/* Thanks go to Dr. Jeff Gunther of the Federal Reserve Bank of Dallas for providing this data. The data here represents a subsample of the data analyzed by Dr. Gunther in his paper "Between a Rock and a Hard Place: The CRA-Safety and Soundness Pinch" that appeared in the Bank's publication ECONOMIC AND FINANCIAL REVIEW, 2nd quarter, 1999, pp. 32 - 41. */ data cra; input rrating loa prl equ roa sec ass metro growth; datalines; 1 0.398216146 0.012070236 0.068825757 0.003436755 0.395789393 11.27347467 0 0.05590794 1 0.622300366 0.005998665 0.109696588 0.008948524 0.329522269 11.57455664 0 0.037608829 1 0.520228877 0.002057797 0.06217486 0.013375959 0.316543741 12.15738123 1 0.059176309 1 0.559964515 0.009662415 0.07120936 0.013882853 0.323822768 10.63844824 0 0.06163979 1 0.653101674 0.003479104 0.111563278 0.01139738 0.269915236 10.76692588 0 0.037608829 1 0.654570147 0.000994884 0.107557956 0.013553286 0.166808793 11.05601968 1 0.077307368 1 0.581330984 0.009515912 0.108572613 0.014815517 0.351508241 11.47698736 0 0.031546187 1 0.544357272 0.000905251 0.091564407 0.014636172 0.171662308 10.30313578 0 0.060334532 1 0.633068609 0.001361438 0.075470234 0.010468801 0.247411477 12.02855951 1 0.101827664 1 0.25072108 0.039950684 0.1214356 -0.015693262 0.495006165 11.38972905 0 0.018209948 1 0.693165873 0.005133246 0.076663757 0.015216985 0.179053678 14.16490325 1 0.081062164 1 0.769697674 0.008704299 0.074335232 0.016698913 0.144208542 11.95031551 0 0.076415439 1 0.476839988 0.002092186 0.120844011 0.016337243 0.364364722 11.02935827 0 0.064899745 1 0.411425954 0 0.147241673 0.009816031 0.263595314 9.634365506 0 0.070313205 1 0.451176271 0.011676146 0.163017203 0.015571515 0.389993524 11.95734843 1 0.039129789 1 0.233299441 0.001906457 0.07282664 0.015309874 0.522165735 10.57999709 1 0.046876896 1 0.491757576 0.010278788 0.106036364 0.011750645 0.445987879 10.62740639 0 0.032264465 1 0.594548298 0.000422035 0.151113428 0.013711796 0.33775229 10.60363517 0 0.052681387 1 0.474161358 0.000631448 0.099430569 0.010582071 0.430309523 11.39284605 0 0.062206311 1 0.633227109 0.022651143 0.094144381 0.005088737 0.286036322 12.71100293 1 0.05137767 1 0.750014017 0.003736746 0.064784552 0.013747352 0.217786646 12.62216442 1 0.075036023 1 0.805994851 0 0.184258919 0.021674408 0.000551673 8.601166625 1 0.068967717 1 0.458243185 0.005764357 0.123786858 0.018229384 0.459386784 11.07764012 0 0.103457879 1 0.560306863 0.024661781 0.075456243 0.009990451 0.26705186 11.63987525 0 0.088972 1 0.559298877 0.008583039 0.078730411 0.013303213 0.32956536 11.35783768 0 0.05855742 1 0.716022606 0.010448166 0.106441993 0.016031128 0.10854831 10.77793494 0 0.055494227 1 0.548072221 0.01492938 0.074119531 0.014935725 0.345255104 11.55494035 1 0.055312715 1 0.53685381 0.004311714 0.096979531 0.01189386 0.359165797 11.38659097 0 0.053993779 1 0.777712454 0.003631822 0.06791683 0.01410413 0.142983513 13.51196601 1 0.074069538 1 0.505237664 0.030760885 0.092517791 0.012668716 0.384075217 13.29698705 1 0.05590794 1 0.56378809 0.016684972 0.076814316 0.011952467 0.262315981 15.39545127 1 0.048093977 1 0.620392954 0.016768293 