Index

Abel, A. B., 165, 314

Accelerationist hypothesis, 441, 441n25

Accelerators, Samuelson multiplier-accelerator model, 5, 427–429, 427n16

Accounting identities, equations as, 35

Acemoglu, D., 264, 265, 267

Adaptive expectations, 7

path of inflation and unemployment under, 440–444

uncertainty and, 273–275

Adaptive learning, 295

AD-AS (aggregate demand–aggregate supply) model, 413, 422–424

Addition, matrix, 661

Additively separable functions, 60, 655, 694

Adjoint matrix, 664

Adjustment costs, investment with, 313–314

choice of optimal investment, 314–317

determinants of q, 317–318

dynamic adjustments, 318–320

gross investment of firm, 315

investment function, 317

marginal product of capital, 317

Rotemberg model, 450, 457n3, 470–473

uncertainty, 320–327

user cost of capital, 317

zero adjustment costs, 317

Adjustment path

Blanchard-Weil model, 173–177

Ramsey model, 143–145

Adjustment speed, 163–164

Adverse selection, 541

Aggregate capital accumulation, 216–218, 231

Aggregate consumption over time, 172

Aggregate demand–aggregate supply (AD-AS) model, 413, 422–424

Aggregate demand policies

aggregate demand function, 422

impact of, 421, 424–426

natural rate of unemployment and, 439–447

rules versus discretion in, 440–444

Aggregate fluctuations, 375–376.

exogenous preference and productivity shocks, 494–504

inflation and aggregate fluctuations under Taylor rule, 492–504

log-linear stochastic growth model, 386–392

monetary policy and government debt, 26–30

monetary policy in postwar period, 31–32

price level and inflation, 22–26

recession frequency and duration, 18–19

simplified stochastic growth model, 383–386

staggered price adjustment, 457–470

stochastic growth model, 376–377n1, 376–383

unemployment rates in booms and recessions, 20–22

Aggregate investment, rational expectations equilibrium and, 325–327

Aghion, P., 258n1, 267n13, 592

Aiyagari, S.

AK models, 236n2, 237n3, 247–248. See also Learning by doing

Akerlof, G., 310n12, 457n2, 457n3

Alesina, A., 586, 589, 591–592

Algebra. See Linear algebra

Allais, M., 153n1

Almost sure convergence, 713

Alogoskoufis, G., 382n5, 395, 403, 404n7, 475n1, 483n11, 499n20, 500n22, 502n24, 503n26, 571n18, 626n6, 628n11

Andolfatto, D., 532, 534

Andres, J., 535

Angeletos, M., 411, 586, 588

“Animal spirits.” See Sunspots

Antidiagonals, 662

Anti-inflationary reputation, 560–562

ARMA (autoregressive moving average), 720

Arrow, K. J., 231, 232–233, 234. See also Arrow-Debreu model; Arrow-Romer model

Arrow-Debreu model, 7

Arrow-Romer model

Arrow-Romer-Blanchard-Weil model, 242–244

Arrow-Romer-Ramsey model, 239–241

convergence in, 247–248

defined, 232–233

endogenous growth rate, 238–239

externalities from capital accumulation, 234–237

fiscal policy, 245–247

production function, 233–234

real interest rate, 237–238

real wages, 237–238

savings rate, 238–239

suboptimality of the competitive equilibrium, 241–242

variables, 233

Asset purchases, 575

Asymmetric information, 541

Asymptotic convergence, 99, 99n7

Augmented matrix, 662, 664–665

Automatic stabilizers, 585–586

Autoregression, vector, 720–721

Autoregressive moving average (ARMA), 720

Autoregressive processes

autoregressive stochastic processes, 718–719

first-order linear expectational models, 279–286

multivariate linear models, 291–293

rational expectations for, 277–279

second-order linear expectational models, 286–291

simplified stochastic growth model, 385–386, 389, 391

Average real interest rate, 131

Azariadis, C., 10, 159n5, 478n6, 612n9, 613, 618, 620n14

Backus, D., 18n31, 561

Backward-looking expectations, 440

Bairoch, P., 13

Balanced budget multiplier, 418

Balanced growth path. See Steady state

Banking school, 552

Bank of Amsterdam, 333

Bank of England, 31, 333

Banks.

Barro. R. J., 6, 43n7, 79n15, 153–154n1, 188, 201n6, 232, 248n6, 266, 267n13, 395, 396n1, 403, 447n30, 503n25, 535, 558, 561, 581, 586, 588, 625. See also Barro tax-smoothing model

Barro tax-smoothing model, 581–583

Barter, 331

Baumol, W. J., 6, 336n5

Behavioral relations, equations as, 35

Bellman, Richard, 698

Bellman equation, 300, 515, 697–699

Bellman principle of optimality, 303

Bellman value function, 698

Benhabib, J., 602n3, 619

Bernanke, B. S., 333n4, 335, 411n10, 412, 543, 553n3, 565n12, 626n7

Bernoulli, Jacob, 708

Bernoulli distribution, 708

Bernoulli equation, 110–111

Beveridge curve, 510, 513, 514, 521, 522, 524–529, 531, 532, 536

Binder, M., 291, 293

Bivariate distribution, 714

Blanchard, O. J., 4n6, 9, 55, 154, 169, 170, 291–292, 483, 457n2, 468, 475n1, 476n4, 478n6, 478n7, 483–486, 502n23, 531, 535, 601n2, 602n4, 625, 626n6, 628. See also Blanchard-Kahn linear model solution method; Blanchard-Weil model

Blanchard-Kahn linear model solution method, 291–294

Blanchard-Weil model

aggregation across generations, 172

assumptions of, 169, 169n8

balanced growth path in, 173–177

discrete time model, 178

dynamic simulations, 177–182, 194–201, 227–229

efficiency units of labor, 173

externalities and endogenous growth in, 242–244

fiscal policy, 191–201

intertemporal utility function, 170–171

monetary growth in, 222–229

time period, 154

variables, 169–170

Bolton, P., 592

Bonds, 77, 540

Borrowing constraints, precautionary savings and, 310–311

Boundary values, 668, 670

Bretton Woods system, 31

British Bank Act (1844), 552

Brumberg, R., 6, 297n1, 307, 311

Brunnermeier, M. K., 544, 601n2, 609n6, 612n8

Bubbles

defined, 281, 601

deterministic, 604–605

versus fundamentals, 603

linear rational expectations model example, 602–603

money market, 609–611

ruling out unstable, 611–612

as self-fulfilling prophecies, 605–607

stochastic bursting, 605

stock market, 607–608

Buchanan, J.

Buchanan, N. S., 271n3, 275n4

Budget constraints

in Blanchard-Weil model, 201

consumer choice under, 645–647

government budget constraint, 185–187

in imperfectly competitive model, 452–453

money in the utility function approach, 351–353

optimization under, 644–651

in Ramsey model, 130–131

in two-period competitive model, 43–44, 57–58, 70, 78

Burns, A. F., 8–9, 627

Bursting bubbles, 605

Business Cycle Dating Committee, 18

Business cycle theory, 55, 68–69

Business gross profits taxation, 203–205

Caballe, J., 254

Caballero, R. J., 310

Cagan, P., 269n1, 283, 365, 368, 609–610. See also Cagan model of money demand

Cagan model of money demand, 283–284, 609–610

Calibrated Blanchard-Weil model, 177–182, 194–201, 227–229

Calibrated Ramsey model, 148–149

Calibrated Solow model, 113–114

Calvo, G. A., 450, 458. See also Calvo model of government debt crises; Calvo model of staggered pricing

Calvo model of government debt crises, 593–598

Calvo model of staggered pricing

assumptions of, 450, 457–461

divine coincidence and optimal monetary policy in, 451, 468–469

dynamic simulation of, 469–470

equilibrium conditions, 461–462

imperfectly competitive model with, 459–461

new Keynesian Phillips curve, 450, 462–463, 468, 493

optimal pricing with, 459–461

real and monetary shocks, 464–468

Taylor rule, 463–464

unemployment modeling and, 489–493

Campbell, J. Y., 307n6, 383, 386

Capital, cost of, 313–314

convex adjustment costs, 313–320

fixed accelerator models, 314n2

investment rate, 313n1

marginal product of capital, 317

uncertainty, 320–327

user cost of capital, 317

Capital accumulation. See also Convex adjustment costs; Human capital accumulation; Learning by doing

Diamond overlapping generations model, 157–159

externalities from, 234–237

log-linear stochastic growth model, 386–387

Ramsey model, 126–128, 216–218

Solow model, 90–95

Capital income taxation

dynamic effects of, 203–205

dynamic simulations of, 205–206

Cardano, Gerolamo, 703

Cash in advance approach

defined, 209n1

overlapping generations (OLG) models, 355–357, 359

representative household growth model, 353–355, 359

two-period competitive model, 69–70, 71n13

Cass, D., 4, 9, 119, 601, 613, 615n12

CDF (cumulative distribution function), 705

CEIS.

Central banks

anti-inflationary reputation, 560–562

constitutions of, 559–560

function and history, 332–333

money supply and, 210, 333–335

Central limit theorem, 712, 714

CES. See Constant elasticity of substitution (CES) production function; Constant elasticity of substitution (CES) utility function

Chain rules

chain rule of probability, 715

defined, 641

Chamley, C., 586

Characteristic equation, 674

Characteristic polynomials, 679

Chari, V. V., 586, 587, 625

Cheron, A., 534

Chicago Board of Trade, 540

China, per capita output and income in, 13–14, 13n27

Christiano, L. J., 291, 293, 546n7, 554n5, 585n2, 625, 626n6

Christoffel, K., 535

Civil War, monetary policy during, 27

Classical dichotomy, 74

Classical money theory, 2–3, 74

Clower, R., 6, 209n1, 353

Cobb, C. W., 40. See also Cobb-Douglas production function

Cobb-Douglas production function

defined, 653

in extended Solow model, 249

in ideas-and-innovations growth models, 259–260

in log-linear stochastic growth model, 388

in one-period competitive model, 40

in Ramsey model, 145, 148

in simplified Diamond model, 159–162

in Solow model, 89–90, 110–111

in stochastic growth model, 377

in two-period competitive model, 48–49

Cobweb model

absence of uncertainty in, 272–273

adaptive expectations hypothesis, 273–275

rational expectations hypothesis, 275–277

supply and demand functions, 271–272

Cochrane, John, 309n11, 624n3

Coefficients, matrices of, 660

Coefficients, undetermined

first-order linear expectational models, 282

second-order linear expectational models, 288–289

Cofactors, 663

Commodity money, 69, 332

Competitive equilibrium models. See Dynamic stochastic general equilibrium (DSGE) models

Competitive models. See Imperfectly competitive model; One-period competitive model; Perfectly competitive model; Two-period competitive model

Complementary function, 672

Complete linear differential equation, 673

Complex conjugates, 674

Concave functions, 644

Conditional convergence, 110–111

Conditional probability mass function, 714

Conflicts of interest, 542

Constant capital stock condition, 318

Constant coefficients, 669–670

Constant elasticity of intertemporal substitution (CEIS) utility function, 655–657

constant relative risk aversion, 46n8

Frisch elasticity of labor supply, 60

in Ramsey model, 123

in two-period competitive model, 46–48, 54

Constant elasticity of substitution (CES) production function, 90n3, 651–654

Constant elasticity of substitution (CES) utility function, 655

Constant gross investment condition, 318

Constant-intercept Taylor rule, 567n13

Constant relative risk aversion utility function, 46n8

Constant returns to scale, 88

Constraints, budget.

