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Article Excerpt
I. INTRODUCTION
Central bankers know that financial intermediation is important for achieving macroeconomic stability. Without a functioning banking system, an economy will grind to a halt. It is the job of regulators and supervisors to ensure that the financial system functions smoothly. But monetary policy and prudential supervisory policy can work at cross-purposes. An economic slowdown can cause deterioration in the balance sheets of financial institutions. Seeing the decline in the value of assets, supervisors will insist that banks should follow the regulation and ensure that they have sufficient capital given their risk exposures. The limit on bank lending set by capital adequacy requirements declines during recessions and increases during booms. And as intermediation falls, the level of economic activity goes down with it. It looks as if regulation deepens recessions. As the Basel Committee on Banking Supervision (2001) put, the capital regulation "has the potential to amplify business cycles."
Blum and Hellwig (1995) provided the first theoretical demonstration that capital requirements can exacerbate business cycle fluctuations. In focusing entirely on the behavior of the banking system, the Blum and Hellwig model provides an important first step, but in the end, their analysis is incomplete. They do not consider the response of the central bank to economic fluctuations. This assumption is critical for their result but certainly unrealistic. What if central banks conduct monetary policy to explicitly account for the impact of capital requirements? (1) Will the procyclical effect of capital requirements remain? Is this the optimal thing to do for central banks? To answer these questions, we derive an optimal monetary policy rule in both a static and a dynamic model where the potential procyclicality of capital requirements is embedded.
Our conclusions are as follows: a country's monetary policymakers should react to the state of their banking system's balance sheet. And when they do, the procyclical effect of prudential capital regulation can be counteracted and completely neutralized. For a given level of economic activity and inflation, the optimal policy reaction dictates setting interest rates lower, the more financial stress there is in the banking system when the economic activity is in the downturn. We present simulation results to give a sense of the magnitude of the required reaction. But when taking this proposition to the data and estimating forward-looking monetary policy reaction functions for the United States, Germany (preunification), and Japan, we find that while monetary policymakers in the United States behave as the theory suggests, lowering interest rates by more in downturns in which the banking system is under stress, by contrast, central bankers in Germany and Japan do not.
We derive optimal interest rate rules with the static model and the dynamic model in Sections II and III, respectively. Section IV reports the simulation results, and Section V discusses the empirical estimation. Section VI concludes.
II. A STATIC MODEL A. The Model
We begin with a static aggregate demand-aggregate supply model modified to include a banking sector. The purpose of this simple model is to highlight the impact of introducing bank capital requirements in their most stripped-down form in order to show the extent to which the banking industry can affect business cycles. The static model also sheds lights on the fruitful approach that solves the dynamic model.
The starting point is an aggregate demand curve that admits the possibility of banks having an impact on the level of economic activity. Following Bernanke and Blinder (1988), we distinguish between policy-controlled interest rate and lending rates and write aggregate demand as:
(1) [y.sup.d] = [y.sup.d](i - [[pi].sup.e], [rho] - [[phi].sup.e], [phi]) + [eta],
where i is the short-term nominal interest rate, [rho] is the nominal loan rate, [[pi].sup.e] is expected inflation, [pi] is the inflation rate, and [eta] is a white noise random variable. We will refer to [eta] as the aggregate demand shock, since in equilibrium it will tend to move output and inflation in the same direction. As we will see in a moment, while the lending rate (P) is determined by the equilibrium in the lending market, the short-term rate (i) is set by the monetary authority and so can be treated as a constant. For future reference, we note that we will make the standard assumption that aggregate demand falls when any of the three arguments in Equation (1) rises. That is, both higher inflation and higher real interest rates result in lower level of aggregate demand.
Turning to the loan market, banks receive deposits and make loans. There are two cases. When the capital requirement is not binding, we write real loan supply when the bank has sufficient capital and is not constrained, [L.sup.s.sub.u], as
(2) [L.sup.s.sub.u] = B + (1 - [theta])D,
where B is real bank capital, D is the level of real deposits, and [theta] is reserve requirement.
When the capital requirement is binding, banks' lending cannot reach the level indicated in Equation (2). (2) Instead, loan supply is constrained to be a multiple of bank capital. That is,
(3) [L.sup.s.sub.c] = cB,
where c is banks' statutory maximum leverage ratio. In equilibrium, loan supply will be the minimum of [L.sup.s.sub.u] and [L.sup.s.sub.c].
