary policy is potent in our model, although in a limited way: only one of the traditional monetary policy tools is effective. In the next section, the models and the relevant comparative static findings are discussed. 3
We then present some model simulations and implications for countries on fixed exchange rate regimes. The Model. The traditional Mundell-Fleming model with fixed exchange rates, in its simplest version, assumes no wealth (or Pigou) effect and perfect capital mobility that fixes the interest rate on bonds, i, at i*, the world interest rate. The model can be written: E(y, i*) = y (1) L(y, i*) = m x B (2) Equation (1) represents the goods market equilibrium (the traditional IS curve). The demand for goods, E, depends on real output (income), y, and the interest rate, i. Equation (2) is the money market equilibrium (the traditional LM curve). The demand for money, L, depends on y and i. The right-hand side of equation (2) is the money supply, expressed as the product of the money multiplier, m, and the monetary base, B. In accordance with Walras Law, a third equation for the bond market is dropped from the model. Following standard assumptions, the money multiplier is a function of banks required reserve ratio, r, their excess reserve ratio, e, and the non-bank public s currency to deposit ratio, c: m = m(r,e,c), where m r, m e, m c < 0. For simplicity, we assume that all three variables affecting the money multiplier are exogenous. This assumption is reasonable given that the interest 4
rate, the primary determinant of the multiplier in most money supply models, is exogenous. The two endogenous variables in the model are B and y. In this model, with i fixed at i*, y is determined in the goods market, so monetary policy tools working through equation (2) cannot affect real income. As B is endogenously determined by the parameters and exogenous variables in the model, the policy tools that might seemingly affect it--open market operations and the discount rate-- are impotent. Moreover, changes in the required reserve ratio that affect the money multiplier produce offsetting movements in B and have no impact on the money supply or on real output, y. Following Bernanke and Blinder s (1988) credit-view model for a closed economy, we add bank loans to this model, treating them and bonds as imperfect substitutes. We modify equation (1) and add equation (3): E(y, i*, ρ, α ) = y (1') L(y, i*, ρ ) = λ (i*, ρ, β ) x (m - 1) x B (3) Equation (1') alters the traditional goods market equation by incorporating the interest rate on bank loans, ρ, as a determinant of the demand for goods. The variable α is an autonomous shock variable. Equation (3) is the equilibrium equation for bank loans. The demand function for bank loans is L. It depends on y, i, and ρ. The right-hand side of (3) represents bank loan supply, which depends on bank credit, (m 1) x B, and the share of bank credit allocated to bank loans (as opposed to bonds), λ. The variable β is an autonomous shock variable. The bank credit multiplier, m 1, is easily derived from 5
the bank balance sheet. 4 The revised model consists of equations (1'), (2) and (3). The variables y, ρ and B are endogenous. We assume the usual signs for the partial derivatives. In addition, following Bernanke and Blinder (1988), E ρ <0, L y >0, L ρ <0, λ ρ >0. It is obvious that policies that affect the monetary base cannot alter y, assuming other exogenous variables unchanged. As in the traditional Mundell-Fleming model, an open-market purchase or a reduction in the discount rate that leads to a rise in B cannot be maintained under the fixed-exchange rate regime and necessitates an equal and opposite change in B in order to return the model to equilibrium at the original exchange rate. Thus, open market operations and discount rate changes that attempt to alter the monetary base are impotent tools. In contrast, no such impotence befalls the reserve requirement, r. Taking the total derivatives of equations (1'), (2) and (3) and applying Cramer s Rule to compute the change in y arising from an autonomous change in m (such as that caused by a change in r), we obtain: 5 dy/dm = - ( λ E ρ B)/D > 0 (6) where, D = - E ρ m L y + (L ρ (m-1)bλ ρ )(m )(E y 1) + λ (m 1)L y E ρ > 0 (7) 6
