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Sve to Jahve bijae zapovjedio svome sluzi Mojsiju, zapovjedio je Mojsije
Joui, a Joua sve izvrio, ne izostavivi nita od svega to Jahve bijae
zapovjedio Mojsiju.
16
Tako
je Joua zauzeo svu zemlju: Gorje, sav Negeb i svu zemlju Goen, efelu,
Arabu, Izraelsko
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then the GMM estimator that minimizes q is the 2SLS estimator. The extension that we can obtain here is
to allow for heteroscedasticity of unknown form. There is no need to rederive the earlier result. If the
disturbances are heteroscedastic, then
Wjj =pl
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timate from the larger sample. The posterior variance is the inverse in brackets, which is 0.000071164.
This is close to the variance of the latter estimate. An HPD interval can be formed in the familiar fashion.
It will be slightly narrower than the cond
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hand calculator whereas the maximum likelihood estimator requires specialized software (only
somewhatit is reasonably common).
16.2.2 BAYESIAN ESTIMATION Parametric formulations present a bit of a methodological dilemma. They
would seem to straightjacket
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of a model: If every equation has its own predetermined variable, the entire model is
identied.Theproossimpleandisleftasanexercise.Foranalexample,weconsider a somewhat larger
model.
Example 15.6 Identication of Kleins Model I The structural coefcients in
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The following model of industry structure and performance was estimated by Strickland and Weiss
(1976). Note that the square of the endogenous variable, C, appears in the rst equation. A = 0
+1M+2Cd+3C+4C2 +5Gr +6D+1, C = 0 +1A+2MES+2, M = 0 +1K +2Gr
+3C+
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There are at least two fully parametric estimators for this model. The maximum likelihood estimator is
discussed in Section 17.6.3. Greene (1997b) presents the following method of moments estimator: For
the regression slopes, excluding the constant term,
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they are labeled limited information methods.
15.5.1 ORDINARY LEAST SQUARES For all T observations, the nonzero terms in the jth equation are yj =
Yj j +Xj j +j = Zjj +j. The M reducedform equations are Y = X+V. For the included endogenous
variables Yj,
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full derivation of the more complex cases.2 The classical normal regression model we have analyzed thus
far is constructed around the conditional multivariate normal distribution N[X,2I]. The interpretation is
different here. In the sampling theory settin
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If this hybrid is to have the same variables as the original, then it must have nonzero elements in the
same places, which can be ensured by taking f0=1, and zeros in the
samepositionsastheoriginalaj.Extractingthethirdandfthblocksofrows,if aj isto be admi
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result is dominated by the sample information, as it should be if there is no prior
information.Intheabsenceofanypriorinformation,themeanoftheposteriordistribution, which is a type of
Bayesian point estimate, is the sampling theory estimator. To generaliz
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CHAPTER 15 SimultaneousEquations Models 403
estimator.17 The implication is that with normally distributed disturbances, 2SLS is fully efcient. The
kclass of estimators is dened by the following form
j,k =
YjYj kVjVj YjXj XjYj XjXj
1Yjyj kVjvj Xjyj
.
We
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1.01 Scientific Method Lab Simulation Report
Bio202A
Turn on Comments (Review>Show Comments Simple Markup) to see the rubric for each graded item.
When using the underlined key terms in your answers, EXPLAIN them. For example: The hypothesis, which is
an
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withinwhichthedensityfunctionishigherthananypointsoutsideit,whichjustiesthe term highest posterior
density (HPD) interval. For the case we have analyzed, which involves a symmetric distribution, we would
form the HPD interval for around the least squares
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assuming that the distribution of X does not depend on or 2. Since g(2) a constant, this density
is the one in (164). For now, write f(2,y,X) h(2)[2]K/22(XX)11/2e(1/2)(b)[2(XX)
1]1(b), (165) where h(2) = [vs2]v+1
(v+1) 1 2v evs2(1/2). (166) For the
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CHAPTER 16 Estimation Frameworks in Econometrics
This density is proportional to a multivariate t distribution6 and is a generalization of
thefamiliarunivariatedistributionwehaveusedatvariouspoints.Thisdistributionhas
adegreesoffreedomparameter,d =nK,mean
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higher powers of the regressors creates many more linearly independent instrumental variables. If an
equation in a linear model fails the rank condition but not the order
17Thisisprovedbyshowingthatbothestimatorsaremembersofthekclassofestimators,allofwhic
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theory estimator. Onemightaskatthispoint,whybother?TheseBayesianpointestimatesareidentical to the
sampling theory estimates. All that has changed is our interpretation of the results. This situation is,
however, exactly the way it should be. Remember that
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CHAPTER 16 Estimation Frameworks in Econometrics 435
Theminimumisfoundbyequatingthisderivativeto0,whence,sinceWisirrelevant, = E[y,X]. This kind of
loss function would state that errors in the positive and negative direction are equally bad, and large
er
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In this setting, the data are viewed as constants whose distributions do not involve the
parametersofinterest.Forthepurposeofthestudy,wetreatthedataasonlyafixedset
ofadditionalinformationtobeusedinupdatingourbeliefsabouttheparameters.[Note the similarity
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that as the amount of data increases, the posterior density, and the estimates thereof, converge to the
sampling theory results.
