Understanding DSGE models

Theory and Applications

Celso Jose Costa Junior

• Publisher: Vernon Art and Science Inc.
• Year: 2016
• ISBN:
  9781622731343
• Edition: 1
• Topic: Economics
• Subtopic: Macroeconomics
• Index: Economics

While the theoretical development of DSGE models is not overly difficult to understand, practical application remains somewhat complex. The literature on this subject has some significant obscure points. This book can be thought of, firstly, as a tool to overcome initial hurdles with this type of modeling. Secondly, by showcasing concrete applications, it aims to persuade incipient researchers to work with this methodology. In principle, this is not a book on macroeconomics in itself, but on tools used in the construction of this sort of models. It strives to present this technique in a detailed manner, thereby providing a step by step course intended to walk readers through this otherwise daunting process. The book begins with a basic Real Business Cycle model. Subsequently various frictions are gradually incorporated into a standard DSGE model: imperfect competition; frictions in prices and in wages; habit formation; non-Ricardian agents; adjustment cost in investment; costs of not using the maximum installed capacity; and finally, Government.

Chapter 1

Introduction

l. 2

Why tell a story using models instead of telling a story using words? According to Professor Fábio Kanczuk of São Paulo University:

"To the older generation of any era, Macroeconomics means telling stories, believing they derive from an accounting equality, without realizing that they are but exactly that: identities. Confusing what is endogenous with what is exogenous, equilibrium with disequilibrium…. To the younger generation, it is important to think in terms of equilibrium and to identify the exogenous shocks, in order to then be able to tell the story. Otherwise, it appears so dishonest that even some consultants would be ashamed. In this case, even with its harsh limitations, DSGE helps us to think. There are people who are intelligent enough to do without models and can perform the identification in their heads. When I try to do that, I notice that I often get confused. I also notice that other people get confused, but don’t realize it". (Blog AC3L, 2013)

l. 8

In short, a model consists of mathematical expressions that have unique, precise definitions. This does not occur when only words are used. Thus, once a mathematical expression is defined, it is represented by a rigid set of rules that concern the relationships that can be made, with no room for subtext or metaphors. This is why a well-defined structure is needed, even when telling stories.

l. 10

During the years that followed Kydland and Prescott’s (1982) seminal article, RBC theory provided the main reference structure for the analysis of economic fluctuations, becoming the center of macroeconomic theory. The impact of the RBC revolution lies in its methodology, which established the use of DSGE models as a central tool for macroeconomic analysis. Behavioral equations describing aggregate variables were replaced by first-order conditions of intertemporal problems faced by households and firms. Ad hoc assumptions in the formation of expectations were replaced by rational expectations.

l. 12

However, this methodology was initially criticized for limiting itself to the analysis of only one type of shock (productivity shocks) and only one type of economic structure (perfect competition), besides not recognizing any role for monetary policy. Therefore, from the perspective of central banks, it was hard to see how these models could contribute to the monetary policy debate. Twenty years later, this controversy has been completely dispelled. The main reason for this is that the technological innovation overlying RBC models introduced frictions that allowed Keynesian principles and new shocks to be incorporated. The success of these new models allowed major economic institutions to develop their own DSGE models, as did the Brazilian Central Bank (SAMBA), the European Central Bank (NAWM), the Bank of Canada (ToTEM), the Bank of England (BEQM), the Bank of Japan (JEM), the Bank of Chile (MAS), and the International Monetary Fund (GEM), among others.

l. 14

The acceptance of this methodology is due to its coherent analysis structure. This coherence is a result of the acceptable behavior that agents maximize when making decisions, and of rational expectations. Its dynamic mechanism is another attraction, as these models are able, clearly and transparently, to represent the intertemporal movement of economic variables. Lastly, these models are not subject to the Lucas critique (Lucas, 1976). For this reason, central banks are striving to make DSGE more and more useful in the analysis of economic policy. To this end, they are taking into account an increasingly sophisticated financial sector (with financial vulnerability and collateral restrictions) and are progressively perfecting the understanding of forecasting.

l. 16

According to Chari et al. (2009), in order for a model to contribute to economic policy analysis, it needs to have two essential characteristics. The first is that the estimated parameters should be structural parameters of the economy, so that they are not affected by policy changes, and the second is that the exogenous shocks used in the model should have a coherent and relevant interpretation. They also state that there are two main approaches for models that meet these two requirements. The first seeks to keep the model as simple as possible with respect to the number of parameters, variables and dynamics. The other is aligned with Christiano et al. (2005) and Smets and Wouters (2003), who seek a so called ”adjustment principle”. In this sense, this second approach argues for the inclusion of several estimation mechanisms with the aim of improving adherence to observed data, such as different types of rigidity and shocks. Thus, the models that are concerned with bringing theory and reality closer together follow this second tradition. They propose frictions and shocks to a degree that is sufficient and necessary for better adjustment to the observed data.

Definition 1.0.1 (Adjustment principle). According to Kocherlakota (2007), by this principle, the better a model’s projected data adheres to observed data,the more preferable it is for policy analysis.

