The Limits of Mathematics and NP Estimation in ... - Chichilnisky

More documents

Recommendations

Info

Instrument Generating Functionand Analysis of Persistent Economic Times Series: Theory and Application 23y y X Y (4)where ( 1,....... p ) , Y ( y , X),and ( , ) . For equation (4), IV estimator isconstructed below1 ˆ Fy ( ) y Fy ( ) X Fy ( ) yˆ Xy XX Xy .where Fy ( ) Fy ( p), Fy ( T)11 T TUnder the null, we have B A , where1ATFy ( ) Fy ( ) XXX ( ) XT T T1T F( yt1) t F( yt1)xt xtxt xttt1 t1 t1 t11BTFy ( ) y Fy ( ) XXX ( ) Xy T T T1T Fy ( ) y Fy ( ) x xx xy t1 t1 t1 t t t t t1t1 t1 t1 t1and the variance ofAT is given by2 ECT , where1CTFy ( ) Fy ( ) Fy ( ) XXX ( ) XFy ( )T T T1T2 Fyt1 Fyt1 xt xx t t xFy t t1t1 t1 t1 t1( ) ( ) ( ) For differenced lagged variables, themselves are used as the instruments without IGFtransformation, details are explained in Chang(2002). The half-life calculated from the valueof (1) assumes that shocks to the data decay monotonically, which is inappropriate for ADFregressions represented by (3), since in general shocks to an AR(p) will not decay at aconstant rate. Murray and Papell (2002) calculate the half-life from the impulse responsefunction of an AR(p) below,py c y (4)t k tk tk1From the IGF estimates of (3), coefficients of (4) can be recalculated as follows:1 1, 2 ( 1 2), 3 ( 2 3), and 1 . (5)pp
24Advances in Econometrics - Theory and ApplicationsWhen the coefficients are obtained, the k-period impulse response function (irf thereafter)for univariate AR(p) regression can be calculated. For convenience, we name (4) by ADF-AR(p).(5) is widely used, for example, Murray and Papell (2002), however, not only is it subject tostrict restriction, but also bias if some of right-hand-side variables of (4) are co-integrated.Therefore, instead of using (3) and (5) to indirectly calculate the coefficients of (4), wepropose a Fully-Modified AR (p) to estimate (4) directly, the model is derived from Fully-Modified VAR of Phillips (1995). Section below continues the study.2.3 Unrestricted fully-modified AR(p)Phillips’ (1995) FM-VAR is a level system regression with/without error correction terms(differenced terms). FM-VAR of Phillips (1995) generalized the asymptotics of Phillips andHansen (1990), allowing full rank I(1) regressors and possible cointegration existed amonglagged dependent variables. Mostly important, the asymptotics of FM-VAR is normal, ormixed normal, which allows us to construct confidence intervals and half life. Themethodology for FM-AR(p) is illustrated below.y ay y u aAy u(6)t 1 t1 p tp 0t t0twhere A is an 1p coefficient vector and y t- is a p(p=p 1 +p 2 )-dimensional vector of lagged y twhich are partitioned below:H y y up 1 11 t1, t1tH y y up 2 12 t2, t2tHere H=[H 1 , H 2 ] is pp orthogonal matrix and rotates the regressor space in (6) so that themodel has the alternative formy A y A y u(7)t 1 1, t2 2, t0tHere A 1 =AH 1 and A 2 =AH 2 . The form of (7) usefully separates out the I(0) and I(1)components of the regressors in (6). However, the direction (H 1 ) in which the regressors arestationary will not be generally known in advance, not even will the rank of thecointegrating space of the regressors. Phillips’ (1995) fully-modified correction has twosteps:The first step is to correct for the serial correlation to the LS estimatorˆA y 1tyt ytytof(7). The endogeneity correction is achieved by modifying the dependent variable y t in (7)with the transformationy y ˆˆ y(8)1t t 0yt ytyttIn (8), ˆ denotes the kernel estimate of the long-run (lr) covariances of the variablesdenoted by the subscript:ˆ 0y lr cov( u0, )tt ytand ˆ y cov( , )t y lr y tt y t. (8)leads us to estimate the equation below
Page 2 and 3: ADVANCES INECONOMETRICS - THEORYAND
Page 4: free online editions of InTechBooks
Page 8 and 9: PrefaceEconometrics is a (sub)disci
Page 10: PrefaceIXLastly, I would like to th
Page 14: 10The Limits of Mathematicsand NP E
Page 17 and 18: 6 Advances in Econometrics - Theory
Page 19 and 20: 8 Advances in Econometrics - Theory
Page 21 and 22: 10 Advances in Econometrics - Theor
Page 27: 16 Advances in Econometrics - Theor
Page 32 and 33: Instrument Generating Functionand A
Page 41 and 42: 30Advances in Econometrics - Theory
Page 44: Recent Developments in SeasonalVola
Page 58 and 59: The Impact of Government-Sponsored
Page 60 and 61: The Impact of Government-SponsoredT
Page 84 and 85:
The Impact of Government-SponsoredT
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Returns to Education and Experience
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Using the SUR Model of Tourism Dema
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
show all

The Limits of Mathematics and NP Estimation in ... - Chichilnisky

Create successful ePaper yourself

Delete template?

Save as template?