recursive residuals, 483

studentized residuals, 482 Reverse regression, 71-72, 459-461 Ridge regression, 281-283 /-square

in dummy dependent variable models, 332-334

in multiple regression models, 131 relationship with F-ratios, 167-168 in simultaneous equation models, 369 in time-series models, 550

Sampling distributions multiple regression, 134-135 from normal populations, 26 simple regression, 76-78

Sargans test, 255

Selection of regressors, 496-502

Serial correlation in autoregressive models, 248 LM test, 250

in rational expectations models, 443-444

in unit root tests, 583 Significance levels

criticism, 32

defined, 29 Sims test, 394 Specification errors

Hausmans test, 506-509

irrelevant variables, 164-165

omitted variables, 161-162

Ramseys test, 478

Sargans test in dynamic models, 255 Specification searches, 491 Spurious trends, 260-261 Stationary time-series, 527-530 Stochastic regressors, 126 Structural change and unit roots, 587

/-distribution, 21 Tests of hypotheses

for cointegration, 598

general theory, 29-32

for linear functions of parameters, 159

in linear regression models, 80, 158-160

for market efficiency, 599-600 nonnested hypotheses, 514-518 for rational expectations hypothesis, 599

for unit roots, 583-587 Theils R criterion, 497 Time series

ARIMA models. 538-541

autoregressive, 533

Box-Jenkins methods, 542-549

forecasting, 544

moving average, 531

R measures, 550-552

stationarity, 527-530 Trace of a matrix, 55 Trends and random walks, 258-261 Truncated variables

criticism of the tobit model, 341

tobit model, 338-342

truncated regression model, 342-343 TSP model, 259 Two-stage least squares, 373

Unbiasedness defined, 23

least squares estimators, 114 under stochastic regressors, 126

Underestimation of standard errors under autocorrelation, 241-243 under heteroskedasticity, 210-211

Unit root tests Dickey-Fuller test, 583 powers of unit root tests, 584 serial correlation, 583 structural change, 587

Unit roots, 581-582

Variance inflation factor (VIF), 274

Vector autoregressions, 578-580

Vector autoregressions and cointegration,

592-597 von Neumann ratio, 245

Wald test, 121-124, 256 Weighted least squares, 212-213 Whites test, 204

Workings concept of identification, 385