INDEX

Cointegration and vector autoregressions,

592-597 Cointegration tests, 598-600 Condition number (in multicoUinearity),

Conditional probability, 14

Confidence intervals defined, 27-28, 79-80 joint and separate intervals, 138-139 relationship with testing of hypotheses, 32-33

Consistency, 24

Correlations relationships with /-ratios, 145-147 simple, partial, and multiple, 147-148

Correlogram, 528

Cramers rule, 50

Cross-validation, 504

Davidson and MacKinnons 7-test, 515-516

Deletion of variables "

pitfalls in using /-ratios, 168

use of F-ratios, 167 Determinants, 44-47 Detrending, 258-259 DFFITS criterion for outliers, 487-488 Diagnostic checking, 476 Dickey-Fuller test, 259, 583 Disproportionate sampling, 330-331 Distributed lags, 408-412 Dropping variables

in multicoUinearity, 289-291

use of F-ratios, 167-168, 500-503 DSP model, 259 Dummy variables

for changes in intercepts, 307-312

for changes in slopes, 313-315

for cross-equation constraints, 315-317

dummy dependent variables, 322-338

under heteroskedasticity and autocorrelation, 321-322

linear discriminant function, 325-326

linear probability model, 323-325

logit model, 327-329

measures of R-, 333-334

for predictions and standard errors of prediction, 319-320

probit model, 327-329

for testing stability, 318-319

Econometrics aims and methodology, 4-7 definition, 1-2

tests of economic theories, 7

types of models, 2-4 Encompassing test, 517 Endogenous variables, 357 Error correction models, 420, 597 Errors in variables

classical model, 449-450

correlated errors, 470

general model, 451-458

grouping methods, 463

Hausmans test for errors in variables, 508

instrumental variable methods, 461-462

Krasker-Pratt criterion, 467 multiple equations, 469 proxy variables, 464-466 reverse regression, 459-461 Estimation interval estimation, 27-28 method of least squares, 69-72, 130-132

method of maximum likelihood (ML), 118

method of moments, 66 point estimation, 22-26 Estimator properties asymptotic unbiasedness, 25 asymptotic variance, 25 BLUE property of least squares, 114-115

consistency, 24

efficiency, 24

unbiasedness, 23 Exogeneity

defined, 390-391

relationship with causality, 394

test for exogeneity, 395 Exogenous variables, 357 Expectations

adaptive expectations, 408-410

expectations and adjustment lags, 415

model-consistent expectations, 433

naive models, 406-408

rational expectadons, 431-433

sufficient expectations, 433 Extraneous estimators, 293

F-distribution, 21 F-ratios

implied by different criteria for model

selection, 500-503 relationship to higher R, 167-168

Instrumental variables, 112, 367-369,

461-462 Inverse of a matrix, 48 Inverse prediction, 101-102 Irrelevant variables, 164-165

Generalized least squares, 212-213, 227, 238

Glejsers test, 204

Goldfeld-Quandt test, 206

Goodness of fit, 131, 332-334, 369, 540-

541, 550-552 Granger casuality, 393 Grangers test, 393 Grid-search method, 239 Grouping methods, 463

Hausmans test, 506-509 Hendrys approach to model

construction, 494-495 Heteroskedasticity

Anscombes test, 204

Breusch and Pagan test, 207-209

consequences, 209-211

deflators, 215-217

estimation of correct variance, 211

Glejsers test, 204

Goldfeld and Quandt test, 206

likeUhood ratio test, 206

maximum likelihood method, 213

Ramseys RESET test, 204

weighted least squares, 212-213

Whites test, 204 Hockings 5p criterion, 498-499 Hypothesis testing

general theory, 27-32

relationship with confidence intervals, 32-33

Idempotent matrices, 55 Identification

necessary and sufficient conditions, 363-364

through reduced form, 358-360

Workings concept. 385 Inference

classical, 22-26

muhiple regression, 134-135

simple regression, 76-78

Joint, marginal, and conditional

distributions, 18 Joint and separate confidence intervals,

7-test, 515-516

Koyck model estimation in autoregressive form, 411 estimation in distribution lag form, 412

Lagrangian multiplier (LM) test, 119-124, 177, 251

Levels vs. first differences, 232-234, 259-263

Likelihood ratio (LR) test, 119-124, 206 Limited information maximum likelihood

(LIML), 381 Limiting distribution, 25 Linear and quadratic forms, 52 Linear probability (LP) model. 323-325 Linear vs. log-linear forms, 96-97, 220-

Liu critique, 389 Logit model, 327-329 Lucas critique, 389

Mallows Cp criterion, 498 Matrix addition, 42 Matrix multiplication, 43 Methods of estimation

generalized least squares, 212-213, 227, 238

indirect least squares, 359-360

instrumental variables, 112, 367-369, 461-462

least squares, 69-72, 130-132

limited information maximum likelihood (LIML), 381

maximum likelihood, 118

moments, 66 Model selection, 492-496 Moving average process, 531

index

MulticoUinearity condition number, 275 definition, 270 dropping variables, 289-291 extraneous estimates, 293 principal component regression, 284-285

problems in measuring, 276 ridge regression, 281-283 Theils measure, 275 Multiple regression analysis of variance, 157 degrees of freedom and R-, 165-168 inclusion of irrelevant variables, 164-165

interpretation, 143-144

omission of relevant variables, 161-162

partial correlation and multiple

correlation, 147-148 prediction, 154-155 statistical inference, 134-135 test for linear functions of parameters,

tests for stability, 170-177 tests of hypotheses, 156-159 Multivariate normal distribution, 54

Nonnested hypothesis tests, 514-518 Normal distribution, 19 Normalization in simultaneous equations, 377

Omitted variables autocorrelation, 253 bias in least squares estimators, 161-163

interpretation of Hausmans test, 510-512

test for, 477 Orthognal matrices, 49 Oudiers

bounded influence estimation. 488 DFFITS criterion, 487-488 illustrated, 89-95

Partial adjustment models, 419-423 PE test, 223

Piecewise regression, 185 Polynomial lags, 423-427

Posterior odds for model selection, 503-505

Principal component regression, 284-285

Probability, 12-14

Probability distributions, 17-21

Probit model, 327-329

Proxy variables, 464-466

PSW test, 513-514

e-statistics, 540-541 Qualitative variables {see Dummy variables)

Ramseys RESET test, 478 Raos score test, 119-124 Rational expectations defined,431-433

estimation of a demand and supply

model, 436-442 serial correlation problem, 443 tests for rationality, 434-435, 599

Rational lags, 429

Recursive systems, 387

Reduced form, 358-360

Regression analysis of variance, 84, 156-157 assumptions and specification, 65 causation in regression, 75-76 censored regression model, 339-342 cointegrating regression, 590-591 interpretation, 143-145 inverse prediction, 101-102 irrelevant variables, 164-165 method of least squares, 69-71 method of moments, 66 outliers, 89-95

prediction, 85, 154-155, 319-320

statistical inference, 76-78, 134-135

tests of hypotheses, 80

truncated regression model, 342-343 Regression fallacy, 105 Regression with no constant term, 83 Residuals

BLUS residuals, 483

predicted residuals, 481

problems with least squares residuals, 479-480