Thoughtout this book, we have focused on the real economy. The methods explained in Chapter 2 are extremely useful, not only for analyzing the real economy, but for analyzing financial markets. In this chapter, we analyze the combinatorial problem that is so crucial in a market with many heterogeneous investors. It has important implications for volatility in the financial market.

Introduction

We have repeated time and again that the behavior of macroeconomic variables emerges as an outcome of aggregation of micro behavior of a large number of interacting agents. Financial markets are no exception. In fact, there has been a veritable explosion of empirical and simulation studies of financial markets – prices, returns, or volumes of transactions – based on the explicit assumption of heterogeneous investors (see Gopikrishnan et al., 1998; Lux and Marchesi, 1999; Mantegna and Stanley, 1994; Takayasu and Sato, 1997). Reported simulation studies of financial markets by multiagent models apparently mimic well many, if not all aspects of the actual behavior of asset returns (see Lux and Marchesi, 1999).

Investors in the markets employ various strategies or trading rules. For convenience, we identify investors with the strategies or the rules they employ, and say that investors of the same type form a group or cluster. Clusters evolve over time as agents switch their decision rules or behavioral patterns in response to changing economic environments. They also change as agents enter or exit.

In the last ten years or so, I have devoted my research efforts to revising the commonly adopted frameworks for modeling and analysis by mainstream macroeconomists. Results of my initial thoughts and proposals were published in 1996, followed by another book in 2002. In these two books I explained my proposed methods for modeling and analyzing stochastic dynamic interactions among economic agents of possibly many different types, and how to analyze aggregate behavior and associated fluctuations. The two books are mostly exposition of concepts and techniques and had only a few suggestive economic examples.

I have realized that more substantive examples are needed to convince mainstream macroeconomists of the usefulness of my approaches. This book, jointly written with Hiroshi Yoshikawa, integrates the methodologies and approaches in these two earlier books with much more detailed analysis of more substantive and substantial macroeconomic examples.

As the subtitle of the book makes clear, our approaches have two components: (1) continuous-time Markov chains to model stochastic dynamic interactions among agents and (2) combinations of stochastic processes and non-classical combinatorial analysis, called combinatorial stochastic processes.

In (1) a version of Chapman–Kolmogorov equations called master equations describes how states of the models evolve stochastically over time. In this sense this part is devoted to applications of some of the concepts and methods from statistical physics.

We begin this chapter by reconsidering the notion of equilibrium in economics. In the standard analysis, optimization by an economic agent is followed by supply and demand; every economic agent or unit is always in his/her best position. The equality of demand and supply in the market then constitutes equilibrium. In the equilibrium, marginal utilities and productivities are equated to prices, and as a consequence, they are all equal. Lucas (1987) describes this equilibrium theory as the economic theory. In this framework, demand does not matter for the determination of the level of aggregate economic activity. It is determined by technology and factor endowments.

In the economy, micro units or economic agents certainly optimize. Some economists stress the limits of rationality of economic agents, and advocate “bounded rationality.” However, in our view, the problem surrounding bounded rationality is irrelevant to macroeconomics. More fundamental are micro fluctuations, uncertainty, and the limits to arbitrage in real economic activities.

In standard economic theory, which ignores microeconomic fluctuations, the outcome of optimization by an economic agent is given by a “point” in some set or space; typically, a point is supported by a price vector. In this chapter, we explain that this approach is not valid because of microeconomic fluctuations.

Given the complexity of the macroeconomy, we must explicitly consider stochastic deviations of microeconomic behavior from its mean. In Chapter 1, we have seen that micro behaviors of individual households and firms are very diverse.

The new approach to macroeconomics and financial markets outlined in Chapter 1 requires mathematical methods and concepts that are quite different from those commonly used in economics. This chapter introduces them to the reader.

Phenomena we can analyze using the methods explained here share one or more of the following three features:

1. A finite but large number of micro units or agents interact.

2. Different “types” of agents are present.

3. New and unknown types of agents, products, or technologies may appear; that is, the number of types of agents, products, or technologies may not be fixed nor known in advance.

