Greene W.H. Econometric Analysis

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Index

1179

Newey, W., 370, 449, 453, 468n3,

474, 480, 481, 481n10,

502n18, 505, 524, 587n28,

707, 858n12, 860n14, 872n24,

892, 920

Newey-West autocorrelation

consistent covariance

estimator, 920

Newey-West autocorrelation robust

covariance matrix, 921

Newey-West estimator, 478

Newton’s method, 201, 555, 572,

1098, 1106

Neyman, J., 588, 619, 721,

722n29, 861

Neyman-Pearson methodology, 111

Nickell, S., 378n17, 496n13

Nijman, T., 735, 736, 883, 885

NIST, 217

NLS, 344

NMAR, 95

Nobel Prize, 2

nominal size, 138

noncentral chi-squared distribution,

527n8, 1022

noncentral F distribution, 1023

nonconstructive test, 276

nonhomogeneous equation system,

990, 992

noninformative prior, 659

nonlinear consumption function,

191–193

nonlinear cost function, 162–165

nonlinear instrumental variable

estimator, 489

nonlinear instrumental variables

estimation, 246–248

nonlinear least squares, 202, 570

nonlinear least squares criterion

function, 187

nonlinear least squares estimator,

184–185, 200–202

nonlinear model with random

effects, 621–623

nonlinear panel data regression

model, 411–415

nonlinear random parameter

models, 641–642

nonlinear regression model,

182–202

applications, 191–199

assumptions, 182–183

asymptotic normality, 188

Box-Cox transformation,

193–196

consistency, 187

deﬁned, 186

F statistic, 190

ﬁrst-order conditions, 185

general form, 182

hypothesis testing/parametric

restrictions, 189–191

interaction effects (loglinear

model for income), 195–199

Lagrange multiplier statistic, 191

large sample properties, 186–189

nonlinear consumption function,

191–193

nonlinear least squares, 202

nonlinear least squares estimator,

184–185, 200–202

Wald statistic, 190

nonlinear restrictions, 131–133, 167

nonlinear systems, 318n37

nonlinear systems of equations,

305–306

nonlinearity, 162–165

nonnegative deﬁnite matrix,

1005–1006

nonnested model, 823

nonnormal disturbance, 127–131

nonparametric average cost

function, 214

nonparametric bootstrap, 612

nonparametric estimation, 444–447

nonparametric regression,

212–215

nonrandom sampling, 221

nonresponse (GSOEP sample), 737

nonresponse bias, 735

nonsample information, 326

nonsingular matrix, 991

nonspherical disturbances and

robust covariance

estimation, 385–389

nonstationary data, 942–972

ARIMA model, 943

bounds test, 964

cointegration. See cointegration

Dickey-Fuller tests, 948–945

integrated process and

differencing, 942–943

KPSS test of stationarity, 958–959

panel data, 410–411, 970–971

random walk, 946

trend stationary process, 946

unit root. See unit root

nonstationary panel data, 410–411,

970–971

nonstationary series, 943

nonstochastic regressor, 23

nontested models, 110, 134–137, 534

nonzero conditional mean of the

disturbances, 20

normal distribution, 513, 1019–1020

normal equation, 33

normal-gamma prior, 663, 675

normality, 23–24

normalization, 319, 511

normally distributed, 23

not missing at random (NMAR), 95

notational conventions, 9–10, 16

null hypothesis, 109–110

null matrix, 974

numerical examples, 9

Nymoen, R., 7n

Oakes, D., 865n17

Oaxaca and Blinder

decomposition, 79

Oberhofer, W., 283, 298n15, 553,

561, 562, 566

Oberhofer-Kmenta conditions, 561,

562, 563n22

observationally equivalent, 322

Obstfeld, M., 468n3, 494

Ohtani, K., 171, 275n16, 295n9

OLS estimator, 250

Olsen, R., 521, 850

Olsen’s reparameterization, 850

omission of relevant variables,

56–58

omitted parameter heterogeneity,

220–221

omitted variable, 57, 219

omitted variable bias, 219

omitted variable formula, 56

omitted variables, 713

one-sided test, 116

one-sided test about a mean, 1066

one-step maximum likelihood

estimator, 1100

one-to-one function, 1014

open form integral, 623

OPG estimator, 522

optimal instruments, 232n1

optimal linear predictor, 53

optimal weighting matrix, 465

optimization, 1010–1013,

1093–1106. See also

computation and

optimization

optimization conditions, 290–291

Orcutt, G., 852, 926

Ord, S., 134n7, 460n1, 514, 515, 517,

1019n1, 1059

order condition, 325, 476

1180

Index

order less than n

, 1089

order n

, 1088

ordered choice models, 682, 760,

784–802

anchoring vignettes, 802

applications, 787

bivariate ordered probit model,

792–793

DIF, 801, 802

essential ingredient, 787

extensions of ordered probit

model, 798–802

generalized, 799–800

ordered probit model, 787–791

ordered probit model with ﬁxed

effects, 794–795

ordered probit model with

random effects, 795–798

panel data applications, 794–798

parallel regression assumption,

791

speciﬁcation test, 791–792

Orea, C., 593

Orme, C., 936

orthogonal partitioned

regression, 33

orthogonal regression, 36

orthogonal vector, 988

orthogonality condition, 185, 186,

238, 483

orthonormal quadratic form, 1043

Osterwald-Lenum, M., 967

outer product of gradients (OPG)