Example 16.3 Bayesian Estimate of the Marginal Propensity to Consume
InExample3.2,anestimateofthemarginalpropensitytoconsumeis
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on the entire system of equations. With normally distributed disturbances, FIML is efcient among all
estimators. The FIML estimator treats all equations and all parameters jointly. To formulate the
appropriate loglikelihood function, we begin with the re
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CHAPTER 15 SimultaneousEquations Models
variables that the conditions are met trivially. In practice, it is simple to check both conditions for a small
model. For a large model, frequently only the order condition is veried. We distinguish three cases: 1
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CHAPTER 15 SimultaneousEquations Models 397
havethevirtueofcomputationalsimplicity,althoughwithmodernsoftware,thisvirtue is extremely modest.
For better or worse, OLS is a very commonly used estimator in this context. We will return to this issue
later i
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that will be an imposter for equation j. Many fjs are already precluded. 1. f1 must be the rst column of
an identity matrix. The rst equation is identied and normalized on y1. 2. In all remaining columns of F,
all elements below the diagonal must be zero,
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where j is a degrees of freedom parameter and 2 is the Bayesian estimate of 2. The prior degrees of
freedom m is a parameter of the prior distribution for 2 that would havebeendeterminedattheoutset.
(Seethefollowingexample.)Onceagain,itisclear
8Note that
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The limited information maximum likelihood (LIML) estimator is based on a single equation under the
assumption of normally distributed disturbances; LIML is efcient among singleequation estimators. A
full (lengthy) derivation of the loglikelihood is pro
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400 CHAPTER 15 SimultaneousEquations Models
columnofZj onX.Thisequationalsoresultsinausefulsimplicationoftheestimated asymptotic covariance
matrix, Est.Asy.Var[ j,2SLS]= jj[ Zj Zj]1. It is important to note that jj is estimated by
jj =
(yj Zj j)(yj Zj j
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Three techniques are generally used for joint estimation of the entire system of equations: threestage
least squares, GMM, and full information maximum likelihood.
15.6.1 THREESTAGE LEAST SQUARES Consider the IV estimator formed from
W= Z=diag[X(XX)1XZ
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naredi im Joua da sijeku drva i nose vodu, sve do danas, za zajednicu i za
rtvenik Jahvin na mjestu
koje se god izabere.
Chapter 10
1
A kad u jeruzalemski kralj AdoniSedek da je Joua zauzeo Aj i da ga je
izruio "heremu",
kletom unitenju, kao to je uinio
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CroatianBibleAnonymous
brojan narod i imate silnu snagu. Zato nee dobiti samo jedan drijeb:
18
neka gora bude tvoja.
Ako je umovita, iskri je pa e obronci biti posjed doma tvoga. Istjerat e
sigurno Kanaance ako
i imaju eljezna kola, ako i jesu jaki."
Chap
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opskrbi, ne pitajui Jahvu to e im rei.
15
Joua uglavi s njima mir i sklopi savez s njima da e
ih potedjeti. I glavari se na to zakunu.
16
A poslije tri dana, poto su sklopili s njima savez, saznalo
se da su im susjedi i da ive usred Izraela.
17
Tada krenu
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Dilean, Hamispe, Jokteel;
39
Laki, Boskat, Eglon;
40
Kabon, Lahmas, Kitli;
41
Gederot,
BetDagon, Naama, Makeda: esnaest gradova s njihovim selima.
42
Libna, Eter, Aan;
43
Jiftah,
Ana, Nesib;
44
Keila, Akzib i Marea: devet gradova s njihovim selima.
45
Ek
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Mea je
Manaeova ila od Aera do Mikmetata, koji lei nasuprot ekemu, a zatim
zavijala desno prema
Jaibu na izvoru Tapuahu.
8
Pokrajina Tapuah pripadae Manaeu, ali sam Tapuah na mei
Manaeovoj pripadae sinovima Efrajimovim.
9
Mea je silazila do potoka Kane. J