مدلسازی نرخ بهره بانک مرکزی در چارچوب تعادل عمومی پویا

This paper incorporates two components of a modern monetary system into a standard real business cycle model: a central bank which lends reserves to commercial banks and charges a repo interest rate; and banks which make loans under a fractional reserve system and thereby create money. We examine the response of our model to shocks in the monetary base, in the currency–deposits ratio and in the required reserve ratio. Our main finding is that all these monetary shocks lead to changes in the composition of total investment between the banking and the non-banking sectors.

Modern monetary systems have two important features. First, there is a central bank which lends reserves to commercial banks and charges a repo interest rate (e.g., the “main refinancing rate” of the European Central Bank). Second, there are banks which make loans under a fractional reserve system and thereby create money. This paper is an attempt to incorporate these elements into a standard Real Business Cycle (RBC) model. RBC models were launched by Kydland and Prescott (1982) and Long and Plosser (1983), and were later given a more consistent framework by Hansen (1985) and King, Plosser and Rebelo (1988). These were dynamic general equilibrium models with a productive sector, intertemporal optimization under rational expectations and perfectly flexible prices — but without money. Later research added new dimensions to the basic model. Cooley and Hansen (1989) first incorporated money into RBC models by using a cash-in-advance constraint to derive the demand for money and assuming that money was supplied through lump-sum transfers from a monetary authority. Fuerst (1992) and Christiano and Eichenbaum, 1992 and Christiano and Eichenbaum, 1995 made further extensions by introducing a banking system which receives cash injections from the central bank and lends money to the economy. However, unlike in the real world, the cash injections received from the monetary authority in their models are costless lump-sum transfers, and banks do not operate under a fractional reserve system. By contrast, this paper extends the standard RBC model by explicitly including (i) a central bank that lends reserves to banks and charges a repo interest rate; and (ii) banks which make loans under a fractional reserve system and thereby create money. This extended framework will allow us to look at the impact of monetary shocks which have not so far been considered in the RBC literature. In particular, we will study how the economy and the banking system are affected by changes in the repo rate and by changes in the money multiplier (arising from variations in the currency–deposits ratio and/or in the required reserve ratio). It should be acknowledged that other work has already modelled the central bank repo rate in a dynamic general equilibrium framework. Notable examples are the flexible-price models of Calvo and Vegh, 1990 and Calvo and Vegh, 1995 and Lahiri and Vegh (2003), and the sticky-price models of Clarida, Gali and Gertler (1999) and McCallum and Nelson (1999). However, unlike the present paper, these models do not include a fractional reserve banking system, nor a productive sector with endogenous capital accumulation. Additionally, the present paper goes beyond the qualitative comparison between the properties of the model and the stylized facts. In the RBC vein, we calibrate our model and then use it to generate artificial data that can be compared with actual data. In this way, the present paper attempts to meet the challenge set forth by Lucas (1980) when he wrote that one of the functions of theoretical economics is to provide fully articulate, artificial economic systems that can serve as laboratories for macroeconomic analysis. 1 We start by modelling the typical behaviour of households, firms and banks. The first order conditions of these agents' decision problems, together with the market clearing conditions, define the competitive equilibrium of the economy. Next, this system is log–linearized around the steady-state values of its variables and then calibrated using Postwar U.S. data. Finally, we examine the response of the model to shocks in the monetary base, in the currency–deposits ratio and in the required reserve ratio. Our main finding is that all these monetary shocks lead to changes in the composition of investment between the banking sector and the non-banking sector. More specifically, an increase in reserves by the central bank which is seen as temporary leads to a strong increase in investment by banks at the expense of investment by non-bank firms. In contrast, an increase in either the currency–deposits ratio or in the required reserve ratio leads to a fall in bank investment in favour of a rise in non-bank investment. The structure of the article is as follows. In Section 2, we characterize the economic environment: economic flows, preferences, technology, resource constraints and market structure. In Section 3, we describe the typical bank's behaviour and its relation with the central bank. 4 and 5 deal respectively with the typical firm's behaviour and with the typical household's behaviour. In Section 6, we write down the market clearing conditions. Section 7 presents the system that describes the competitive equilibrium and Section 8 reports the calibration of the model. In Section 9, we look at the impacts of increases in central bank liquidity, and of changes in the currency–deposits ratio and in the required reserve ratio. Section 10 provides an overview and concludes.

This paper has been an attempt to incorporate the main ingredients of a monetary system into a standard RBC model: a reserves market in which the central bank lends reserves to commercial banks; and a bank loans market in which banks make loans and create deposits (money) under a fractional reserve system. We examined the response of our model to several types of monetary shocks: increases in central bank reserves, increases in the currency–deposits ratio and increases in the required reserve ratio. In our model, increases in reserves by the central bank which are seen as temporary lead to a fall in interest rates. This result, which has been difficult to replicate in general equilibrium models, is in accordance with the findings of the empirical literature. In turn, lower interest rates lead to an increase in bank lending and thus in the money supply. This causes prices to rise and leaves real variables (in particular, real output) almost unaffected — a result which is common in flexible price models. On the other hand, the increase in liquidity has a significant effect on the composition of investment expenditure. Specifically, the resulting fall in the central bank repo rate makes investment by banks so attractive that significant amounts of investment are switched from non-bank firms to banking firms. Increases in the currency–deposits ratio and in the required reserve ratio in our model also have significant effects on the composition of investment. Indeed, an increase in either ratio raises the amount of monetary base necessary to support a given amount of bank credit. As a result, the value of the marginal product of capital in banks decreases, and this shifts investment expenditure from banks to non-bank firms. One shortcoming of our model is the prediction that a temporary increase in reserves leads to a fall in investment by non-bank firms. Although the predicted effect is small, it is still in contrast with our empirical finding of a slight positive correlation between movements in the monetary base and in non-bank investment. We believe that this difficulty points to the need for further research in at least two directions. First, our short empirical study followed the literature by using simple correlations to obtain some indication as to the impact of monetary policy on bank and non-bank investment in the U.S. economy. It would be of value to carry out a more profound econometric study concerning the impact of monetary policy on the composition of investment expenditure. In particular, this study should control for other influences on investment, besides monetary policy, within a multivariate modelling framework. Second, in the class of models to which our model belongs, the way in which investment expenditure is modelled is still rudimentary. In particular, firms are all alike and therefore the investment expenditure corresponds to each firm using part of its own output to increase capital. As a consequence, there is no firm investment financed by loans. Hence, one possible research avenue is to model firm heterogeneity so as to create the need in some firms to borrow in order to finance investment. It could then be verified whether, in this improved scenario, expansionary monetary policy no longer has a negative impact on firm investment, but still produces a stronger effect on bank investment than on firm investment.