Consumer price index (CPI) inflation

in postwar period, 31–32

stagflation, 24, 31, 434

trends and fluctuations in, 22–26

Consumption. See also Demand for money; Euler equation for consumption; Keynesian models; Ramsey representative household model; Utility function

aggregate over time, 172

Blanchard-Weil model, 170–171

consumption capital asset pricing model, 298, 302–303, 307–308

consumption-labor supply in two-period model, 62–69

consumption-leisure choice in one-period model, 56–62

Gray-Fischer-Taylor unemployment model, 478–481

under income constraints, 645–647

life cycle theory, 6

life cycle theory of, 6, 307, 311

marginal propensity to consume, 416

optimal intertemporal path of, 121–124

permanent income theory, 6, 306–307, 517–519

portfolio choice under uncertainty, 297–311

random walk model of, 301–302

smoothing, 45, 305

Consumption beta, 307

Consumption capital asset pricing model (CAPM), 298, 302–303, 307–308

Continuous functions, 635

Continuous probability distributions, 705–706

Continuous time analysis, 83–84

optimal control method in, 696–697

optimal savings in continuous time, 700–702

Continuous uniform distribution, 594, 708–709

Contour maps, 635

Contracts, long-term, 478

Control variables, 693

Convergence

almost sure, 713

asymptotic, 99, 99n7

with Cobb-Douglas production function, 110–111

conditional convergence, 110

in distribution, 713

in probability, 713

Ramsey model, 143–145

for random variables, 712–713

speed of, 104–106

strong, 713

weak, 713

Convertibility, currency, 27, 29–30

Convex adjustment costs, 313–314

choice of optimal investment, 313–317

determinants of q, 317–318

dynamic adjustments, 318–320

gross investment of firm, 315

investment function, 317

marginal product of capital, 317

Rotemberg model, 450, 457n3, 470–473

uncertainty, 320–327

user cost of capital, 317

zero adjustment costs, 317

Convex functions, 644

Copernicus, 343

Correlation coefficient, 715

Costly price adjustment, 450, 457n3, 470–473

Cost of capital. See Capital, cost of

Covariance, 715

Cowles Commission, 8

CPI inflation. See Consumer price index (CPI) inflation

Cramer’s rule, 664

Cukierman, A., 592

Cumulative distribution function (CDF), 705

Currency school, 552

Current savings and investment per efficiency unit of labor, 92

Damped oscillations, 429

Debt, government. See Government debt

Decentralized competitive equilibrium, 126–128

Deficits, 185–187, 201n6. See also Government debt

Demand for money, 6, 336. See also Euler equation for consumption; Money supply

aggregate capital accumulation, 216–218

Cagan model of money demand, 283–284, 609–610

cash in advance approach, 69–70, 71n13, 209n1, 353–359

classical money theory, 2–3, 74

factors determining, 329–330, 336–339

first-order conditions for optimum, 212–213

inflation and growth rate of money supply, 214–215

money demand function, 213–214, 336–339, 336n5, 420–421, 480

money in the utility function approach, 71n13, 209n1, 211–212

neutrality of money, 71–74, 209–211

opportunity cost of real money balances, 212

perfectly competitive models, 400

quantity theory of money, 71

real money balances, 336

real versus nominal variables, 69, 209

superneutrality of money, 210, 220–221

welfare costs of inflation, 221–222, 345

De Moivre’s theorem, 688

Derivatives of functions, 635–642

Descartes, Rene, 634

Determinants, 662–663

Deterministic bubbles, 604–605

Deterministic models, 7–10, 273. See also Overlapping generations (OLG) models; Representative household growth model

Diagonals and diagonalization, 661–662, 665

Diamond, D., 543

Diamond, P., 4, 9, 55, 119n2, 121, 153, 154, 531, 601. See also Diamond overlapping generations model

Diamond overlapping generations model

assumptions of, 153–154

balanced growth path in, 159–160

basis of, 153n1

capital accumulation and dynamic adjustment, 157–159

dynamic inefficiency in, 164–165

dynamic simulations of calibrated Diamond model, 165–168

intertemporal utility function, 155–156

markets and household behavior, 156–157

population growth, 161–162

production function, 155

pure rate of time preference, 160–161

self-fulfilling expectations, 159n5

simplified, 159–164

time period, 154

total factor productivity, 162

variables, 155

welfare implications, 164–165

Difference equations

first-order linear, 686–687, 689–692

lag operators, 683–685

second-order linear, 687–689

Differential equations

boundary values, 668

defined, 667–669

first-order linear, 669–672, 675–682

general solutions, 668

linear versus nonlinear, 668

particular solutions, 668

second-order linear, 673–675

Differentiation, 637

Digital money, 69

Direct finance, 540

Discrete probability distributions, 704–705

Discrete time. See also Stochastic processes

Blanchard-Weil model in, 178

intertemporal models in, 82–84

Ramsey model in, 146–148

Solow model in, 112–113

Discrete uniform distribution, 707–708

Discretionary aggregate demand policies, 414

Discretionary monetary and fiscal policy, 429–430

credibility issues, 556

with full employment target, 431–432

Tinbergen-Theil theory, 431

Distortionary taxation, 76, 201–203

Distribution, convergence in, 713

Distributional considerations, politics and, 589–590

Distributions, probability. See Probability distributions

Divergent oscillations, 429

Diversification, 541

Divine coincidence, 451, 468–469, 501–502

Dixit, A. K., 454n1, 482n10, 633n1, 693n1

Domar, E. D., 4, 87, 106, 653

Douglas, P. H., 40

Downsian median voter models, 590

Drachma, monetary reform of, 346

Drazen, A., 590, 592

Dreze, J., 310

Driffill, J., 561

DSGE. See Dynamic stochastic general equilibrium (DSGE) models

Dybvig, P., 543

Dynamic inefficiency, 101, 164–165

Dynamic programming, 697–699

Dynamic Ramsey approach, 586–587

Dynamic simulations

Blanchard-Weil model, 177–182, 194–201, 227–229

Calvo model of staggered pricing, 469–470

Diamond model, 165–168

Gray-Fischer-Taylor unemployment model, 504–506

log-linear stochastic growth model, 391–392

Ramsey model, 149–152

Solow model, 114–117

Dynamic stochastic general equilibrium (DSGE) models, 7, 375–376. See also Gray-Fischer-Taylor unemployment model; Imperfectly competitive model; Perfectly competitive model

history of, 7–10

log-linear stochastic growth model, 386–392

policy evaluation and, 628–629

shortcomings of, 625–626, 626n8

simplified stochastic growth model, 383–386

stochastic growth model, 376–377n1, 376–383

Dynamic stochastic models under rational expectations. See also Stochastic processes

characteristics of, 269–271

first-order linear expectational models, 279–286

learning dynamics, 295

multivariate linear models, 291–293

rational expectations for linear autoregressive processes, 277–279

rational expectations hypothesis, 275–277

second-order linear expectational models, 286–291

Econometric models, 5, 627

Econometrics, 8n21

Economic growth process, Kaldor facts of, 107, 265–266

Edgeworth, F. Y., 552

Education, spending on, 249–250

Effective federal funds rate, 566

Efficiency units of labor

in Blanchard-Weil model, 173

in Solow model, 91–92

in stochastic growth model, 378–380

Efficiency wage theories, 477–478

Efficient markets hypothesis (EMH), 308–310

Eggerstsson, G. B., 544, 573, 574, 585n2

Eigenvalues, 665, 676–682

Eigenvectors, 665, 679–682

Elasticity of labor supply, 397

Elasticity of steady state output, 101–102

Elasticity of substitution. See also Constant elasticity of intertemporal substitution (CEIS) utility function

constant elasticity of substitution (CES) production function, 90n3, 651–654

constant elasticity of substitution (CES) utility function, 655

Electoral factors, fiscal policy and, 590–592

Elements, matrix, 660

EMH (efficient markets hypothesis), 308–310

Empirical macroeconomics, role of, 626–628

Employment. See Labor market; Unemployment modeling; Unemployment rates

Endogenous-growth models, 231–232. See also Learning by doing; Solow model

defined, 96

extended Solow model, 249–252

ideas-and-innovations growth models, 258–262

institutions and long-run growth, 263–265

Jones model of human capital accumulation, 252–253

Kaldor facts of economic growth, 265–266

Lucas model, 253–258

savings rate and, 238–239

unified growth theory, 262–263

Endogenous variables, 35, 634, 663–666

Endowment economies, 347–351

Endowments, household, 36–38

Envelope theorem, 300

Equilibrium conditions. See also Equilibrium unemployment; General intertemporal equilibrium