To analyze these phenomena, we must depart from the standard methods of model construction and analysis in mainstream economics. Specifically, in this book, we formulate models as continuous-time Markov chains, also known as jump Markov processes. This approach gives us new insight, and often yields more information on the behavior of the macroeconomy than the traditional approach can offer.

The standard approach in “micro-founded” macroeconomics formulates complicated intertemporal optimization problems facing the representative agent. By so doing, it ignores interactions among nonidentical agents. Also, it does not examine a class of problems in which several types of agents simultaneously attempt to solve similar but slightly different optimization problems with slightly different sets of constraints. When these sets of constraints are not consistent, no truly optimal solutions exist.

Unemployment is one of the most important problems in economics. Macroeconomics as a discipline was born through economists' efforts to better understand unemployment. Despite piles of works on the subject, it is still a matter of dispute. Some economists see unemployment as nothing but a particular type of rational economic activity, namely job search. Others take it as a sign of waste of the most important production factor; it costs both the unemployed and the economy as a whole.

This chapter explains that the approach we propose gives us a new perspective on the labor market and unemployment. It follows the tradition of search theory, but differs from the existing literature in one important respect. As explained in Chapter 3, our model is based on the notion of stochastic equilibrium which is conditioned by aggregate demand. In this chapter, extending the model in Chapter 6, we show that unemployment due to demand deficiency and “structural” unemployment cannot be so clearly separated as one might think. This suggests that the natural unemployment may not be defined clearly independent of the level of aggregate demand.

We also show that Okun's law, which puzzles many, can be quite naturally explained. In our analysis, the notion of equilibrium as distribution plays the central role. The equilibrium distribution is conditioned by aggregate demand.

Background

There are different approaches to labor market and unemployment. Let us begin with the assumption that the labor market were a single homogeneous market.

Introduction

Business cycles, or fluctuations of aggregate economic activities, have long attracted economists' attention. A glance at Haberler (1964) reveals that all kinds of theories had already been advanced by the end of the 1950s.

Some theories consider monetary factors, such as changes in money supply, the fundamental factor causing business cycles whereas others consider real factors, such as technical progress, fundamental. Some theories emphasize the role played by exogenous shocks. The famous theory of Jevons (1884), for example, singled out sun spots as the ultimate factor, and traced the chain of causation from sun spots to weather conditions, weather conditions to harvests, and finally from harvests to general business conditions. In contrast, other theorists purged exogenous factors, and constructed models in which endogenous cycles are generated. Goodwin's (1951) model of the nonlinear accelerator is a primary example of such models, Kaldor (1940) is another. More recently, Grandmont (1985) offers another example in which persistent deterministic cycles appear in a purely endogenous fashion without any exogenous shocks. Endogenous cycles produced in these models all rest on the particular nonlinearity of behavior of the representative agent.

Earlier, following the lead of Frisch (1933), Samuelson (1939) demonstrated that the second-order ordinary linear difference equation based on the multiplier and accelerator could generate cycles. Introducing the “ceiling” and the “floor” into such a model, Hicks (1950) ingeniously got around “explosions,” and showed that the model could account for a dazzling variety of cycles.

In Chapters 3 and 6, we have shown that demand affects the level of total output. As the old Keynesian economics claims, demand is relevant. However, the claim is normally taken to be relevant only for the short run. The long run is the realm of the neoclassical economics, whereby economic growth is determined solely by supply factors. In this chapter, we challenge this standard neoclassical view, and argue that demand actually plays a central role in the process of economic growth.

Introduction

In the standard literature, the fundamental factor restraining economic growth is diminishing returns to capital in production or R&D technology. In this chapter, we present a model suggesting that “saturation of demand” is another important factor restraining growth.

In the less mathematical literature and casual discussions, the idea of demand saturation has been popular. Every businessman would acknowledge saturation of demand for an individual product. In fact, plot a time series of production of any representative product such as steel and automobiles, or production in any industry, against year, and, with few exceptions, one obtains a S-shaped curve. Figure 8.1, from Rostow (1978), demonstrates this stylized fact. The experiences of diffusion of such consumer durables as refrigerators, television sets, cars, and personal computers tell us that deceleration of growth comes mainly from saturation of demand rather than diminishing returns in technology.