0.072594851 0.007294375 0.156825881 10.98597046 1 0.041928778 1 0.91350671 0.018813639 0.086927855 0.013537465 0.04338151 11.80160954 1 0.075036023 1 0.598615144 0.021182339 0.063649393 0.015451285 0.302592882 11.58476229 1 0.053243524 1 0.671794631 0.005058516 0.091158575 0.012449296 0.252096887 13.00891693 0 0.054020816 1 0.682852374 0.001239418 0.048777318 0.009583616 0.213719057 14.76838468 1 0.078967786 1 0.622175235 0.001960266 0.082815735 0.009868068 0.289062156 10.72331144 0 0.083474419 1 0.544126075 0.007020057 0.089875836 0.010282173 0.380468004 9.949416484 1 0.092594736 1 0.698397947 0.00889538 0.082403965 0.008881175 0.236922464 10.71867536 0 0.042110475 1 0.37633213 0.006017828 0.144318937 0.016593824 0.539801434 12.49203699 0 0.09298712 1 0.588033297 0.004782366 0.074198594 0.013919053 0.273314036 10.92631611 0 0.056023293 1 0.679953942 0.013488321 0.08986731 0.009736129 0.208356179 9.811262609 0 0.08743253 1 0.52354888 0.002121521 0.080278344 0.012742799 0.34428038 10.06764514 0 0.030872864 1 0.478109868 0.027180891 0.062197367 0.008483588 0.293900156 11.76975134 1 0.046338009 1 0.590591291 0.021773871 0.079854175 0.005149646 0.212095485 9.904686833 0 0.048769005 1 0.437676403 0.001837873 0.110141122 0.013114647 0.437938956 10.32449787 0 0.057938248 1 0.413081988 0.00350365 0.11850283 0.010858516 0.468870171 12.97843989 1 0.060334532 1 0.579250109 0.010431908 0.176929177 0.016075726 0.258441022 11.40236255 1 0.03929008 1 0.726369211 0.01007965 0.089800522 0.0124533 0.174596462 9.560081331 0 0.069191128 1 0.453717262 0.014141076 0.08454941 0.016050286 0.434319304 13.07744969 1 0.057938248 1 0.652107409 0.008179164 0.112914591 0.012208856 0.227860082 14.30880216 1 0.074069538 1 0.633713684 0.003274161 0.077874884 0.015744674 0.289547032 13.21834606 0 0.044657369 1 0.647552858 0.005559906 0.082184808 0.004824549 0.24986296 10.84114831 1 0.086326054 1 0.613907642 0.00619161 0.055556967 0.012544892 0.198926595 14.88468511 1 0.115898624 1 0.542254216 0.075638807 0.051213997 -0.015792504 0.289557907 14.9011916 1 0.003202055 1 0.772594212 0.015291313 0.062276899 0.007928077 0.088697027 11.30172284 0 0.039449857 1 0.536039074 0.003863607 0.079295074 0.012613464 0.218184469 10.91274026 1 0.052478014 1 0.721390049 0.016718901 0.065470237 0.009986591 0.157556543 13.80523596 0 0.044039387 1 0.372866884 0.005196326 0.086507849 0.012944051 0.488649809 11.31424279 0 0.056306546 1 0.364053356 0.006484948 0.089102125 0.01090604 0.392418411 9.850455906 0 0.086736045 1 0.515203873 0.001581398 0.098049934 0.010316188 0.342795691 12.63565459 1 0.04658721 1 0.689039289 0.000684128 0.068192924 0.008062978 0.19556294 10.6195697 0 0.062206311 1 0.712116381 0.005300917 0.064846552 0.010403474 0.154364289 10.13022464 0 0.046338009 1 0.625300121 0.001249526 0.067359237 0.015599477 0.218385511 12.36516396 1 0.081062164 1 0.569569424 0.00246498 0.103582173 0.012629613 0.288786991 11.23131824 0 0.101827664 1 0.857195866 0.004302635 0.066027942 0.011440491 0.065852835 12.38778152 1 0.08743253 1 0.329139414 0.009147531 0.083717082 0.01790822 0.5905309 11.06759103 1 0.046876896 1 0.624650856 0.007490732 