... 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 ... restrictions on W)?
8. 7. With definitions (8. 14) and (8. 15), show that system 2SLS and 3SLS are
numerically identical whenever
^
WW is a diagonal matrix.
8. 8. Consider...
... (2. 48) ?
2.4. For random scalars u and v and a random vector x, suppose that Eðu jx; vÞ is a
linear function of ðx; vÞ and that u and v each have zero mean and are uncorrelated
with the elements of x. Show ... 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 (...
... 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...
... possible. See Newey (1 985 ),
Tauchen (1 985 ), and Pagan and Vella (1 989 ) for general treatments and applications
of conditional moment tests. White’s (1 982 a) information matrix test can often be
viewed ... given x.
13 .8. 1 Setup for Panel Data
For panel data applications we let y denote a T Â 1 vector, with generic element y
t
.
Thus, y
i
is a T Â1 random draw vector fr...
... Review of Economic Studies 47,
225–2 38.
Chamberlain, G. (1 982 ), ‘‘Multivariate Regression Models for Panel Data, ’’ Journal of Econometrics 18,
5–46.
Chamberlain, G. (1 984 ), ‘ Panel Data, ’’ in Handbook ... (1995), ‘ Data and Econometric Tools for Development Analysis, ’’ in Handbook of Develop-
ment Economics, Volume 3A, ed. J. Berhman and T. N. Srinivasan. Amsterda...
... 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 ... W
N
@
a
w
2
Q
.
The method of establishing equation (3 .8) , given that statement (3.3) holds, is often
called the delta method, and it is used very often in econometrics. It gets...
... 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 ex...
... 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. ... shown by Hansen (1 982 ) and White (1 982 b,
1 984 ). In fact, even if x is exogenous and Assumption OLS.3 holds, OLS is not gen-
erally asymptotically e‰cient if, for x H...
... confuse a
pooling of independent cross sections with a di¤erent data structure, panel data,
which we treat starting in Chapter 7. Briefly, in a panel data set we follow the same
group of individuals, ... data in HPRICE.RAW, which is a subset of the data
used by Kiel and McClain (1995). The file conta ins housing prices and characteristics
for two years, 19 78 and...