in Calvo model of government debt crises, 593

in Calvo model of staggered pricing, 461–462

equations as, 35

with high inflation, 368

in IS-LM model, 419, 420

in labor market, 62, 66

in Lucas model, 403–406

in market for goods and services, 417

in perfectly competitive model, 398–400

in product market, 61–62, 66

rational expectations equilibrium, 325–327

short-run equilibrium in money market, 339–342

in Solow model, 85–86

staggered price adjustment and, 461–462

sunspots, 601–602, 612–620

time-consistent equilibrium, 561

time-inconsistent reputational equilibrium, 561

Equilibrium state. See Steady state

Equilibrium unemployment, 509–510

Beveridge curve, 510, 513

dynamic adjustment to steady state, 527–534

firms and creation of vacancies, 513–517

flows into and out of employment, 512–513

job destruction, 527

labor market flows, 512–513

labor market tightness, 509

labor productivity, 523–525

matching function, 510–512

nominal rigidities and, 534–535

numerical simulations of, 532–534

real interest rate and, 527

unemployed job seeker behavior, 517–519

unemployment benefit, 525–526

wage bargaining and wage equation, 519–521

wage determination and equilibrium unemployment, 521–522

Equity premium puzzle, 308

Erceg, D. J., 462n6, 468n11, 476n3, 502n23, 554n5

Estimation errors, 569

Euler equation for consumption, 702

distortionary taxation and, 202–203

monetary model, 215–216

Ramsey model, 122–123, 129–130, 147

stochastic growth model, 383–384, 387

two-period competitive model, 45–46, 50, 64, 72

Euro, creation of, 346

Evans, G. W., 295

Events

defined, 705

interaction with ideas, 623–630

Excess output, 465

Exchanges, 540

Exogenous growth models, 109. See also Individual models

Exogenous stochastic shocks, optimal monetary policy in, 562–564

Exogenous variables, 35, 284–286, 634

Expectational models. See also Rational expectations hypothesis

adaptive expectations, 273–275

cobweb model, 271–277

expectations theory of the term structure, 567

first-order linear, 279–286

static expectations, 273

Expectations-augmented Phillips curve, 7, 476, 487–488, 501, 547, 554

Expected aggregate employment, 484–485

Expected duration of unemployment, 512

Expected values, 706–707

Expenditure, government. See Government expenditure

Exponential function, derivative of, 640

Extended Ramsey model, 377

Extended Solow model, 553n3

balanced growth path in, 250–251

endogenous growth in, 251–252

spending on education/training, 249–250

External finance premium, 542–543

Externalities from capital accumulation. See also Learning by doing

Arrow-Romer model, 234–239

Blanchard-Weil model, 242–244

Ramsey model, 239–241

Ezekiel, M., 271n3, 275n4

Factorization

first-order linear expectational models, 281

second-order linear expectational models, 287–288

Faia, E., 535

Fama, E. F., 308n9, 309–310

Farmer, R. E. A., 10, 602n3, 607n5, 619, 620n14

Federal funds rate, 565–566

Federal Open Market Committee, 566

Federal Reserve System, 28, 31, 335, 565–566

Feenstra, R. C., 209n1

Financial accelerator model, 543

Financial intermediation, 541–543

Financial market frictions

finance markets, role of, 539–541

financial intermediation and, 541–543

links between financial sector and real activity, 543–544

in model with unemployment persistence and nominal wage contracts, 546–548

in new Keynesian model with staggered pricing, 544–546

open market operations, 565–566

stock market bubbles, 607–611

zero lower bound on interest rates, 571–576, 585–586

Firm behavior. See also Investment decisions of firms; Production functions

creation of vacancies, 513–517

in one-period competitive model, 38–40

perfectly competitive model, 397–398

in stochastic growth model, 377–378

technology and optimal output path, 48–49

in two-period competitive model, 65–66

value of firm under uncertainty, 321–323

First difference operator, 83

First moment of random variable, 706–707

First-order linear difference equations

general solutions, 686–687

n first-order, 690–692

pair of, 689–690

First-order linear differential equations

constant coefficients, 669–670

convergence and stability of, 672–673

homogenous, 671–672

nonhomogenous, 671–672

nth-order system of, 678–682

pair of, 675–678

variable coefficients, 671

variable right-hand side, 670–671

First-order linear expectational models

economic examples of, 282–284

exogenous variables, evolution of, 284–286

expectational models and, 286

factorization method, 281

law of iterated expectations, 279

repeated substitutions, 279–281

undetermined coefficients method, 282

Fiscal policy, 183–184. See also Government debt

in Blanchard-Weil model, 191–201

business gross profits taxation, 203–206

capital income taxation, 203–206

discretionary, 429–433

distortionary taxation, 201–203

endogenous growth and, 245–247

fiscal theory of price level, 363

government budget constraint, 185–187

government debt, 26–30

implications of, 81–82

income taxes and aggregate savings, 78–81

income taxes and labor supply, 76–77

nondistortionary taxation, 201–203

in one-period economy, 74–76

politics in, 589–592

in Ramsey model, 188–191

Ricardian equivalence, 78–81, 183–184, 187–191, 188n2, 579–580

in two-period economy, 77–78

Fischer, S., 169n7, 221n4, 333n3, 365n14, 457n3, 475, 483, 553n2. See also Gray-Fischer-Taylor unemployment model

Fisher, Irving, 3, 42, 55, 119, 121, 153n1, 154n3, 156, 157n4, 212, 269n1, 402n5, 419n9, 435n19, 543, 546, 548, 552, 553. See also Fisher equation; Fisher rule

Fisher equation, 72, 72n14, 212, 218, 220, 400, 401, 456, 494,

Fisher rule, 402n5

Fixed accelerator models, 314n2

Fixed inflation rule, 559

Fixed nodes, 678

Fixed-proportions production function, 653

Fixed-proportions utility function, 655

Flexible accelerator model, 6, 314n2

investment under uncertainty, 323–327

value of firm under uncertainty, 321–323

Flood, R. P., 612

Flows into and out of employment, 512–513

Forcing terms, 671

Foresight, perfect, 272–273

Forward guidance, 574

Forward shift operator, 325

Free entry, 516–517

Friedman, M., 6, 221n4, 269n1, 297n1, 307, 311, 333n4, 336n5, 359, 412, 415, 424n13, 437–441, 448, 456, 552, 553, 558n8, 585, 629

Friedman, Milton, 344, 439

Frisch, R., 1n1, 3, 8–9, 8n21, 58–60, 376

Frisch demand for leisure, 60

Frisch elasticity of labor supply, 60, 67, 76, 397, 453

Full employment target, monetary policy with, 431–432

Full rank matrix, 662

Functions, 633–634. See also Production functions; Utility function

additively separable, 694

Bellman value function, 698

complementary, 672

conditional probability mass function, 714

constraints, optimization under, 644–651

continuous, 635

cumulative distribution, 705

defined, 634–635

derivatives and partial derivatives of, 635–642

Hamilton, 695–696, 700–702

joint probability mass function, 714

marginal probability mass function, 715

matching, 510–512

maxima/minima, 642–643

objective, 644

probability density, 705–706

probability mass, 705

rational, 684

slope of, 637

stationary points, 642–643

total differential of, 642

Functions, defined, 35. See also Individual functions

Fundamental solutions, 280, 601

Fundamental solutions, defined, 603

Future mathematical expectations operator (F), 281, 287

Gali, G., 7n17, 462n6, 464n7, 464n8, 468, 498n19, 502n23, 535, 554n4, 625

Galor, O., 8n19, 262, 263, 267n13

Garber, P. M., 612

Gauss-Jordan elimination, 664

GDP (gross domestic product). See Gross domestic product (GDP)

Geanakoplos, J., 543

General intertemporal equilibrium

concept of, 33

and determination of output and employment, 61–62, 66–68

one-period competitive model, 40–42

perfectly competitive model, 398–400

two-period competitive model, 49–55

Generalized Solow model, 109n13, 232

General solutions, 668, 670

General Theory of Employment, Interest and Money, The (Keynes), 1, 3, 413, 416, 416n3, 475–476, 623. See also Keynesian models

