Welcome to SHAZAM - Version 9.0 - DEC 2003 SYSTEM=WIN-XP PAR= 2000 CURRENT WORKING DIRECTORY IS: C:\ECONOM~1\Berndt |_FILE PATH CHAP6.DAT\ |_TIME 1952 4 |_SAMPLE 1952.1 1986.4 |_READ (KOPCKE) DATE JS JE F IS IE /SKIPLINES=1 UNIT 88 IS NOW ASSIGNED TO: CHAP6.DAT\KOPCKE 6 VARIABLES AND 140 OBSERVATIONS STARTING AT OBS 1 |_GENR FJE=F/JE |_GENR IELAG=LAG(IE) ..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO |_SAMPLE 1952.2 1986.4 |_OLS IE IELAG FJE /RSTAT DLAG RESID=U REQUIRED MEMORY IS PAR= 16 CURRENT PAR= 2000 OLS ESTIMATION 139 OBSERVATIONS DEPENDENT VARIABLE= IE ...NOTE..SAMPLE RANGE SET TO: 2, 140 R-SQUARE = 0.9951 R-SQUARE ADJUSTED = 0.9951 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.27212E+08 STANDARD ERROR OF THE ESTIMATE-SIGMA = 5216.5 SUM OF SQUARED ERRORS-SSE= 0.37008E+10 MEAN OF DEPENDENT VARIABLE = 0.16092E+06 LOG OF THE LIKELIHOOD FUNCTION = -1385.50 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 136 DF P-VALUE CORR. COEFFICIENT AT MEANS IELAG 0.88557 0.1832E-01 48.35 0.000 0.972 0.8726 0.8756 FJE 0.13676 0.1878E-01 7.281 0.000 0.530 0.1314 0.1883 CONSTANT -10271. 1766. -5.815 0.000-0.446 0.0000 -0.0638 DURBIN-WATSON = 1.7833 VON NEUMANN RATIO = 1.7962 RHO = 0.09893 RESIDUAL SUM = -0.13506E-08 RESIDUAL VARIANCE = 0.27212E+08 SUM OF ABSOLUTE ERRORS= 0.52745E+06 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9951 RUNS TEST: 49 RUNS, 63 POS, 0 ZERO, 76 NEG NORMAL STATISTIC = -3.5886 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 1.1945 |_* Calculate P-value for h-statistic |_GEN1 H=$DURH ..NOTE..CURRENT VALUE OF $DURH= 1.1945 |_DISTRIB H /TYPE=NORMAL NORMAL DISTRIBUTION - MEAN= 0.0000 VARIANCE= 1.0000 DATA Z PDF CDF 1-CDF H ROW 1 1.1945 1.1945 0.19546 0.88386 0.11614 |_* |_* Perform a Breusch-Godfrey LM test of an AR(1) process. |_* Regress U on Y and U lagged. |_* Run auxiliary regression. |_OLS U U(1.1) IELAG FJE REQUIRED MEMORY IS PAR= 17 CURRENT PAR= 2000 OLS ESTIMATION 138 OBSERVATIONS DEPENDENT VARIABLE= U ...NOTE..SAMPLE RANGE SET TO: 3, 140 R-SQUARE = 0.0112 R-SQUARE ADJUSTED = -0.0110 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.27039E+08 STANDARD ERROR OF THE ESTIMATE-SIGMA = 5199.9 SUM OF SQUARED ERRORS-SSE= 0.36232E+10 MEAN OF DEPENDENT VARIABLE = -43.782 LOG OF THE LIKELIHOOD FUNCTION = -1374.57 TESTS ON LAGGED COEFFICIENTS VARIABLE SUM(COEFS) STD ERROR T-RATIO P-VALUE | MEAN LAG| JOINT-F P-VALUE U 0.10547 0.875E-01 1.21 0.230 | 1.000 | 1.45 0.230 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 134 DF P-VALUE CORR. COEFFICIENT AT MEANS U 0.10547 0.8752E-01 1.205 0.230 0.104 0.1054 0.1126 IELAG -0.73518E-02 0.1878E-01 -0.3915 0.696-0.034 -0.1039 26.8163 FJE 0.83734E-02 0.1936E-01 0.4324 0.666 0.037 0.1146 -42.5402 CONSTANT -727.28 1817. -0.4003 0.690-0.035 0.0000 16.6113 |_* One version of the test is an ordinary t-test on ULAG. |_* Another is an LM test on NR2, which is asymptotically chi-square. |_GEN1 LM = $N*$R2 ..NOTE..CURRENT VALUE OF $N = 138.00 ..NOTE..CURRENT VALUE OF $R2 = 0.11161E-01 |_DISTRIB LM /TYPE=CHI DF=1 CHI-SQUARE PARAMETERS- DF= 1.0000 MEAN= 1.0000 VARIANCE= 2.0000 MODE= 0.0000 DATA PDF CDF 1-CDF LM ROW 1 1.5402 0.14883 0.78541 0.21459 |_* |_* The AUTO command also generates an h-statistic. |_AUTO IE IELAG FJE /RSTAT DLAG REQUIRED MEMORY IS PAR= 18 CURRENT PAR= 2000 DEPENDENT VARIABLE = IE ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS DLAG OPTION IN EFFECT - FIRST INDEPENDENT VARIABLE MUST BE LAGGED