estimator, 522

outliers, 101–102

overdispersion, 805–806

overdispersion parameter, 439

overidentiﬁcation, 238–239

overidentiﬁcation of labor supply

equation, 239

overidentiﬁed, 167, 484, 487

overidentiﬁed cases, 466

overidentifying restrictions,

189, 479

overview of book. See textbook

Pagan, A., 276, 298, 304, 348, 376,

417n27, 444n2, 447, 448, 453,

468n3, 561, 564, 575, 647,

858n12, 860n13, 933, 1051

paired bootstrap, 612

Pakes, A., 603, 753n42, 771, 782

Panattoni, L., 932n19, 936n24

panel data binary choice models,

716–738

panel data literature, 344n2

panel data random effects

estimator, 728

panel data sets, 1048. See models

for panel data

Pappell, D., 410

paradigm of econometrics, 1–3

parameter heterogeneity, 416–426,

733–734. See also random

parameter models

parameter space, 110, 434,

449–450, 524

parametric bootstrap, 612

parametric estimation and

inference, 434–439, 443

parametric hazard function, 866

parametric models, 258

Parsa, R., 436

partial correlation, 38

partial correlation coefﬁcient, 36

partial differences, 925

partial effects, 346

partial ﬁxed effects model, 425

partial likelihood estimator, 870

partial regression, 32–39

partial regression coefﬁcient, 34

partialing out, 34

partially censored distribution, 846

partially linear regression, 210–212

partially linear translog cost

function, 211

participation equation, 852

partitioned matrix, 992–995

partitioned regression, 32–35

Passmore, W., 463

path diagram, 11

Patterson, K., 433n1

PCGets computer program, 139

pdf, 1016

Peacock, B., 1019n1

Pedroni, P., 410, 970, 971

Peel, D., 593, 595, 596

Penn World Tables, 343

percentile method, 613

perfect multicollinearity, 153

period, 606

Perron, P., 955

persistence, 729

Persistence of Memory (Dali), 109

personalized system of instruction

(PSI), 590, 694–696

Pesaran, H., 134n8, 136, 344n2, 964

Pesaran, M., 134n9, 220, 290, 410,

422, 423, 424, 425, 970, 971

Petersen, D., 858

Petersen, T., 863n16

Phillips, A., 904

Phillips, G., 305n16

Phillips, P., 328, 410, 945, 946,

955, 958

Phillips curve, 904–905

Phillips-Perron test, 957

piecewise continuous, 159

piecewise linear regression, 158–160

Pike, M., 723n30

pivotal quantity, 1061

pivotal statistic, 76

placebo effect, 156

plan of the book, 7–8

Ploberger, W., 647

Plosser, C., 947n6

point estimate, 1055

point estimation, 51, 664–665,

1055–1060

Poirier, D., 159n4, 433, 625n5,

656n2, 881n32, 1019n1,

1048n1

Poisson distribution, 608, 1026

Poisson-normal mixture model, 827

Poisson regression model, 803–804

Poisson regression model with

random effects, 633

Polachek, S., 176

Pollard, D., 753n42

pooled model, 299–300

pooled regression model, 349–359

between-groups estimator, 358

binary choice, 717–718

clustering and stratiﬁcation,

352–354

estimation with ﬁrst differences,

355–356

event counts, 816–817

least squares estimation, 349–350

robust covariance matrix

estimation, 350–352

robust estimation using group

means, 354–355

within-groups estimator, 357

population averaged model, 349

population moment equation, 483

population orthagonality

conditions, 52–53

population quantity, 26

population regression, 26

population regression equation, 12

positive deﬁnite matrix, 257

positive duration dependence, 865

posterior density, 657

posterior density function, 664

posterior mean, 668

Potter, S., 142

Index

1181

Powell, A., 309n23

Powell, J., 204n11, 208n14, 443, 860,

860n14, 872n24

Powell, M., 1103n23

Powell’s censored LAD

estimator, 443

power of the test, 111, 617, 1063

powers (matrix), 1000–1002

practice of econometrics, 3–4

Prais, S., 268n8, 558, 926, 927

Prais and Winsten estimator, 927

Prais and Winsten FGLS

estimator, 560

Prais and Winsten

transformation, 558

precision matrix, 667

precision parameter, 521

predetermined variable, 317, 320

predicting movie success, 93

prediction, 80–87

prediction criterion, 44, 140

prediction error, 81

prediction interval, 81

prediction variance, 81

predictive density, 667

predictive test, 170

predictive test of model stability,

174–175

Prentice, R., 587n27, 860, 862n15,

865, 867, 868, 870

Press, S., 763

Press, W., 606, 608, 1003, 1089n2,

1092, 1093, 1094n11

pretest estimation, 91–92

pretest estimator, 92

principal components, 92–94

principal minor, 987n4

principle of maximum likelihood,

511–513

prior

conjugate, 661, 662

hierarchical, 675

improper, 675

informative, 659

noninformative, 659

normal-gamma, 663, 675

uniform, 664

uniform-inverse gamma, 674

prior beliefs, 657

prior distribution, 659

prior odds ratio, 666

prior probabilities, 666

private capital coefﬁcient, 645

probability and distribution theory,

1015–1047

analysis of variance, 1037

beta distribution, 1025

bivariate normal distribution,

1037–1038

chi-squared distribution,

1021, 1022

classical normal linear regression

model, 1042–1043

conditioning in bivariate

distribution, 1034–1036

cumulative distribution function

(cdf), 1016

discrete random variable, 1026

distribution of function of

bivariate random variables,

1032–1033

distribution of function of

random variable, 1026–1028

expectations of random variable,

1017–1019

exponential distribution, 1024

F distribution, 1021, 1045

full rank quadratic form,

1045–1046

