Part I
Introduction
Chapter 1
Background and Overview
Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science.
—Henri Poincaré
1.1 Background
The seminal contribution of Kydland and Prescott (1982) marked a sea change in the way macroeconomists conduct empirical research. Under the empirical paradigm that remained predominant at the time, the focus was either on purely statistical (or reduced-form) characterizations of macroeconomic behavior, or on systems-of-equations models that ignored both general-equilibrium considerations and forward-looking behavior on the part of purposeful decision makers. But the powerful criticism of this approach set forth by Lucas (1976), and the methodological contributions of, for example, Sims (1972) and Hansen and Sargent (1980), sparked a transition to a new empirical paradigm. In this transitional stage, the formal imposition of theoretical discipline on reduced-form characterizations became established. The source of this discipline was a class of models that have come to be known as dynamic stochastic general equilibrium (DSGE) models. The imposition of discipline most typically took the form of “cross-equation restrictions,” under which the stochastic behavior of a set of exogenous variables, coupled with forward-looking behavior on the part of economic decision makers, yield implications for the endogenous stochastic behavior of variables determined by the decision makers. Nevertheless, the imposition of such restrictions was indirect, and reduced-form specifications continued to serve as the focal point of empirical research.
Kydland and Prescott turned this emphasis on its head. As a legacy of their work, DSGE models no longer serve as indirect sources of theoretical discipline to be imposed upon statistical specifications. Instead, they serve directly as the foundation upon which empirical work may be conducted. The methodologies used to implement DSGE models as foundational empirical models have evolved over time and vary considerably. The same is true of the statistical formality with which this work is conducted. But despite the characteristic heterogeneity of methods used in pursuing contemporary empirical macroeconomic research, the influence of Kydland and Prescott remains evident today.
This book details the use of DSGE models as foundations upon which empirical work may be conducted. It is intended primarily as an instructional guide for graduate students and practitioners, and so contains a distinct how-to perspective throughout. The methodologies it presents are organized roughly following the chronological evolution of the empirical literature in macroeconomics that has emerged following the work of Kydland and Prescott; thus it also serves as a reference guide. Throughout, the methodologies are demonstrated using applications to three benchmark models: a real-business-cycle model (fashioned after King, Plosser, and Rebelo, 1988); a monetary model featuring monopolistically competitive firms (fashioned after Ireland, 2004a); and an asset-pricing model (fashioned after Lucas, 1978).
1.2 Overview
The empirical tools outlined in the text share a common foundation: a system of nonlinear expectational difference equations representing a DSGE model. The solution to a given system takes the form of a collection of policy functions that map a subset of the variables featured in the model— state variables—into choices for the remaining subset of variables—control variables; the choices represent optimal behavior on the part of the decision makers featured in the model, subject to constraints implied by the state variables. Policy functions, coupled with laws of motion for the state variables, collectively represent the solution to a given DSGE model; the solution is in the form of a state-space representation.
Policy functions can be calculated analytically for only a narrow set of models, and thus must typically be approximated numerically. The text presents several alternative methodologies for achieving both model appr...