Dynamic stability conditions require a positive sign on D (see the Appendix for details). In this modified model, an autonomous increase in the money multiplier produces an increase in aggregate demand. For example, a decrease in reserve requirements (causing an autonomous increase in the multiplier) leads to a increase in bank loans, a lower equilibrium bank loan rate, ρ, and a higher aggregate demand, y. Inspection of equation (2) reveals that the higher y (and, consequently, higher money demand) must yield a higher money supply in the new equilibrium. In contrast to the standard Mundell- Fleming model, the induced change in the endogenous monetary base fails to fully offset the change in the money multiplier. The reason that the change in the multiplier is no longer neutral in this credit view model centers on the differential effect of the multiplier change on the money supply and on bank loans. A change in the monetary base alone cannot bring the money and loan markets both back into equilibrium simultaneously. Hence, changes in the other endogenous variables are needed to reestablish overall equilibrium. Figure 1 presents graphically the effect of an increase in the money multiplier on y and ρ. We solve equation (2) for B and insert this function into equation (3). The model is now reduced to two equations and two unknowns, y and ρ. The endogenous variable B is suppressed and determined at the intersection of the remaining two functions. The modified equation (3) (and curve in Figure 1) is labeled FA, denoting the overall "financial asset market." At every point on the FA curve the money and loan markets clear. An increase in the money multiplier for instance, from a reduction in reserve requirements--shifts the FA curve downward and to the right causing the 7
equilibrium y to rise and ρ to fall, as the equilibrium moves from intersection 1 to intersection 2 in the figure. ρ, FA 1 FA' 2 IS y Figure 1. Effect of an increase in the money multiplier Table 1 reports how various shocks affect income, the rate on bank loans, the monetary base and the money supply. Among other results, the comparative static analysis reveals that an autonomous rise in λ, the percentage of bank assets held in loans, increases equilibrium y. This result is consistent with the findings from the Bernanke-Blinder closed-economy model. 6 The next section provides simulation estimates for the impact of a change in the reserve requirement on aggregate demand. 8
Table 1. Effects of Shocks on Endogenous Variables Income Loan rate Monetary base Money supply Exogenous (y) ( ρ ) (B) (mb) change in: Money multiplier + -? + (m) Loan ratio + - + + ( β ) Goods demand + + + + (α ) Simulations. Our foregoing analysis of the credit-view model indicates that changes in reserve requirements affect aggregate demand, even in a setting with fixed exchange rates. However, without empirical evidence we cannot say whether the connection between bank reserve requirements and aggregate demand is economically significant. In an effort to shed some light on this issue, we assume a set of plausible values for the variables and parameters in equation (6). For this simple illustration, we selected values that seem roughly representative of the current American economy. The results, and further discussion of our assumptions, are contained in Table 2. The baseline values assumed for the components of equation (6) suggest the following: a 50 percent reduction in reserve requirements (e.g., from 10 percent to 5 percent of bank deposits), would increase real aggregate demand by 1.7%, an impact sufficiently large to help reverse even severe recessionary forces. 9
Table 2 also shows the results of some simple sensitivity analyses. The suggestion is that the strength of the connection between reserve requirements and aggregate demand does not depend critically on any one parameter or variable value. While variations in the assumed values for the components of equation (6) produce noticeable changes in the estimated impact of reserve requirement changes, they do not produce wild swings in those estimates. Concluding Remarks. The open-economy credit-view model with fixed exchange rates provides various predictions that deviate substantially from the predictions of the traditional Mundell- Fleming model. First, consistent with the Bernanke-Blinder closed-economy model, autonomous bank portfolio shifts between bonds and loans affect aggregate demand and are a potential source of instability in the economy. Second, autonomous changes in the money multiplier cause changes in real aggregate demand. According to the model, monetary policy can affect aggregate demand, but only through changes in the reserve requirement. Autonomous changes in the other determinants of the money multiplier also produce changes in real aggregate demand. This result suggests, for example, that a country adhering to a fixed-exchange rate regime and experiencing an increase in its currency-to-deposit ratio would encounter an adverse demand shock despite equilibrating increases in the monetary base. Thus, our analysis reveals a previously unidentified determinant of aggregate demand for small, open economies and suggests a new area for empirical research. 10
Table 2 Effect of Reserve Requirement Changes on Real Income: Simulation Results Parameter or Variable Predicted Percentage Change in Real Income from a 50 Percent Reduction in Reserve Requirements All equal to baseline values a 1.7%? (0.4) 0.2 0.7% 0.6 3.4% m (7) 6 2.3% 8 1.3% E y (0.6) 0.5 1.3% 0.7 2.4% e mr (-0.2) -0.1 0.8% -0.3 2.5% e E? (-0.2) -0.1 0.8% -0.3 2.8% e?? (0.5) 0.25 2.9% 0.75 1.2% e Ly (0.5) 0.25 1.3% 0.75 2.3% ely (0.3) 0.15 2.0% 0.45 1.5% el? (-0.2) -0.1 2.0% -0.3 1.4% 11