gamma distribution, 1024

idempotent quadratic forms,

1043–1045

independence of linear and

quadratic forms, 1046–1047

joint distribution, 1030–1034

large degrees of freedom,

1023–1024

linear functions of normal

regression, 1043

logistic distribution, 1025

marginal and conditional normal

distributions, 1041–1042

marginal distribution, 1030

moments, 1038–1039

multivariate distribution,

1038–1040

multivariate normal distribution,

1041–1047

normal distribution, 1019–1020

probability distribution,

1015–1016

quadratic forms, 1043–1045

random variable, 1015

representations of a probability

distribution, 1028–1029

t distribution, 1022

Wishart distribution, 1025

probability density function (pdf),

1016

probability distribution, 1015–1016

probability limits, 67, 457, 1074

probability model, 694–695

probit model, 442, 444

basic form, 688

bivariate, 738–752

bivariate ordered, 792–793

Gibbs sampler, 673

HOPIT model, 800

multinomial, 770–771

multivariate, 752–755

ordered, 787–791

prediction, 703

robust covariance matrix

estimation, 693

problem of endogeneity, 224

problem of identiﬁcation, 317,

321–326

PROC MIXED package, 642

product copula, 438

product innovation, 753–755

product limit estimator, 870

product rule, 1074

production function, 124–126

production function model, 638–639

proﬁt maximization, 308

projection, 31–32, 382, 989

projection matrix, 31

propensity score matching, 894–896

proportional hazard model,

870, 871

proxy variable, 221

proxy variables, 242–246

Prucha, I., 392

pseudo differences, 925

pseudo-log-likelihood function, 545

pseudo maximum likelihood

estimator, 637

pseudo-MLE, 547, 548, 937–938

pseudo R

, 533

pseudo-random number generator,

605–606

pseudoinverse, 1003

pseudoregressors, 184, 186

PSI, 590, 694–696

PSID, 344

public capital, 300–304

Pudney, S., 787, 794n10, 799, 800

pure space recursive model, 391

Puterman, M., 652n10

Pythagorean theorem, 988

Q test, 923, 924

QMLE, 692, 693

QR model, 683

quadratic approximation, 1007

quadratic hill-climbing

method, 1098

1182

Index

quadrature

approximating integrals,

1092–1093

bivariate normal

probabilities, 627

Gauss-Hermite, 582, 583, 1093

Gauss-Laguerre, 1093

Gaussian, 1093

MLE, 580–584

quadrature abscissa, 1093

quadrature weight, 1093

qualiﬁcation indices, 176

qualitative response (QR)

model, 683

Quandt, R., 181n2, 459, 470n4,

1093n7, 1094, 1096, 1097,

1098, 1099n16, 1102n21,

1103n23

quantile regression, 204, 442

quantile regression model, 207–210

quasi differences, 925

quasi-maximum likelihood

estimator (QMLE), 692, 693

quasi-Newton method, 1099

Quester, A., 846, 851

, 42–45, 139

Raftery, A., 141

Raj, B., 612

Ramaswamy, V., 593, 652n10

Ramsey, J., 459, 470n4

Ramsey’s RESET test, 137–138

random coefﬁcients, 771

random coefﬁcients model, 417–420

random draws, 625–627

random effects geometric

regression model, 584

random effects in nonlinear model,

621–623

random effects linear regression

model, 633

random effects model, 347, 370–385

binary choice, 718–720

Chamberlain’s approach,

381–384

cluster (and panel) robust

covariance matrix, 388–389

error components model, 371

event counts, 818–821

FGLS, 374–376

generalized least squares,

373–374

Hausman test, 379–380

heteroscedasticity, 387–388

least squares estimation, 372–373

Mundlak’s approach, 381

nonlinear regression, 414–415

simulation-based estimation,

629–633

testing for random effects,

376–379

random effects negative binomial

(RENB) model, 819

random number generation,

605–609

random parameter models, 343,

347, 416–426, 634–652

Bayesian estimation, 676–678

discrete distributions, 650–652

hierarchical linear models,

639–641

individual parameter estimates,

642–649

latent class models, 650–652

linear regression model,

634–639

nonlinear models, 641–642

random parameters logit (RPL)

model, 771–772

random parameters wage

equation, 636

random sample, 457, 1048

random utility, 2, 681, 683

random utility models, 684–685

random variable, 1015

random walk, 915, 946

random walk with drift, 942, 946

rank condition, 325, 476

rank two correction, 1099

rank two update, 1099

Rao, A., 423

Rao, C., 520, 587n27, 1082, 1092,

1100n19

Rao, P., 268, 617n3, 927

Rasch, G., 722

rating schemes, 784

ratio rule, 1074

Ray, B., 344n2

real estate sales, 392–393

recursive model, 319, 746

reduced form, 316, 319

reduced-form disturbances, 321

reduced form equation, 232, 243

regional production model (public

capital), 300–304

regressand, 12

regression, 21, 1034. See also

regression modeling

bivariate, 29

difference in differences, 155–158

heteroscedastic, 269

instrumental variable, and,

229–230

intrinsically linear, 166

kitchen sink, 139

linearly transformed, 46–47

median, 203, 204

modiﬁed zero-order, 95

multiple, 30

nonparametric, 212–215

orthogonal, 36

orthogonal partitioned, 33

partial, 32–39

partially linear, 210–212

partitioned, 32–35

piecewise linear, 158–160

pooled, 346

population, 26

regression discontinuity, 897–898

regression function, 12

regression modeling, 8

analysis of variance, 41, 42

censored regression model,

848–850

classical normal linear regression

model, 1042–1043

functional form. See functional

form

generalized regression model.

