* MANKIW.RAT * REPRISE DE L'ÉTUDE DE MANKIW ET CAMPBELL (1987) * CAL 1947 1 4; ALL 89:1 COMPUTE NBEG=47:1 , NEND=85:4 OPEN DATA C:\T837\DAT\USAQ.RAT DATA(FORMAT=RATS) NBEG NEND RGNP * SET RGNPD NBEG+1 NEND = 400*( LOG(RGNP) - LOG(RGNP{1}) ) SET TREND NBEG NEND = T * GRAPH(HEADER='PREMIERE DIFFERENCE DU PIB REEL U.S.') 1 # RGNPD NBEG+1 NEND * * Choix des retards * * 1ère méthode: critère d'Akaike * COMPUTE NLAG=6 , I=0 * LINREG(NOPRINT) RGNPD NBEG+1+NLAG NEND # CONSTANT COMPUTE AIC = LOG(%RSS/FLOAT(%NOBS)) + 2*(%NREG-1)/(FLOAT(%NOBS)) DISPLAY 'RETARD ' I 'AKAIKE' AIC RETARD 0 AKAIKE 3.02878 * DO I=1,NLAG LINREG(NOPRINT) RGNPD NBEG+1+NLAG NEND # CONSTANT RGNPD{1 TO I} COMPUTE AIC = LOG(%RSS/FLOAT(%NOBS)) + (2*(%NREG-1))/(FLOAT(%NOBS)) DISPLAY 'RETARD ' I 'AKAIKE' AIC END DO I RETARD 1 AKAIKE 2.89320 RETARD 2 AKAIKE 2.88789 RETARD 3 AKAIKE 2.87571 RETARD 4 AKAIKE 2.88112 RETARD 5 AKAIKE 2.89317 RETARD 6 AKAIKE 2.90499 * * Persistence avec première différence * LINREG(DEFINE=1) RGNPD NBEG+5 NEND RES1 # CONSTANT RGNPD{1 TO 3} Dependent Variable RGNPD - Estimation by Least Squares Quarterly Data From 1948:02 To 1985:04 Usable Observations 151 Degrees of Freedom 147 Centered R**2 0.175761 R Bar **2 0.158939 Uncentered R**2 0.452438 T x R**2 68.318 Mean of Dependent Variable 3.2182280044 Std Error of Dependent Variable 4.5424453876 Standard Error of Estimate 4.1658473184 Sum of Squared Residuals 2551.0797304 Regression F(3,147) 10.4488 Significance Level of F 0.00000284 Durbin-Watson Statistic 2.021390 Q(36-0) 20.779253 Significance Level of Q 0.98003058 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 1. Constant 2.027684144 0.468788524 4.32537 0.00002797 2. RGNPD{1} 0.341159317 0.081380250 4.19216 0.00004752 3. RGNPD{2} 0.190343893 0.084577418 2.25053 0.02589949 4. RGNPD{3} -0.161619409 0.081291521 -1.98815 0.04865257 CORRELATE(NUMBER=12,QSTATS,DFC=3) RES1 NBEG+4 NEND Correlations of Series RES1 Quarterly Data From 1948:01 To 1985:04 Autocorrelations 1: -0.0130734 0.0032135 0.0450811 -0.0679731 -0.0755717 0.0049579 7: 0.0490919 -0.0727796 -0.1095936 0.0922283 0.0157510 -0.0788286 Ljung-Box Q-Statistics Q(12) = 7.6430. Significance Level 0.57048737 * IMPULSE(INPUT) 1 12 # 1 IMP_A # 1.0 Entry RGNPD 1 1.000000000000 2 0.341159316893 3 0.306733572363 4 0.007963199675 5 0.005963614892 6 -0.046023809417 7 -0.015853321331 8 -0.015132695238 9 -0.000741901998 10 -0.000571318479 11 0.002109610122 12 0.000730871927 * MODIFY 1 2 VREPLACE RGNPD BY RGNP DIFFERENCE 1 IMPULSE(INPUT) 1 12 # 2 # 1.0 * * 2ème méthode: critère de Schwarz * COMPUTE I=0 LINREG(NOPRINT) RGNPD NBEG+1+NLAG NEND # CONSTANT COMPUTE SWZ = LOG(%RSS/FLOAT(%NOBS)) + ((%NREG-1)*LOG(%NOBS))/FLOAT(%NOBS) DISPLAY 'RETARD ' I 'SCHWARZ' SWZ RETARD 0 SCHWARZ 3.02878 * DO I=1,NLAG LINREG(NOPRINT) RGNPD NBEG+1+NLAG NEND # CONSTANT RGNPD{1 TO I} COMPUTE SWZ = LOG(%RSS/FLOAT(%NOBS)) + ((%NREG-1)*LOG(%NOBS))/FLOAT(%NOBS) DISPLAY 'RETARD ' I 'SCHWARZ' SWZ END DO I RETARD 1 SCHWARZ 2.91337 RETARD 2 SCHWARZ 2.92821 RETARD 3 SCHWARZ 2.93619 RETARD 4 SCHWARZ 2.96176 RETARD 5 SCHWARZ 2.99398 RETARD 6 SCHWARZ 3.02595 * * Persistence avec première différence * LINREG(DEFINE=1) RGNPD NBEG+2 NEND RES1 # CONSTANT RGNPD{1} Dependent Variable RGNPD - Estimation by Least Squares Quarterly Data From 1947:03 To 1985:04 Usable Observations 154 Degrees of Freedom 152 Centered R**2 0.135697 R Bar **2 0.130011 Uncentered R**2 0.428562 T x R**2 65.999 Mean of Dependent Variable 3.2125595891 Std Error of Dependent Variable 4.5021166241 Standard Error of Estimate 4.1992690600 Sum of Squared Residuals 2680.3468171 Regression F(1,152) 23.8642 Significance Level of F 0.00000260 Durbin-Watson Statistic 2.102745 Q(36-0) 24.310919 Significance Level of Q 0.93088152 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 1. Constant 2.0301453721 0.4160424581 4.87966 0.00000266 2. RGNPD{1} 0.3683480896 0.0754023242 4.88510 0.00000260 CORRELATE(NUMBER=12,QSTATS,DFC=1) RES1 NBEG+2 NEND Correlations of Series RES1 Quarterly Data From 1947:03 To 1985:04 Autocorrelations 1: -0.0518590 0.1821455 -0.0778667 -0.0571008 -0.1026415 -0.0125132 7: 0.0210056 -0.0566044 -0.0682671 0.0660580 0.0078325 -0.0585771 Ljung-Box Q-Statistics Q(12) = 11.5672. Significance Level 0.39703602 * IMPULSE(INPUT) 1 12 # 1 IMP_S # 1.0 Entry RGNPD 1 1.0000000000000 2 0.3683480895660 3 0.1356803150869 4 0.0499775848540 5 0.0184091479021 6 0.0067809744603 7 0.0024977589878 8 0.0009200447514 9 0.0003388967265 10 0.0001248319618 11 0.0000459816146 12 0.0000169372399 * MODIFY 1 2 VREPLACE RGNPD BY RGNP DIFFERENCE 1 IMPULSE(INPUT) 1 12 # 2 # 1.0 * * 3ème méthode: retard maximal significatif * DO I=NLAG,1,-1 LINREG(NOPRINT) RGNPD NBEG+1+NLAG NEND # CONSTANT RGNPD{1 TO I} DISPLAY 'Retard = ' I 'Test-t = ' $ %BETA(1+I)/(SQRT(%SEESQ)*SQRT(%XX(1+I,1+I))) END DO I Retard = 6 Test-t = 0.47809 Retard = 5 Test-t = -0.44288 Retard = 4 Test-t = -1.07645 Retard = 3 Test-t = -1.93908 Retard = 2 Test-t = 1.66178 Retard = 1 Test-t = 4.85990 * * Persistence avec première différence * LINREG(DEFINE=1) RGNPD NBEG+4 NEND RES1 # CONSTANT RGNPD{1 TO 3} Dependent Variable RGNPD - Estimation by Least Squares Quarterly Data From 1948:01 To 1985:04 Usable Observations 152 Degrees of Freedom 148 Centered R**2 0.175556 R Bar **2 0.158844 Uncentered R**2 0.452954 T x R**2 68.849 Mean of Dependent Variable 3.2135727081 Std Error of Dependent Variable 4.5277429765 Standard Error of Estimate 4.1525996326 Sum of Squared Residuals 2552.1243889 Regression F(3,148) 10.5049 Significance Level of F 0.00000263 Durbin-Watson Statistic 2.026750 Q(36-0) 21.045032 Significance Level of Q 0.97773576 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 1. Constant 2.020579404 0.466405357 4.33224 0.00002710 2. RGNPD{1} 0.340287786 0.081044138 4.19880 0.00004613 3. RGNPD{2} 0.191192342 0.084237954 2.26967 0.02467221 4. RGNPD{3} -0.161483147 0.081031117 -1.99285 0.04811612 CORRELATE(NUMBER=12,QSTATS,DFC=1) RES1 NBEG+2 NEND * IMPULSE(INPUT) 1 12 # 1 IMP_T # 1.0 Entry RGNPD 1 1.000000000000 2 0.340287785581 3 0.306988119073 4 0.008041579257 5 0.006479486274 6 -0.045831029054 7 -0.015655490754 8 -0.015136241897 9 -0.000742949393 10 -0.000618652232 11 0.002091681938 12 0.000713466051 * MODIFY 1 2 VREPLACE RGNPD BY RGNP DIFFERENCE 1 IMPULSE(INPUT) 1 12 # 2 # 1.0 * GRAPH(HEADER='IMPACT DU CHOIX DU RETARD SUR LES IMPULSES',KEY=UPRIGHT,$ NODATES) 3 # IMP_A # IMP_S # IMP_T * * Choix des retards par le test du LR: modèle avec * tendance linéaire selon Blanchard * * Modèle non contraint * LINREG(NOPRINT) RGNP NBEG+6 NEND RES6 # CONSTANT TREND RGNP{1 TO 6} * LINREG(NOPRINT) RGNP NBEG+6 NEND RES4 # CONSTANT TREND RGNP{1 TO 4} RATIO(DEGREES=2) NBEG+6 NEND # RES6 # RES4 Covariance\Correlation Matrices RES6 RES6 537.0541568921 RES4 RES4 538.0520308822 Log Determinants are 6.286099 6.287955 Chi-Squared(2)= 0.278449 with Significance Level 0.87003267 * LINREG(NOPRINT) RGNP NBEG+6 NEND RES2 # CONSTANT TREND RGNP{1 TO 2} RATIO(DEGREES=2) NBEG+6 NEND # RES4 # RES2 Covariance\Correlation Matrices RES4 RES4 538.0520308822 RES2 RES2 560.8724717013 Log Determinants are 6.287955 6.329494 Chi-Squared(2)= 6.230743 with Significance Level 0.04436201 * LINREG(NOPRINT) RGNP NBEG+6 NEND RES0 # CONSTANT TREND RATIO(DEGREES=2) NBEG+6 NEND # RES2 # RES0 Covariance\Correlation Matrices RES2 RES2 560.8724717013 RES0 RES0 7804.211307577 Log Determinants are 6.329494 8.962419 Chi-Squared(2)= 394.938783 with Significance Level 0.00000000 * * Persistence avec une tendance selon Blanchard * LINREG(DEFINE=3) RGNP NBEG+4 NEND # CONSTANT TREND RGNP{1 TO 4} Dependent Variable RGNP - Estimation by Least Squares Quarterly Data From 1948:01 To 1985:04 Usable Observations 152 Degrees of Freedom 146 Centered R**2 0.999029 R Bar **2 0.998996 Uncentered R**2 0.999904 T x R**2 151.985 Mean of Dependent Variable 2233.3835526 Std Error of Dependent Variable 743.2392454 Standard Error of Estimate 23.5494112 Sum of Squared Residuals 80967.916297 Regression F(5,146) 30052.6197 Significance Level of F 0.00000000 Durbin-Watson Statistic 1.997031 Q(36-0) 29.617962 Significance Level of Q 0.76483313 Variable Coeff Std Error T-Stat Signif ******************************************************************************* 1. Constant 57.20022143 20.13551649 2.84076 0.00514412 2. TREND 1.02132966 0.38376276 2.66136 0.00865423 3. RGNP{1} 1.23882072 0.08260086 14.99767 0.00000000 4. RGNP{2} -0.09086147 0.12981167 -0.69995 0.48507334 5. RGNP{3} -0.26356505 0.12997341 -2.02784 0.04439563 6. RGNP{4} 0.05697158 0.08298486 0.68653 0.49346796 * COMPUTE [RECTANGULAR] PHI = || %BETA(3), %BETA(4), %BETA(5), %BETA(6) | $ 1, 0, 0, 0 | $ 0, 1, 0, 0 | $ 0, 0, 1, 0 || WRITE PHI 1.2388 -0.0909 -0.2636 0.0570 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 EIGEN(CVALUES=CEIGEN) PHI WRITE CEIGEN ( 0.8770, 0.0000) ( 0.5590, 0.0000) ( -0.4535, 0.0000) ( 0.2562, 0.0000) * SUMMARIZE # RGNP{1 TO 4} Summary of Linear Combination of Coefficients RGNP Lag(s) 1 to 4 Value 0.941365786881 t-Statistic 40.91812 Standard Error 0.023006087210 Signif Level 0.00000000 IMPULSE(INPUT) 1 12 # 3 IMP # 1.0 Entry RGNP 1 1.0000000000000 2 1.2388207177089 3 1.4438153027487 4 1.4125021943380 5 1.3491115479081 6 1.2330036439264 7 1.1148584411490 8 0.9939710521371 9 0.8819386162641 10 0.7786586139739 11 0.6860234099999 12 0.6032898609262