-------------------------------------------------------------------------------- log: C:\Documents and Settings\Patricia_Anderson\My Documents\ECON 20\I > nClass\nov25.log log type: text opened on: 25 Nov 2002, 11:14:20 . use hseinv . desc Contains data from hseinv.dta obs: 42 vars: 14 13 Sep 2000 15:31 size: 2,310 (100.0% of memory free) ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- year int %9.0g 1947-1988 inv float %9.0g real housing invest., millions $ pop float %9.0g population, 1000s price float %9.0g housing price index; 1982 = 1 linv float %9.0g log(inv) lpop float %9.0g log(pop) lprice float %9.0g log(price) t byte %9.0g time trend: t=1,...,42 invpc float %9.0g per capita invest., inv/pop linvpc float %9.0g log(invpc) lprice_1 float %9.0g lprice[t-1] linvpc_1 float %9.0g linvpc[t-1] gprice float %9.0g lprice - lprice_1 ginvpc float %9.0g linvpc - linvpc_1 ------------------------------------------------------------------------------- Sorted by: . **simple model . reg linvpc lprice Source | SS df MS Number of obs = 42 -------------+------------------------------ F( 1, 40) = 10.53 Model | .254364572 1 .254364572 Prob > F = 0.0024 Residual | .966255373 40 .024156384 R-squared = 0.2084 -------------+------------------------------ Adj R-squared = 0.1886 Total | 1.22061994 41 .029771218 Root MSE = .15542 ------------------------------------------------------------------------------ linvpc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lprice | 1.240944 .3824192 3.24 0.002 .4680455 2.013842 _cons | -.5502345 .0430266 -12.79 0.000 -.6371945 -.4632745 ------------------------------------------------------------------------------ . **add a trend . reg linvpc lprice t Source | SS df MS Number of obs = 42 -------------+------------------------------ F( 2, 39) = 10.08 Model | .415945135 2 .207972568 Prob > F = 0.0003 Residual | .804674809 39 .020632687 R-squared = 0.3408 -------------+------------------------------ Adj R-squared = 0.3070 Total | 1.22061994 41 .029771218 Root MSE = .14364 ------------------------------------------------------------------------------ linvpc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lprice | -.3809609 .6788352 -0.56 0.578 -1.754035 .992113 t | .0098287 .0035122 2.80 0.008 .0027246 .0169328 _cons | -.9130595 .1356134 -6.73 0.000 -1.187363 -.6387556 ------------------------------------------------------------------------------ . **review detrending . reg linvpc t Source | SS df MS Number of obs = 42 -------------+------------------------------ F( 1, 40) = 20.19 Model | .409447014 1 .409447014 Prob > F = 0.0001 Residual | .81117293 40 .020279323 R-squared = 0.3354 -------------+------------------------------ Adj R-squared = 0.3188 Total | 1.22061994 41 .029771218 Root MSE = .14241 ------------------------------------------------------------------------------ linvpc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- t | .0081459 .0018129 4.49 0.000 .0044819 .0118098 _cons | -.8412918 .044744 -18.80 0.000 -.9317228 -.7508608 ------------------------------------------------------------------------------ . predict linvpcdt, resid . reg lprice t Source | SS df MS Number of obs = 42 -------------+------------------------------ F( 1, 40) = 107.57 Model | .120404028 1 .120404028 Prob > F = 0.0000 Residual | .044774118 40 .001119353 R-squared = 0.7289 -------------+------------------------------ Adj R-squared = 0.7222 Total | .165178146 41 .004028735 Root MSE = .03346 ------------------------------------------------------------------------------ lprice | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- t | .0044173 .0004259 10.37 0.000 .0035565 .0052781 _cons | -.188386 .0105121 -17.92 0.000 -.2096318 -.1671401 ------------------------------------------------------------------------------ . predict lpricedt, resid . **run the detrended regression . reg linpcdt lpricedt variable linpcdt not found r(111); . reg linvpcdt lpricedt Source | SS df MS Number of obs = 42 -------------+------------------------------ F( 1, 40) = 0.32 Model | .00649812 1 .00649812 Prob > F = 0.5730 Residual | .804674807 40 .02011687 R-squared = 0.0080 -------------+------------------------------ Adj R-squared = -0.0168 