Table 2 (continued) a The baseline values are indicated in parentheses, next to the parameter/variable symbol. The predicted impacts on real income in this table are based upon estimates of dy/dr, and its corresponding elasticity (? yr ). In calculating this elasticity (and others using y), we assumed that y (= E) = $10 trillion and r = 0.1. In computing dy/dr, we relied up the values for?, m, and E y (the marginal propensity to consume out of income) shown in the table. In addition, quantification of dy/dr requires values for several other partial derivatives. These we developed by assuming plausible values for the corresponding elasticities (shown in the above table). We also assumed values for the levels of the following variables: ρ = 0.05; B = $650 billion; L = 4.6 trillion; L = 2.4 trillion. 12
References Bernanke, Ben S. Nonmonetary Effects of the Financial Crisis in the Propagation of the Great Depression, American Economic Review, June 1983, 73, 257-76. Bernanke, Ben S. and Blinder, Alan S., Credit, Money, and Aggregate Demand, American Economic Review, May 1988, 78, 435-39. Brunner, Karl and Meltzer, Allan H., Liquidity Traps for Money, Bank Credit and Interest Rates, Journal of Political Economy, 1968, 76(1), 1-37. Eichengreen, Barry. Golden Fetters: The Gold Standard and the Great Depression, 1919-1939 (New York: Oxford University Press, 1992).. Still Fettered After All These Years, NBER Working Paper No. 9276, October 2002. Mishkin, Frederic S. The Economics of Money, Banking and Financial Markets (7 th edition), (Boston: Pearson, Addison Wesley, 2004). 13
APPENDIX Let α and β be autonomous shift parameters. The model is: E(y, i*, ρ,α ) = y (1) L(y, i*) = mb (2) L(y, i*, ρ ) = λ (i*, ρ, β ) (m 1) B (3) Proof that dy/dm > 0 Total differentiation of the model and arranging exogenous variables on the right-hand side yields: (E y 1)dy + E ρ d ρ = - E α dα (1') L y dy mdb = Bdm (2') L y dy + (L ρ - (m-1)bλ ρ ) d ρ - λ (m-1)db = λ Bdm + (m-1)bλ β d β (3') The denominator for Cramer s Rule is: E y 1 E ρ 0 L y 0 -m L y L ρ - (m-1)b λ ρ - λ (m-1) 14
Or, D = E ρ (-m) L y + (L ρ - (m-1)b λ ρ )m(e y 1) + λ (m-1) L y E ρ The sign for D is ambiguous as the first two terms are positive while the last term is negative. Dynamic stability, however, requires that D > 0 (shown below). The matrix numerator for dy/dm is: 0 E ρ 0 B 0 -m λ B L ρ - (m-1)b λ ρ -λ (m-1) Or, -me ρ λ B + λ (m-1)be ρ This reduces to: -E ρ λ B > 0 Thus, dy/dm is unambiguously positive if D > 0. 15
Proof that D > 0 The solution to the numerator matrix for dy/dα is -me α (L ρ - (m-1)bλ ρ ). This is unambiguously positive. Thus, an autonomous rise in the demand for goods can lower y if and only if D < 0. This, however, is a dynamically unstable possibility. Solve equation (2) for B and substitute into equation (3). We now have one equation in two unknowns, ρ and y. When this new equation (designated FA) holds, the money and loan markets clear. The FA curve may be upward or downward sloping. However, if it is downward sloping, it must be flatter than the IS curve for dynamic stability. Figure A-1 below shows what happens if the FA curve is steeper than IS and an autonomous increase in goods expenditures occurs. The comparative static prediction is that income (y) falls. In the figure, the equilibrium moves from point 1 to 2. If we make the dynamic assumption that the money and loan markets always clear, then the economy will always be positioned on the FA curve. A rightward shift in IS will leave the economy on the FA curve, but below the IS curve (point 1). This represents excess demand in the goods market causing an increase in y and a movement away from the predicted comparative static equilibrium at point 2. Thus, when FA is more steeply sloped than IS, the model predicts a fall in y when autonomous expenditure demand increases. This is a dynamically unstable case and is rejected. This case only occurs if D < 0, since the numerator for dy/dα is unambiguously positive. As a result, D < 0 is rejected and D is signed positive. 16
FA ρ 2 1 IS' IS y Figure A.1- Dynamically unstable case (D < 0) ENDNOTES: 1 Mishkin (2004, p. 490). 2 See, e.g., Eichengreen (1992, 2002). 3 Eichengreen (2002) reviews the various papers supporting this view. 4 Bank assets are reserves (R) + bank credit (BC) while liabilities are deposits, D. D equals the money supply, M, minus currency held outside the banks, C. R + BC = M - C, so BC = M - R C. Since B = R - C, BC = M - B. And since M = mxb, BC = (m - 1) x B. See also the seminal work by Brunner and Meltzer (1968). 5 See the mathematical appendix for details. 6 The open-economy model s finding that an autonomous decrease in λ reduces aggregate demand adds additional theoretic support to the Bernanke (1983) hypothesis that a reduction in the bank lending ratio in the U.S. during the Great Depression exacerbated recessionary forces. 17