Geometric polynomials, 684–685

Gertler, M., 333n4, 535, 543, 544, 626n7

Ghironi, F., 625, 626n7

Global maximums, 644

Global minimums, 644

GNI. See Gross national income (GNI) per capita

Goldberger, A., 5, 8, 627

Golden rule capital stock, 100

Golden rule savings rate, 99–101

Gold standard, 23, 26–30, 552

Goodfriend, M., 7, 461n5, 494n14, 625

Gordon, D., 447n30, 478n6, 503n25, 558, 561

Gould, J., 314

Government budget constraints, 185–187

Government debt

in Blanchard-Weil model, 191–194

bonds, 77, 540

burden of, 592–593

Calvo model of government debt crises, 593–598

debt-default conditions, 593

debt-deflation theory, 543

debt-holding conditions, 593

debt-holding curve, 594

Keynesian stabilization policy, 585–586

long-run effects, 201n6

monetary policy and, 26–30

multiple equilibria, 580–581, 599–600

optimal dynamic Ramsey taxation, 586–589

overlapping generations models and, 184

in Ramsey model, 188–191

Ricardian equivalence, 78–81, 183–184, 187–191, 188n2, 579–580

rise in, 580

solvency and, 185–187

tax smoothing, 195, 581–584

in two-period competitive model, 77–82

Government deficits, 185–187, 201n6

Government expenditure. See also Fiscal policy

in Blanchard-Weil model, 191–192

in one-period economy, 74–76

primary, 78

in Ramsey model, 188–191

in stochastic growth model, 378–380

in two-period competitive model, 77–78

Government intertemporal budget constraint, 78

Gray, J. A., 475

Gray-Fischer-Taylor unemployment model

alternative views of labor market, 477–478

assumptions of, 475–477

dynamic simulations, 504–506

firm pricing and production, 481–483

household consumption and demand, 478–481

inflation and aggregate fluctuations under Taylor rule, 494–502

monetary and real shocks, 504–506

optimal Taylor rule, 502–504

Phillips curve, 488

staggered price adjustment, 489–492

staggered pricing with periodic nominal wage contracts, 492–494

unemployment persistence and wage determination, 485–488

wage setting, 483–487

Great Depression

causes of, 412

government debt during, 28–29

Lucas model and, 410–411

persistence of, 411n10

severity and duration of, 19

theories of, 543

unemployment rates, 20–21

Great Recession (2008–2009), 28–29, 412, 624

Greece, monetary reforms in, 346

Greenbacks, 27

Grilli, V., 592

Gross domestic product (GDP), 11n26, 28. See also Recessions

Grossman, H., 6, 535

Grossman, G.M., 258n7

Gross national income (GNI) per capita

cross-country differences, 11–13

defined, 11n26

economic growth and convergence since 1820, 14–17

evolution over time, 13–14

growth rates, 14n28

Growth theory

new growth theory, 8, 8n19

two-period representative household model and, 55

unified growth theory, 8

Guerrieri, V., 544

Haavelmo, T., 8, 418, 627

Half-life, convergence, 106

Hall, R. E., 535

Hamilton function, 121–122, 128–129, 695–696, 700–702

Hansen, A. H., 3, 3n5, 5, 413, 419n8

Hansen G., 262n10, 382n5, 478n8

Hansen L.P., 307n6,

Harrod, R. F., 4n2, 87, 653. See also Harrod–Domar model

Harrod–Domar model, 87, 106

Harrod neutral technical progress, 88

Hayashi, F., 314

Hicks, J. R., 3, 5, 58, 89, 231n1, 333n4, 413, 419

Hicksian substitution effect, 58–59

Higher moments, 707

High-powered money, 334

History of macroeconomics

deterministic and stochastic dynamic general equilibrium models, 7–10

Keynesian macroeconomics, 4–5

microeconomic foundations, 6–7

new classical macroeconomics, 7

pre-Keynesian macroeconomics, 2–4

research focus, 1–2

Hodrik, R. J., 18n31, 386

Homogeneous nonstationary stochastic processes, 718

Homogenous differential equations

first-order, 671–672

second-order, 673–674

Honkapohja, S., 295

Household model. See Representative household growth model

Human capital accumulation, 232, 248–249

extended Solow model, 249–252

Jones model, 252–253

Lucas model, 253–258

Hume, D., 2, 3, 25, 343

Huygens, Christiaan, 703

Hyperbolic absolute risk aversion (HARA) utility functions, 303

Hyperinflation

Cagan model of money demand, 283–284, 609–610

causes of, 368–371

tackling, 371–372

Ideas-and-innovations growth models

balanced growth path in, 261–262

characteristics of, 258

key elements of, 259–261

key features of, 258–259

nonrivalrous ideas, 258

rate of technical progress, 261

Ideas/events interaction, 623–624

empirical macroeconomics, role of, 626–628

financial crisis and, 624–626

policy evaluation and DSGE models, 628–629

Identity matrix, 662

Imperfectly competitive model, 446

assumptions of, 451–452

characteristics of, 449–451

full price flexibility, 455–456

natural rates, 455–457

representative firms, 454–455

representative households, 452–454

Implementation errors, 569

Impulse response function, 98–99, 98n6, 116–117

Inada conditions, 88, 94–96, 654

Income effect, 133

Income taxes

aggregate savings and investment and, 81

distortionary taxation, 76

labor supply and, 76–77

Indeterminacy

price level, 361–364

sunspots and, 612–620

Index sets, 715

Inefficiency, dynamic, 101

Infinite horizon growth models. See also Ramsey representative household model; Solow model

infinite-horizon transversality condition, 132

infinite-period intertemporal models, 82–84

Inflation

adaptive expectations, 440–444

central bank anti-inflationary reputation, 560–562

equilibrium, 73

fixed inflation rule and monetary policy, 559

growth rate of money supply, 214–215

hyperinflation, 283–284, 368–372

inflationary bias, 444, 558

inflation-based nominal interest rate rule, 401–402

inflation tax, 216–218

long-run neutrality of money, 343–347

money market bubbles and, 609–611

optimal inflation theory, 502–504

in postwar period, 31–32

rational expectations hypothesis, 446–447

relation with monetary growth and seigniorage, 365–367

social welfare loss from, 555–556

stabilization of, 501–502

stagflation, 24, 31, 434

Taylor rule and, 494–504

trends and fluctuations in, 22–26

in two-period competitive model, 69–74

welfare cost of, 221–222, 346

Informational frictions, 411

Initial conditions, 670

Inner products, 661

Insider-outsider model, wage setting in, 483–488

Institutions, long-run growth and, 263–265

Instruments, policy, 429–430

Integrating factor, 669

Integration, 637

Interest rates

average real, 131

Fisher equation, 72, 72n14, 400–401, 456

interest rate pegging and price level indeterminacy, 361–364

in learning-by-doing models, 237–238

nominal, 357–361, 401–402

opportunity cost of real money balances, 212

prime rate, 566

in Ramsey model with money, 216

real, 357–361

in Solow model, 96–97

Taylor rule, 450–451, 463–464, 464n7

term structure of, 566–567

Wicksell interest rate rule, 362–363, 363n12, 401

zero lower bound on, 571–576, 585–586

Intertemporal budget constraints. See Budget constraints

Intertemporal logarithmic utility function, 657

Intertemporal model, infinite-period, 82–84

Intertemporal model, one-period

assumptions of, 33–34

consumption and labor supply, 56–62

general equilibrium, 40–42

government expenditure and taxes, 74–77

nature and components of, 34–35

optimal behavior of households, 36–38

profit-maximizing behavior of firms, 38–40

Intertemporal model, two-period

consumption and labor supply, 62–69

fiscal policy, 74–82

general equilibrium, 49–55

implications for growth and business cycle theory, 55

saving and investment, 42–55

Intertemporal optimization

dynamic programming and Bellman equation, 697–699

form of problems, 693–694

optimal control method, 694–697

optimal intertemporal path of consumption, 121–124

optimal savings in continuous time example, 700–702

Intertemporal substitution effect

Ramsey model, 133

stochastic growth model, 381–382, 382n5

Intertemporal utility function. See Utility function

Inversion, matrix, 661–663

Investment decisions of firms, 313–314. See also Human capital accumulation; Labor market; Savings and investment

convex adjustment costs, 313–320

fixed accelerator models, 314n2

investment rate, 313n1

marginal product of capital, 317

uncertainty, 320–327

user cost of capital, 317

IS-LM model, 3, 3n5, 5, 413, 419–421

equilibrium conditions, 419, 420

neo neoclassical synthesis IS-LM functions, 494

Isoquants, 635, 652

Iterated expectations, law of, 279

Japan, per capita GNI (gross national income), 14–17

Jevons, W. S., 552, 613n10

Jevons sunspot theory, 613n10

Jobs. See Labor market

Joint probability distributions, 714–715

Joint probability mass function, 714

Jones, C. I., 11n25, 107n11, 109n13, 111n14, 232, 252, 258n7, 265–267. See also Jones model of human capital accumulation

Jones model of human capital accumulation, 252–253

Jorgenson, D., 6, 313, 314

Judd, K. L., 291, 293

Jung, T., 573

Justiniano, A., 544

Kahn, C., 291–293, 466

Kaldor, Nicholas, 107, 107n12, 238, 265–266, 271n3, 274

Kaldor facts of economic growth, 107, 265–266

Kehoe, P. J., 18n31, 586–587, 625

Keynes, John Maynard, 1–4, 123n4, 333n4, 336n5, 344, 367n16, 413, 416n3, 417n4, 418n7, 419, 421n10, 424n11, 475–476, 572, 613, 623, 629. See also General Theory of Employment, Interest and Money, The (Keynes); Keynesian models; Keynes-Ramsey rule