The idea of Representative Agents and Lifespan

l. 24

It is a fact that every consumer is different in relation to his/her preferences for goods and services. The same holds true for firms with regard to the technology used in the production process. In other words, agents in an economy are heterogeneous. However, considering these characteristics, a potential theoretical problem of flexibility emerges, rendering the theoretical modelling of each economic agent’s individual choices impossible. Furthermore, it would be impossible to know each individual agent’s exact choices. The fact is that any economic model is a simplified description of a complex phenomenon.

l. 27

The solution found was to group economic agents into larger categories, for example, in the case of a study regarding consumers, forming groups with similar consumption characteristics (high, average and low-income consumers) would be recommended. This procedure within DSGE modelling is called introducing a representative agent. In this approach, it is assumed that a large quantity of identical economic agents exists. This is clearly a significant simplification of reality. However, by adopting such a procedure, macroeconomic modelling is a lot simpler, at least enough to fulfill the purpose of macroeconomic studies, such as how household consumption reacts to rising interest rates.

l. 29

Thus, the aim of DSGE modelling is to build relatively small theoretical models (using representative agents) that include households, firms, government, the financial sector and the foreign sector. Aggregating these types of agent enables one to see how they interact, allowing for a detailed analysis of a certain macroeconomic policy effects.

l. 31

Now that the issue of how economic agents are defined in DSGE models has been described, it is necessary to consider each agent’s lifespan, which, for the purpose of these models, means the temporal reference that agents use to make their decisions. It is assumed that they have infinite time horizons. Obviously, firms and governments do not exist forever. However, when a government decides upon its budget, it does not expect that it will cease to exist. Firms act likewise; when deciding their budgets, they do not consider that they will go bankrupt in the future. This assumption in relation to consumers is simpler. Although it is assumed that each consumer has a finite lifespan, when considering the family structure in which members periodically are born and die, the ”family” representative agent becomes infinite.

l. 34

Teaching DSGE models in undergraduate and graduate courses

l. 35

Macroeconomics is complex, and complex systems, as is common knowledge, are difficult to analyze. However, is the macroeconomics being taught in undergraduate courses consistent with reality? Are models such as the IS-LM and Mundell-Fleming models, among others, really able to represent how the macroeconomy works? Is the macroeconomics taught in undergraduate courses different from that taught in postgraduate courses?

l. 38

At the beginning of the 1970s, macroeconomic theory received a jolt. The neoclassical synthesis model, which was almost universally accepted as the basic paradigm up to the end of the sixties, is today not considered scientifically respectable. The popularity of this model began to wane because of to its inability to explain certain economic events, especially failing to appropriately deal with factors such as inflation and supply shocks. The waning enthusiasm for these models is also a result of the theoretical and empirical progress of an alternative approach to the behavior of households and firms, grounded in the concepts of optimization of agents’ behavior and market adjustments.

l. 40

Although models based on the neoclassical synthesis have fallen out of favor with economists over the last 25 years, they continue to be the main tools used in undergraduate course textbooks. Although it is true that some manuals now include material about macroeconomics with microfoundations (Romer, 2012; Blanchard and Fischer, 1989 and Benassy, 2011 for graduate courses; and Barro, 1997; Williamson, 2008 and Barron et al., 2006 for undergraduate courses, among others) it is still insufficient, even in postgraduate courses. In summary, modern macroeconomics is not being taught in an orderly manner owing to a lack of textbooks that direct the study of this methodology systematically.

l. 42

Generally speaking, mathematics cannot be accredited with being the reason for modern macroeconomics barely being taught in undergraduate economics courses, as the basic tools in these models (derivatives, maximization, etc.,) are taught in the majority of courses, even undergraduate courses. Textbooks such as ”Fundamental Methods of Mathematical Economics” by Chiang and Wainwright (2005) or ”Mathematics for Economists” by Simon and Blume (1994), very popular in math classes and in economics courses, fulfill the necessary and sufficient conditions for a good understanding of macroeconomic modelling.

l. 44

Dynare

l. 45

Dynare is a software platform for handling a wide range of economic models, in particular DSGE models and overlapping generations (OLG) models. The models solved by Dynare include those relying on the rational expectations hypothesis, wherein agents form their expectations about the future in a way consistent with the model. But Dynare is also able to hand models where expectations are formed differently: at one extreme, models where agents perfectly anticipate the future; at the other, models where agents have limited rationality or imperfect knowledge of the state of the economy and, hence, form their expectations through a process of learning.

l. 48

This platform offers an easy way to describe these models, capable of performing simulations given the calibration of the model parameters or forecasting these parameters given a dataset. In practice, the user will write a text file containing the list of variables, dynamic equations, computing tasks and the desired graphical or numerical outputs.

l. 50

Dynare is a free software, which means that it can be downloaded free of charge, that its source code is freely available, and that it can be used for both non-profit and profitable purposes. It is available for the Windows, Mac and Linux platforms and is fully documented by way of a user guide and reference manual. Part of Dynare is programmed in C++, while the rest is written using the Matlab programming language. The latter implies that commercially-available Matlab software is required in order to run Dynare. However, as an alternative to Matlab, Dynare is also able to run on top of Octave(basically a free clone of Matlab). The development of Dynare is mainly done at Cepremap by a core team of researchers who devote part of their time to software development.

l. 52

In short, Dynare is a preprocessor and collection of routines that operate on Matlab, which has advantages for reading and writing DSGE models, almost as if one were writing an academic article. Not only does this make the presentation of models easier, it also easily allows for code sharing. Figure 1.1 is an overview of how Dynare works. Basically, the models and its related attributes, such as the shock structure, are written equation by equation in a text editor. The result is a file.mod¹. This file is loaded by Matlab, which initiates Dynare’s preprocessor, translating the file.mod so it can be used by Matlab’s routines to solve or estimate the model. Finally, the results are shown by Matlab.

The structure of the book

As mentione...

Table of contents

• 1 Introduction
• I Basic principles
• II Extensions