CHAPTER 10 Nonspherical Disturbances 195
2. The largest characteristic root of is nite for all n. For the heteroscedastic model, the variances are
the characteristic roots, which requires them to be nite. For models with autocorrelation, the
requirements
But there are two problems with this estimator, one theoretical, which applies toQ as well, and one
practical, which is specic to the latter. Unlike the heteroscedasticity case, the matrix in (1015) is 1/n
times a sum of n2 terms, so it is difcult to con
and the instrumental variables estimator.
10.2.3 ASYMPTOTIC PROPERTIES OF NONLINEAR LEAST SQUARES If the regression function is nonlinear,
then the analysis of this section must be applied to the pseudoregressors x0 i rather than the
independent variables
Asy.Var[ GMM]=[(XZ) V(ZX)]1.
We conclude this discussion by tying together what should seem to be a loose end. The GMM estimator
is computed as the solution to Min q = m()Asy.Var[n m()]1 m(), which suggests that the
weighting matrix is a function of the t
not to estimate Q, but to nd a function of the sample data that will be arbitrarily close to this
function of the population parameters as the sample size grows large. The distinction is important. We
are not estimating the middle matrix in (1010) or (10
asymptotically, then
plimbIV = +QXX.Z plim1 n
Z
= .
This result is exactly the same one we had before. We might note that at the several points where we
have established unbiasedness or consistency of the least squares or instrumental variables estimator,
completely unknown, both as to its structure and the specic values of its elements. In this situation,
least squares or instrumental variables may be the only estimator available, and as such, the only
available strategy is to try to devise an estimator f
the sum, the weights in the sum grow smaller as we move away from the diagonal. If we think of the
sum of the weights rather than just the number of terms, then this sum falls off sufciently rapidly that
as n grows large, the sum is of order n rather than
the same as that of
vn,LS =Q1 1 nX =Q1 1 n
n
i=1
xii, (109)
where x i is a row of X (assuming, of course, that the limiting distribution exists at all). The question now
is whether a central limit theorem can be applied directly to v. If the disturbances
this point, we no longer require that E[i xi] = 0. Instead, we adopt the instrumental variables
formulation in Section 10.2.4. That is, our model is yi = x i +i E[i zi] = 0 for K variables in xi and for
some set of L instrumental variables, zi, where L
Corn Starch Osmosis
Weight of corn starch
Weight of water
Dialysis tube (before)
Dialysis tube (after)
Volume of dialysis tube (before)
Volume of dialysis tube (after)
Volume of water in beaker (before)
Volume of water in beaker (after)

6.16g
93.6g
95.1
Codeine
Slang/Street Names of
Codeine
Purple
Lean
Drank
Syrup
History of Codeine
Codeine is found in opium
Was synthesized(manmade) in 1830
JeanPierre Robiquet, a Frenchman created
codeine to replace raw opium for medical
purposes
Purpose of Codeine
Can
Part of Frankenstein
Chapter/Page
Number/Quote
Song
Victors obsession with
Elizabeth
Chapter 1 Page 21
since to death she was to
be mine only
Chapter 5 Page 43
How could I describe my
emotions at this
catastrophe
Chapter 8 Page 76
The 1st victims to my
un
Economics Food
Project
Food Wasted
Food Wasted
Food Wasted
(Never used)
Food Wasted
Food Wasted
Plates of Food that I Ate
(Same
exact thing
as
The last
slide)
Plates of Food that I Ate
Plates of Food that I Ate
(Had the waste
the milk, was
running late fo