Next, we need to model the relationship between bank deposits and bank capital on the one hand and macroeconomic variables like output, interest rates, and inflation on the other. We assume that the level of real bank deposits (D) depends on both the level of real output and the real short-term interest rate. We write this as:
(4) D = D(y, i - [[pi].sup.e]),
where the function is increasing in the first argument and decreasing in the second argument. As for bank capital, it is assumed to rise and fall with aggregate economic activity.
That is, a rise in real output results in an increase in the value of bank assets. This could be because of an increase in the value of tradable securities or because borrowers are now more able to repay their debts. Using the established notation, this is
(5) B = B(y),
where the function is upward sloping. (3)
To complete the story of banks and the loan market, we turn to the demand side. We assume that real loan demand depends on the real loan rate and the level of real economic activity, so
(6) [L.sup.d] = [L.sup.d]([rho] - [[pi].sup.e], y).
The higher the real loan rate ([rho]), the lower loan demand, and the higher aggregate output (y), the higher the loan demand.
We use a standard supply curve in which output depends positively on unanticipated inflation plus an additive white noise error. That is,
(7) [y.sup.s] = [y.sup.s]([pi] - [[pi].sup.e]) + [epsilon],
where a white noise random variable [epsilon] is mean zero and uncorrelated with the aggregate demand shock [eta]. The shock [epsilon] is a common aggregate supply shock, as it pushes output and inflation in opposite directions.
To determine the impact of capital requirements on aggregate fluctuations, we need to compute the impact of a shock on output both when banks are constrained by the capital requirement and when they are not. This requires solving two versions of a linearized version of the model, which we write as
(8a) [y.sup.d] = [y.sup.d.sub.[rho]] ([rho] - [[pi].sup.e]) - [y.sup.d.sub.i](i - [[pi].sup.e]) - [y.sup.d.sub.[pi]] + [eta], [y.sup.d.sub.[rho]] > 0, [y.sup.d.sub.[pi]] > 0, [y.sup.d.sub.i] > 0,
(8b) D = [D.sub.y] y - [D.sub.i](i - [[pi].sup.e]), [D.sub.y] > 0, [D.sub.i] > 0,
(8c) B = [B.sub.y]y, [B.sub.y] > 0,
(8d) [L.sup.s] = min[[L.sup.s.sub.u], [L.sup.s.sub.c]]; where
[L.sup.s.sub.u] = B + (1 - [theta])D and [L.sup.s.sub.c] = cB,
(8e) [L.sup.d] = -[L.sub.[rho]] ([rho] - [[pi].sup.e]) + [L.sub.y]y, [L.sub.[rho]] > 0, [L.sub.y] > 0,
(8f) [y.sup.s] = [beta]([pi] - [[pi].sup.e]) + [epsilon], [beta] > 0,
(8g) [y.sup.s] = [y.sup.d] = y,
(8h) [L.sup.s] = [L.sup.d],
where [X.sub.h] denotes partial derivative of X with respect to h evaluated at the equilibrium for the endogenous variables in the absence of shocks, which we normalize to be zero.
To solve this model, we first assume that agents have rational expectations but are unaware of the shocks e and q. This means that they expect inflation and output to be zero. That is, [[pi].sup.e] = 0. Next, using the loan and goods market equilibrium conditions, we solve for output and inflation in terms as functions of the two shocks and the nominal interest rate (i). We write the resulting two solutions in compact form as:
(9a) [pi] = -[a.sup.j.sub.[pi]]i - [b.sup.j.sub.[pi]][epsilon] + [c.sup.j.sub.[pi]][eta], [a.sup.j.sub.[pi]] [greater than or equal to] 0,
[b.sup.j.sub.[pi]] [greater than or equal to] 0, [c.sup.j.sub.[pi]] [greater than or equal to] 0,
(9b) y = -[a.sup.j.sub.y]i + [b.sup.j.sub.y][epsilon] + [c.sup.j.sub.y][eta], [a.sup.j.sub.y] [greater than or equal to] 0,
[b.sup.j.sub.y] [greater than or equal to] 0, [c.sup.j.sub.y] [greater than or equal to] 0,
where the j superscript...
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