Understanding DSGE models

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 8 Open economy New-Keynesian model 8.1 Brief theoretical review: open economy 8.1.1 National accounts 8.1.2 Basics of the balance of payments 8.1.3 Introducing open economy in DSGE models 8.2 The model 8.2.1 Households 8.2.2 Firms 8.2.3 Government 8.2.4 Exports and Foreign Debt 8.2.5 Equilibrium conditions 8.2.6 Steady state 8.2.7 Log-linearization (Uhlig's method) 8.3 Shocks to productivity, to exports, to international interest rate and to international price level 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