Welcome to SHAZAM - Version 9.0 - DEC 2003 SYSTEM=WIN-XP PAR= 2000 CURRENT WORKING DIRECTORY IS: C:\ECONOM~1\Berndt |_FILE PATH C:\ESL\USER\ |_READ (DATA9-5) year output labor land machines energy fert seedfeed others UNIT 88 IS NOW ASSIGNED TO: C:\ESL\USER\DATA9-5 ...SAMPLE RANGE IS NOW SET TO: 1 46 |_GENR loutput = log(output) |_GENR llabor = log(labor) |_GENR lland = log(land) |_GENR lmachine=log(machines) |_GENR lenergy=log(energy) |_GENR lfert=log(fert) |_GENR lseedfd=log(seedfeed) |_GENR lothers=log(others) |_* Estimate doulbe-log model, and test for first-order serial correlation using |_* the Durbin Watson test |_OLS loutput llabor lland lmachine lenergy lfert lseedfd lothers /LOGLOG DWPVALUE RESID=U REQUIRED MEMORY IS PAR= 29 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= LOUTPUT ...NOTE..SAMPLE RANGE SET TO: 1, 46 DURBIN-WATSON STATISTIC = 1.39325 DURBIN-WATSON POSITIVE AUTOCORRELATION TEST P-VALUE = 0.001527 NEGATIVE AUTOCORRELATION TEST P-VALUE = 0.998473 R-SQUARE = 0.9779 R-SQUARE ADJUSTED = 0.9738 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.15758E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.39696E-01 SUM OF SQUARED ERRORS-SSE= 0.59879E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -111.560 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 38 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR -0.68199 0.8221E-01 -8.296 0.000-0.803 -1.0638 -0.6820 LLAND 1.0126 0.3949 2.564 0.014 0.384 0.1515 1.0126 LMACHINE -0.30153 0.1006 -2.996 0.005-0.437 -0.2513 -0.3015 LENERGY 0.15796 0.1221 1.294 0.204 0.205 0.0828 0.1580 LFERT -0.25112E-01 0.7638E-01 -0.3288 0.744-0.053 -0.0377 -0.0251 LSEEDFD 0.82284E-01 0.1454 0.5660 0.575 0.091 0.0614 0.0823 LOTHERS 0.85184E-01 0.1037 0.8212 0.417 0.132 0.0484 0.0852 CONSTANT 3.0091 1.562 1.926 0.062 0.298 0.0000 3.0091 |_* Confirm the Durbin-watson test with the Breusch-Godfrey test. |_SET MISSVALU=0 |_GENR U1=LAG(U) ..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO |_OLS u u1 llabor lland lmachine lenergy lfert lseedfd lothers /DLAG ..WARNING..OBSERVATION 1 OF U1 HAS MISSING DATA VALUE= 0. REQUIRED MEMORY IS PAR= 13 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= U ...NOTE..SAMPLE RANGE SET TO: 1, 46 R-SQUARE = 0.1006 R-SQUARE ADJUSTED = -0.0938 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.14555E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.38151E-01 SUM OF SQUARED ERRORS-SSE= 0.53853E-01 MEAN OF DEPENDENT VARIABLE = -0.14330E-17 LOG OF THE LIKELIHOOD FUNCTION = 89.9822 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 37 DF P-VALUE CORR. COEFFICIENT AT MEANS U1 0.33941 0.1668 2.035 0.049 0.317 0.3376*********** LLABOR -0.18668E-01 0.7954E-01 -0.2347 0.816-0.039 -0.1958*********** LLAND 0.14080 0.3858 0.3650 0.717 0.060 0.1416*********** LMACHINE -0.31768E-01 0.9797E-01 -0.3243 0.748-0.053 -0.1781*********** LENERGY 0.35259E-01 0.1186 0.2973 0.768 0.049 0.1242*********** LFERT 