The ABCs of RBCs is the first book to provide a basic introduction to Real Business Cycle (RBC) and New-Keynesian models. These models argue that random shocks—new inventions, droughts, and wars, in the case of pure RBC models, and monetary and fiscal policy and international investor risk aversion, in more open interpretations—can trigger booms and recessions and can account for much of observed output volatility.

George McCandless works through a sequence of these Real Business Cycle and New-Keynesian dynamic stochastic general equilibrium models in fine detail, showing how to solve them, and how to add important extensions to the basic model, such as money, price and wage rigidities, financial markets, and an open economy. The impulse response functions of each new model show how the added feature changes the dynamics.

The ABCs of RBCs is designed to teach the economic practitioner or student how to build simple RBC models. Matlab code for solving many of the models is provided, and careful readers should be able to construct, solve, and use their own models.

In the tradition of the “freshwater” economic schools of Chicago and Minnesota, McCandless enhances the methods and sophistication of current macroeconomic modeling.

PART ONE BASIC MODELS AND SOLUTION METHODS
1  The Basic Solow Model      7
1.1 The Basic Model  7
1.2 Technological Growth  10
1.3 The Golden Rule   11
1.4 A Stochastic Solow Model  12
1.5 Log-Linear Version of the Solow Model  14
1.5.1 Capital  15
1.5.2 Output  16
1.6 Reprise   18
2  Savings in an OLG Model       19
2.1 The Basic OLG Model   20
2.1.1 An Example Economy  26
2.2 Dynamics    27
2.3 A Stochastic Version  28
2.4 Reprise   32
2.5 Matlab Code Used to Produce Figure 2.2  32
3   Infinitely Lived Agents     33
3.1 A Robinson Crusoe Economy with Fixed Labor   34
3.1.1 Variational Methods  34
3.2 A Robinson Crusoe Economy with Variable Labor  38
3.2.1 The General Model  38
3.2.2 Solution for a Sample Economy  40
3.3 A Competitive Economy    41
3.4 The Second Welfare Theorem     44
3.4.1 An Example Where the Representative Agent Economy and the
Decentralized Economy Are Not Equal  45
3.5  Reprise   49
4   Recursive Deterministic Models        50
4.1 States and Controls  51
4.2 The Value Function    52
4.3 A General Version   55
4.4 Returning to Our Example Economy     58
4.4.1 Another Version of the Same Economy  59
4.5 An Approximation of the Value Function  60
4.6 An Example with Variable Labor   63
4.7 Reprise    66
4.8 Matlab Code for Figures 4.2 and 4.3  67
5   Recursive Stochastic Models       69
5.1 Probability   70
5.2 A Simple Stochastic Growth Model   71
5.3 A General Version   74
5.3.1 The Problem of Dimensionality  76
5.4 The Value Function for the Simple Economy   77
5.4.1 Calculating the Value Functions  78
5.5 Markov Chains     80
5.6  Reprise   86
5.7 Matlab Code     87
6   Hansen's RBC Model         89
6.1 Hansen's Basic Model    90
6.2 Log Linearization Techniques   94
6.2.1 The Basics of Log Linearization  95
4   6.2.2 Uhlig's Method of Log Linearization  98
6.3  Log-Linear Version of Hansen's Model    100
6.3.1 Solution Using Jump Variables  104
6.3.2  Calibration of the Log-Linear Model  106
6.3.3  Variances of the Variables in the Model  109
6.4  Hansen's Model with Indivisible Labor   112
6.4.1 Stationary State  115
6.4.2 Log-Linear Version of the Indivisible Labor Model  118
6.5 Impulse Response Functions      120
6.6  Reprise    124
6.7  Appendix 1: Solving the Log-Linear Model    124
6.8  Appendix 2: Blanchard and Kahn's Solution Method     128
6.8.1  General Version  129
6.8.2  Stochastic Shocks  131
6.8.3  Hansen's Model and Blanchard-Kahn  132
6.8.4  The Generalized Schur Method  134
6.9  Matlab Code     142
6.9.1 Solution to Basic Hansen Model  142
6.9.2 Approximating the Variances  143
6.9.3  Code for Appendix 2  144
7   Linear Quadratic Dynamic Programming               146
7.1  Taylor Approximations of the Objective Function   147
7.2  The Method of Kydland and Prescott    148
7.2.1 AnExample     151
7.2.2  Solving the Bellman Equation  154