See generalized regression

model and

heteroscedasticity

goodness of ﬁt, 39–46

heteroscedastic regression

model, 268

hypothesis testing. See hypothesis

testing and model selection

latent regression model, 686–687

least squares estimation. See

Least squares estimation

least squares regression, 26–32

linear regression model. See

linear regression model

linearly transformed regression,

46–47

median regression, 203, 204

multivariate regression

model, 307

negative binomial regression

model, 806–807

nonlinear regression model. See

nonlinear regression model

nonparametric regression,

212–215

partial regression, 32–39

partially linear regression,

210–212

Index

1183

partitioned regression, 32–35

Poisson regression model,

803–804

pooled regression model. See

pooled regression model

quantile regression model,

207–210

structural change, 168–175

SUR model. See seemingly

unrelated regression (SUR)

model

truncated regression model,

837–839

regression variance, 1037

regression with constant term, 35

regressor, 12

regular densities, 515–516

regularity conditions, 514–515

rejection region, 111, 1062

Renault, E., 712n24, 858n12

RENB model, 819

Renfro, C., 930n16, 932n19, 938n28,

1089n1

reservation wage, 2

RESET test, 137–138

residual, 26

residual correlation, 353

residual inclusion method, 828

residual maker, 31

residual variance, 1037

residual variance (regression), 1036

response, 155

restricted investment equation, 120

restricted least squares estimator,

121–122

restrictions, 326

returns to schooling, 397

Revankar, N., 205, 216, 294n8,

309n23

revealed preference data, 782

Revelt, D., 771, 782

reverse equation, 334

reverse regression, 176, 177

Rice, N., 222, 697, 698, 735, 736,

794, 795, 798, 884, 887

Rich, R., 3, 951, 953

Richard, J., 135, 317, 968, 969

Ridder, G., 496n13, 885

right censoring, 813

Rilstone, P., 92

Riphahn, R., 3, 195, 345, 411, 540,

569, 571, 705, 735, 794,

807n14, 809, 820, 826, 827

risk set, 870

Rivers, D., 858n12

Robb, L., 313n31, 609, 610, 749, 793

Roberts, H., 176

Robertson, D., 422

Robins, J., 887

Robins, R., 930, 932

Robinson, C., 685n3

Robinson, P., 860n14

robust covariance matrix

estimation, 350–352, 692–693

robust estimation, 269, 276

robust estimator (wage equation),

355, 356

robust standard errors, 389

robustness to unknown

heteroscedasticity, 279

Rodgers, J., 1094n13

Rodriguez-Poo, J., 685n3, 693

Rogers, W., 71, 204

root mean squared error, 88

Rose, A., 410

Rose, J., 761, 772n6, 782

Rosen, H., 502n18, 505

Rosen, S., 685n3, 892n34

Rosenbaum, P., 895

Rosenblatt, D., 446

Rosett, R., 848n10

Rossi, P., 656n2, 761

rotating panel, 344

Rothenberg, T., 956, 957

Rothschild, M., 930n16

Rothstein, J., 229

Rotnitzky, A., 887

row vector, 973

Rowe, B., 706n20, 746n41

Roy’s identity, 184

RPL model, 771–772

RPL procedure, 642

RPM procedure, 642

Rubin, D., 94, 96, 656n2, 678, 814,

895, 1104, 1106

Rubin, H., 328n42, 335, 567, 948

Rubin’s causal model, 889

Runkle, D., 628n7, 716n27, 773, 883

Rupert, P., 232, 351

Ruud, P., 433n1, 435, 468n3, 628,

693, 712n24, 858n12, 916

Sala-i-Martin, X., 142, 143,

410, 970

Salem, D., 1024n5

Salmon, M., 277

sample discrepancy, 114

sample information, 434

sample midrange, 1048

sample selection, 872–887

attrition, 886–887

bivariate distribution, 873

common effects, 884

labor supply, 874, 878–879

maximum likelihood estimation,

877–878

nonlinear models, 880–883

panel data applications, 883

regression, 873–876

treatment effects. See evaluation

of treatment effects

two-step estimation, 876–877

