Understanding DSGE models: Theory and Applications
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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 applic
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Understanding DSGE models - Celso Jose Costa Junior
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.
Understanding DSGE
Celso José Costa Junior
Centro Macro Brasil Escola de Economia de São Paulo, FGV
Vernon Series in Economic Methodology
Copyright © 2016 by Vernon Press on behalf of the author.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Vernon Art and Science Inc.
www.vernonpress.com
Vernon Press is an imprint of Vernon Art & Science Inc.
Library of Congress Control Number: 2015952652
Vernon Series in Economic Methodology
ISBN 978-1-62273-134-3
Product and company names mentioned in this work are the trademarks of their respective owners. While every care has been taken in preparing this work, neither the authors nor Vernon Art and Science Inc. may be held responsible for any loss or damage caused or alleged to be caused directly or indirectly by the information contained in it.
Contents
Introduction
The idea of Representative Agents and Lifespan
Teaching DSGE models in undergraduate and graduate courses
Dynare
The structure of the book
Real Business Cycle (RBC) model
Brief theoretical review: Real Business Cycles
Model with two goods
: consumption and leisure
Dynamic structure of consumption-savings
Input markets
The model
Households
Firms
The model’s equilibrium conditions
Steady state
Log-linearization (Uhlig’s method)
Productivity shock
Basic New-Keynesian (NK) model
Brief theoretical review: New-Keynesians
Differentiated Products and the Consumption Aggregator
Firms in monopolistic competition
Price stickiness
The model
Households
Firms
The model’s equilibrium condition
Steady state
Log-linearization (Uhlig’s method)
Productivity shock
New-Keynesian model with wage stickiness
Brief theoretical review: wage stickiness
Why would wages be rigid in the short term?
The model
Households
Firms
The model’s equilibrium condition
Steady state
Log-linearization (Uhlig’s method)
Productivity shock
Is there an interpretation problem related to the assumption of the presence or absence of frictions in the model’s prices and wages?
New-Keynesian model with habit formation and non-Ricardian agents
Brief theoretical review: household rigidity
Habit formation
Non-Ricardian agents
The model
Households
Firms
The model’s equilibrium conditions
Steady state
Log-linearization (Uhlig’s method)
Productivity shock
Is there an interpretation problem related to the presence or absence of household frictions (habit formation and non-Ricardian agents)?
New Keynesian Model with adjustment costs on investment and the under-utilization of maximum installed capacity
A brief theoretical review: adjustment costs on investment and the under-utilization of maximum installed capacity
Adjustment Cost on Investment
Cost of under-utilization of maximum installed capacity
The model
Households
Firms
The model’s equilibrium condition
Steady state
Log-linearization (Uhlig’s method)
Productivity Shock
New-Keynesian Model with government
A brief theoretical review: Government
Introducing taxes into the DSGE models
Government budget constraints
Public investment
Alternative forms of government in the DSGE models
Taylor’s Rule
The model
Households
Firms
Government
Model’s equilibrium condition
Steady state
Log-linearization (Uhlig’s Method)
Monetary and fiscal policy productivity shocks and analysis of the Laffer curve
Productivity and monetary shocks
Fiscal policy shocks
Using taxation for fiscal adjustment
The Laffer curve
References
List of Figures
1.1 The file.mod is read by Dynare’s preprocessor, which calls the Mat- lab routines required to perform the desired operations and display the results. Source: Modified from Griffoli (2011).
2.1 Indifference curve map for consumption and leisure.
2.2 Budget constraint line for the consumption-leisure model..
2.3 Optimal choice of consumption and leisure.
2.4 With a rise in real wages from w1 to w2, the individual chooses more consumption and less leisure.
2.5 With a rise in real wages from w2 to w3, the individual chooses more consumption and the same amount of leisure.
2.6 With a rise in real wages from w3 to w4, the individual chooses more consumption and more leisure.
2.7 Sections at which the income and substitution effects dominate.
2.8 Intertemporal representation of the events of a two-period consumption structure.
2.9 An individual’s intertemporal budget constraint.
2.10 Interaction between the intertemporal budget constraint and an individual’s preference to determine optimal intertemporal consumption.
2.11 Isoquant map.
2.12 Steady state market adjustment structure. The dashed lines represent the labor, capital goods and consumer goods markets.
2.13 Effects of a productivity shock. Results of a Dynare simulation (impulse-response functions).
2.14 Leisure-wage locus. The x and y axes measure deviation in relation to the variable’s steady state in percentage terms. Point I is the inflection point between where the substitution effect and income effect dominate.
2.15 Leisure-consumption locus. The x and y axes measure deviations in relation to the variable’s steady state in percentage terms. Point I is the inflection point between where the substitution effect and income effect dominate.
2.16 Consumption-income locus. The unit on the x and y axes measures percentage deviations in relation to the variable’s steady state. Point I is the inflection point between which the substitution effect and income effect dominate.
2.17 Leisure-income locus. The unit on the x and y axes measure, in percentage terms, deviations in relation to the variable’s steady state. Point I is the inflection point between which the substitution effect and income effect dominate.
3.1 Graph describing the elasticity of substitution between two goods. Moving from point A to point B along the indifference curve (U = U0), both the ratio (c1∕c2) and the MRS will change. Elasticity of substitution ψ is defined as the ratio between these proportional changes. This parameter measures the curvature of an indifference curve.
3.2 A firm in monopolistic competition faces a negatively sloped demand curve for its product. The marginal revenue (MR) curve is below the demand curve, and a profit-maximizing firm’s choice of production occurs when MR=MC. At this point, price exceeds marginal cost (MC).