0.073967803 0.011366304 0.305850389 10.58106414 0 0.056023293 1 0.612648414 0.008435527 0.0830875 0.018058856 0.315722749 10.62174189 0 0.054067221 1 0.659960816 0.002723754 0.065800163 0.017859112 0.144072251 9.94879547 0 0.046338009 1 0.445407534 0.005134434 0.078249508 0.01038204 0.362354846 10.90299748 0 0.039752868 1 0.657165674 0.005874286 0.068833688 0.01421437 0.262736351 12.97037469 1 0.086326054 1 0.512047924 0.019756707 0.062670276 -0.014148415 0.134525558 15.68314112 1 0.047605068 1 0.703174811 0 0.087776759 0.011183431 0.207083279 10.03884852 0 0.052681387 1 0.504707098 0.010070775 0.107823921 0.014302338 0.419573803 11.54797403 0 0.049447755 1 0.689516809 0.008446373 0.091540989 0.022066502 0.241943298 11.46112678 0 0.083474419 1 0.72150612 0.010781213 0.081489543 0.017686487 0.149264184 13.58468886 0 0.074069538 1 0.518702612 0.002836282 0.10519517 0.013056603 0.41207526 10.48038178 0 0.08743253 1 0.375820374 0.003245827 0.110322443 0.011840158 0.556855472 10.93439186 0 0.030872864 1 0.586780054 0.007880594 0.124767759 0.025671928 0.185243837 11.29224139 0 0.055312715 1 0.665243387 0.007662489 0.07890816 0.01280355 0.250811076 11.95144488 0 0.037608829 1 0.589781559 0.013931245 0.125914406 0.024004632 0.171661708 14.14999439 1 0.070313205 1 0.557069109 0.004796003 0.079134055 0.011825017 0.286727727 10.30978565 0 0.032670961 1 0.622647059 0.008568628 0.078921569 0.016187173 0.302980392 11.53272809 0 0.074707343 1 0.588936204 0.008465506 0.082263996 0.012323849 0.255838182 12.07627143 1 0.06163979 1 0.458822405 0.031133001 0.061707797 0.002541155 0.416038044 12.68928244 1 0.086736045 1 0.523622542 0.004303575 0.088945781 0.013068786 0.389410693 11.06143736 0 0.075036023 1 0.405725403 0.001389661 0.05 0.001960479 0.360116732 10.49071851 1 0.073824177 1 0.7137121 0 0.074962851 0.010027782 0.095039363 10.3618297 0 0.009844162 1 0.656110563 0.056705712 0.069353437 0.003171446 0.235429964 12.63180433 1 0.038240561 1 0.689182302 0.01436626 0.069601504 0.014002906 0.186602109 11.0474874 0 0.071429065 1 0.65538465 0.004860869 0.082004658 0.010803558 0.248736962 11.39496366 0 0.052681387 1 0.491038862 0.047587184 0.039465743 -0.041375657 0.393712771 11.24135293 1 0.030349396 1 0.708639358 0.00292774 0.102950456 0.017853969 0.195767396 11.28026174 0 0.076415439 1 0.59042935 0.005522691 0.073985933 0.011372916 0.31459698 11.79330343 0 0.035290104 1 0.694881516 0.0218863 0.125472694 0.009104027 0.168524999 12.23306018 1 0.039129789 1 0.547906977 0.010523256 0.066453488 0.005521531 0.145406977 9.752664663 0 0.070313205 1 0.329475861 3.98E-05 0.107571781 0.009416342 0.562793287 10.13245412 0 0.045694435 1 0.642005643 0.020140784 0.068925133 0.009916446 0.197452015 16.18638335 1 0.053788556 1 0.732053862 0.010555642 0.100201207 0.013735968 0.170778517 10.3829773 0 0.03929008 2 0.63628522 0.001081721 0.07092268 0.011062304 0.235950446 12.27593914 1 0.060334532 2 0.401950202 0.000539724 0.151896229 0.018815144 0.496887594 10.92565067 0 0.075567041 2 0.385824784 0.008798659 0.091358203 0.014518599 0.438598705 10.92347141 0 0.064899745 2 0.635406016 0.020426176 0.063120985 0.006482801 0.039752667 