Keynesia models, 4–5. See also New Keynesian models

AD-AS model, 413, 422–424

aggregate demand policies, 414, 421, 424–426, 439–447

characteristics of, 413–415

discretionary monetary and fiscal policy, 429–433

IS-LM model, 413, 419–421

Keynesian cross, 413, 416–419, 417n5, 419n8

Keynesian revolution, 4n6

liquidity preference, 336n5

liquidity traps, 421, 421n10, 572–573

new Keynesian Phillips curve, 450

Phillips curve, 414–415, 435–439, 435n19

Samuelson multiplier-accelerator model, 5, 419, 427–429

stabilization policy, 585–586

Keynes-Ramsey rule, 123n4

King, R. G., 7, 377n1, 625, 627

Kiyotaki, N., 457n2, 543, 544

Klein, L. R., 4n6, 5n8, 8, 627–628

Klein, M., 633n1, 659n1, 667n1, 683n1, 693n1

Klein, P., 291, 293. See also Klein linear model solution method

Klein linear model solution method, 293

Kocherlakota, N. R., 587n3, 588

Kolmogorov, Andrey Nikolaevich, 704

Koopmans, T., 4, 9, 119

Koyck, L. M., 269n1

Krause, M. U., 535

Krishnamurti, A., 544

Krugman, Paul R., 544, 573, 574, 576n21, 585n2, 624n3, 625n4

Kurtosis, 707

Kydland, F. E., 7, 377n1, 446, 447n30, 503n25, 552, 558, 588, 629

Labor, efficiency units of

in Blanchard-Weil model, 173

in Solow model, 91–92

Labor market, 478, 509–510. See also Labor supply; Unemployment modeling; Wages

Beveridge curve, 510, 513

dynamic adjustment to steady state, 527–534

equilibrium conditions in, 62, 66

firms and creation of vacancies, 513–517

flows into and out of employment, 512–513

job creation, 513–517

job destruction, 527

labor augmenting technical progress, 88

labor productivity, 523–525

matching function, 510–512

nominal rigidities and, 534–535

real interest rate and, 527

tightness of, 509

unemployed job seeker behavior, 517–519

unemployment benefits, 525–526

wage bargaining and wage equation, 519–521

wage determination and equilibrium unemployment, 521–522

Labor supply

efficiency units of labor, 91–92, 173

efficiency wage theories, 477–478

Frisch elasticity of, 60, 397, 453

income and substitution effects on, 58–60

income taxes and, 76–77

intertemporal substitution in, 381–382, 382n5

long-term contracts, 478

new Keynesian Phillips curve, 450, 462–463, 468, 493

in one-period competitive models, 56–62

search or matching theories, 478

in stochastic growth model, 380–382

in two-period competitive model, 62–69

Laffer, Arthur, 367n16

Laffer curve, 367–368, 367n16

Lag operators, 281, 683–685

Lagrange, Joseph Louis, 636

Lagrange method, 647–651

in Lucas-Prescott model, 324

in money in the utility function of representative household, 351–352

in one-period competitive model, 37, 57

optimization of, 694–696

in Ramsey model, 147

in Samuelson OLG model with money, 615

in stochastic growth model, 380, 381

in two-period competitive model, 44–45, 63, 70–71

in unemployment model, 480

Langot, F., 534

La’O, J., 411

Laplace, Pierre, 703

Large numbers, law of, 713

Law of iterated expectations, 279

Law of large numbers, 713

Learning approach to expectations, 295

Learning by doing, 231

Blanchard-Weil model, 242–244

convergence in, 247–248

defined, 232–233

endogenous growth rate, 238–239

externalities from capital accumulation, 234–237

fiscal policy, 245–247

production function, 233–234

Ramsey model, 239–241

real interest rate, 237–238

real wages, 237–238

savings rate, 238–239

suboptimality of the competitive equilibrium, 241–242

variables, 233

Leeper, E. M., 363

Leibniz, Gottfried Wilhelm, 636

Leijonhufvud, A., 6

Leisure

consumption-leisure choice in one-period model, 56–58

Frisch demand for, 60

Marshallian demand for, 58–60

Leland, H., 310

Lenders of last resort, 552

Leontieff, W., 87

Leontieff production function, 87, 90, 106, 653

Leverage, 542–543

L’Hopital’s rule, 46, 46n9, 125, 653, 655, 657

Lian, C., 411

Life cycle theory, 6, 307, 311

Linear algebra

example with two endogenous variables, 663–666

matrix addition, 661

matrix elements, 660–661

matrix inversion, 661–663

matrix multiplication, 661

matrix subtraction, 661

Linear autoregressive processes

autoregressive stochastic processes, 718–719

first-order linear expectational models, 279–286

multivariate linear models, 291–293

rational expectations for, 277–279

second-order linear expectational models, 286–291

Linear difference equations

first-order, 686–687, 689–692

second-order, 687–689

Linear differential equations

characteristics of, 668

first-order, 669–672, 675–682

second-order, 673–675

Linear functions, derivative of, 638

Linear intertemporal utility function, 657

Linear models

bubbles in, 281, 601–612

defined, 659–660

Linear production function, 653

Linzert, T., 535

Liquidity effect, 340–341, 360–361

Liquidity preference, 336n5

Liquidity traps, 421, 421n10, 572–573

Lira, monetary reform of, 346

Local maxima/minima, 642–644

Location parameters, 706

Lockwood, B., 592

Logarithmic function, derivative of, 640

Logarithmic preferences

portfolio choice under uncertainty, 303–304

simplified Diamond model, 159–162

Log-linear stochastic growth model

capital accumulation process, 386–387

dynamic simulations, 391–392

production function, 386

steady state, 388–391

Long-run economic growth. See also Solow model

cross-country differences in per capita output and income, 11–13

economic growth and convergence since 1820, 14–17

evolution in per capita output and income over time, 13–14

growth rates, 14n28

in pre-Keynesian macroeconomics, 2

Long-run neutrality of money, 25–26, 343–347

Long-term contracts, 478

Lorenzoni, G., 544

Lubik, T. A., 535

Lucas, R. E., Jr., 7–9, 8n19, 25, 64n11, 221n4, 232, 253–254, 262n10, 269n1, 307n7, 314, 323, 325, 327, 353, 377n1, 382n5, 395, 403, 404n7, 406n9, 410, 411n10, 412, 446n29, 449–451, 462–463, 468, 473–474, 499n21, 581, 586, 588, 624n3, 625, 627–629, 716. See also Lucas and Raping equilibrium labor market model; Lucas model; Lucas-Prescott model

Lucas and Raping equilibrium labor market model, 411n10

Lucas model

competitive equilibrium under imperfect information, 403–406

equilibrium conditions, 403–406

Great Depression and, 410–411

history of, 403

human capital accumulation, 253–258

informational frictions and rational inattention, 411

monetary shock effects, 407–410

optimal monetary policy in, 410

output and employment, 406–407

Lucas-Prescott model, 323–327

Lump sum taxes, 75

Machowiak, B., 411

Macroeconomic models, concept of, 33–34, 633–634. See also Individual models

Maddison, A., 11n26, 13–14

Maddison Project, 14

Main diagonals, 661

Malthus, T. R., 2

Mankiw, N. G., 7, 106, 109n13, 232, 248n6, 249, 266, 307n6, 377n1, 411, 457n2, 625, 629

Marginal change, 637

Marginal probability mass function, 715

Marginal propensity to consume, 416

Marginal propensity to save, 416

Marginal rate of substitution (MRS), 46

Marginal utility, 637

Marshall, A., 3n3, 40, 552

Marshallian demand for leisure, 58–60

Matching frictions in labor market. See Matching models of labor market

Matching function, 510–512

Matching models of labor market, 478, 509–510, 535–537

Beveridge curve, 510, 513

dynamic adjustment to steady state, 527–534

firms and creation of vacancies, 513–517

flows into and out of employment, 512–513

job destruction, 527

labor market flows, 512–513

labor market tightness, 509

labor productivity, 523–525

matching function, 510–512

nominal rigidities and, 534–535

numerical simulations of, 532–534

real interest rate and, 527

unemployed job seeker behavior, 517–519

unemployment benefits, 525–526

wage bargaining and wage equation, 517–519

wage determination and equilibrium unemployment, 521–522

Mathematical expectation, 706

Mathematical functions. See Functions

Mathematical macroeconomic models, concept of, 33–34, 633–634. See also Individual models

