... right-hand side accounts for possible serial correlation
in the score. The first term on the right-hand side of equation (13. 51) can be replaced
by one of the other two estimators in equation (13. 50). ... or
X
N
i¼1
Aðx
i
;
^
yyÞ
"#
À1
13: 32Þ
and the asymptotic standard errors are the square roots of the diagonal elements of
any of the matrices. We discussed each of th...
... e¤ect of w on
Eðy jw; cÞ, holding c fixed, is easily estimated.
Unfortunately, complications often arise in the collection and analysis of economic
data because of the nonexperimental nature of economics. ... function of x.Wheny and x are random, it makes sense to use
the right-hand side of equation (2.8), but where f ðxÞ is the conditional mean, mðxÞ.
Therefore, the (parti...
... the cross section
sample size, N; for an example, see Problem 8.8. We cover general panel data appli-
cations in Chapter 11. (As in Chapter 7, the label ‘‘systems of equations’’ is not es-
pecially ... y
i
, X
i
, and u
i
can represent di¤erent time periods for the same cross-
sectional unit (so G ¼ T, the total number of time periods). Therefore, the following
analysis...
... section units. Often there are ele-
ments of x
it
that are constant across time for a subset of the cross section. For ex-
ample, if we have a panel of adults and one element of x
it
is education, ... time-constant factors
that are not of direct interest.
In panel data analysis the term ‘‘time-varying explanatory variables’’ means that
each element of x
it
varies ov...
... Asymptotic Variance of Semiparametric Estimators,’’ Econometrica 62, 134 9–
138 2.
Newey, W. K., and D. McFadden (1994), ‘‘Large Sample Estimation and Hypothesis Testing,’’ in Hand-
book of Econometrics, ... Model of Crime with Panel Data, ’’ Re-
view of Economics and Statistics 76, 360–366.
Cosslett, S. R. (1981), ‘‘E‰cient Estimation of Discrete-Choice Models,’’ in St...
... cross section analysis the asymptotics is as the number of observations, denoted
N throughout this book, tends to infinity. Usually what is meant by this statement is
obvious. For panel data analysis, ... the time series dimension and let the cross section dimension grow. The
research on asymptotic analysis with these kinds of panel data sets is still in its early...
... square root of the appropriate diagonal ele-
ment of
^
VV
N
=N. The asymptotic standard errors can be loosely thought of as estimating
the standard deviations of the elements of
^
yy
N
, and they ... Limiting Behavior of Estimators and Test Statistics
In this section, we apply the previous concepts to sequences of estimators. Because
estimators depend on the random outcomes...
... Linear Model and OLS Estimation 53
II LINEAR MODELS
In this part we begin our econometric analysis of linear models for cross section and
panel data. In Chapter 4 we review the single-equation linear ... for cross section data
as well as begin our analysis of panel data. Chapter 8 builds on the framework from
Chapter 7 but considers the case where some expl...
... quarters of birth and various interactions of these with year of birth and
state of birth—are very weak, and they are too numerous relative to their contribu-
tion in explaining years of education. ... linear combination of interest, say
y 1 a
1
b
1
þ a
2
b
2
þÁÁÁþa
K
b
K
, and then to write one of the b
j
in terms of y and the
other elements of b. Then, substitute...
... obtained by taking h
i
to be all nonconstant, unique elements of x
i
and
x
0
i
x
i
: the levels, squares, and cross products of the regressors in the conditional mean.
The Breusch-Pagan and White ... case of the White test because ð
^
yy
i
;
^
yy
2
i
Þ con-
tains two linear combinations of the squares and cross products of all elements in x
i
.
Additional Single-Equati...