Greg Duffee January 26, 2001 Term Premia and Interest Rate Forecasts in Affine Models forthcoming, Journal of Finance Supplementary information This file contains parameter estimates for all unconstrained models estimated for the paper. The models are, using Dai and Singleton's notation, Completely affine A_0(3) A_1(3) A_2(3) A_3(3) Essentially affine A_0(3) A_1(3) A_2(3) The parameter estimates are reported in the order that these models are listed. No standard errors are reported. I only trust the standard errors on the preferred (restricted) specifications, which are reported in the paper. Here is the ordering of the parameters. In an effort to confuse everyone, all indexes start at 0, not 1. (This is a residual from writing the code in C.) Therefore the only indexes that correspond to the indexes used in the paper are for the delta vector. (See the equation just above equation (1) in the paper.) alpha vector, indexes 0, 1, 2 delta vector, indexes 0 through 3. ktheta vector, indexes 0 through 2 the K matrix, indexes (0,0) through (2,2) the Sigma matrix, indexes (0,0) through (2,2). This is always an identity matrix. the Beta matrix, indexes (0,0) through (2,2) the Lambda_1 vector, indexes 0 through 2 the Lambda_2 matrix, indexes (0,0) through (2,2) The Cholesky decomposition of the variance-covariance matrix of cross-sectional yield errors. I call this matrix 'l', which is really stupid, since it looks like a one. Indexes (0,0) through (2,2). Only the lower triangle is shown. The last column is whether the variable is estimated (1) or fixed (0). Some of the fixed parameters are, in principle, free, but they were estimated at the boundary of their parameter space. Completely affine A_0(3) alpha0 1 0 alpha1 1 0 alpha2 1 0 delta0 0.0461700347234856 1 delta1 0.00326314077331176 1 delta2 0.0210176082277978 1 delta3 0.0101240630745222 1 ktheta0 0 0 ktheta1 0 0 ktheta2 0 0 kmatrix00 0.561739743659122 1 kmatrix01 0 0 kmatrix02 0 0 kmatrix10 -1.66735041646807 1 kmatrix11 1.6414710184576 1 kmatrix12 0 0 kmatrix20 -0.125451617947379 1 kmatrix21 0.179007747037869 1 kmatrix22 0.00213846527113638 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 0 0 beta01 0 0 beta02 0 0 beta10 0 0 beta11 0 0 beta12 0 0 beta20 0 0 beta21 0 0 beta22 0 0 lambda10 -0.0361262287952509 1 lambda11 -0.587599896439474 1 lambda12 -0.163162901204163 1 lambda200 0 0 lambda201 0 0 lambda202 0 0 lambda210 0 0 lambda211 0 0 lambda212 0 0 lambda220 0 0 lambda221 0 0 lambda222 0 0 100 0.00226143008836088 1 l10 -0.000493187385346933 1 l11 0.000840522842789615 1 l20 8.44357099856492e-06 1 l21 -0.000166918068749196 1 l22 0.000938083321053357 1 Completely affine A_1(3) alpha0 0 0 alpha1 1 0 alpha2 1 0 delta0 0.0217683425440843 1 delta1 0.000880200939615894 1 delta2 0.000539121699830161 1 delta3 0.00354033968623057 1 ktheta0 0.163856234806784 1 ktheta1 -0.523264997201019 0 ktheta2 0.27277130415955 0 kmatrix00 0.0297648492594678 1 kmatrix01 0 0 kmatrix02 0 0 kmatrix10 -0.0950522498140507 1 kmatrix11 0.322528041959425 1 kmatrix12 