In this study, we focus on the impact of the US monetary policy regime on the real economy and particularly on the business cycle. Starting from a neo-classical monetary standard (MPS) , we move to a neoclassical MPS (NMPS) regime. In both cases, the monetary policy is made in terms of a Taylor-type rule. We obtain an economic equilibrium in a single-good economy with heterogeneous firms and consumers in order to quantify the impact of the NMPS on both aggregate and industry level. We show that under a NMPS monetary policy regime, the monetary authority tends to target aggregate factors, while under a MPS regime, monetary authorities tend to target industry specific factors. The impact of this behavioral difference is reflected on the variance of the GDP time series. Finally, our model could be extended to the case of a multi-sector economy with heterogeneous firms.
***Keywords***: Business cycle, Business cycle models, Modeling, Real business cycle, Taylor-type rule, Variability of the output
author:
- 'Paolo Pin[^1]'
title: Modeling Monetary Policy Regimes
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Introduction {#Intro}
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The business cycle is a central issue in macroeconomics, and several economic theory formalizations have been proposed to study it. One of the most popular is the *real business cycle* approach, introduced by the *National Bureau of Economic Research* (NBER). Following that tradition, in this paper we focus on a simple model with a neoclassical money supply, which is one of the most important tools for monetary policy [@NBER].
Several empirical results show that there are some asymmetries in monetary policy which may lead to a real business cycle (RBC). Such asymmetries may come from the nature of the monetary policy instrument, from central banks’ attitude and from the behavior of agents in the private sector. In this work we focus on the attitude of central banks and their monetary policy, which affects the quantity of money. Moreover, we study the role of consumers’ and producers’ behavior in the business cycle.
In order to understand the endogenous role of central banks’ monetary policy (i.e. how monetary policy affects the aggregate level of the economy), we study in this paper a simple *real business cycle* model, extending the idea of real business cycle introduced by [@McGrattan-RePEc:oup:jemepra:v:29:y:2009:i:1:p:139-157]. The model allows for a single-good economy. This model also can be extended to a multi-sector economy with heterogeneous firms and consumers.
The paper is organized as follows. In Section \[Theory\], we first explain the main features of the basic model with the Taylor-type policy rule. Then we extend the model to include heterogeneous firms and consumers. In Section \[Analysis\], we present and discuss the simulation results. Finally, in Section \[Conclusions\], we provide concluding remarks.
The main model {#Theory}
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The model {#Model}
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We consider a single-good economy with a monopolist producing a single product with homogeneous firms, i.e. each firm produces only one good with a constant marginal productivity $a$. The firms face a decreasing trend in their demand. Firms produce the good until the price reaches the marginal cost of production $C$. To ensure the existence of all firms, we require that the MPC is non-negative, i.e. $aC \geq 1$, otherwise, we say that there is an empty spot on the market.
The economy can be described by the following system of equations: $$\begin{aligned}
\label{eq:model1}
Y(t) &= A(t), \\ \nonumber
A(t) &= \int_0^t\left(1-f_M(t,T)L(t)\right)F_M(t,T)dt,\end{aligned}$$ where $A$ is the aggregate production, $Y$ is output, and $F_M$ is the average marginal product of capital. The investment function $F_M$ can be written in an equation form: $$F_M(t,T) = \frac{f_L(t,T)C(t)}{a},$$ where $C$ is the average cost of production. The money function $L$ can be written as $L(t) = \sum_n \psi_n q_n(t) L_n$, where $q_n$ is the relative quantity of the good that the firm $n$ produces, and $L_n$ is the money of firm $n$.
As shown in Appendix \[App1\], equation (\[eq:model1\]) is sufficient to compute a functional relation between the output and the money.
In our model, we introduce a policy rule, which influences the rate of growth. We assume that the change in $L$ is proportional to the rate of growth of the output $Y$, so that $$\frac{dL(t)}{dt} = -\eta (Y(t)-y),$$ where $\eta>0$ is a parameter, and $y$ is the exogenous reference rate. This can be regarded as a Taylor-type rule (e.g. see [@Taylor]). This is the central object in this paper, and represents a simple rule to influence the rate of growth. The above equation is integrated to find $$L(t) = \int_0^t -\eta (Y(s)-y) F_M(s,t)ds,$$ and then used to compute the total output and the average capital, since $$A(t) = F_M(t,t)L(t)$$ and $$F_M(t,t) = \frac{f_L(t,t)C(t)}{a}.$$
To ensure an endogenous output adjustment, we make the usual assumptions of decreasing returns to scale and increasing marginal returns to scale. Hence the production function becomes $$\label{eq:model2}
F_M(t,T) = \frac{f_L(t,T)C(t)}{a\left(1-\frac{f_L(t,T)C(t)}{a}\right)}.$$
Firms may change their quantities after taking into account their time preference (time discount factor) in choosing an appropriate quantity. Hence, the production function can be written as: $$\label{eq:model3}
F_M(t,T) = \frac{f_L(t,T)C(t)}{a\left[1-\frac{f_L(t,T)C(t)}{a}+q(t)\left(\frac{f_L(t,T)C(t)}{a}\right)^{\delta}\right]}.$$ Here $q(t)$ is the time preference function, where $0