DEP. VAR. VARIANCES COMPUTED USING DHRYMES THEOREM 7.1 DN OPTION IN EFFECT - DIVISOR IS N LEAST SQUARES ESTIMATION 139 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100 ITERATION RHO LOG L.F. SSE 1 0.00000 -1385.50 0.37008E+10 2 0.09893 -1384.75 0.36609E+10 3 0.11032 -1384.74 0.36603E+10 4 0.11207 -1384.74 0.36602E+10 5 0.11234 -1384.74 0.36602E+10 LOG L.F. = -1384.74 AT RHO = 0.11234 THEORETICAL DIFFERENCE DUE TO DHRYMES ADJUSTMENT= 0.262912E+08 COVARIANCE BETWEEN RHO AND LAGGED DEPVAR=-0.467032E-03 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.11234 0.00761 0.08726 1.28741 R-SQUARE = 0.9952 R-SQUARE ADJUSTED = 0.9951 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.26333E+08 STANDARD ERROR OF THE ESTIMATE-SIGMA = 5131.5 SUM OF SQUARED ERRORS-SSE= 0.36602E+10 MEAN OF DEPENDENT VARIABLE = 0.16092E+06 LOG OF THE LIKELIHOOD FUNCTION = -1384.74 ASYMPTOTIC VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR -------- P-VALUE CORR. COEFFICIENT AT MEANS IELAG 0.87697 0.2065E-01 42.47 0.000 0.964 0.8641 0.8671 FJE 0.14548 0.2108E-01 6.900 0.000 0.509 0.1398 0.2003 CONSTANT -10822. 1957. -5.530 0.000-0.428 0.0000 -0.0672 DURBIN-WATSON = 2.0868 VON NEUMANN RATIO = 2.1019 RHO = -0.05528 RESIDUAL SUM = -721.52 RESIDUAL VARIANCE = 0.26336E+08 SUM OF ABSOLUTE ERRORS= 0.51520E+06 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9952 RUNS TEST: 55 RUNS, 63 POS, 0 ZERO, 76 NEG NORMAL STATISTIC = -2.5580 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -5.9290 MODIFIED FOR AUTO ORDER=1 WITH LAGGED DEPVAR |_GEN1 H=$DURH ..NOTE..CURRENT VALUE OF $DURH= -5.9290 |_DISTRIB H /TYPE=NORMAL NORMAL DISTRIBUTION - MEAN= 0.0000 VARIANCE= 1.0000 DATA Z PDF CDF 1-CDF H ROW 1 -5.9290 -5.9290 0.92770E-08 0.15235E-08 1.0000 |_* These results sugest the presence of autocorrelation even after correcting for an AR(1) process. |_* |_* The Breusch-Godfrey LM test can check for a higher order process, e,g,AR(4). |_OLS U U(1.4) IELAG FJE LAG FOR U RANGE = 1 4 ORDER= 0 ENDCON=0 REQUIRED MEMORY IS PAR= 21 CURRENT PAR= 2000 OLS ESTIMATION 135 OBSERVATIONS DEPENDENT VARIABLE= U ...NOTE..SAMPLE RANGE SET TO: 6, 140 R-SQUARE = 0.2993 R-SQUARE ADJUSTED = 0.2664 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.18999E+08 STANDARD ERROR OF THE ESTIMATE-SIGMA = 4358.8 SUM OF SQUARED ERRORS-SSE= 0.24318E+10 MEAN OF DEPENDENT VARIABLE = -135.17 LOG OF THE LIKELIHOOD FUNCTION = -1319.25 TESTS ON LAGGED COEFFICIENTS VARIABLE SUM(COEFS) STD ERROR T-RATIO P-VALUE | MEAN LAG| JOINT-F P-VALUE U 0.68104 0.125 5.43 0.000 | 2.431 | 13.5 0.000 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 128 DF P-VALUE CORR. COEFFICIENT AT MEANS U 0.87981E-01 0.8426E-01 1.044 0.298 0.092 0.0883 0.0795 U 0.41869 0.8494E-01 4.929 0.000 0.399 0.4252 0.2366 U -0.32961E-01 0.8929E-01 -0.3692 0.713-0.033 -0.0324 -0.0570 U 0.20733 0.9304E-01 2.228 0.028 0.193 0.2004 0.1467 IELAG -0.37058E-01 0.1745E-01 -2.123 0.036-0.184 -0.5292 44.3188 FJE 0.41278E-01 0.1835E-01 2.250 0.026 0.195 0.5626 -68.7154 CONSTANT -3377.9 1699. -1.988 0.049-0.173 0.0000 24.9907 |_GEN1 LM = $N*$R2 ..NOTE..CURRENT VALUE OF $N = 135.00 ..NOTE..CURRENT VALUE OF $R2 = 0.29927 |_DISTRIB LM /TYPE=CHI DF=4 CHI-SQUARE PARAMETERS- DF= 4.0000 MEAN= 4.0000 VARIANCE= 8.0000 MODE= 2.0000 DATA PDF CDF 1-CDF LM ROW 1 40.402 0.17029E-07 1.0000 0.35744E-07 |_*Note that the AR(1) tests do not detect the presence of higher-order autocorrelation. ..INPUT FILE COMPLETED..TYPE A NEW COMMAND OR TYPE: STOP