partial
regression coefficients,
191–192
specification bias, 200–201
standardized variables, regression on,
199–200
Threshold GARCH (TGARCH), 799
Threshold level, 566
Time derivative, 714n
Time effect, 598
Time sequence plot, 430
Time series, 290
Time series data, 737–769, 773–799
approaches to, 773–775
Box–Jenkins methodology, 777–784
cointegration, 762–765
and cross-section data, 591
and cross-sectional data, 343
defined, 21–23
economic applications, 765–768
examples of, 796–798
key concepts with, 739
modeling, 775–777
spurious regression phenomenon with,
747–748
stationarity, tests of, 748–754
stochastic
processes, 740–747
transforming nonstationary time series
to, 760–762
unit root tests, 754–760
U.S. economy, 738–739
vector autoregression, 784–790
volatility measurement in, 791–796
Time series econometrics, 22, 345
Time-invariant variable, 595, 596
Time-series regression, 270
Time-to-event data analysis, 580
Time-variant variable, 596
Tobit model, 574–577
Tolerance, 340
Total sum of squares (TSS), 74
Toxicity study, 586
TPF (transcendental production
function), 267
Traditional econometric methodology, 2–3
Transcendental production function
(TPF), 267
Transformation
of variables, 344–345
Transposition, 839
Transposition, matrix, 843
Trend stationary, 745
Trend stationary process (TSP), 745
Trend stationary (TS) stochastic processes,
745–746
Trends, 22
Trend-stationary processes, 761–762
Trial-and-error method, 527–529
Triangular (arithmetic) distributed-lag
model, 661
Triangular models, 712, 713n
Trichotomous variable, 542
True
level of significance, 475–476
Truncated sample, 574n
TS stochastic processes (
see
Trend
stationary stochastic processes)
TSP (trend stationary process), 745
TSS (total sum of squares), 74
2SLS (
see
Two-stage least squares)
2-
t
rule of thumb, 120
Two-sided hypothesis, 113–114
Two-stage least squares (2SLS),
718–724, 736
Two-tail hypothesis test, 113–114
Two-tail test of significance, 117
Two-variable linear regression model, 13
Two-variable regression analysis, 21, 34–48
examples of, 45–47
linearity in, 38–39
population
regression function, 37–38
sample regression function, 42–45
stochastic disturbance in, 41–42
stochastic specification of PRF, 39–41
Two-variable regression model, 147–175
elasticity measurement, 159–162
estimation problem, 55–85
classical linear regression model, 61–69
coefficient of determination
r
2
, 73–78
examples, 78–83
Gauss–Markov theorem, 71–73
Monte Carlo experiments, 83–84
ordinary least squares method, 55–61
precision/standard errors, 69–71
functional models of, 159
log-linear model, 159–162
reciprocal models, 166–172
selection, 172–173
semilog models, 162–166
growth measurement, 162–166
hypothesis testing, 113–124
accepting/rejecting hypothesis, 119
choosing level of significance,
121–122
confidence-interval approach, 113–115
exact level of significance, 122–123
forming null/alternative hypotheses, 121
selection of method, 124
statistical vs. practical significance,
123–124
test-of-significance approach,
115–119
zero null hypothesis/2-
t
rule, 120
hypothetical example of, 34–37
interval estimation, 107–112
confidence intervals, 109–112
statistical prerequisites, 107
regression through the origin, 147–153
and scaling/units
of measurement,
154–157
on standardized variables, 157–159
and stochastic error, 174–175
Two-way fixed effects model, 598
Type I error, 108n, 114n, 121, 122, 833, 834
Type II error, 121, 122, 833
U
Unbalanced panel, 25, 593
Unbiasedness, 520–521, 826, 827
assumption regarding, 189, 367
of BLUE, 72
of least-squares estimators, 92–93
Unconditional expected value, 35
Underdifferencing, 761
Underfitting, of model, 471–473
Underidentification, 692–694
Underprediction, 8
Ungrouped data, 561–566, 570–571,
589–590
Unit change in value of regressor in,
199–200, 571
Unit matrix, 840
Unit root problem, 744
Unit root stochastic processes, 744
Unit root tests:
augmented Dickey–Fuller test,
757–758
critique, 759–760
F
test, 758
1% and 5% critical Dickey–Fuller
t
and
F
values for, 893
Phillips–Perron, 758
structural changes testing, 758–759
time series data, 754–760
Units of measurement, 157
Universal regression, law of, 15
University of Michigan, 22
Unobservable variable, 603
Unobserved effect, 595
Unrestricted residual sum of squares
(RSS
UR
), 257–258
Upper confidence limit, 108
Upward trend, 164
U.S. Census Bureau, 22, 901
U.S. Department of Commerce,
23, 27
U.S. economic time series, 738–739
U.S. inflation rate, 797–798
U.S. Treasury bills examples,
767–768
Utility index, 566
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922
Subject Index
V
Vagueness, of theory, 41
Validity, of instruments, 669–670
VAR model (
see
Vector autoregression
model)
Variables:
dropping, 343–344
measurement
scales of, 27–28
orthogonal, 355
standardized, 183–184
transformation of, 344–345
Variance:
of individual prediction, 146, 862
of least-squares estimators, 93
of mean prediction, 145–146, 862
of OLS estimators, 194–195
of probability distribution, 810–811
variation vs., 74n
Variance-covariance matrix, 852–853,
856–857, 875
Variance-inflating factor (VIF), 328, 340
Variation, variance vs., 74n
Vector autoregression (VAR) model, 653,
655, 773, 775
causality, 787–788
estimation, 785–786
forecasting, 786–787
problems with, 788–789
Texas economy application, 789–790
time series data, 784–790
Venn diagram, 73, 74
VIF (
see
Variance-inflating factor)
Volatility, 791
Volatility clustering, 773
Volatility measurement:
ARCH presence, 795
Durbin–Watson
d
and ARCH effect, 796
in financial time series, 791–796
GARCH model, 796
NYSE price changes example, 794–795
U.S./U.K. exchange rate example, 791–794
Von Neumann ratio, 454
W
Wage
equations, 614
Wald test, 259–260, 299n
Weakly exogenous regressors, 468
Weakly stationary, 740
Weekly data, 22
Weierstrass’ theorem, 645
Weighted least squares (WLS), 373,
389–390, 409–410
WG estimator (
see
Within-group estimator)
White noise error, 419, 750
White noise process, 741
White’s general heteroscedasticity test,
386–389, 396, 398–399
White’s heteroscedasticity-consistent
standard errors, 391, 411, 503
Wide sense, stochastic process, 740
Wiener–Granger causality test, 653n
Within-group (WG) estimator, 599–602
WLS (
see
Weighted least squares)
WLS estimators, 373
World Fact Book,
901
World Wide Web resources, 900–901
X
X
(explanatory variable), 21
assumption on nature of, 68
independence of, 62–63, 316–317
Y
Y
(dependent variable), 21
Z
Z
test, 836–837
Zellner
SURE estimation technique, 714n
Zero contemporaneous correlation, 713
Zero correlation, 77
Zero mean value of
u
i
(assumption 3),
63–64, 317
Zero null hypothesis, 120
Zero-intercept model, 148–150
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