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Handbook ò econometrics

Handbook of Econometrics Vols1-5 _ Chapter 1 pdf

Handbook of Econometrics Vols1-5 _ Chapter 1 pdf

... matrices of order L X L and K X L, respectively: r YII Y 21 Y12-.*YIL PI1 Pl2-.-PIL Y22 Y2L P 21 P22 P2L YLI r= YL2 where n X L P,, P,L_ XB=E, Yll Y 21 _Y nl (2.3) matrices of the two sets of ... modeling of a disturbance covariance matrix 9 .1 Rational random behavior 9.2 The asymptotics of rational random behavior 9.3 Applications to demand and supply 10 The Moore-Penrose 10 .1 10.2 10 .3 10 .4 ... y,_s_, + A*x, + AA*+, + + A”A*x ,_, + u, + Au ,_, + + AS~t_s (7 .16 ) If all roots of A are less than in absolute value, so that A” converges to zero as s -+ cc and (7 .15 ) holds, the limit of...
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Handbook of Econometrics Vols1-5 _ Chapter 2 ppsx

Handbook of Econometrics Vols1-5 _ Chapter 2 ppsx

... (2ncf;)- 2 exp{-(x2-P2 )2/ 2~~ ,2) (2. 56) and f(xJx2;)= [27 ro:(1-p2)]- 2 Xexp{-[x,-~,-p, .2( x2- ~2) 12/ 2(1-p2)o:}, (2. 57) where p, = a,p/u, From (2. 56), it is seen that the marginal pdf for Z2 is normal ... (2~ )-“ 21 G,111~2exp{- (2. 67a) and dx,lce,) = w- m2’ - %GII’ 21 G 22 G 121 1/2w{- Q2 /2) , (2. 67b) with mi the number of elements in xi, i = 1 ,2, ml + m2 = m, Q,, and Q2 as defined in (2. 65) and (2. 66), ... conditional variance - p2 Since t, = (2, - p2)/u2 the conditional pdf for Z2, given Z,, is normal, that is, f(x,lx,J)= [2nu;(1-PZ)]- 2 Xexp{-[x2- ~2 - _2 .~(x~-11.~) 12/ 2(1-P2)u 22} ~ u2), wheree’ (P,P,,...
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Handbook of Econometrics Vols1-5 _ Chapter 4 docx

Handbook of Econometrics Vols1-5 _ Chapter 4 docx

... replace ,) Conditions 4. 4.2 and 4. 4.3 by those similar to Conditions 4. 3.2 and 4. 3.3 to keep the system identified Or we may rely on [Kohn (1979)]: Theorem 4. 4.2 Under Condition 4. 4.1 and 0, = Zc, ... constant and (4. 32) and (4. 33) hold Combining Lemma 4. 2.1 and Lemma 4. 4.1 we obtain the following proposition about observationally equivalent structures with regard to model (4. 1) Lemma 4. 4.2 Twostructures,S=[B(L) ... identification of those rows of A Similarly for Condition 4. 3.3’ below “For instance, Condition 4. 3.2 implied Condition 6.2.1 of Fisher (1966) 250 C Hsiao 4. 3.1 by Condition 4. 3.3’ For each row of A,...
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Handbook of Econometrics Vols1-5 _ Chapter 5 pot

Handbook of Econometrics Vols1-5 _ Chapter 5 pot

... fall into one of four categories, each of which measures different aspects of the problem.4 (1) (2) (3) (4) Measures of Measures .of Measures of Measures of the the the the “quality of the design” ... Hypotheses by Goodness of Fit”, Economics Journal, 85, 877-882 Ch 5: Model Choice 329 Neyman, Jerzy (1 958 ) “The Use of the Concept of Power in Agricultural Experimentation”, Indian Society of ... Problem”, Annals of Mathematical Srarisrics, 33, 255 -2 65 of an Ad Hoc Procedure for Estimating Parameters Ando, A and G M Kaufman (I 966) “Evaluation of Some Linear Models”, Review of Economics and...
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Handbook of Econometrics Vols1-5 _ Chapter 6 ppsx

Handbook of Econometrics Vols1-5 _ Chapter 6 ppsx

... x/S> a T_ K) ’ (2 .65 ) Note that j? actually drops out of the denominator of (2 .65 ), which makes the computation of the confidence region simple in this case In analogy to (2 .65 ), Hartley (1 964 ) ... Z)-‘ ](y-f) ...
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Handbook of Econometrics Vols1-5 _ Chapter 7 pot

Handbook of Econometrics Vols1-5 _ Chapter 7 pot

... is found in Goldberger (1 970 ), Geraci (1 977 ,1 978 ), Hausman (1 977 ), and Hsiao (1 976 ) Also, see Aigner, Hsiao, Kapteyn and Wansbeek (Chapter 23 in this Handbook) Ch 7: Simultaneous Equation Models ... the case of restrictions on Xl4 14Hsiao (Chapter models He discusses in this Handbook) also discusses the case of errors in variables also identification of simultaneous equation Ch 7: Simultaneous ... 38Malinvaud (1 970 , pp 678 - 679 ) derives the concentrated Rothenberg (1 973 , p 78 ) derives the Cramer-Rao bound log-likelihood function for this case 428 J A Hausman term p”ui which is, of course,...
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Handbook of Econometrics Vols1-5 _ Chapter 8 pps