Matrices of coefficients, 660

Matrix addition, 661

Matrix inversion, 661–663

Matrix multiplication, 661

Matrix subtraction, 661

Maturity premiums, 540

Maxima of functions, 642–643

Maximum principle, 695–696

McCallum, B. T., 291, 293, 363, 553n3, 564

Mean values, 706–707

Measure theory, 704

Meltzer, A., 333n4, 553, 592

Merton, R. C., 298, 303, 307n7, 311

Merz, M., 532, 534

Metallic monetary systems, 26

Method of substitution, 465–468, 665, 675–676

Method of undetermined coefficients, 673

Mexico, monetary reforms in, 346

Michaillat, P., 535

Mill, J. S., 2, 3, 343, 552

Minima of functions, 642–643

Mirlees, J. A., 588

Mises, Richard von, 704

Mises, L. von, 3

Mitchell, W. C., 8–9, 627

Models, concept of, 33–34, 633–634. See also Individual models

Modified golden rule, 138–139

Modigliani, F., 3, 5n10, 6, 297n1, 307, 310–311, 333n4, 413, 422, 572

Monetarism, 344

Monetary authorities

functions of, 332–333

money supply and, 210, 333–335

Monetary base, 333–334

Monetary policy, 468–469, 551

Bretton Woods system, 31

convertibility, 27, 29–30

discretionary, 429–433

divine coincidence and, 468–469

financial market frictions, 571–576

financial markets and open market operations, 565–566

gold standard, 26–30

government debt and, 26–30

interest rate term structure, 566–567

liquidity traps, 421, 421n10, 572–573

in Lucas model, 410

monetarism, 344

monetary reforms, 346

in new Keynesian models, 468–469, 554–562

optimal policy rules, 569–570

policy errors, 569–570

in postwar period, 31–32

rules versus discretion in, 552–562

staggered pricing mode and, 554n5

stochastic shocks and, 562–564

Taylor rule and, 567–569

transmission mechanisms, 333n4

zero lower bound on interest rates, 571–576, 585–586

Monetary shock effects

new Keynesian models, 464–468

perfectly competitive models, 395, 405n8

in rational expectations equilibrium, 407–410

stochastic growth models, 376

unemployment modeling, 504–506

Monetary theory, 2–3, 74

Money demand function, 213–214, 336–339, 336n5, 420–421, 480

Money in the utility function approach, 71n13, 209n1, 211–212

defined, 209n1

money and price level, 351–353

nominal and real interest rates, 357–359

Money market, 329–330. See also Demand for money; Money supply

bubbles in, 609–611

central banks, 210, 332–335, 560–562

commodity money, 332

fiscal theory of price level, 363

functions of money, 331

interest rate pegging and price level indeterminacy, 361–364

liquidity effect, 340–341, 360–361

monetary base, 333–334

nominal interest rates, 339–342, 345, 357–361

price level and, 347–357, 363

quantity theory of money, 337n6, 343–344

real interest rates, 357–361

seigniorage, 27–28, 217, 330

short-run equilibrium, 339–342

Money multiplier, 334

Money supply, 331. See also Demand for money; Inflation

Blanchard-Weil model, monetary growth in, 222–229

defined, 334

inflation and, 214–215

liquidity effect, 340–341, 360–361

monetary growth, 364–372

money multiplier, 334

neutrality of money, 71–74, 209–211, 343–347

nominal interest rates, 357–361

in perfectly competitive model, 400–401

in Ramsey model, 218–222

real interest rates, 357–361

seigniorage, 364–372

superneutrality of money, 210, 220–221

Monopolistic competition model, 454n1, 457n2

Montagu, Charles, First Earl of Halifax, 333

Moore, J., 543

Moral hazards, 541

Mortensen-Pissarides model, 509–510, 512n3, 558n9

Beveridge curve, 510, 513

dynamic adjustment to steady state, 527–534

firms and creation of vacancies, 513–517

flows into and out of employment, 512–513

job destruction, 527

labor market tightness, 509–510

labor productivity, 523–525

matching function, 510–512

numerical simulations of, 532–534

real interest rate and, 527

unemployed job seeker behavior, 517–519

unemployment benefits, increase in, 525–526

wage bargaining and wage equation, 517–519

wage determination and equilibrium unemployment, 521–522

Moving average processes, 717

Moyen, S., 535

MRS (marginal rate of substitution), 46

Muellbauer, J., 6

Mulligan, C. B., 254

Multiple balanced growth paths, 159

Multiplication, matrix, 661

Multiplication, scalar, 661

Multipliers

Keynesian cross, 417–419

Samuelson multiplier-accelerator model, 5, 419, 427–429

Multivariate distribution, 714

Multivariate linear models, 291–293

Muth, J. F., 7, 269n1, 271n3, 275, 446

Napoleonic Wars, monetary policy during, 27

National Bureau of Economic Research (NBER), 18

Natural interest rate, 494–495

Natural rate of unemployment, 7. See also Rational expectations hypothesis

adaptive expectations, 440–444

discretionary policies, 439–440

full price flexibility and, 455–456

inefficiency of, 456–457

rules versus discretion, 444–446

Neftci, S. N., 386

Neoclassical production function, 635

in Diamond model, 155

in one-period competitive models, 38–40

in Ramsey model, 124–125

in Solow model, 87–89

Neoclassical synthesis, 5–6, 424n14

Nerlove, M., 271n3, 275n4

Net expected profits

from existing jobs, 514–515

from vacancies, 515

Neutrality of money, 71–74, 209–211, 343–347

New classical models, 7, 375–376

log-linear stochastic growth model, 386–392

Lucas model, 403–411

perfectly competitive models, 395–402

simplified stochastic growth model, 383–386

stochastic growth model, 376–377n1, 376–383

New dynamic public finance, 588

New growth theory, 8, 8n19

New Keynesian models, 7

assumptions of, 451–452

characteristics of, 449–451

divine coincidence, 451, 468–469, 501–502

financial frictions in, 544–546

full price flexibility, 455–456

natural rates, 455–457

new Keynesian IS curve, 459–462, 461n5

new Keynesian Phillips curve, 450, 462–463, 468, 493

representative firms, 452–454

representative households, 452–454

Rotemberg model of convex costs of price adjustment, 470–473

rules versus discretion in, 554–562

staggered price adjustment, 457–470

Taylor rule, 450–451, 463–464, 464n7

two-period intertemporal model and, 68–69

New neoclassical synthesis, 625–626, 626n6

New York Stock Exchange (NYSE), 540

n first-order difference equations, 690–692

n first-order linear differential equations, 678–682

Nominal distortion, 476

Nominal interest rates, 339–342, 345

cash in advance in OLG models, 359

cash in advance in representative household model, 359

liquidity effect in representative household models, 360–361

money in the utility function of representative household, 357–359

opportunity cost of real money balances, 212

perfectly competitive model, 401–402

Nominal rigidities, 534–535

Nominal variables, 69, 209

Nominal wage contracts, 492–494

Nonaccelerating inflation rate of unemployment. See Natural rate of unemployment

Nondistortionary taxation, 201–203

Nonfundamental solutions, 280

Nonhomogenous differential equations

first-order, 671–672

second-order, 674–675

Nonlinear differential equations, 668

Nonlinear models, 612–619

Nonrivalrous ideas, 258–259

Nonsatiation, 37, 56, 645–646

Nonstationary stochastic processes, 718

Non-Walrasian equilibrium modeling, 6

Normal distribution, 709–710

North, D. C., 263, 264n11

NYSE (New York Stock Exchange), 540

Objective functions, 644

Okun’s Law, 503

Okun-type relations, 488, 493, 496n17, 500–501, 548

OLG. See Overlapping generations (OLG) models

One-period competitive model

assumptions of, 33–34

consumption and labor supply, 56–62

general equilibrium, 40–42

government expenditure and taxes, 74–77

nature and components of, 34–35

optimal behavior of households, 36–38

profit-maximizing behavior of firms, 38–40

Open market operations, 565–566

Operators

first difference, 83

forward shift, 325

future mathematical expectations (F), 281, 287

lag, 281, 683–685

Opportunistic incentives, 590

Opportunity cost of real money balances, 212

Optimal control method, 694–697

Optimal dynamic Ramsey taxation, 586–589

Optimal intertemporal path of consumption, 121–124

Optimality, principle of, 698

Optimal least squares projections, 407

Optimal savings in continuous time, 700–702

Optimal Taylor rule, 502–504

Optimal time-consistent contingent policy, 503–504, 503n26

Optimization

under constraints, 644–651

intertemporal, 121–124, 693–699, 700–702

Orphanides, A., 553, 554n4, 569n16

Oscillations, 429

OTC (over the counter) markets, 540

Output

AD-AS model, 424–425, 424n13

developed versus less developed economies, 108–109

excess, 465

general equilibrium and, 61–62, 66–68

in Lucas model, 406–407

output gap, 465

in Solow model, 93–95

technology and, 48–49

Overlapping generations (OLG) models, 153–154. See also Blanchard-Weil model; Diamond overlapping generations model

characteristics of, 153–154

government debt, 184

history of, 4–5

monetary growth in, 222–229

money and price level, 347–351, 355–357

nominal and real interest rates, 359

Pigou effect, 364

Ricardian equivalence and, 579–580

Samuelson OLG model with money, 347–351, 614–619

taxation, 184

Over the counter (OTC) markets, 540

Papademos, L., 333n4,

Paper currency, 69, 332–333

Parameters, 35, 634

Partial derivatives of functions, 642

Particular integrals, 672

Particular solutions, 668

Partisanship, fiscal policy and, 590–592

Passalacqua, A., 586, 589, 592

Patinkin, D., 3, 5n10, 6, 209n1, 351, 364, 413, 424

PDF (probability density function), 705–706

Per capita GNI (gross national income)

cross-country differences, 11–13

developed versus less developed economies, 108–109

economic growth and convergence since 1820, 14–17

evolution over time, 13–14

growth rates, 14n28

Perfect competition, assumption of, 259n8

Perfect consumption smoothing, 305

Perfect foresight, 42, 272–273

Perfectly competitive model

equilibrium conditions, 398–400

general equilibrium, 398–400

history of, 395–396

money demand function, 400

money supply, 400–401

nominal interest rates, 401–402

optimal monetary policy, 402

representative firms, 397–398

representative households, 396–397

Periodic nominal wage contracts, 492–494

Permanent income theory, 6, 306–307, 517–519

Perotti, R., 592

Perpetual youth model

aggregation across generations, 172

assumptions of, 169, 169n8

balanced growth path in, 173–177

discrete time model, 178

dynamic simulations, 177–182

efficiency units of labor, 173

intertemporal utility function, 170–171

variables, 169–170

Persson, T., 558n7, 591–592

Pesaran, M. H., 291, 293

Peso, monetary reform of, 346

Phelps, E. S., 6–7, 100n8, 258n7, 415, 437–438, 440, 448

Phillips, A. W., 6, 414. See also Phillips curve

Phillips curve, 6, 403n6

deviations of output, 488

expectations-augmented, 7, 476, 487–488, 501, 547, 554

history of, 6–7, 414–415, 627

inflationary expectations from, 435–439, 435n19

new Keynesian, 450, 462–463, 468, 493

staggered pricing and nominal wage contracts, 492–494

Pigou effect, 364

Pissarides, C. A., 509, 515n5, 527, 531. See also Mortensen-Pissarides model

Points of inflection, 642–644

Poisson frequency distribution, 511

Policy evaluation, DSGE models and, 628–629

Politics, fiscal policy and

distributional considerations, 589–590

electoral factors and partisan differences, 590–592

Polynomials, geometric, 684–685

Poole, W., 553n3, 564

Population growth

in Diamond overlapping generations model, 161–162

in Ramsey model, 142–143

in Solow model, 90, 104

in stochastic growth model, 378–380

Portes, R., 6

Portfolio choice under certainty. See Ramsey representative household model

Portfolio choice under uncertainty, 297–298

Bellman equation, 300

consumption capital asset pricing model, 298, 302–303, 307–308

efficient markets hypothesis, 308–310

envelope theorem, 300

hyperbolic absolute risk aversion (HARA) utility functions, 303

logarithmic preferences, 303–304

permanent-income hypothesis, 306–307

precautionary savings and borrowing constraints, 310–311

quadratic preferences and certainty equivalence, 305–306

random walk model of consumption, 301–302

stochastic dynamic programming, 298–301

Power function, derivative of, 639

Preferences, household, 36–38

Pre-Keynesian macroeconomics, 2–4

Prescott, E. C., 7, 18n31, 262n10, 308n8, 314, 325, 327, 377n1, 386, 389, 446, 447n30, 503n25, 552, 558, 589, 627, 629. See also Lucas-Prescott model

Price level. See also Calvo model of staggered pricing

costly price adjustment, 450, 457n3, 470–473

fiscal theory of, 363

in Gray-Fischer-Taylor unemployment model, 481–483

in imperfectly competitive model, 452–456

indeterminacy, 361–364

in Lucas model, 403–406

monetary and fiscal policy with price level target, 432–434

money and, 347–357, 614–619

money market bubbles and, 609–611

Rotemberg model, 450, 457n3, 470–473

staggered price adjustment, 450, 457–470

trends and fluctuations in, 22–26

in two-period competitive model, 69–74

Primary government deficit, 186–187

Primary government expenditure, 78

Prime rate, 566

Principle of optimality, 698

Probability

concept of, 703–704

probability density function (PDF), 705

probability mass function, 705

probability space, 704

Probability distributions

Bernoulli, 708

continuous, 705–706

continuous uniform, 708–709

defined, 704

discrete, 704–705

discrete uniform, 707–708

higher moments, 707

joint, 714–715

mathematical expectation, 706

normal, 709–710

standard normal, 710–712

standard uniform, 708–709

variance, 706–707

Production functions. See also Cobb-Douglas production function

aggregate capital accumulation, 216

constant elasticity of substitution (CES), 90n3, 651–654

fixed-proportions, 653

in Gray-Fischer-Taylor unemployment model, 481–483

in Jones model, 252–253

in learning-by-doing models, 233–234

Leontieff, 87, 106, 653

linear, 653

in log-linear stochastic growth model, 386

neoclassical, 38–40, 87–89, 124–125, 155, 635

optimal decision of firms and, 61

in Solow model, 653–654

Productivity

shocks, 495–500

total factor, 38, 102–104

Product market, equilibrium conditions in, 61–62, 66

Profit-maximizing behavior of firms, 38–40, 48–49

Pure rate of time preference, 43, 656–657

in Diamond model, 160–161

in Ramsey model, 139–141

Pythagorean theorem, 688

q model of investment, 6, 313–314

convex adjustment costs, 314–320

marginal product of capital, 317

uncertainty, 320–327

user cost of capital, 317

Quadratic preferences

certainty equivalence, 305–306

consumption capital asset pricing model, 307–308

permanent-income hypothesis with, 306–307

Quantity theory of money, 25–26, 71, 337n6, 343–344

Ramsey, F. P., 4, 9, 55, 119–121, 586, 700. See also Dynamic Ramsey approach; Keynes-Ramsey rule; Ramsey representative household model; Ramsey representative household model with money