7.2.3  Calibrating the Example Economy  155
7.3  Adding Stochastic Shocks    157
7.3.1  The Example Economy  160
7.3.2  Calibrating the Example Economy  163
7.4  Hansen with Indivisible Labor   166
7.5 Impulse Response Functions      172
7.5.1  Vector Autoregressions  174
7.6  An Alternative Process for Technology   176
7.7  Reprise    178
7.8  Matlab Code     178
PART TWO     EXTENSIONS OF THE BASIC RBC MODEL
8   Voney: Cash in Advance           183
8.1  Cooley and Hansen's Model     184
8.2  Finding the Stationary State  190
8.3  Solving the Model Using Linear Quadratic Methods    195
8.3.1  Finding a Quadratic Objective Function  196
8.3.2 Finding the Economy Wide Variables  199
8.4  Solving the Model Using Log Linearization   202
8.4.1  The Log Linearization  202
8.4.2  Solving the Log-Linear System  205
8.4.3 Impulse Response Functions  209
8.5  Seigniorage    210
8.5.1  The Model   212
8.5.2  The Stationary State  215
8.5.3  Log-Linear Version of the Model  218
8.6  Reprise    222
8.7  Appendix 1: CES Utility Functions   223
8.8  Appendix 2: Matrix Quadratic Equations    230
8.9  Matlab Code for Solving the CES Model with Seigniorage   233
9   Money in the Utility Function         236
9.1  The Model     237
9.2  Stationary States  240
9.3  Log-Linear Version of the Model   242
9.4  Seigniorage    246
9.4.1  The Full Model  248
9.4.2  Stationary States  248
9.4.3  Log Linearization  251
9.5  Reprise    256
10   Staggered Pricing Model          258
10.1  The Basic Model     259
10.1.1  The Final Goods Firms  259
10.1.2  The Intermediate Goods Firms  261
10.1.3  TheFamily   266
10.1.4 Equilibrium Conditions  267
10.1.5  The Full Model  269
10.2  The Stationary State   270
10.3  Log Linearization    273
10.3.1 fog Linearization of the Firm's Problem  273
10.3.2  The Final Goods Pricing Rule  273
10.3.3  The Intermediate Goods Pricing Rule  273
10.3.4 Inflation Equation (Phillips Curve)  275
10.3.5  Log Linear Version of the Model  277
10.4  Solving the Log Linear Model    279
10.4.1 Impulse Response Functions  285
10.5  Inflation Adjustment for Nonoptimizing Firms    290
10.5.1  The Stationary State  291
10.5.2  Log Linearization  293
10.5.3  Solving the Model  295
10.5.4 Impulse Response Functions  300
10.6  Reprise    304
11   Staggered Wage Setting          306
11.1  The Labor Bundler     307
11.1.1 First-Order Conditions for Families  310
11.1.2  TheRest of the Model  312
11.1.3 Equilibrium Conditions  313
11.1.4  The Full Model  314
11.2  The Stationary State   315
11.3  Log Linearization    317
11.4  Solving the Model    321
11.4.1 Impulse Response Functions  325
11.5  Reprise    327
12   Financial Markets and Monetary Policy             329
12.1  Working Capital    331
12.1.1 Households   331
12.1.2 Firms    333
12.1.3 Financial Intermediaries  334
12.1.4  The Full Model  334
12.1.5  The Stationary State  336
12.1.6  Log Linear Version of the Model  340
12.1.7 Impulse Response Functions  345
12.1.8 Economy with Annual Inflation of 100 Percent  347
12.1.9  Comparative Impulse Response Functions  349
12.2  Central Banking and Monetary Policy Rules    352
12.2.1  The Model with a Taylor Rule  353
12.2.2  Stationary States  356
12.2.3  Log-Linear Version and Its Solution  357
12.2.4  Comparing a Taylor Rule to a Friedman Rule  362
12.3  Reprise    368
13   Small Open Economy Models              370
13.1  The Preliminary Model     371
13. 1. I1 The Household  371
13.1.2  The Firm   374
i     13.1.3 Equilibrium Conditions  374
13.1.4  Stationary State  374
13.1.5  The Dynamic (Log-Linear) Model  376
13.2  Model with Capital Adjustment Costs    379
13.3  Closing the Open Economy       386
13.3.1 Interest Rates and Country Risk  386
13.3.2  The Dynamic Version  388
13.4  The "Closed" Open Economy with Money        393
13.4.1  The Open Economy Conditions  394
13.4.2  The Household   395
13.4.3 Firms    396
13.4.4 Equilibrium Conditions  396
13.4.5  The Full Model  397
13.4.6  The Stationary State  398
13.4.7 Log-Linear Version ofFull Model  400
13.5  Reprise     410
References     411
Index     417