Understanding DSGE models

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.

1 Introduction
1.1 The idea of the Representative Agent and his or her lifetime
1.2 Teaching DSGE models at undergraduate and graduate levels
1.3 Dynare
1.4 The structure of this book
2 Basic Real Business Cycle Model (RBC)
2.1 Brief theoretical review: Real Business Cycle
2.1.1 "Two-good" model: consumption and leisure
2.1.2 Dynamic structure of the consumption-saving trade-off
2.1.3 Input markets
2.2 The model
2.2.1 Households
2.2.2 Firms
2.2.3 Equilibrium conditions
2.2.4 Steady state
2.2.5 Log-linearization (Uhlig's method)
2.3 Productivity shocks
3 Basic New-Keynesian model (NK)
3.1 Brief theoretical review: New-Keynesians
3.1.1 Differentiated goods and consumption aggregator
3.1.2 Monopolistically competitive firms
3.1.3 Price stickiness
3.2 The model
3.2.1 Households
3.2.2 Firms
3.2.3 Equilibrium conditions
3.2.4 Steady state
3.2.5 Log-linearization (Uhlig's method)
3.3 Productivity shocks
4 New-Keynesian model with sticky wages
4.1 Brief theoretical review: sticky wages
4.1.1 Why would wages be sticky in the short run?
4.2 The model
4.2.1 Households
4.2.2 Firms
4.2.3 Equilibrium conditions
4.2.4 Steady state
4.2.5 Log-linearization (Uhlig's method)
4.3 Productivity shocks
4.3.1 How costly would it be in terms of the lack of realism to pick a model without these price and wage frictions over a model including them?
5 New-Keynesian model with habit formation and non-ricardian agents
5.1 Brief theoretical review: household-related frictions
5.1.1 Habit formation
5.1.2 Non-ricardian agents
5.2 The model
5.2.1 Households
5.2.2 Firms
5.2.3 Equilibrium conditions
5.2.4 Steady state
5.2.5 Log-linearization (Uhlig's method)
5.3 Productivity shocks
5.3.1 How costly would it be in terms of the lack of realism to pick a model without these household-related frictions (habit formation and non-ricardian agents) over a model including them?
6 The New-Keynesian model with investment adjustment costs and variable capital utilization
6.1 Brief theoretical review: investment adjustment costs and variable capital utilization
6.1.1 Investment adjustment costs
6.1.2 Variable capital utilization costs
6.2 The model
6.2.1 Households
6.2.2 Firms
6.2.3 Equilibrium conditions
6.2.4 Steady state
6.2.5 Log-linearization (Uhlig's method)
6.3 Productivity shocks
7 New-Keynesian model with government
7.1 Brief theoretical review: Government
7.1.1 Introducing taxes into DSGE models
7.1.2 Government budget constraint
7.1.3 Public Investment
7.1.4 Alternative ways of government in DSGE models
7.1.5 Taylor rule
7.2 The model
7.2.1 Households
7.2.2 Firms
7.2.3 Government
7.2.4 Equilibrium conditions
7.2.5 Steady state
7.2.6 Log-linearization (Uhlig's method)
7.3 Shocks to productivity, to monetary and fiscal policies and Laffer curve analysis
7.3.1 Shocks to productivity and to monetary policy
7.3.2 Shocks to fiscal policy
7.3.3 Using taxes in the fiscal adjustment
7.3.4 Laffer curve
References
Appendices
A Mathematical tools.
A.1 Lagrange optimization
A.1.1 An example
A.2 Matrix and eigenvalue operations
A.2.1 Matrix addition and subtraction
A.2.2 Matrix multiplication
A.2.3 Inverse matrix calculation
A.2.4 Eigenvalues
B Basic ideas about DSGE
B.1 Calibration
B.2 Blanchard e Kahn (BK)'s condition for the existence of a unique stable solution
B.2.1 A textbook example: Chapter 2's RBC model

Celso Costa is Lecturer and Associated Researcher at the Brazilian Macro Center - São Paulo School of Economics (EESP) – FGV recognized as one of the top schools of economics in Latin America. And Adjunct Professor at Universidade Estadual de Ponta Grossa - UEPG. Prior to his present roles, he completed a Post-doctorate in Economics at EESP. He holds a PhD in Economic Development from Universidade Federal do Paraná - UFPR, a Masters degree in Economics from Universidade Estadual Paulista – UNESP and a Bachelor degree in Geophysics from Universidade de São Paulo – USP.