partial adjustment models, 634
example using, 627–629, 631
mean lag in, 627
median lag in, 627
and partial adjustment model, 632–633
Koyck transformation, 626
Kruskal’s theorem, 376n, 422
Kurtosis, 131, 132, 815, 816
K
-variable linear regression model, 849–851
L
Labor economics, 17, 18
Labor force participation (LFP), 51, 541,
549–551, 872
Lag(s):
and autocorrelation, 416–417
in economics, 618–622
length of, 753
reasons for, 622–623
Lag operator, 744n
Lagged endogenous variables, 690
Lagged values, 417
Lagrange multiplier (LM) model, 678
Lagrange multiplier (LM) test, 259–260,
481–482 (
See also
Breusch–
Godfrey test)
Lag-weighted average of time, 627
Large sample theory, 510
Large-sample properties, 96, 828–831
Latent variable, 566, 603
Law of gravity, 19
Law of iterated expectations, 815
Law of universal regression, 15
LB (Ljung–Box) statistic, 754
Lead terms, 667
Leamer–Schwarz critical values, 836
Least-squares criterion, 56
Least-squares dummy variable (LSDV)
model, 596–599
Least-squares estimates:
derivation of, 92
precision/standard errors of, 69–71
two-stage (
see
Two-stage least squares)
Least-squares estimator(s), 59
consistency of, 96
linearity/unbiasedness of, 92–93
minimum variance of, 95–96
ordinary (
see
Ordinary least squares)
properties of, 71–73
for regression through the origin,
182–183
of
σ
2
, 93–94
variances/standard errors of, 93
Leptokurtic, 816
Level form, 418
Level of significance, 108, 824, 834
choosing, 121–122
exact, 122–123
in presence of data mining, 475–476
Leverage, 497, 498
LF (
see
Likelihood function)
LFP (
See
Labor force participation)
LGDP time series, 751–752
Life-cycle permanent income hypothesis, 10
Likelihood function (LF), 103, 590, 825
Likelihood ratio (LR) statistic, 563
Likelihood ratio (LR) test, 259–260,
274–276
Limited dependent variable regression
models, 574
Limited information methods, 711
Linear equality restrictions testing,
248–254
F
-test approach, 249–254
t
-test approach, 249
Linear function, 38n
Linear in parameter (assumption 1), 62
Linear population regression function, 37
Linear PRF, 37
Linear probability model (LPM), 543–549
alternatives to, 552–553
applications of, 549–552
defined, 543
effect of unit change on regressor
value in, 571
example, 547–549
goodness of fit, 546–547
heteroscedastic variances of
disturbances, 544–545
nonfulfillment of
E
between 0 and 1, 545
non-normality of disturbances, 544
Linear regression model(s), 38, 39
estimation of, 527
example of, 4
log–linear vs., 260–261
nonlinear vs., 525–526
Linear trend model, 164
Linearity, 38–39
of BLUE, 71
of least-squares estimators, 92–93
in parameters, 38–39
in variables, 38
Linearization method, 537–538
Lin–log model, 162, 164–166
Ljung–Box (LB) statistic, 754
LLF (
See
Log-likelihood function)
LM (Lagrange multiplier) model, 678
LM test (
see
Lagrange multiplier test)
Log hyperbola model, 172
Logarithmic reciprocal model, 172
Logarithms, 184–186
Logistic distribution function, 526, 554
Logistic growth model, 532
Logit model, 553–555
effect of unit change on regressor
value in, 571
estimation of, 555–558
grouped, 558–561
ML estimation, 589–590
multinomial, 580
ordinal, 580
probit vs., 571–573
ungrouped data, 561–566
Log-likelihood function (LLF), 590, 825
Log-lin model, 162–164
Log-linear model, 159–162, 260–261
Log-log model, 159
Log-normal distribution, 174
Long panel, 593
Longitudinal data (
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