12.24207665 1 0.027880249 2 0.591101168 0.043085591 0.095285442 0.010810591 0.106968266 10.09154264 0 0.076400237 2 0.357097936 0.051798068 0.064718998 0.009327321 0.384826482 9.769441742 0 0.04076748 2 0.586297323 0.007181396 0.077804738 0.01139424 0.328189052 11.79587636 0 0.052681387 2 0.473754324 0.009873613 0.124942628 0.011549315 0.445040245 11.40008146 1 0.070322572 2 0.657343237 0.005384212 0.099373223 0.01245511 0.250931883 10.4972839 1 0.036468568 2 0.564694296 0.004684714 0.101945753 0.011176179 0.300886369 10.53393452 0 0.031546187 2 0.541669407 0.040715648 0.105295008 0.001874169 0.314490561 11.23868597 0 0.051431825 2 0.574158129 0.007781092 0.072666753 0.01038529 0.323045001 10.04901545 0 0.062695144 2 0.595054614 0.000469075 0.072103465 0.005474453 0.350465724 9.610658926 0 0.029533934 2 0.596635588 0.049777697 0.079282657 0.000284013 0.237366867 11.69986965 1 0.018874969 2 0.53501517 0.031711068 0.07086156 0.008487739 0.220439716 10.08834755 0 0.04113205 2 0.475052025 0.009485554 0.078562326 0.014626003 0.164722773 11.03471223 1 0.067843366 2 0.407724351 0.003355876 0.109912237 0.01585925 0.522619334 11.82826891 0 0.041752168 2 0.766477452 0.008483128 0.070009461 0.008866444 0.122768843 11.05753455 1 0.046589154 2 0.769150923 0.020763598 0.110243948 0.007472597 0.173299401 13.65151407 1 0.04286767 2 0.648577594 0.001636945 0.096802996 0.013531406 0.049281976 10.6045781 0 0.084214206 2 0.744089926 0.013770859 0.092359394 0.005005271 0.013075556 10.854682 1 0.021316413 2 0.615800274 0.018780014 0.098925174 0.014239703 0.273916554 12.37921049 0 0.048160317 2 0.625577939 0.007719617 0.109643329 0.014829419 0.241908851 10.09509916 0 0.038100122 2 0.594345334 0.002441879 0.132688893 0.013641155 0.296214078 10.8107779 1 0.052681387 2 0.588959344 0.011642777 0.104118932 0.013539085 0.29701071 10.53300247 1 0.074707343 2 0.365771158 0.000894388 0.088900844 0.009430016 0.497306748 11.90971976 0 0.009844162 2 0.548603042 0.013470853 0.075076866 0.007885865 0.319022695 11.48500941 0 0.080857113 2 0.219349249 0.003967913 0.087122163 0.017225608 0.497226931 12.5805045 1 0.060334532 2 0.650599854 0.014144789 0.072440798 0.011793869 0.204582301 13.72098557 0 0.077307368 2 0.652382638 0.026060794 0.08355825 0.010853224 0.207280651 11.41204379 0 0.05346025 2 0.451171155 0.005658634 0.072925985 0.013458347 0.46723441 13.69496082 1 0.05855742 2 0.29594265 0.004551133 0.090279017 0.017406179 0.665774288 10.42281692 0 0.031320677 2 0.444541195 0.053696563 0.085416926 0.0087308 0.409462205 10.09067227 0 0.090869605 2 0.510990227 0.034888438 0.132804721 0.019662172 0.36695556 10.90098954 0 0.067097122 2 0.604790594 0.00026322 0.117893074 0.018456376 0.279100374 10.43974698 1 0.04633174 2 0.649739403 0 0.079608874 0.011092498 0.212628569 9.98419158 0 0.083474419 2 0.684964693 0.015952786 0.133859079 0.007518896 0.176949642 10.56622707 1 0.048360613 2 0.378319708 0.025495358 0.09533047 0.009059804 0.392730128 9.982806922 0 0.068621215 2 0.411408926 0.003077184 0.072154666 0.004115552 0.385496912 10.76047404 0 0.07824569 2 0.546239211 0.010378134 0.083083788 0.010051625 0.276437085 11.12908485 