17.6585045588126 1 kmatrix20 0.0495495136952904 1 kmatrix21 -0.0182805352346403 1 kmatrix22 1.86319219004572 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 1 0 beta01 0 0 beta02 0 0 beta10 42.0946222672517 1 beta11 0 0 beta12 0 0 beta20 0.3203633065162 1 beta21 0 0 beta22 0 0 lambda10 -0.0404276914442228 1 lambda11 -0.0166532360515313 1 lambda12 -0.114338823899613 1 lambda200 0 0 lambda201 0 0 lambda202 0 0 lambda210 0 0 lambda211 0 0 lambda212 0 0 lambda220 0 0 lambda221 0 0 lambda222 0 0 l00 0.00226092431013116 1 l10 -0.000491526635190178 1 l11 0.000840169136550654 1 l20 3.06055915771452e-06 1 l21 -0.00016773371829613 1 l22 0.000938109502773196 1 Completely affine A_2(3) alpha0 0 0 alpha1 0 0 alpha2 1 0 delta0 0.0146159466479317 1 delta1 0.00064532130394747 1 delta2 0.00134585163844205 1 delta3 0.00315624055743921 1 ktheta0 1e-9 0 ktheta1 0.249723327649198 1 ktheta2 -3.21818967262527 0 kmatrix00 0.136320457655394 1 kmatrix01 -0.306477113259958 1 kmatrix02 0 0 kmatrix10 -0.164801573990814 1 kmatrix11 0.481206432544043 1 kmatrix12 0 0 kmatrix20 0.870114679314744 1 kmatrix21 -3.38276556760561 1 kmatrix22 1.73247485891024 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 1 0 beta01 0 0 beta02 0 0 beta10 0 0 beta11 1 0 beta12 0 0 beta20 0 0 beta21 4.33343968710089 1 beta22 0 0 lambda10 -0.0293878905216973 1 lambda11 -0.0543695117090512 1 lambda12 -0.107396018901534 1 lambda200 0 0 lambda201 0 0 lambda202 0 0 lambda210 0 0 lambda211 0 0 lambda212 0 0 lambda220 0 0 lambda221 0 0 lambda222 0 0 l00 0.00226741607638635 1 l10 -0.000498032457854663 1 l11 0.000841654024302121 1 l20 2.07248824884736e-05 1 l21 -0.000170405785026805 1 l22 0.000935729622110194 1 Completely affine A_3(3) alpha0 0 0 alpha1 0 0 alpha2 0 0 delta0 -0.00526279445984055 1 delta1 0.00142838718297943 1 delta2 0.000304462485123162 1 delta3 0.00890797595942737 1 ktheta0 0.827362758937972 1 ktheta1 0 1 ktheta2 0.34292201045988 1 kmatrix00 0.547634502612035 1 kmatrix01 -0.0715846536055385 1 kmatrix02 0 1 kmatrix10 0 1 kmatrix11 0.0406766930971768 1 kmatrix12 -0.118488917506276 1 kmatrix20 -1.83641468682856 1 kmatrix21 0 1 kmatrix22 2.02338800980501 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 1 0 beta01 0 0 beta02 0 0 beta10 0 0 beta11 1 0 beta12 0 0 beta20 0 0 beta21 0 0 beta22 1 0 lambda10 -0.048930986245714 1 lambda11 -0.0296251617178005 1 lambda12 -0.321237639623551 1 lambda200 0 0 lambda201 0 0 lambda202 0 0 lambda210 0 0 lambda211 0 0 lambda212 0 0 lambda220 0 0 lambda221 0 0 lambda222 0 0 l00 0.00226826756587856 1 l10 -0.000499832382736162 1 l11 0.000843327212223429 1 l20 1.58323598568115e-05 1 l21 -0.000173108290177128 1 l22 0.00093390194720705 1 Essentially affine A_0(3) alpha0 1 0 alpha1 1 0 alpha2 1 0 delta0 0.0475173934412961 1 delta1 0.0165258952044111 1 delta2 0.0136622174886877 1 delta3 0.0081364807525488 1 ktheta0 0 0 ktheta1 0 0 ktheta2 0 0 kmatrix00 0.745997409906114 1 kmatrix01 0 0 kmatrix02 0 0 kmatrix10 -1.00177592850232 1 kmatrix11 3.3517459589244 1 kmatrix12 0 0 kmatrix20 -0.37682399330276 