Total | .811172927 41 .019784706 Root MSE = .14183 ------------------------------------------------------------------------------ linvpcdt | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lpricedt | -.3809608 .6702961 -0.57 0.573 -1.73568 .9737581 _cons | 1.02e-10 .0218855 0.00 1.000 -.0442322 .0442322 ------------------------------------------------------------------------------ . reg linvpc lprice t Source | SS df MS Number of obs = 42 -------------+------------------------------ F( 2, 39) = 10.08 Model | .415945135 2 .207972568 Prob > F = 0.0003 Residual | .804674809 39 .020632687 R-squared = 0.3408 -------------+------------------------------ Adj R-squared = 0.3070 Total | 1.22061994 41 .029771218 Root MSE = .14364 ------------------------------------------------------------------------------ linvpc | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lprice | -.3809609 .6788352 -0.56 0.578 -1.754035 .992113 t | .0098287 .0035122 2.80 0.008 .0027246 .0169328 _cons | -.9130595 .1356134 -6.73 0.000 -1.187363 -.6387556 ------------------------------------------------------------------------------ . use fertil3, clear . desc Contains data from fertil3.dta obs: 72 vars: 24 13 Sep 2000 15:30 size: 6,264 (100.0% of memory free) ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- gfr float %9.0g births per 1000 women 15-44 pe float %9.0g real value pers. exemption, $ year int %9.0g 1913 to 1984 t byte %9.0g time trend, t=1,...,72 tsq int %9.0g t^2 pe_1 float %9.0g pe[t-1] pe_2 float %9.0g pe[t-2] pe_3 float %9.0g pe[t-3] pe_4 float %9.0g pe[t-4] pill byte %9.0g =1 if year >= 1963 ww2 byte %9.0g =1, 1941 to 1945 tcu float %9.0g t^3 cgfr float %9.0g change in gfr: gfr - gfr_1 cpe float %9.0g pe - pe_1 cpe_1 float %9.0g cpe[t-1] cpe_2 float %9.0g cpe[t-2] cpe_3 float %9.0g cpe[t-3] cpe_4 float %9.0g cpe[t-4] gfr_1 float %9.0g gfr[t-1] cgfr_1 float %9.0g cgfr[t-1] cgfr_2 float %9.0g cgfr[t-2] cgfr_3 float %9.0g cgfr[t-3] cgfr_4 float %9.0g cgfr[t-4] gfr_2 float %9.0g gfr[t-2] ------------------------------------------------------------------------------- Sorted by: . **simple version . reg gfr pe ww2 pill Source | SS df MS Number of obs = 72 -------------+------------------------------ F( 3, 68) = 20.38 Model | 13183.6215 3 4394.54049 Prob > F = 0.0000 Residual | 14664.2739 68 215.651087 R-squared = 0.4734 -------------+------------------------------ Adj R-squared = 0.4502 Total | 27847.8954 71 392.223879 Root MSE = 14.685 ------------------------------------------------------------------------------ gfr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- pe | .08254 .0296462 2.78 0.007 .0233819 .1416981 ww2 | -24.2384 7.458253 -3.25 0.002 -39.12111 -9.355684 pill | -31.59403 4.081068 -7.74 0.000 -39.73768 -23.45039 _cons | 98.68176 3.208129 30.76 0.000 92.28003 105.0835 ------------------------------------------------------------------------------ . reg gfr pe ww2 pill t Source | SS df MS Number of obs = 72 -------------+------------------------------ F( 4, 67) = 32.84 Model | 18441.2357 4 4610.30894 Prob > F = 0.0000 Residual | 9406.65967 67 140.397905 R-squared = 0.6622 -------------+------------------------------ Adj R-squared = 0.6420 Total | 27847.8954 71 392.223879 Root MSE = 11.849 ------------------------------------------------------------------------------ gfr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- pe | .2788778 .0400199 6.97 0.000 .1989978 .3587578 ww2 | -35.59228 6.297377 -5.65 0.000 -48.1619 -23.02266 pill | .9974479 6.26163 0.16 0.874 -11.50082 13.49571 t | -1.149872 .1879038 -6.12 0.000 -1.524929 -.7748146 _cons | 111.7694 3.357765 33.29 0.000 105.0673 118.4716 ------------------------------------------------------------------------------ . **look at pattern of fertility . graph gfr t . ** use fancier trend terms . reg gfr pe ww2 pill t tsq tcu Source | SS df MS Number of obs = 72 -------------+------------------------------ F( 6, 65) = 57.07 Model | 23405.1282 6 3900.8547 Prob > F = 0.0000 Residual | 4442.76724 65 68.3502652 R-squared = 0.8405 -------------+------------------------------ Adj R-squared = 0.8257 Total | 27847.8954 71 392.223879 Root MSE = 8.2674 ------------------------------------------------------------------------------ gfr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- pe | .1619068 .0413053 3.92 0.000 .0794145 .2443991 ww2 | -19.04674 5.042 -3.78 0.000 -29.11631 -8.977167 pill | -25.00967 5.345633 -4.68 0.000 -35.68564 -14.33371 t | -5.612221 .5427627 -10.34 0.000 -6.696193 -4.528249 tsq | .1553794 .0203037 7.65 0.000 .11483 .1959288 tcu | -.0012898 .0001894 -6.81 0.000 -.0016682 -.0009115 _cons | 142.7955 4.337744 32.92 0.000 134.1324 151.4586 ------------------------------------------------------------------------------ . **try fdl of order 2 . reg gfr pe pe_1 pe_2 ww2 pill t tsq tcu Source | SS df MS Number of obs = 70 -------------+------------------------------ F( 8, 61) = 47.58 Model | 22402.4771 8 2800.30964 Prob > F = 0.0000 Residual | 3589.95575 61 58.8517336 R-squared = 0.8619 -------------+------------------------------ Adj R-squared = 0.8438 Total | 25992.4329 69 376.701926 Root MSE = 7.6715 ------------------------------------------------------------------------------ gfr | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- pe | .0155381 .0759508 0.20 0.839 -.1363349 .167411 pe_1 | -.03621 .0839206 -0.43 0.668 -.2040196 .1315995 pe_2 | .176656 .069089 2.56 0.013 .038504 .314808 ww2 | -4.17593 6.396479 -0.65 0.516 -16.96648 8.61462 pill | -26.76372 5.054231 -5.30 0.000 -36.87028 -16.65716 t | -6.622622 .6144521 -10.78 0.000 -7.851295 -5.393949 tsq | .183325 .0215221 8.52 0.000 .140289 .226361 tcu | -.0015103 .0001947 -7.76 0.000 -.0018995 -.001121 _cons | 152.4889 5.235048 29.13 0.000 142.0208 162.957 ------------------------------------------------------------------------------ . **joint test . test pe pe_1 pe_2 ( 1) pe = 0.0 ( 2) pe_1 = 0.0 ( 3) pe_2 = 0.0 F( 3, 61) = 8.21 Prob > F = 0.0001 . **really want to test the LR impact propensity . test pe+pe_1+pe_2=0 ( 1) pe + pe_1 + pe_2 = 0.0 F( 1, 61) = 16.19 Prob > F = 0.0002 . use phillips, clear . desc Contains data from phillips.dta obs: 49 vars: 11 13 Sep 2000 15:34 size: 2,254 (100.0% of memory free) ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- year int %9.0g 1948-1996 unem float %9.0g civilian unemployment rate inf float %9.0g CPI inflation rate unem_1 float %9.0g unem lagged once inf_1 float %9.0g inf lagged once unem_2 float %9.0g unem lagged twice inf_2 float %9.0g inf lagged twice cunem float %9.0g unem - unem_1 cinf float %9.0g inf - inf_1 cunem_1 float %9.0g cunem lagged once cinf_1 float %9.0g cinf lagged once ------------------------------------------------------------------------------- Sorted by: . **static phillips curve . reg inf unem Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 1, 47) = 2.62 Model | 25.6369575 1 25.6369575 Prob > F = 0.1125 Residual | 460.61979 47 9.80042107 R-squared = 0.0527 -------------+------------------------------ Adj R-squared = 0.0326 Total | 486.256748 48 10.1303489 Root MSE = 3.1306 ------------------------------------------------------------------------------ inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | .4676257 .2891262 1.62 0.112 -.1140212 1.049273 _cons | 1.42361 1.719015 0.83 0.412 -2.034602 4.881822 ------------------------------------------------------------------------------ . predict uhat, resid . **get the lag . gen uhat=uhat[_n-1] uhat already defined r(110); . gen uhat_1=uhat[_n-1] (1 missing value generated) . **simple test . reg uhat uhat_1 Source | SS df MS Number of obs = 48 -------------+------------------------------ F( 1, 46) = 24.34 Model | 150.91704 1 150.91704 Prob > F = 0.0000 Residual | 285.198412 46 6.19996547 R-squared = 0.3460 -------------+------------------------------ Adj R-squared = 0.3318 Total | 436.115452 47 9.27905217 Root MSE = 2.49 ------------------------------------------------------------------------------ uhat | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- uhat_1 | .5729695 .1161334 4.93 0.000 .3392052 .8067338 _cons | -.1133967 .359404 -0.32 0.754 -.8368393 .610046 ------------------------------------------------------------------------------ . *check for AR(2) serial corr . gen uhat_2=uhat[_n-2] (2 missing values generated) . reg uhat uhat_1 uhat_2 Source | SS df MS Number of obs = 47 -------------+------------------------------ F( 2, 44) = 22.01 Model | 203.88313 2 101.941565 Prob > F = 0.0000 Residual | 203.755041 44 4.63079639 R-squared = 0.5002 -------------+------------------------------ Adj R-squared = 0.4774 Total | 407.638171 46 8.86169938 Root MSE = 2.1519 ------------------------------------------------------------------------------ uhat | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- uhat_1 | .7813238 .1274284 6.13 0.000 .5245087 1.038139 uhat_2 | -.1923933 .1242322 -1.55 0.129 -.4427669 .0579803 _cons | .0849247 .3142431 0.27 0.788 -.5483907 .71824 ------------------------------------------------------------------------------ . **adjust to be valid without strict exog . reg uhat uhat_1 uhat_2 unem Source | SS df MS Number of obs = 47 -------------+------------------------------ F( 3, 43) = 16.15 Model | 215.940675 3 71.980225 Prob > F = 0.0000 Residual | 191.697496 43 4.45808131 R-squared = 0.5297 -------------+------------------------------ Adj R-squared = 0.4969 Total | 407.638171 46 8.86169938 Root MSE = 2.1114 ------------------------------------------------------------------------------ uhat | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- uhat_1 | .7972073 .1254019 6.36 0.000 .5443102 1.050104 uhat_2 | -.0938253 .1358316 -0.69 0.493 -.3677558 .1801052 unem | -.392191 .2384746 -1.64 0.107 -.8731208 .0887389 _cons | 2.348028 1.410215 1.67 0.103 -.4959424 5.191998 ------------------------------------------------------------------------------ . **alternative test . reg inf uhat_1 uhat_2 unem Source | SS df MS Number of obs = 47 -------------+------------------------------ F( 3, 43) = 18.72 Model | 250.411019 3 83.4703398 Prob > F = 0.0000 Residual | 191.697501 43 4.45808141 R-squared = 0.5664 -------------+------------------------------ Adj R-squared = 0.5362 Total | 442.10852 46 9.61105478 Root MSE = 2.1114 ------------------------------------------------------------------------------ inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- uhat_1 | .7972073 .1254019 6.36 0.000 .5443102 1.050104 uhat_2 | -.0938253 .1358316 -0.69 0.493 -.3677558 .1801052 unem | .0754347 .2384746 0.32 0.753 -.4054952 .5563646 _cons | 3.771638 1.410215 2.67 0.011 .9276677 6.615608 ------------------------------------------------------------------------------ . **let's try newey-west errors with AR(1) . newey inf unem, t(year) lags(1) option lag() required r(198); . newey inf unem, lags(1) option lag() required r(198); . newey inf unem, lag(1) t(year) Regression with Newey-West standard errors Number of obs = 49 maximum lag : 1 F( 1, 47) = 2.70 Prob > F = 0.1069 ------------------------------------------------------------------------------ | Newey-West inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | .4676257 .2844517 1.64 0.107 -.1046173 1.039869 _cons | 1.42361 1.556447 0.91 0.365 -1.707558 4.554778 ------------------------------------------------------------------------------ . **if you set lag=0, it's the same as robust . reg inf unem, robust Regression with robust standard errors Number of obs = 49 F( 1, 47) = 3.29 Prob > F = 0.0763 R-squared = 0.0527 Root MSE = 3.1306 ------------------------------------------------------------------------------ | Robust inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | .4676257 .2579888 1.81 0.076 -.0513809 .9866323 _cons | 1.42361 1.491135 0.95 0.345 -1.576167 4.423387 ------------------------------------------------------------------------------ . newey inf unem, lag(0) t(year) Regression with Newey-West standard errors Number of obs = 49 maximum lag : 0 F( 1, 47) = 3.29 Prob > F = 0.0763 ------------------------------------------------------------------------------ | Newey-West inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | .4676257 .2579888 1.81 0.076 -.0513809 .9866323 _cons | 1.42361 1.491135 0.95 0.345 -1.576167 4.423387 ------------------------------------------------------------------------------ . . newey inf unem, lag(3) t(year) Regression with Newey-West standard errors Number of obs = 49 maximum lag : 3 F( 1, 47) = 2.57 Prob > F = 0.1155 ------------------------------------------------------------------------------ | Newey-West inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | .4676257 .2916056 1.60 0.115 -.119009 1.05426 _cons | 1.42361 1.515019 0.94 0.352 -1.624215 4.471435 ------------------------------------------------------------------------------ . ***try Cochrane-Orcutt by hand . *est rho . reg uhat uhat_1 Source | SS df MS Number of obs = 48 -------------+------------------------------ F( 1, 46) = 24.34 Model | 150.91704 1 150.91704 Prob > F = 0.0000 Residual | 285.198412 46 6.19996547 R-squared = 0.3460 -------------+------------------------------ Adj R-squared = 0.3318 Total | 436.115452 47 9.27905217 Root MSE = 2.49 ------------------------------------------------------------------------------ uhat | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- uhat_1 | .5729695 .1161334 4.93 0.000 .3392052 .8067338 _cons | -.1133967 .359404 -0.32 0.754 -.8368393 .610046 ------------------------------------------------------------------------------ . **create the quasi-dif vars . gen infqd=inf-.573*inf_1 (1 missing value generated) . consqd=1-.573 unrecognized command: consqd r(199); . gen consqd=1-.573 . gen unemqd=unem-.573*unem_1 (1 missing value generated) . **get the estimates . reg infqd consqd unemqd, nocons Source | SS df MS Number of obs = 48 -------------+------------------------------ F( 2, 46) = 12.26 Model | 136.11224 2 68.0561202 Prob > F = 0.0001 Residual | 255.276046 46 5.54947926 R-squared = 0.3478 -------------+------------------------------ Adj R-squared = 0.3194 Total | 391.388287 48 8.15392264 Root MSE = 2.3557 ------------------------------------------------------------------------------ infqd | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- consqd | 5.512996 2.037525 2.71 0.010 1.411672 9.614321 unemqd | -.27988 .321916 -0.87 0.389 -.9278632 .3681033 ------------------------------------------------------------------------------ . **have stata do this . tsset year time variable: year, 1948 to 1996 . prais inf unem, corc two Iteration 0: rho = 0.0000 Iteration 1: rho = 0.5727 Cochrane-Orcutt AR(1) regression -- twostep estimates Source | SS df MS Number of obs = 48 -------------+------------------------------ F( 1, 46) = 0.75 Model | 4.17856886 1 4.17856886 Prob > F = 0.3901 Residual | 255.315974 46 5.55034727 R-squared = 0.0161 -------------+------------------------------ Adj R-squared = -0.0053 Total | 259.494543 47 5.5211605 Root MSE = 2.3559 ------------------------------------------------------------------------------ inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | -.2793123 .3219114 -0.87 0.390 -.9272865 .3686618 _cons | 5.50983 2.037318 2.70 0.010 1.408922 9.610738 -------------+---------------------------------------------------------------- rho | .5727355 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.802700 Durbin-Watson statistic (transformed) 1.217816 . **don't use any options . prais inf unem Iteration 0: rho = 0.0000 Iteration 1: rho = 0.5727 Iteration 2: rho = 0.7307 Iteration 3: rho = 0.7719 Iteration 4: rho = 0.7792 Iteration 5: rho = 0.7803 Iteration 6: rho = 0.7805 Iteration 7: rho = 0.7805 Iteration 8: rho = 0.7805 Iteration 9: rho = 0.7805 Prais-Winsten AR(1) regression -- iterated estimates Source | SS df MS Number of obs = 49 -------------+------------------------------ F( 1, 47) = 7.39 Model | 37.9720609 1 37.9720609 Prob > F = 0.0092 Residual | 241.618458 47 5.14081826 R-squared = 0.1358 -------------+------------------------------ Adj R-squared = 0.1174 Total | 279.590519 48 5.82480248 Root MSE = 2.2673 ------------------------------------------------------------------------------ inf | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- unem | -.715659 .3134522 -2.28 0.027 -1.346244 -.0850744 _cons | 8.295912 2.23143 3.72 0.001 3.806854 12.78497 -------------+---------------------------------------------------------------- rho | .7805446 ------------------------------------------------------------------------------ Durbin-Watson statistic (original) 0.802700 Durbin-Watson statistic (transformed) 1.909865 . log close log: C:\Documents and Settings\Patricia_Anderson\My Documents\ECON 20\I > nClass\nov25.log log type: text closed on: 25 Nov 2002, 12:14:32 -------------------------------------------------------------------------------