0.11361E-01 0.7362E-01 0.1543 0.878 0.025 0.1146*********** LSEEDFD -0.46244E-01 0.1416 -0.3267 0.746-0.054 -0.2321*********** LOTHERS -0.99517E-02 0.9981E-01 -0.9970E-01 0.921-0.016 -0.0380*********** CONSTANT -0.37678 1.513 -0.2490 0.805-0.041 0.0000*********** DURBIN-WATSON = 1.9683 VON NEUMANN RATIO = 2.0121 RHO = 0.00128 RESIDUAL SUM = -0.87499E-14 RESIDUAL VARIANCE = 0.14555E-02 SUM OF ABSOLUTE ERRORS= 1.2958 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.1006 RUNS TEST: 22 RUNS, 25 POS, 0 ZERO, 21 NEG NORMAL STATISTIC = -0.5488 ...DURBIN H STATISTIC CANNOT BE COMPUTED |_GEN1 LMAR1 = $N*$R2 ..NOTE..CURRENT VALUE OF $N = 46.000 ..NOTE..CURRENT VALUE OF $R2 = 0.10064 |_DISTRIB LMAR1 /TYPE=CHI DF=1 CHI-SQUARE PARAMETERS- DF= 1.0000 MEAN= 1.0000 VARIANCE= 2.0000 MODE= 0.0000 DATA PDF CDF 1-CDF LMAR1 ROW 1 4.6294 0.18319E-01 0.96857 0.31429E-01 |_* Now test for third-order serial correlation, first using the Durbin-Watson test |_OLS loutput llabor lland lmachine lenergy lfert lseedfd lothers /LOGLOG DWPVALUE ORDER=3 REQUIRED MEMORY IS PAR= 28 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= LOUTPUT ...NOTE..SAMPLE RANGE SET TO: 1, 46 3 ORDER TEST GAP AFTER OB. NO. 0 0 MISSING OBS DURBIN-WATSON STATISTIC = 1.82220 DURBIN-WATSON POSITIVE AUTOCORRELATION TEST P-VALUE = 0.306329 NEGATIVE AUTOCORRELATION TEST P-VALUE = 0.693671 R-SQUARE = 0.9779 R-SQUARE ADJUSTED = 0.9738 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.15758E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.39696E-01 SUM OF SQUARED ERRORS-SSE= 0.59879E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -111.560 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 38 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR -0.68199 0.8221E-01 -8.296 0.000-0.803 -1.0638 -0.6820 LLAND 1.0126 0.3949 2.564 0.014 0.384 0.1515 1.0126 LMACHINE -0.30153 0.1006 -2.996 0.005-0.437 -0.2513 -0.3015 LENERGY 0.15796 0.1221 1.294 0.204 0.205 0.0828 0.1580 LFERT -0.25112E-01 0.7638E-01 -0.3288 0.744-0.053 -0.0377 -0.0251 LSEEDFD 0.82284E-01 0.1454 0.5660 0.575 0.091 0.0614 0.0823 LOTHERS 0.85184E-01 0.1037 0.8212 0.417 0.132 0.0484 0.0852 CONSTANT 3.0091 1.562 1.926 0.062 0.298 0.0000 3.0091 |_* Now confirm with the Breusch-Godfrey test |_GENR U2=LAG(U,2) ..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO |_GENR U3=LAG(U,3) ..NOTE.LAG VALUE IN UNDEFINED OBSERVATIONS SET TO ZERO |_OLS u u1-u3 llabor lland lmachine lenergy lfert lseedfd lothers /DLAG ..WARNING..OBSERVATION 1 OF U1 HAS MISSING DATA VALUE= 0. ..WARNING..OBSERVATION 1 OF U2 HAS MISSING DATA VALUE= 0. ..WARNING..OBSERVATION 2 OF U2 HAS MISSING DATA VALUE= 0. ..WARNING..OBSERVATION 1 OF U3 HAS MISSING DATA VALUE= 0. ..WARNING..OBSERVATION 2 OF U3 HAS MISSING DATA VALUE= 0. ..WARNING..OBSERVATION 3 OF U3 HAS MISSING DATA VALUE= 0. REQUIRED MEMORY IS PAR= 14 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= U ...NOTE..SAMPLE RANGE SET TO: 