1 kmatrix21 -0.796080254496088 1 kmatrix22 0.0967251903685535 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 0 0 beta01 0 0 beta02 0 0 beta10 0 0 beta11 0 0 beta12 0 0 beta20 0 0 beta21 0 0 beta22 0 0 lambda10 -0.482611462157918 1 lambda11 -0.374829642760271 1 lambda12 -0.138686026562958 1 lambda200 -0.581793424615619 1 lambda201 1.33557827557625 1 lambda202 -0.0832466240107103 1 lambda210 0.593010932776235 1 lambda211 -1.39550617895028 1 lambda212 -0.0814282618866247 1 lambda220 0.405926651643426 1 lambda221 0.899949768171279 1 lambda222 -0.103454415602115 1 100 0.00227027641822878 1 l10 -0.000498668150562055 1 l11 0.000841705443149033 1 l20 6.96873898128997e-06 1 l21 -0.000170676239463131 1 l22 0.000931985955036401 1 Essentially affine A_1(3) alpha0 0 0 alpha1 1 0 alpha2 1 0 delta0 0.0158083214053012 1 delta1 0.000918407248178146 1 delta2 0.0011441075475783 1 delta3 0.00306975748565371 1 ktheta0 0.169283797366344 1 ktheta1 -1.98577156656332 0 ktheta2 0.522792129907272 0 kmatrix00 0.0300645513315913 1 kmatrix01 0 0 kmatrix02 0 0 kmatrix10 -0.352670084937656 1 kmatrix11 0.577203459081355 1 kmatrix12 4.75453382700887 1 kmatrix20 0.0928471068695082 1 kmatrix21 -0.0243287924662819 1 kmatrix22 3.31302653655854 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 1 0 beta01 0 0 beta02 0 0 beta10 10.5574366070543 1 beta11 0 0 beta12 0 0 beta20 0.275057801468444 1 beta21 0 0 beta22 0 0 lambda10 -0.0409538747847809 1 lambda11 -6.01166111772206 1 lambda12 -0.00961644747968307 1 lambda200 0 0 lambda201 0 0 lambda202 0 0 lambda210 63.4883135068499 1 lambda211 -0.100852707527274 1 lambda212 5.84644714780988 1 lambda220 -0.0644642248960533 1 lambda221 0.0146661533429004 1 lambda222 -1.68450019104249 1 l00 0.00226512006365017 1 l10 -0.00049381552108709 1 l11 0.000840601589783602 1 l20 -3.41550193036534e-06 1 l21 -0.000167962457186848 1 l22 0.000935745843830377 1 Essentially affine A_2(3) alpha0 0 0 alpha1 0 0 alpha2 1 0 delta0 0.0137395368719474 1 delta1 0.000628119999089547 1 delta2 0.00134505979083574 1 delta3 0.0032906573385547 1 ktheta0 0.04070653964243 1 ktheta1 0.193049782455795 1 ktheta2 -2.76699434105645 0 kmatrix00 0.144512567722334 1 kmatrix01 -0.307916294439045 1 kmatrix02 0 0 kmatrix10 -0.17200092498936 1 kmatrix11 0.470790737401452 1 kmatrix12 0 0 kmatrix20 0.8112824544491 1 kmatrix21 -3.02239266799591 1 kmatrix22 1.61561814243312 1 sigma00 1 0 sigma01 0 0 sigma02 0 0 sigma10 0 0 sigma11 1 0 sigma12 0 0 sigma20 0 0 sigma21 0 0 sigma22 1 0 beta00 1 0 beta01 0 0 beta02 0 0 beta10 0 0 beta11 1 0 beta12 0 0 beta20 0 0 beta21 3.81400332257606 1 beta22 0 0 lambda10 -0.029235360343917 1 lambda11 -0.0530009742924989 1 lambda12 -0.71862833862579 1 lambda200 0 0 lambda201 0 0 lambda202 0 0 lambda210 0 0 lambda211 0 0 lambda212 0 0 lambda220 0.068359970367799 1 lambda221 2.15019556335019 1 lambda222 0.122745915390323 1 l00 0.00226729376829335 1 l10 -0.000498049586248364 1 l11 0.000841743095945217 1 l20 2.07728797976459e-05 1 l21 -0.000170739219788606 1 l22 0.000935943182586275 1