Ramsey representative household model. See also Ramsey representative household model with money

adjustment path and speed of convergence, 143–145

aggregate fluctuations in, 377

balanced growth path in, 135–139

business gross profits taxation, 203–206

calibrated, 148–149

capital accumulation and, 126–128

capital income taxation, 203–206

consumption function, 133–135

decentralized competitive equilibrium, 126–128

discrete time model, 146–148

distortionary and nondistortionary taxation, 201–203

dynamic simulations of, 149–152

Euler equation for consumption, 122–123, 129–130, 147

externalities and endogenous growth in, 239–241

fiscal policy, 188–191

history of, 4–5

infinite-horizon transversality condition, 132

interest rate pegging and price level indeterminacy, 361–362

intertemporal budget constraints, 130–131

liquidity effect, 360–361

modified golden rule, 138–139

nominal and real interest rates, 357–361

optimal dynamic Ramsey taxation, 586–589

optimal intertemporal path of consumption, 121–124

population growth rate, 142–143

production function, 124–125

pure rate of time preference, 139–141

Ricardian equivalence and, 187–191

Solow model compared to, 119–120

total factor productivity, 141–142

transversality condition, 121, 131–132

utility function, 125–126

utility maximization, 128–129

variables, 124

Ramsey representative household model with money

aggregate capital accumulation, 216–218

Euler equation for consumption and, 215–216

inflation, 221–222

money supply, 218–222

private consumption and money demand, 211–216

Random variables

Bernoulli distribution, 708

central limit theorem, 712, 714

continuous probability distributions, 705–706

continuous uniform distribution, 708–709

convergence of, 712–713

defined, 704

discrete probability distributions, 704–705

discrete uniform distribution, 707–708

higher moments, 707

joint probability distributions, 714–715

law of large numbers, 713

mathematical expectation, 706

normal distribution, 709–710

standard normal distribution, 710–712

standard uniform distribution, 708–709

variance, 706–707

Random walks, 301–302, 717

Rapping, L., 64n11, 377n1, 382n5, 411n10

Rational expectations hypothesis, 7, 42n6

adaptive learning approach, 295

bubbles in, 602–607

concept of, 269n1, 270–271, 275–277

first-order linear expectational models, 279–286

inflation and unemployment under, 446–447

linear autoregressive processes, 277–279

in Lucas-Prescott model, 325–327

monetary shock effects, 407–410

multivariate linear models, 291–293

second-order linear expectational models, 286–291

Rational functions, 684

Rational inattention, 411

Ratio of two functions, derivative of, 641

Real and distinct roots, 674

Real business cycle (RBC) theories, 3, 7. See also Stochastic growth model

Real distortion, 476

Real interest rates

average, 131

cash in advance in OLG models, 359

cash in advance in representative household model, 359

job creation and, 527

in learning-by-doing models, 237–238

liquidity effect in representative household models, 360–361

money in the utility function approach, 357–359

natural and equilibrium, 494–495

opportunity cost of real money balances, 212

in Ramsey model with money, 216

in Solow model, 96–97

Realization, 715

Real money balances, 336

Real numbers, 35, 634

Real shocks, 504–507

Real variables, 69, 209

Real wages

learning-by-doing models, 237–238

Ramsey model with money, 216

Solow model, 96–97

wage bargaining and wage equation, 517–519

Rebelo, S., 7n16, 236n2, 237n3, 377n1, 627. See also Rebelo model

Rebelo model, 236n2, 237n3

Recent developments in macroeconomics, 623–624

empirical macroeconomics, role of, 626–628

financial crisis and, 624–626

policy evaluation and DSGE models, 628–629

Recessions. See also Great Depression

defined, 18

frequency, severity, and duration of, 18–20

government debt during, 28

Great Recession (2008-2009), 28–29, 412, 624

unemployment rates in, 20–22, 20n33

Rectangular distribution, 708

Recurrence relation, 685

Reduced form, 665

Reduced linear differential equation, 673

Reis, R., 411, 625

Repeated substitutions, 279–281

Replacement rate, 523

Representative firms

concept of, 36

in Gray-Fischer-Taylor unemployment model, 481–483

in imperfectly competitive model, 452–454

in one-period competitive model, 38–40, 56–62

in perfectly competitive model, 397–398

in stochastic growth model, 377–378

technology and optimal output path, 48–49

in two-period competitive model, 62–69

Representative household growth model. See Ramsey representative household model

Representative households. See also One-period competitive model; Two-period competitive model

concept of, 36

in Diamond model, 156–157

in Gray-Fischer-Taylor unemployment model, 478–481

in imperfectly competitive model, 452–454

in perfectly competitive model, 396–397

in stochastic growth model, 378, 380–383

Reputational equilibrium, 560–562

Research and development (R&D) models. See Ideas-and-innovations growth models

Reserve banks. See Central banks

Ricardian equivalence, 78–81, 183–184, 187–191, 188n2, 579–580

Ricardo, D., 2, 79, 188n2

Riksbanken, 333

Rogoff, K., 447n30, 503n25, 559, 590–591

Romer, C., 21n34

Romer, D., 7, 457, 625, 629

Romer, P. M., 8n19, 231, 232, 236n2, 239, 243, 258–259, 265–267. See also Arrow-Romer model

Rotemberg, J. J., 450. See also Rotemberg model

Rotemberg model, 450, 457n3, 470–473

Roubini, N., 592

Rules versus discretion in monetary policy

central bank anti-inflationary reputation, 560–562

central bank constitutions, 559–560

credibility issues, 556–558

historical debate, 552–553

new Keynesian model example, 553–554

policy under fixed inflation rule, 559

social welfare loss from inflation and unemployment, 555–556

Sachs, J. D., 365n14, 368, 425n15, 592

Saddle paths, 678, 682

Saddle points, 672, 678, 682, 687

Saddle vectors, 682

Saez, E., 535

Sahuk, J. G., 535

Sala-i Martin, X., 111n14, 254, 267n13

Sample space, 704

Samuelson, P. A., 1n1, 2n2, 3–4, 5n10, 6, 119n2, 153n1, 298–299, 308n9, 311, 314n2, 414, 417n5, 435, 436, 448. See also Samuelson multiplier-accelerator model; Samuelson OLG model

Samuelson-Diamond model. See Diamond overlapping generations model

Samuelson multiplier-accelerator model, 5, 419, 427–429, 427n16

Samuelson OLG model. See also Overlapping generations (OLG) models

money and price level, 347–351

self-fulfilling prophesies and sunspot equilibria, 612–620

Sandmo, A., 310

Sannikov, Y., 544

Santos, M. S., 254

Sargent, T. J., 327n4, 361, 364–365, 372, 396n1, 403, 553n3, 564, 625, 683n1

Savings and investment. See also q model of investment; Solow model

balanced growth path in, 98–99

dynamic inefficiency, 101

elasticity of steady state output, 101–102

in flexible accelerator model, 6

golden rule, 99–101

implications of, 97–98

impulse response function, 98–99, 98n6

income taxation and, 81

learning-by-doing models, 238–239

marginal propensity to save, 416

in two-period competitive model, 42–55

Scalar multiplication, 661

Schmitt-Grohe, S., 291, 293

Schwartz, A. J., 344n7, 412, 629

Search externalities, 512

Search or matching models of labor market. See Matching models of labor market

Second-order linear autoregressive process, 719

Second-order linear difference equations, 687–689

Second-order linear differential equations, 673–675

Second-order linear expectational models, 286–287

economic examples of, 290–291

factorization method, 287–288

undetermined coefficients method, 288–289

Seigniorage

defined, 217, 330

equilibrium with high inflation, 368

history of, 27–28

Laffer curve, 367–368, 367n16

relation with monetary growth and inflation, 365–367

Self-fulfilling prophesies

bubbles as, 605–607, 607n5

in Diamond model, 159n5

multiple equilibria and, 598–600

sunspots, 612–620

Separation of variables, 668

Shell, K., 258n7, 601, 613

Shiller, R. J., 309–310, 612

Shimer, R., 532, 535, 626n2

Short-run equilibrium, 339–342

Sibert, A., 590–591

Sidrauski, M., 210n2, 220, 344, 351

Simons, H., 552–553

Simplified Diamond model

Cobb-Douglas production function, 159–162

logarithmic preferences, 159–162

speed of adjustment in, 163–164

Simplified stochastic growth model, 383–386

Sims, C. A., 291, 293, 363, 411, 627, 721. See also Sims linear model solution method

Sims linear model solution method, 293

Skewness, 707

Slope of indifference curves, 650

Slutsky, E. E., 8–9, 58–59, 376. See also Slutsky substitution effect

Slutsky substitution effect, 59

Smets, F., 554n5, 626n6, 627

Smith, Adam, 1, 2

Smoothing, consumption, 45, 305

Social welfare costs

of Diamond model, 164–165

from inflation and unemployment, 221–222, 346, 555–556

Solow, R. M., 4–6, 10n22, 85–87, 119, 414, 432. See also Solow model

Solow model, 110–111. See also Generalized Solow model

assumptions of, 4, 106–107

balanced growth path in, 85, 92–93, 104–106

calibrated, 113–114

Cobb-Douglas production function, 89–90, 110–111

competitive markets, 96–97

convergence process, 110–111

discrete-time model, 112–113

dynamic simulations of, 114–117

equilibrium conditions, 85–86

exogenous growth model, 109

extended, 249–252

generalized, 109n13

growth rate of capital and output, 93–95

impulse response function, 98–99, 98n6, 116–117

Inada conditions, 94–96

Kaldor facts of economic growth, 107, 265–266

neoclassical production function, 87–89

per capita output and income, differences in, 108–109

population growth, 90, 104

production function in, 653–654

real interest rate, 96–97

representative household growth model compared to, 119–120

savings and capital accumulation, 90–92, 97–102

strengths and weaknesses, 85–87, 117–118

technical progress, 90

total factor productivity, 102–104

variables in, 87

Solow-Swan model. See Solow model

Solutions, fundamental versus nonfundamental, 280

Solvency, government deficits and, 185–187

Square matrices, 660

Stabilization policy, 585–586

Stable nodes, 672, 686

Stagflation, 24, 31, 434

Staggered price adjustment

assumptions of, 450, 457–461

divine coincidence and optimal monetary policy, 451, 468–469

dynamic simulation of, 469–470

equilibrium conditions, 461–462

financial frictions and, 544–546

imperfectly competitive model with, 463–464

new Keynesian Phillips curve, 462–463, 468

optimal pricing with, 459–461

real and monetary shocks, 464–468

Taylor rule, 463–464

unemployment modeling and, 489–494

Staggered wage contracts, 45n2

Standard normal distribution, 710–712

Standard uniform distribution, 708–709

State space, 715

State variables, 693

Static expectations, 273, 440

Stationary points, 642

Stationary state, 672

Stationary stochastic processes, 717

Steady state

in Blanchard-Weil model, 173–177

convergence process, 92–93

defined, 85, 672, 678

in Diamond model, 159–160

elasticity of, 101–102

in extended Solow model, 250–251

in ideas-and-innovations growth models, 261–262

investment per efficiency unit of labor, 92

in log-linear stochastic growth model, 388–391

in matching models of labor market, 527–534

in Ramsey model, 135–139

in Ramsey model with money, 219–220

savings rate and, 98–99

speed of convergence toward, 104–106

steady state capital locus, 137

steady state consumption locus, 136

tax smoothing implications, 583–584

Stiglitz, J. E., 454n1, 478n5, 482n10, 542n1, 625n4, 626n7

Stochastic bursting bubbles, 605

Stochastic dynamic programming, 298–301

Stochastic expectational model. See also Dynamic stochastic models under rational expectations