sample selection bias, 221, 735

sampling

continuous distributions, 607–608

discrete populations, 608–609

multivariate normal

population, 608

standard uniform population, 606

sampling distribution, 1051–1055

sampling distribution (least squares

estimator), 54–55

sampling theory estimator, 665

sampling variability, 1053

sampling variance, 58, 1055

sampling variance (two-variable

regression model), 59

sandwich estimator, 545, 693

Savin, E., 305n16, 533n10

Savin, N., 947n8

Saxonhouse, G., 420n30

scalar matrix, 973

scalar multiplication, 976

scaled log-likelihood function, 469

scatter diagram, 1049

scedastic function, 1035

Schimek, M., 213

Schipp, B., 305n16

Schmidt, P., 124n4, 153, 171, 292n3,

305n16, 329n43, 332n45,

359n5, 382n24, 402, 497, 499,

502, 503, 505, 761, 763, 833,

839, 840, 841, 843, 852,

858, 958

Schur product, 635

Schwarz criterion, 139, 140

Schwert, W., 933, 955

score test, 530

score vector, 517

Scott, E., 588, 619, 721,

722n29, 861

Seaks, T., 122, 152n1, 193n5

season of birth, 254

second derivatives matrix, 1008

second-generation random

coefﬁcients model, 417n28

seed, 605

1184

Index

seemingly unrelated generalized

regression model, 304–305

seemingly unrelated regression

(SUR) model, 292–304

assumptions, 292

basic form, 292

dynamic SUR model, 305n16

FGLS, 296

generalized least squares,

293–295

generalized SUR model, 304–305

GMM estimation, 491–492

identical regressors, 295

MLE, 560–567

pooled model, 299–300

speciﬁcation test, 297–299

testing hypothesis, 296–297

Segerson, K., 307n19

Selden, T., 410, 970

selection bias, 881

selection methods. See sample

selection

selection on unobservables, 736, 891

selectivity effect, 244

self-reported data, 95

self-selected data, 95

semilog equation, 150, 160

semilog market, 17

semiparametric, 63, 183

semiparametric estimation, 439–444

semiparametric models of

heterogeneity, 731–733

Sepanski, J., 731n35

serial correlation, 258, 903–941

analysis of time-series data,

905–909

AR(1) disturbance, 910–912,

926–927

ARCH model, 930–933

asymptotic results, 912–917

autocorrelation. See

autocorrelation

Box-Pierce test, 922–923

central limit theorem, 915–917

convergence of moments,

913–915

convergence to normality,

915–917

disturbance processes, 909–912

Durbin-Watson test, 923, 924

ergodicity, 914, 915

estimation when  known,

924–926

estimation when  unknown,

926–930

GARCH model, 933–937

GMM estimation, 921–922

lagged dependent variable,

929–930

least squares estimation, 918–921

LM test, 922, 924

Q test, 923, 924

Sevestre, P., 344n2

share equations, 312

Shaw, D., 810, 811, 834n2

Shea, J., 250

Shephard, R., 311

Shephard’s lemma, 311

Shetty, C., 1093n7

Shields, M., 787, 794, 794n10, 799,

800

Shin, Y., 410, 422, 958, 970, 971

short rank, 19

short rank matrix, 985

shufﬂing, 606

sibling studies, 244

Sickles, R., 153, 171, 312n29, 416,

731n35, 843

Siegfried, J., 792, 793

signiﬁcance level, 1063

signiﬁcance of the regression, 126

signiﬁcance test, 115

Silva, J., 136n11

Silver, J., 307n20

Silverman’s rule of thumb, 213

“Simple Message to

Autocorrelation Correctors:

Don’t, A” (Mizon), 906

simple-to-general approach to

model building, 138

simplex methods, 1094

simulated annealing, 1094

simulated log likehihood

function, 630

simulation-based estimation,

603–634

bootstrapping, 611–615

functions, 603

GHK simulator, 627–629

Halton sequences, 625–627

Krinsky and Robb technique,

609–611

Monte Carlo integration,

623–633

Monte Carlo studies, 615–621

MSL. See maximum simulated

likelihood (MSL)