Handbook of Econometrics Vols1-5 _ Chapter 8 pps

... background The concept of using a polynomial approximation of 8, in terms of the elements of m to produce an approximate distribution for 8, can also be used to approximate the moments of 8, , where these ... approximations by using an expansion of 8, (in the case of the k-class estimator) in terms of increasing powers of o, where IJ* is a scalar multiple of the covariance matrix of the errors in the model ... matrices, as in the work of Davis (1 980 a, 198Ob) and Chikuse ( 1 98 1) Ch 8: Exact Small Sample Theory 471 problems of underflow and overflow in the computer evaluations of the coefficients in...
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Handbook of Econometrics Vols1-5 _ Chapter 9 doc

Handbook of Econometrics Vols1-5 _ Chapter 9 doc

... Richard 5.5 An application 555 5.6 Normalization and invariance 557 5 59 561 561 561 563 567 568 571 5 79 5 79 5 79 581 585 5 89 595 596 5.1 Two generalizations Full information analysis 6.1 Introduction ... and Richard ( 197 3) See also Dreze ( 197 6), Kaufman ( 197 5), and Maddala ( 197 6) for the analysis of Tintner’s model of supply and demand for meat; and Zellner, Kmenta and Dreze ( 196 6) as well as ... underidentified models of the complete marginal Ch 9: Bayesian Analysis of Simultaneous Equation Systems 5 39 with associated parameter spaces S’, i, 9 and %rr o (i = 1,2) When 9 = Gj”, we could...
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Handbook of Econometrics Vols1-5 _ Chapter 10 pdf

Handbook of Econometrics Vols1-5 _ Chapter 10 pdf

... “ ,/ p(e,&ct = 0.05 “‘ \.-.\ ‘ \ /;‘ -I _ h_ ‘ L - ._ _ i;c, /’ p(e,&ol=o.l ‘ = _ “ ‘ , ., -. -. -_ -. -_ _ I _ Y P(P b) 200 -$ $f I 0 I I I I 10 15 20 25 30 x Hypothesis Error X = S’ S/~CT* ... as discussed in Chapter of this Handbook by Zellner, we usually compare the posterior probability of the null hypothesis with that of the alternative hypothesis, which may be of the nested variety ... previous sections of this chapter, the transformation of an unbiased estimator often results in a biased estimator of the transformed parameter In this context and in the face of nearly collinear...
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Handbook of Econometrics Vols1-5 _ Chapter 11 ppt

Handbook of Econometrics Vols1-5 _ Chapter 11 ppt

... matrix of explanatory variables p: p X column vector of regression parameters E: n X column vector of errors * : error variance Additional notation x,: i th row of X matrix same same b: estimate of ... average number of rooms squared proportion of owner-occupied units built prior to 1940 logarithm of the weighted distances to five employment centers in the Boston region logarithm of index of accessibility ... helpful information of both positive and negative import Figure 7.2 for NOXSQ, a variable of major concern, reveals a scatter which is not obviously SCATTER FLOT Of YRES_NOXSCi VS XRES_NOXSO ! 00 i...
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Handbook of Econometrics Vols1-5 _ Chapter 12 ppsx

Handbook of Econometrics Vols1-5 _ Chapter 12 ppsx

... approximations 8.3 Evaluation of multivariate 8.4 and other false optima Special cases of the multivariate The generation of random 9.1 The generation of uniformly 9.2 The generation of normally References ... solving Ab = c The computation of each of the above estimators, as well as of many others, requires the inverse of A Error in the inversion process accumulates as a result of rounding error in each ... where the columns of U and V are orthonormal eigenvectors of XX’ and of X’ X, respectively, and where is diagonal and contains the square roots (positive) of the eigenvalues of X’ and XX’ If X...
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Handbook of Econometrics Vols1-5 _ Chapter 13 potx

Handbook of Econometrics Vols1-5 _ Chapter 13 potx

... - p,n ,_, - - $$_p The test for (p + r,O) or (p, r) error process can be calculated as TR2 of the regression of Et on it, cr_i , , iit_p, E,_i , , ‘&-r, where Zr= x, - yix,_i - $,x ,_~ Just ... case: h = a,, + a,C ;_ + + api&, = z,a This is really much like that discussed above as ii ,_ = y ,_ - x ,_ ,p and both yr_ ‘Adrian Pagan has suggested and used this model Ch 13: Wuld, Likelihood ... written in terms of (56) and the score is simply: where U has rows U, = (ii_ i, iir_ z, , ii ,_, ) From the form of (57) it is clear that the LM test views C: as an omitted set of variables from...
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Handbook of Econometrics Vols1-5 _ Chapter 14 pps

Handbook of Econometrics Vols1-5 _ Chapter 14 pps

... commonly of most interest Let G be the set of \cI of primary interest and the complement of G relative to L, denoted by L - G, be the set of J, in L of secondary interest It is assumed that this twofold ... the origin The length of the major axis of the elliptical region (2.20) and the length of the sides of the square become infinite as the absolute value of r tends to one Ch 14: Multiple Hypothesis ... contain all the boundary points of the square In addition to these two pairs of parallel lines of support, there are an infinite number of pairs of parallel lines of support where each line contains...
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Handbook of Econometrics Vols1-5 _ Chapter 16 pdf

Handbook of Econometrics Vols1-5 _ Chapter 16 pdf

... to the stochastic equivalent (evaluate the mean of a random variable) Quandt in Chapter 12 of this Handbook discusses the numerical evaluation of integrals in general Rather clearly, distribution ... T) in (7) As perusal of recent finite sample distributional results will reveal (see, for example, Phillips, Chapter in this Handbook, and Rothenberg, Chapter 15 in this Handbook) , functions ... discussion of the numerical aspects of random number generation, see Quandt, Chapter 12 in this Handbook) : Z r+l = bz; (mod r), i=O,1 ,-*-, m, 09) D F Hendry 948 n, = zr/r E [O,l] The choices of b...
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