0 0.046591266 2 0.407644705 0.024097439 0.068093853 0.000988733 0.411209027 10.73053168 1 0.046338009 2 0.664862154 0.009836126 0.076627579 0.013079252 0.197144587 12.00443982 0 0.046798472 2 0.656210892 0.001009245 0.082253442 0.015175702 0.152597796 10.81057607 1 0.05346025 2 0.608877964 0.004735396 0.106998265 0.022842931 0.281376518 10.22788721 1 0.037608829 2 0.47578425 0.007023984 0.075609784 0.013655512 0.398814986 11.38814425 1 0.054067221 2 0.41377962 0.013294753 0.084930007 0.007073723 0.443731915 10.14933149 0 0.04076748 2 0.502358366 0.040489692 0.083178759 0.005440218 0.417828184 10.53842282 0 0.078092035 2 0.545297693 0.014833127 0.093608364 0.005414757 0.232720437 10.56699993 1 0.069191128 2 0.772911205 0.003848627 0.079020529 0.005898182 0.087024487 11.5236181 1 0.073296746 2 0.339273483 0.000507806 0.118366046 0.009253155 0.553544014 11.34661111 1 0.067569532 2 0.685308191 0.01164927 0.107992974 0.005919517 0.065877935 10.81035402 1 0.076420513 2 0.696606036 0.003607875 0.080918319 0.012667922 0.240986443 12.81304901 0 0.043274078 2 0.424094343 0.0093352 0.112793987 0.016899388 0.416426142 11.56151561 0 0.041752168 2 0.271649805 0.003307031 0.093403174 0.00888803 0.672294267 12.74344575 1 0.03969397 2 0.529239545 0.027028659 0.121002671 0.005329679 0.132170291 11.10138695 1 0.05590794 2 0.572073254 0.006572388 0.068544367 0.007796695 0.33162355 11.24148413 1 0.051211711 2 0.492286727 0.000545108 0.098282911 0.012670484 0.364786045 9.817112337 0 0.067843366 2 0.342993422 0.005768502 0.094534559 0.001407813 0.53822709 10.96947334 0 0.058660456 2 0.68408827 0.028435027 0.072326662 0.005233685 0.209072739 11.90558898 1 0.057988428 2 0.620324414 0.002313755 0.087110737 0.016600904 0.2922535 12.00641977 0 0.078237519 2 0.323591399 0.000230513 0.093555504 0.013889849 0.598462146 11.01425895 0 0.029533934 2 0.288078217 0.003995832 0.097048262 0.01194106 0.602899301 11.92276101 0 -0.023194617 2 0.671661833 0.002137716 0.124728757 0.018504361 0.188860243 11.44132205 0 0.076415439 2 0.660702833 0.005756164 0.085959755 0.011522646 0.205882435 14.40203254 0 0.058365444 2 0.736466598 0.012521362 0.089520913 0.011733851 0.162927153 11.94403883 1 0.06163979 2 0.735354174 0.034835608 0.102087363 0.008335219 0.081367843 11.77360369 1 0.038240561 2 0.718313981 0.003916996 0.0657515 0.011361272 0.212805424 12.31092353 1 0.058655366 2 0.473567804 0.009280541 0.104514506 0.000741198 0.186825101 10.04581143 0 0.038354529 2 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0.643578644 8.738254577 0 0.020808136 4 0.37963982 0.013856929 0.116458229 0.005701487 0.48144072 9.902987428 1 0.046591266 4 0.500435115 0.007029944 0.11681511 0.013036744 0.40730539 11.79168535 1 0.051211711 4 0.369468339 0.017152037 0.119286973 0.007158048 0.333298787 9.867756743 1 0.054923763 4 0.090275381 0 0.179446477 0.020858767 0.71378287 9.58114502 0 0.03537013 4 0.079053721 0.003055693 0.279940858 0.014603515 0.853326762 9.224736252 0 0.037608829 4 0.124696645 0.062027124 0.088151321 0.009860219 0.666880799 10.24067382 1 0.053293724 4 0.256824953 0.00091202 0.108773637 0.007795912 0.465556029 9.707898369 1 