overview, 604–605

random draws, 625–627

random effects in nonlinear

model, 621–623

random effects model, 629–633

random number generation,

605–609

simulation-based statistical

inference, 609–611

simultaneous equations bias, 220,

316n35

simultaneous equations models,

314–336

complete system of

equations, 316

GMM estimation, 493–496

Granger causality, 318

Klein’s model I, 332

LIML estimator, 327, 328

matrix form, 318

MLE, 567–568

notational conventions,

318–321

problem of identiﬁcation,

321–326

single equation estimation and

inference, 326–329

structural form of model, 318

system methods of estimation,

329–334

systems of equations, 315–318

3SLS estimator, 331, 332

2SLS estimator, 327, 328

weak instruments, 334–336

Singer, B., 595, 726, 732, 862n15, 869

single index function, 414

singular value decomposition

(SVD), 1003

singularity of the disturbance

covariance matrix, 313

Siow, A., 666n14, 667

size of the test, 111, 617, 1063

skewness, 1018, 1049

Sklar, A., 437

Sklar’s theorem, 437

Slutsky theorem, 68, 241, 457, 472,

918, 1073

small T asymptotics, 362

smearing, 225

smearing estimator, 83

Smith, M., 437, 878

Smith, R., 220, 290, 410, 411, 422,

423, 424, 425, 971

smoothing functions, 213

smoothing techniques, 212

Snow, J., 228

Snyder, J., 687n5

sociodemographic differences, 393

software and replication, 9

Solow, R., 179, 180, 345n4

Song, S., 391, 578

Index

1185

Sorbom, D., 1089n1

Spady, R., 443

spanning vector, 983

spatial autoregression

coefﬁcient, 390

spatial correlation, 389–394

spatial error correlation, 393

spatial lags, 393

speciﬁcation error, 56, 806, 874

speciﬁcation test, 108, 233–239

AR, 328n42

Hausman, 234–237, 379–380, 397

hypothesis testing, 137–138, 1066

moment restrictions, 480

ordered choice models, 791–792

overidentiﬁcation, 238–239

SUR model, 297–299

Wu, 234–237

speciﬁcity, 617

Spector, L., 590, 673, 694

spectral decomposition

(matrix), 997

spherical disturbance, 21–23

spherical disturbances, 258

spherical normal distribution, 1041

spline function, 159

square matrix, 973

squeezing, 1103

Srivastava, K., 294

Srivistava, V., 292n2, 296n13

stabilizing transformation, 1078

Staiger, D., 204, 232n1, 249n10,

250, 334

Stambaugh, R., 933

standard deviation, 1018, 1048

standard error, 62, 1055

standard error of the regression, 62

standard normal cumulative

distribution function,

1090–1091

standard normal distribution, 1020

standard uniform population, 606

starting values, 202

state dependence, 729

state effect, 352

stated choice experiment, 782

statewide productivity, 579–580

stationarity, 909

ergodic, 524

KPSS test, 958–959

strong, 913

weak, 913

statistic, 1052

statistical properties, 51

statistically independent, 24

statistically signiﬁcant, 116

statistics. See estimation and

inference; probability and

distribution theory

steepest ascent, 1097–1098

Stegun, I., 462n2, 583, 607, 1089n2,

1091, 1092, 1093

Stengos, T., 742n40

step size, 1103

stepwise model building, 139

Stern, H., 656n2, 678

Stern, S., 92, 628n7

Stewart, M., 729n34

Stirling’s approximation, 1092

stochastic elements, 6

stochastic frontier model, 435–436,

624, 839–845

stochastic regressors, 60–61

stochastic volatility, 930

Stock, J., 141, 142, 204, 232n1,

249n10, 250, 334, 956, 957,

963, 964

Stone, R., 307n19

Stone’s expenditure system, 307

Strand, I., 810

Strang, G., 996n7

stratiﬁcation, 352–354

Strauss, J., 410

Strauss, R., 761, 763

streams as instruments, 228–229

Street, A., 173, 358, 362

strict exogeneity, 346

strike duration, 871–872

strong stationarity, 913

strongly exogenous, 318

structural change, 168–175

change in subset of

coefﬁcients, 170

Chow test, 168n10, 170, 171

different parameter vectors,

168–169

example (gasoline market),

172–173

example (World Health Report),

173–174

insufﬁcient observations, 169–170

predictive test of model stability,

174–175

unequal variances, 171

structural disturbances, 318

structural equation, 315

structural equation system, 232

structural form, 318

structural model, 243

structural speciﬁcation, 222

structural vs. nonstructural models,

315n34

Stuart, A., 134n7, 460n1, 514, 515,

517, 1019n1, 1059

study of twins, 244

subjective well-being (SWB), 797

sufﬁcient condition for an

optimum, 1010

sufﬁcient statistics, 460

Suits, D., 152n1, 363n9

sum rule, 1074

summability, 917

subspace, 983

superconsistent, 965

SUR model. See seemingly

unrelated regression (SUR)

model

survey questions, 784, 794

survival distribution, 866

survival function, 863,

866, 1028

survival models (strike duration),

871–872

survivorship bias, 221

Susin, S., 870

SVD, 1003

Swait, J., 761, 769n5

Swamy, P., 417n27, 418, 425

Swamy estimator, 425

SWB, 797

Swidinsky, R., 742n40

Swiss railroads, 843–845

symmetric matrix, 973

symmetry restrictions, 307n20

Symons, J., 422

system methods of estimation,

329–334

systems of demand equations,

307–314

systems of equations, 290–342

Cobb-Douglas cost function,

307–310

complete system of equations,

316

ﬂexible function forms,

310–314

Granger causality, 318

Klein’s model I, 332

LIML estimator, 327, 328

nonlinear systems of equations,

305–306

overview, 291–292, 336–337

panel data, 415–416

pooled model, 299–300

problem of identiﬁcation,

321–326

seemingly unrelated generalized

regression model, 304–305

1186

Index

systems of equations (continued)

simultaneous equations models.

See simultaneous equations

models

Stone’s expenditure system, 307

SUR model. See seemingly

unrelated regression (SUR)

