ABSTRACT
It is a fundamental principle of empirical sciences that theory cannot be divorced from measurement. A natural measure of the fluctuation of positive data series (such as work hours and output in macroeconomic data) is the relative deviation, the ratio of the standard deviation of the series to its mean.2 According to the law of large numbers and the central limit theorem, the relative deviation is in the order of
1 N
for a system with N independent elements. We will call this general rule the Principle of Large Numbers.3 This principle immediately calls into question the idea of explaining macroeconomic fluctuations as the aggregation of microeconomic fluctuations. The number of households and firms in the US economy is so large that the aggregation of microeconomic variations will produce a relative deviation several orders of magnitude smaller than observed macroeconomic fluctuations. This chapter focuses on Lucas’ (1972) model of an island economy (the LMI model) as the benchmark model of the microfoundations approach in businesscycle theory and gives only a brief discussion of the RBC model with a representative agent. In modeling stochastic processes, we extend our scope from statistics theory with stationary probability distribution (i.e., the i.i.d. model in econometrics) to probability theory with nonstationary probability distribution (here we use the linear birth-death process) for understanding macroeconomic fluctuations with growth, so that our empirical analysis can be applied to both the new classical model and the RBC model of macroeconomic fluctuations. In the next two sections of this chapter, we will show that the Principle of Large Numbers is valid for stationary stochastic process like the system of the LMI model as well as for the linear stochastic process of growth studied in the RBC literature (Kydland and Prescott 1990). There is little empirical evidence in favor of a microfoundation explanation of fluctuations in the US output and employment. In section 13.4, we will discuss some theoretical issues raised by the LMI model. We will argue that, contrary to the claims of the LMI model, a rational expectations mechanism cannot be expected to generate perfectly correlated behavior among intelligent agents when they have market information and arbitrage opportunities. Certain fundamental factors underlying market movements, such as unequal distribution, economic complexity, and multiple time scales, cannot be ignored in business-cycle theory, as the LMI theory seems to claim. The equilibrium framework based on microfoundations, rational expectations, and efficient markets is therefore not capable of providing a consistent explanation of business cycles. We must consider other alternatives, including the idea that the macroeconomy is undergoing chaotic deterministic dynamics and the idea that structures intermediate (financial intermediate and industrial organization) between micro (households and firms) and the macro economy play a crucial role in business-cycle fluctuations.