absence of uncertainty in, 272–273

adaptive expectations hypothesis, 273–275

defined, 273

rational expectations hypothesis, 275–277

supply and demand functions, 271–272

Stochastic growth model, 375–376

defined, 376–377

efficiency of labor, 378–380

extended Ramsey model, 377

government expenditure, 378–380

history of, 376–377n1

labor supply of representative household, 380–382

log-linear stochastic growth model, 386–392

representative firms, 377–378

representative households, 378

shortcomings of, 625–626

simplified stochastic growth model, 383–386

two-period intertemporal model and, 68–69

uncertainty and household behavior, 382–383

Stochastic processes

autoregressive, 718–719

autoregressive moving average, 720

defined, 715–716

homogeneous nonstationary stochastic processes, 718

moving average, 717

nonstationary, 718

random walks, 718

stationary, 717

vector, 720–721

white noise, 717

Stochastic shocks, monetary policy and, 562–564

Stochastic variables. See Random variables

Stock market

bubbles, 607–612

organization of, 540

stock prices in, 282–283

Stokey, N., 581, 586, 588

Store of value, money as, 331

Strong convergence, 713

Structural form, 665

Stylized facts of economic growth, 107, 265–266

Suboptimality of the competitive equilibrium, 241–242

Substitution. See also Constant elasticity of intertemporal substitution (CEIS) utility function

constant elasticity of substitution (CES) production function, 90n3, 651–654

constant elasticity of substitution (CES) utility function, 655

intertemporal substitution effect, 133, 381–382

labor supply and, 58–60

method of substitution, 465–468, 665, 675–676

repeated, 279–281

Subtraction, matrix, 661

Summers, L. H., 483

Sum of two functions, derivative of, 641

Sunspots

defined, 601–602

in Diamond model, 159n5

implications of, 612–614

Superneutrality of money, 210, 220–221

Supply of money. See Money supply

Supply shocks, 425–426, 425n15

Sustainability criterion, 186

Svensson, L. E., 575, 591

Sveriges Riksbank, 333

Swan, T. W., 4, 85. See also Solow model

Symmetallism, 552

Systems method, 465–466

Tabellini, G., 558n7, 561, 591–592

Target price-level paths, 574n19

Targets, policy, 429–430

Taxation

in Blanchard-Weil model, 192–194

business gross profits, 203–206

capital income, 203–206

distortionary, 76, 201–203

inflation tax, 216–218

nondistortionary, 201–203

in one-period economy, 74–77

optimal dynamic Ramsey, 586–589

overlapping generations models and, 184

Ricardian equivalence, 78–81, 187–191, 188n2, 579–580

tax smoothing, 195, 581–584

in two-period competitive model, 77–78

Tax smoothing, 195

Barro tax-smoothing model, 581–583

steady state implications of, 583–584

Taylor, J. B., 18n31, 333n4, 363, 450, 457n3, 475. See also Gray-Fischer-Taylor unemployment model; Taylor principle; Taylor rule

Taylor principle, 464, 466–467, 498, 568

Taylor rule

constant-intercept, 567n13

equilibrium fluctuations with exogenous shocks, 495–500

in imperfectly competitive model, 463–464, 464n7

inflation stabilization and divine coincidence, 501–502

nominal interest rate and, 450–451

optimal inflation theory, 502–504

optimal monetary policy and, 553–554, 567–569

staggered pricing and inflation persistence, 500–501

Technical progress

Harrod neutral, 88

in ideas-and-innovations growth models, 258–262

labor augmenting, 88

optimal output path and, 48–49

in Solow model, 90

Technical rate of substitution, 652

Terminal conditions, 670

Term structure, interest rates, 566–567

Theil, H., 414, 430, 433, 553n3

Theoretical models, 5

Thomas, C., 535

Thomas, R. P., 263

Tightness, labor market, 509

Time. See also Discrete time

continuous time analysis, 83–84

discrete time models, 82–84, 112–113, 146–148, 178

time-consistent equilibrium, 561

time-inconsistent reputational equilibrium, 561

time separability, 43, 43n7

Tinbergen, J., 8, 414, 429, 553n3, 627

Tinbergen-Theil theory of discretionary policy, 431–434

Tirole, J., 612

Tobin, J., 6, 210n2, 314, 336n5. See also q model of investment

Total differential, 642

Total factor productivity

in Diamond overlapping generations model, 162

in one-period competitive model, 38

in Ramsey model, 141–142

in Solow model, 102–104

Training, spending on, 249–250

Transposition, 661

Transversality condition

in Blanchard-Weil model, 223

defined, 121, 131

dynamic optimization and, 694

with infinity time horizon, 132

sustainability criterion for fiscal policy, 186

Treadway, A. B., 314

Trigari, A., 534, 535

Trigonometric functions, derivative of, 640

Truncated normal distribution, 595

Turkey, monetary reforms in, 346

Two-period competitive model

consumption and labor supply, 62–69

demand for money, 69–71

fiscal policy, 74–82

general equilibrium, 49–55

implications for growth and business cycle theory, 55

savings and investment, 42–55

Two-period model of government debt crises, 593–598

Uhlig, H., 291, 293

Uncertainty

adaptive expectations hypothesis, 273–275

consumption under, 297–311

investment under, 323–327

stochastic growth model, 382–383

value of firm under, 321–323

Undetermined coefficients

first-order linear expectational models, 282

method of, 673

second-order linear expectational models, 288–289

Unemployment modeling. See also Equilibrium unemployment; Matching models of labor market

alternative views of labor market, 477–478

assumptions of, 475–477

firm pricing and production, 481–483

household consumption and demand, 478–481

monetary and real shocks, 504–506

natural and equilibrium real interest rate, 494–495

permanent income of job seekers, 517–519

Phillips curve and, 488

social welfare loss, 555–556

staggered price adjustment, 489–494

staggered wage contracts, 45n2

Taylor rule and, 494–505

unemployment persistence and financial frictions, 546–548

unemployment persistence and wage determination, 485–488

wage setting, 483–487

Unemployment rates. See also Natural rate of unemployment

in AD-AS model, 424–425, 424n13

in booms and recessions, 20–22

defined, 20n33

dynamic adjustment of, 530–532

dynamic simulations of, 504–506

flows into and out of employment, 512–513

general equilibrium and, 61–62, 66–68

in Lucas model, 406–407

monetary and fiscal policy with full employment target, 431–432

natural rate of, 439–446, 455–457

probability of filling vacancies, 511

probability of unemployed job seeker finding job, 511–512

Unified growth theory, 8, 262–263

United Kingdom

government debt in, 26–30

monetary policy in postwar period, 31–32

per capita GNI (gross national income), 14–17

price level and inflation in, 22–26

recession frequency and duration in, 18–20

unemployment rates in, 20–22

United States

government debt in, 26–30

Great Depression, 19

monetary policy in postwar period, 31–32

per capita GNI (gross national income), 14–17

price level and inflation in, 22–26

recession frequency and duration in, 18–19

unemployment rates in, 20–22

Unit of account, money as, 331

Univariate stochastic processes. See Stochastic processes

Unstable bubbles, ruling out, 611–612

Uribe, M., 291, 293

US Civil War, monetary policy during, 27

User cost of capital, 317

Utility function. See also Utility maximization

in Blanchard-Weil model, 170–171, 223

constant elasticity of intertemporal substitution (CEIS), 46–48, 46n8, 54, 60, 123, 655–657

constant elasticity of substitution (CES), 655

continuous time analysis, 83

in Diamond model, 155–156

fixed-proportions, 655

in imperfectly competitive model, 453

money in the utility function approach, 71n13, 209n1, 211–212, 351–353

in one-period competitive model, 36–38, 56–58, 60

in Ramsey model, 125–126, 128–129, 146

in Samuelson OLG model, 347–348

in stochastic growth model, 378

in two-period competitive model, 43–45, 43n7, 63, 69, 75

Utility maximization

in one-period competitive model, 36–38

in Ramsey model, 128–129

in two-period competitive model, 43–45, 63, 69, 75

Uzawa, H., 253–254, 258n7

Vacancies

creation of, 513–517

dynamic adjustment of, 530–532

net expected profits from, 515

probability of filling, 511

Variables. See also Random variables

in Blanchard-Weil model, 169–170

control, 693

defined, 35

in Diamond overlapping generations model, 155

endogenous, 634, 663–666

exogenous, 284–286, 634

in learning-by-doing models, 233

nominal, 69, 209

in Ramsey model, 124

real, 69, 209

separation of, 668

in Solow model, 87

state, 693

variable coefficients, 671

vectors of, 660

Variance, 706–707

Vectors, 634

autoregressions, 720–721

defined, 660

of variables, 660

vector stochastic processes, 720–721

Velasco, A., 590, 592

Wages

efficiency wage theories, 477–478

labor supply and, 58–60

periodic nominal wage contracts, 492–494

permanent income, 517–519

real, 96–97, 216, 237–238, 517–519

staggered wage contracts, 45n2

wage bargaining and wage equation, 517–519

wage determination and equilibrium unemployment, 521–522

wage equation, 517–519

wage setting model, 483–487

Wallace, N., 361, 362n11, 364, 553n3, 564

Walrasian general equilibrium theory, 6

Walsh, C. E., 330n1, 534

Weak convergence, 713

Weil, P., 9, 55, 154, 169–170, 612. See also Blanchard-Weil model

Welfare costs

of Diamond model, 164–165

from inflation and unemployment, 221–222, 346, 555–556

White noise process, 717

Wicksell, K., 3, 40n5, 333n4, 361–363, 363n12, 401, 552–554. See also Wicksell interest rate rule

Wicksell interest rate rule, 362–363, 363n12, 401, 495, 495n15

Wiederholt, M., 411

Woodford, M., 4n6, 7n17, 359n10, 363, 411, 464n8, 498n19, 553n3, 554n4, 564n11, 569n15, 573, 574, 625

Wouters, R., 554n5, 626n6, 627

Wright, R., 625, 626n7

Yun, T., 458n4

Zero lower bound on interest rates

concept of, 571–576

fiscal implications of, 585–586