3.3 Effects of a productivity shock. Dynare simulation results (Impulse-response functions).
3.4 Comparison between impulse-response functions in the RBC and NK models.
3.5 Leisure-wages locus. The x and y axes measure the variable’s deviation in relation to the steady state in percentage terms. Point I is the inflection point between which the substitution effect and income effect dominate.
4.1 An example of contractual wages being higher than market equilibrium wages.
4.2 Effects of a productivity shock. Dynare simulation results (Impulse-response functions).
4.3 Comparison between the RBC, NK and NKWR’s impulse-response functions.
4.4 Leisure-wage locus. The x and y axes measure the variable’s deviation in relation to the steady state in percentage terms. Point I is the inflection point between the periods in which the substitution effect and income effect are predominant.
4.5 Negative productivity shock. The gray area represents the difference between the NKWR and RBC models’ results.
5.1 Impulse-response functions for the NK model with habit formation and non-Ricardian agents.
5.2 Comparison of the RBC, NKWR and NKFR models’ impulse-response functions.
5.3 Leisure-wage locus. The x and y axes measure the variable’s deviation in relation to the steady state in percentage. Point I is the inflection point between which the substitution effect and income effect dominate.
5.4 Counterfactual analysis of habit formation.
5.5 Counterfactual analysis of non-Ricardian agents.
6.1 NK IRF Model with adjustment costs on investment and under-utilization of maximum installed capacity.
6.2 Comparison between the Impulse Response Functions for the RBC, NKFR and NKIR models.
7.1 Steady state market adjustment structure with government. The dashed lines represent the labor, capital goods and consumer goods markets.
7.2 Productivity shock.
7.3 Expansionist monetary shock.
7.4 Government spending shock (G, IG and TRANS).
7.5 Tax rate shocks (τc, τl and τk).
7.6 Share of taxes in the adjustment of the economy given a positive productivity shock.
7.7 Laffer curve for tax on consumption.
7.8 Laffer curve for tax on labor income.
7.9 Laffer curve for the tax on capital income.
List of Tables
2.1 Structure of the model.
2.2 Values of the structural model’s parameters.
2.3 Values of variables at the steady state.
2.4 Structure of the log-linear model.
3.1 Model structure.
3.2 Values of the structural model’s parameters.
3.3 Values of variables at the steady state.
3.4 Structure of the log-linear model.
4.1 Structure of the model.
4.2 Values of the structural model’s parameters.
4.3 Values of variables at the steady state.
4.4 Structure of the log-linear model.
5.1 Structure of the model.
5.2 Values of the structural model’s parameters.
5.3 Values of variables at the steady state.
5.4 Structure of the model.
6.1 Structure of the model.
6.2 Values of the structural model’s parameters.
6.3 Values of Variables at the steady state.
6.4 Structure of the log-linear model.
7.1 Distortionary rates for OECD countries, in 2005.
7.2 Model structure
7.3 Structural model parameter values.
7.4 Variable values in steady state.
7.5 Structure of the log-linear model.
When one resolves to write a book, and hopes that it will be well accepted, one issue arises that should definitely be addressed: What makes this book different from those that have gone before?
This preface seeks to answer this question.
Dynamic Stochastic General Equilibrium (DSGE) models have become a point of reference in modern macroeconomics. What currently makes this methodology so important is its ability to answer any question regarding the behavior of a particular economic phenomenon.
If, on the one hand, the theoretical development of DSGE models is not overly complex to understand, on the other, their practical application is rather more difficult. The literature on this subject presents important, yet obscure points, which are difficult to comprehend. Generally, articles begin with a presentation of the agents’ object functions and of the equations that solve the maximization problem, while their resolution is not shown. In many cases, it is difficult to identify both the exact theoretical model and its application. Thus, the most important part of this type of exercise is overcoming these barriers of obscurity.
Although this methodology has become so popular in the current economic literature, there is no manual that reveals, step-by-step, how this black box
works. This deficiency poses an important challenge, as many young researchers give up this line of research on account of the initial difficulty.
Some books, although not manuals as such, aid in understanding this methodology. Wickens’s Macroeconomic Theory: A Dynamic General Equilibrium Approach
(2011) presents a view of modern macroeconomics that seeks to integrate macroeconomics and microeconomics. It is firmly rooted in general equilibrium models and demonstrates an understanding of the changes that macroeconomic methods are facing. The following four books follow practically the same logic. They begin with a basic model and, as one progresses through the book, several types of friction are incorporated. The books are: Computational Macroeconomics for the Open Economy
by Lim and McNelis (2008); The ABCs of RBCs
by McCandless (2008); Monetary Policy, Inflation, and the Business Cycle
by Galí (2008); and Introduction to Dynamic Macroeconomic General Equilibrium Models
by Torres (2014). There are a further two books that deal with the methodology’s behind the scenes
aspects: Structural Macroeconometrics
by DeJong and Dave (2007), and Methods for Applied Macroeconomic Research
by Canova (2007).
In short, this work takes the best bits from each of the aforementioned books: Lim and McNelis (2008) – organization; McCandless (2008) – presentation of log-linearization and solutions; and Torres (2014) – educational methodology, in a quest for tools that are useful for overcoming initial obstacles to the study of DSGE modeling and persuading young researchers to work with this methodology. In principle, this is not a macroeconomics book per se, but one that presents the tools used in the development of these models. The idea is that it acts as a complement to the books mentioned in the previous paragraph while at the same time presenting the models in greater detail, offering a step-by-step course. The target audiences are advanced undergraduate students, graduate students and experienced economists prepared to learn this methodology. The book begins with a basic Real Business Cycle model and, gradually, the frictions of a standard DSGE model are incorporated: imperfect competition, price and wage frictions, habit formation, non-Ricardian agents, investment adjustment costs, capacity underutilization costs, and lastly, government.
Chapter 1
Introduction
Why tell a story using models instead of telling a story using words? According to