0.053181502 4 0.110065113 0.001725896 0.899584216 0.020863793 0.852906566 9.453051229 1 0.008561914 ; /* It should be noted that the results produced by proc logistic are the same as produced by the ordered probit/logit routine in EVIEWS except the SIGNS of the coefficients are opposite of each other and the limit points are different (reflecting the different signing conventions of the two computer programs). To get the same answers between the two programs you can use the "descending" option on each of the proc logistic statements as in: proc logistic data=cra descending; However, using the descending option in proc logistic produces the cumulative probabilites of class 4 first then classes 4 and 3, then classes 4, 3, and 2 in that order. Since that presentation of cumulative probabilites is somewhat awkward, let's just note the correspondences between EVIEWS and proc logistic in SAS and skip using the descending option here. */ /* Here we are fitting various ordered multinomial probit models. We use the backward selection technique manually. */ proc logistic data=cra; model rrating = loa prl equ roa sec ass metro growth/link=normit; proc logistic data=cra; model rrating = loa prl equ sec ass metro growth/link=normit; proc logistic data=cra; model rrating = loa prl equ ass metro growth/link=normit; output out=result pred=pred; /* Here we print out the probabilities of each classification by observation using the last ordered multinomial probit model above. */ proc print data=result; /* Here we are fitting various ordered multinomial logit models. We use the backward selection technique manually. */ proc logistic data=cra; model rrating = loa prl equ roa sec ass metro growth/link=logit; proc logistic data=cra; model rrating = loa prl equ sec ass metro growth/link=logit; proc logistic data=cra; model rrating = loa prl equ ass metro growth/link=logit; output out=result pred=pred; /* Here we print out the probabilities of each classification by observation using the last ordered multinomial logit model above. */ proc print data=result; /* Here we just see if the automatic backward and forward selection techniques for the ordered multinomial probit model result in the same final model chosen. */ proc logistic data=cra; model rrating = loa prl equ roa sec ass metro growth/link=normit selection=backward; proc logistic data=cra; model rrating = loa prl equ roa sec ass metro growth/link=normit selection=forward; /* Here we just see if the automatic backward and forward selection techniques for the ordered multinomial logit model result in the same final model chosen. */ proc logistic data=cra; model rrating = loa prl equ roa sec ass metro growth/link=logit selection=backward; proc logistic data=cra; model rrating = loa prl equ roa sec ass metro growth/link=logit selection=forward; /* Wow! It is amazing! You get similar results using the two different link functions = normit and logit. Also amazingly enough, the forward and backward selection procedures result in the same final models, irregardless of the choice of the link function. Of course, this need not happen in other applied problems. */ run;