Modeling GDP fluctuations with agent-based model

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Highlights

  • Modeling GDP fluctuations with agent-based model is proposed.

  • Obtain the analytical solutions for the model using a (forced) damped pendulum.

  • The solutions stipulate the recovery speed from external shocks and business cycle duration.

  • Estimation technique employed in the paper is shown to be more efficient.

  • Key empirical features of the GDP growth in the US and China are well captured.

Abstract

This paper offers a new approach to calibrating parameters of an agent-based model proposed by Ormerod (2002) and conducts a comparative analysis of the US and Chinese business cycles for the period 1993–2014 using annual percentage changes in real gross domestic product. Depending on the underlying conditions of the system, the agent-based model is transformed to a damped pendulum, or a forced damped pendulum, through which we get the analytical solutions. These analytical solutions stipulate the speed of recovery from external shocks and the length of a business cycle. After pinning down two parameters in the analytical solutions, we calibrate the model using the Bayesian estimation technique. Our calibration approach captures the fundamental features of the economic fluctuations reasonably well. In particular, we find that the Chinese economy is more volatile and less persistent than the US economy: China has a shorter average duration of business cycles and recovers faster from external shocks; and the two countries move synchronously.

Introduction

Economic fluctuations have long attracted the attention of a large number of economic researchers. The business cycle refers to the downward and upward movement of gross domestic product (GDP) around its long-term growth trend. The mainstream view that short-run fluctuations are nothing but a series of random shocks fails to explain some crucial properties of economic fluctuations, such as the length and amplitude of the business cycle [1]. In recent years, more and more econophysicists investigate agent-based models (ABM), a computerized simulation-based model of a number of decision-makers and institutions interacting under prescribed rules [[2], [3], [4], [5], [6]]. In this paper, we follow the ABM proposed by Ormerod [7], who models an economy based on heterogeneous agents to explain the empirical features of the business cycle in the US.

Traditional theories of the business cycle postulate that the cycles are caused by a series of external random shocks such as technology and monetary policy shocks. For example, Hansen explores a growth model with technology shocks to show that the economy could display large fluctuations in working hours and relatively small fluctuations in productivity [8]. Christiano et al. point out that there is considerable agreement about the qualitative effects of a monetary policy shock on economic fluctuations [9]. Recent research, however, has shown that besides external sources, business cycles can also be intrinsic to the system itself. Dosi et al. introduce an evolutionary model of industry dynamics that generates endogenous business cycles with ‘Keynesian’ features [10]. Russo et al. present an agent-based computational model wherein both firms and workers are boundedly rational and show that aggregate macroeconomic features could emerge from the localized interactions of individual entities [11]. Employing an ABM that accounts for the key features of the output growth rate in the business cycle in the 20th century, Ormerod shows that business cycles are an internal feature of the system arising from the level of industrial concentration of the agents and the interactions among them [7]. Ormerod claims that the durations and sizes of recessions in 17 capitalist countries follow the power-law and exponential distributions. This feature is the result of interactions among agents [[1], [12]]. To better describe the business cycle and enable future investigation on interaction between agents, we have chosen ABM in our research.

Existing literature provides different ABMs. Ormerod introduces an ABM in which the agents decide their own output growth and sentiment in each time period, and simulates the business cycle in the US economy [7]. Gatti et al. show that an ABM with heterogeneous firms and a representative bank is able to replicate (i) the power-law distribution of firm sizes and (ii) the Laplace distribution of aggregate growth rates with high statistical precision [4]. Li and Gao offer a parsimonious ABM that provides a good approximation to some basic features of the short-run economic fluctuations, such as the distribution of firm sizes, range and autocorrelation of GDP growth, and duration and magnitude of recessions [13].

Previous research, however, has focused on simulating the economic fluctuations without analytical investigation. Most of the ABMs calibrate parameters through numerical simulation, which is intrinsically inefficient. Even though the calibration results could capture part of the stylized facts reasonably well, the calibration process itself might be time-consuming and unstable. In addition, none of the studies in the ABM literature have conducted a comparative analysis between developing and developed economies. While those studies focus only on the US and other 17 capitalist economies, the ABM framework has not been applied to developing countries, and therefore, the economic implications of the different parameter estimates and resultant models for different countries remain largely unexplored.

In this paper, we investigate the ABM proposed by Ormerod [7], and derive the analytical solutions for China and the US. Our work contributes to the related literature by providing a different approach to calibrating the parameters and making a comparison between the Chinese and US economies. Our extensive approach is more efficient without sacrificing the accuracy in capturing the stylized facts. We derive the analytical solutions under different assumptions, providing new indicators to measure periodicity, speed of decay and comovement of the two economies.

The rest of the paper is organized as follows. Section 2 introduces the model and derives the analytical solutions. Section 3 describes the data and calibration process. Section 4 gives a brief conclusion.

Section snippets

Model setup

For our analysis, we employ an ABM in line with Ormerod wherein the interaction among firms is the source of the business cycle [7]. Instead of relying on a real business cycle (RBC) model based on multi-period optimization, we introduce Keynesian style agents to our model: at any given time, each agent acts according to her current standing, the state of the world, and the rules governing her behavior.

The model is populated by N agents with each evolving period by period. Agents decide two

Data

Our data consist of the quarterly growth rates of the real GDP and the business cycle indicators of the US and China. We use the real GDP growth rate as a proxy for the aggregate output growth. The recession period is defined by OECD recession indicators. The quarterly nominal GDP of China is obtained from the Wind database. The nominal GDP of the US and the consumer price indices (CPI) for both countries come from the Federal Reserve Bank of St. Louis (FRED). The monthly OECD-based recession

Conclusion

This paper investigates the analytical solution for the ABM proposed by Ormerod [7]. Assuming that the relative size of each agent remains relatively static, we derive three analytical solutions under different economic conditions. When the forcing term F=0, i.e. in a steady state, the system becomes a damped pendulum. This provides indicators to measure the periodicity and decay speed of an economy. When F=F0cos(ωt), the system converges to a forced damped pendulum, in which case the

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