model

systems of demand equations,

307–314

3SLS estimator, 331, 332

translog cost function, 310–314

2SLS estimator, 327, 328

weak instruments, 334–336

systems of linear equations, 989–990

t distribution, 1022

t ratio, 116

Tahmiscioglu, A., 422

Tandon, A., 173, 607

Taubman, P., 245

Tauchen, H., 370, 719

Tavlas, G., 417n27

Taylor, L., 203n10

Taylor, W., 236, 268, 272n10,

379n20, 394, 395, 397,

407, 499

Taylor series, 312, 462

Taylor series approximation, 1007

television and autism, 252

Telser, L., 293n4

Tennessee STAR experiment, 155

Terza, J., 787, 794n10, 799, 800,

807n14, 813, 880, 881,

883, 8210

test statistic, 617–618

testable implications, 110

testing hypothesis. See hypothesis

testing and model selection

tetrachoric correlation, 741

Teukolsky, S., 606, 608, 1003,

1089n2, 1092, 1093, 1094n11

textbook

notational conventions, 9–10

numerical examples, 9

overview/plan, 7–8

software and replication, 9

Thayer, M., 640

Theil, H., 88n12, 106n6, 242n6,

296n13, 329n43, 331, 334,

567, 663n10, 826, 1003n13,

1087n7

Theil U statistic, 88

theorem

Bernstein-von Mises, 668

Cauchy-Schwarz inequality, 1074

Chebychev’s inequality, 1068

Chebychev’s weak law of large

numbers, 1071

cosine law, 989

covariance, 1035

Cram´er-Rao lower bound,

520, 1059

Cramer-Wold device, 1078

ergodic, 914

ergodicity of functions, 915

Frisch-Waugh-Lovell, 33

Gauss-Markov, 60, 61

generalized Chebychev’s

inequality, 1073

Gordin’s central limit, 917

Granger representation, 964n13

Jensen’s inequality, 1074

Khinchine’s weak law of large

numbers, 1070

Kolmogorov’s strong law of large

numbers, 1071

law of iterated expectations, 1035

Liapounov central limit, 1082

likelihood inequality, 518

Lindeberg-Feller central

limit, 1079

Lindeberg-Levy central

limit, 1079

Markov’s inequality, 1068

Markov’s strong law of large

numbers, 1072

Martingale difference central

limit, 916

minimum mean squared error

predictor, 54

multivariate Lindeberg-Fuller

central limit, 1083

multivariate Lindeberg-Levy

central limit, 1082

orthogonal partitioned

regression, 33

orthogonal regression, 36

Slutsky, 1073

transformed variable, 47

Wold’s decomposition, 1004

theoretical econometrics, 3

three-stage least squares (3SLS)

estimator, 331, 332, 568

threshold effects/categorical

variables, 154–155

Thursby, J., 171n15, 313n31

Tibshirani, R., 611n2, 613

time effects, 363

time invariant, 351, 360

time-invariant variable (TIV), 364

time proﬁle, 158

time series, 1048

time-series cross-sectional

data, 344

time-series data, 257

time-series modeling. See

macroeconometric methods

time-series panel data

literature, 970

time-series process, 907

time space dynamic model, 392

time space recursive model, 391

time space simultaneous model, 392

time-varying covariate, 863

time window, 907

TIV, 364

Tobias, J., 50, 145, 178, 646, 656n2,

793, 895n40

Tobin, J., 845, 848

tobit model, 443, 814–815,

848–855, 858

Todd, P., 895n40

Tomes, N., 685n3

Topel, R., 537, 710, 793, 854, 877n31

total variation, 40

Toyoda, T., 171, 275n16

trace (matrix), 1000

TRACE test, 967

Train, K., 603, 623, 625, 668, 677,

683n2, 761, 771, 772, 782

transcendental logarithmic

(translog) function, 312

transformed variable, 47

translog cost function, 146,

310–314

translog demand system, 183–184

translog function, 312

translog model, 18

transpose, 974

travel mode choice, 773–779

treatment, 15, 155

treatment effect, 356

treatment effects, 155–158. See

evaluation of treatment

effects

treatment group, 156

Trebbi, F., 334

trend stationary process, 946

Trethaway, M., 194

triangular matrix, 973

triangular system, 319

trigamma function, 462n2, 1092

Trivedi, P., 7n3, 97, 251n11, 353,

436, 437, 438, 439, 441, 534,

542, 547, 597, 612, 613, 619,

623, 656, 668, 674, 683,

Index

1187

804n12, 805, 806, 807, 808,

810, 818, 862n15, 878, 888

Trognon, A., 387, 542n12, 545,

712n24, 858n12, 938

Trotter, H., 1098

true vs. asymptotic

distribution, 1085

truncated distribution, 834

truncated lognormal income

distribution, 836–837

truncated mean, 836

truncated normal distribution, 624,

834, 835

truncated random variable, 834

truncated regression model,

837–839

truncated standard normal

distribution, 834

truncated uniform distribution, 835

truncated variance, 836

truncation, 833–845

event counts, 810–812

incidental. See sample selection

moments, 835–837

stochastic frontier model,

839–845

truncated distribution, 834

truncated regression model,

837–839

when it arises, 833

truncation bias, 221, 811

Tsay, R., 3, 787, 942n1

Tunali, I., 685n3

twin studies, 244

twins festivals, 244

two-part models, 821–826, 852–857

two-stage least squares (2SLS),

230–232

two-stage least squares (2SLS)