History shows us that the economy can be trapped in long stagnation. In the nineteenth century, the British economy suffered from the Great Depression for almost a quarter of century (1873–96). The Great Depression in the 1930s attacked the whole world. And since the beginning of the 1990s, the Japanese economy has stagnated for more than a decade.

In every episode, various policies were discussed and tried. Yet the economy did not revive, falling into long stagnation. Certainly, in each case, there must have been policy mistakes. Granted, it appears that once the economy is trapped into a deep depression, the effectiveness of standard policy measures weakens. Irving Fisher (1933), for example, in relation to his famous debt-deflation theory made the following argument.

In this chapter, we focus on uncertainty.

In his 1844 essay, “On the Influence of Consumption upon Production,” J. S. Mill endeavored to refute the belief that, “A great demand, a brisk circulation, a rapid consumption (three equivalent expressions) are a cause of national prosperity.” In this book, we take up the old belief and propose that aggregate demand does matter in the determination of total output. The argument requires a drastic turn in macroeconomic, theory and introduces new methods. The purpose of this book is to explain the new approach. Readers will see how new methods and concepts broaden the scope of macroeconomics and shed new light on old problems such as demand deficiency, inflexible prices, business cycles, and asset prices.

The idea that demand matters was, of course, established by Keynes (1936) – indeed, macroeconomics used to be synonymous with Keynesian economics. Alas, no more! Keynes' principle of effective demand – that aggregate demand determines the level of aggregate production or output – is in stark contrast to the neoclassical doctrine that aggregate output is determined solely by supply factors such as factor endowments and technology, and that demand is relevant only with respect to composition of outputs. Despite its empirical attractiveness, Keynesian economics has long been charged with lacking microeconomic foundations. The need for microeconomic foundations meant that the optimization of agents had to be explicitly considered in models.

Many economists have come to believe that the first principle of economics is the optimization of economic agents such as household and firm.

The standard approach such as RBC is based on the premise that the microeconomic behavior of the optimizing agent mimics dynamics of the macroeconomy. In Chapter 1, we explain that this premise is incorrect, and that the macro and micro behaviors are fundamentally different.

In this chapter, we focus on a particular aspect of the macroeconomy, namely the speed of adjustment. The premise of the standard approach is that rational economic agents must respond quickly to any change in economic environment. And it is taken for granted that this micro behavior should translate itself into the macroeconomy. Thus, one expects that the speed of adjustment in the economy as a whole is also fast in normal conditions. In this way, the standard approach does not make any distinction between the speed of adjustment of micro agents and that of the macroeconomy.

Let us take up prices as an example. Since the publication of Keynes's General Theory (1936), “inflexibile” or “rigid” prices have been always a focal point of macroeconomics. Modigliani (1944), one of the first economists, coined the proposition that what distinguishes Keynesian economics from neoclassical economics is the assumption of inflexible prices (to be precise, rigid nominal wages in his case).

Many economists take inflexibility of prices as a sign of irrationality. Aside from monopoly power or institutional barriers such as regulations, healthy market forces should make prices flexible. In this chapter, we will explain that slow changes in prices are a necessity in the macroeconomy.

Macroeconomics has gone astray. I suspect that many economists, or at least half of macroeconomists who are old enough to know the “Old Macroeconomics,” feel that way. In the past 30 years, macroeconomics has become less relevant.

The mainstream macroeconomics today begins with optimization of the representative consumer. The real business cycle (RBC) theory is the foremost example. The optimum growth theory once meant to be normative is now being taught as a descriptive theory. It is the neoclassical equilibrium theory. Preferences and technologies certainly move the economy. The prediction of the neoclassical doctrine seems often right for the very long run. However, saying that something moves eastward, and saying that it reaches the east end, are wholly different matters. Most of the time, the real economy must move on a bumpy road. It is misleading and wrong to analyze such problems as business cycles, unemployment, and deflation – the subject matters of macroeconomics – with the neoclassical equilibrium theory.

Contrary to the belief held by some economists, we need a new approach for macroeconomics, different from the standard equilibrium theory. The purpose of this book is to explain it. Having sound “microeconomic foundations for macroeconomics” has been long taken as building sophisticated optimization of an individual economic agent into a macro model. This agenda is on the wrong track. The new approach we advance in this book is based on the methods of statistical physics.