estimator, 317, 327, 328

two-step estimation, 876–877

two-step MLE, 536–542

two-way ﬁxed effects model, 427

two-way random effects model, 428

Type I error, 617, 1062

Type II error, 617, 1062

Type-II tobit model, 853

Uhler, R., 701n14

Ullah, A., 444n2, 447, 448, 453,

933, 1051

UMP test, 1064

unbalanced panel, 348

unbalanced sample, 702

unbiased estimation, 55–56

unbiased estimator, 1056

unbiased test, 1064

unbiasedness, 448

uncentered moment, 457

uncorrelatedness, 22, 184

underidentiﬁed, 483

uniform-inverse gamma prior, 674

uniform prior, 674

uniformly most powerful

(UMP), 1064

unit root, 946

economic data, 947–948

example (testing for unit roots),

951–954

GDP, 957, 958–959

unobserved effects model, 380–381

unordered choice models. See

multinomial choice

updating formula, 992

U.S. gasoline market, 17

U.S. manufacturing, 313

utility maximization, 2

vacation expenditures, 443–444

van Praag, B., 750, 880

van Soest, A., 204n11, 443, 794, 795,

846, 853, 858n12, 860

variable

censored, 846

dependent, 12, 1007

dummy. See binary variable

endogenous, 316, 317

exogenous, 316, 317

explained, 12

explanatory, 12

identical explanatory, 294

independent, 12, 1007

latent, 848

omitted, 57, 219

predetermined, 317, 320

proxy, 221, 242–244

random, 1015

time-invariant, 364

transformed, 47

variable addition test, 236, 381

variable metric algorithm, 1099

Varian, H., 416

variance, 21

asymptotic, 520

conditional, 264, 1035

decomposition of, 1036

least squares estimator, 58–59,

61–62

prediction, 81

random variable, 1017

regression, 1037

residual, 1037

sampling, 58, 1055

truncated, 836

variance decomposition formula, 22

variance inﬂation factor, 90

Veall, M., 612, 701n14

vector, 973

vector autoregression models,

291, 506

vector multiplication, 975

vector spaces, 979–980

Vella, F., 468n3, 729n34, 858n12,

860n13, 872n24, 884, 885

Verbeek, M., 729n34, 735, 736, 883,

884, 885

Verbon, H., 416

Vetterling, W., 606, 608, 1003,

1089n2, 1092, 1093, 1094n11

Vilcassim, N., 771

Vinod, H., 201, 612

Volinsky, C., 141

Volker, P., 137n12

Vuong, Q., 534, 823, 858n12

Vuong’s statistic, 823

Vuong’s test, 140, 534–536

Vytlacil, E., 251n12, 587n28, 895n40

wage data panel, 647

wage determination, 290

wage equation, 351–352, 355, 356,

576, 636

Wahba, S., 895

Wald, A., 913, 948

Wald criterion, 118

Wald distance, 115

Wald statistic, 130, 171, 190, 297,

481, 482

Wald test, 115–121, 171, 189

Waldman, D., 277, 858

Walker, J., 860n14, 872n24

Walker, M., 307n19

Wallace, T., 375n15

Wallis, K., 7n, 923n13

Wambach, A., 3, 195, 345, 411, 540,

569, 571, 705, 735, 794,

807n14, 809, 820, 826, 827

Wan, G., 416

Wang, P., 652n10

Wansbeek, T., 326, 496n13, 885

Waterman, R., 818

Watson, G., 923n12

Watson, M., 141, 142, 204, 250,

959n12, 963, 964

Waugh, F., 34

1188

Index

weak instruments, 249–251,

334–336

weak stationarity, 913

weakly exogenous, 317

weakly stationary, 907

Webster, C., 1077n4, 1082

Wedel, M., 593, 652n10

Weeks, M., 134n8, 136, 964

Weibull model, 867, 868

Weibull survival model, 869

weighted endogenous sampling

maximum likelihood

(WESML) estimator, 710,

711n22

weighted least squares, 471

weighting matrix, 265, 464,

471n7, 486

Weinhold, D., 290, 425, 426

Weiss, A., 938

well-behaved data, 65

well-behaved panel data,

348–349

Welsh, R., 90, 100, 101

Wertheimer, R., 852

WESML estimator, 710, 711n22

West, K., 480, 481, 498n16, 920

White, H., 65n4, 134n8, 232n1, 272,

273, 274n14, 275, 318n37,

370, 474, 542n12, 692, 693,

914, 916, 918, 938, 1067,

1084n5

white noise, 910

White’s test, 283

Wichern, D., 93, 299

Wickens, M., 243, 468n3

Wildman, B., 173

willingness to pay (WTP),

779–781

willingness to pay space, 781

Willis, J., 726

Willis, R., 685n3, 892n34, 1025n7

Windmeijer, F., 804n12, 805

Winkelmann, R., 785n8, 794, 795,

797, 799, 801, 806,

807n14, 809

Winsten, C., 558, 926, 927

Winston, R., 309n23

Wise, D., 714n26, 768, 839n6, 883,

886, 887

Wishart density, 676

Wishart distribution, 1025

with zeros (WZ) model,

821n15

within-groups estimator, 357

Witte, A., 719, 846

Wold’s decomposition

theorem, 1004

Wood, D., 313, 314n32

Wooldridge, J., 20, 231, 318n37,

381n23, 382n24, 534, 696,

717, 718n28, 727, 729, 736,

798, 855, 883, 883n39, 885,

886, 887, 894, 938n28

Working, E., 229

World Health Report (2000),

173–174

Wright, J., 141, 142, 249n10

WTP, 779–781

Wu, D., 234, 236

Wu, J., 410

Wu, S., 410, 971

Wu speciﬁcation test,

234–237

Wu test, 236

Wynand, P., 750, 880

WZ model, 821n15

Yaron, A., 471n7, 476

Yatchew, A., 210, 211, 712, 717

Yogo, M., 249n10, 334

Young’s theorem, 1008

Yule-Walker equation, 919

Zabel, J., 884

ZAP model, 821n15

Zarembka, P., 193

Zavoina, R., 701n14, 787, 829

Zeger, S., 716n27

Zellner, A., 142, 166, 205, 216,

293n4, 294, 296n11, 331,

342n51, 342n251, 430, 655,

656n2, 658n3, 659n4, 660n5,

661n7, 663n12, 666n14, 667,

674, 675, 677, 1048n1

Zellner’s efﬁcient estimator (ZEF),

296n11

zero-altered Poisson (ZAP) model,

821n15

zero correlation, 742

zero inﬂated Poisson (ZIP) model,

821n15

zero inﬂation models, 821–824, 825

zero matrix, 974

zero-order method, 95

zero overall mean assumption,

20–21

Zhao, X., 787, 823n16

Zimmer, D., 439

Zimmer, M., 685, 879

Zimmermann, K., 701n14

ZINB model, 823

ZIP model, 821n15

Zoega, G., 7n