1, 46 R-SQUARE = 0.1007 R-SQUARE ADJUSTED = -0.1563 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.15386E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.39225E-01 SUM OF SQUARED ERRORS-SSE= 0.53850E-01 MEAN OF DEPENDENT VARIABLE = -0.14330E-17 LOG OF THE LIKELIHOOD FUNCTION = 89.9834 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 35 DF P-VALUE CORR. COEFFICIENT AT MEANS U1 0.33677 0.1834 1.837 0.075 0.297 0.3349*********** U2 0.55115E-02 0.1892 0.2914E-01 0.977 0.005 0.0054*********** U3 0.45519E-02 0.1904 0.2390E-01 0.981 0.004 0.0044*********** LLABOR -0.17181E-01 0.9000E-01 -0.1909 0.850-0.032 -0.1802*********** LLAND 0.13731 0.4191 0.3276 0.745 0.055 0.1381*********** LMACHINE -0.32021E-01 0.1028 -0.3115 0.757-0.053 -0.1795*********** LENERGY 0.36168E-01 0.1247 0.2899 0.774 0.049 0.1274*********** LFERT 0.11919E-01 0.7787E-01 0.1531 0.879 0.026 0.1202*********** LSEEDFD -0.44399E-01 0.1525 -0.2911 0.773-0.049 -0.2229*********** LOTHERS -0.10308E-01 0.1039 -0.9926E-01 0.921-0.017 -0.0394*********** CONSTANT -0.37994 1.598 -0.2378 0.813-0.040 0.0000*********** DURBIN-WATSON = 1.9649 VON NEUMANN RATIO = 2.0085 RHO = 0.00293 RESIDUAL SUM = 0.48017E-14 RESIDUAL VARIANCE = 0.15386E-02 SUM OF ABSOLUTE ERRORS= 1.2952 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.1007 RUNS TEST: 22 RUNS, 25 POS, 0 ZERO, 21 NEG NORMAL STATISTIC = -0.5488 ...DURBIN H STATISTIC CANNOT BE COMPUTED |_GEN1 LMAR3=$N*$R2 ..NOTE..CURRENT VALUE OF $N = 46.000 ..NOTE..CURRENT VALUE OF $R2 = 0.10069 |_DISTRIB LMAR3 /TYPE=CHI DF=3 CHI-SQUARE PARAMETERS- DF= 3.0000 MEAN= 3.0000 VARIANCE= 6.0000 MODE= 1.0000 DATA PDF CDF 1-CDF LMAR3 ROW 1 4.6315 0.84732E-01 0.79915 0.20085 |_* It appears that there is first-order serial correlation, but no second or third-order |_* serial correlation. |_* Estimate an AR(1) model using Cochrane-Orcutt. |_AUTO loutput llabor lland lmachine lenergy lfert lseedfd lothers /LOGLOG REQUIRED MEMORY IS PAR= 14 CURRENT PAR= 2000 DEPENDENT VARIABLE = LOUTPUT ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 46 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100 ITERATION RHO LOG L.F. SSE 1 0.00000 -111.560 0.59879E-01 2 0.29971 -109.154 0.53820E-01 3 0.34219 -109.111 0.53684E-01 4 0.35014 -109.111 0.53679E-01 5 0.35171 -109.112 0.53678E-01 6 0.35202 -109.112 0.53678E-01 LOG L.F. = -109.112 AT RHO = 0.35202 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.35202 0.01905 0.13800 2.55075 R-SQUARE = 0.9802 R-SQUARE ADJUSTED = 0.9765 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.14126E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.37584E-01 SUM OF SQUARED ERRORS-SSE= 0.53678E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -109.112 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 38 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR -0.71070 0.9074E-01 -7.832 0.000-0.786 -1.1085 -0.7107 LLAND 1.1919 0.3974 2.999 0.005 0.438 0.1783 1.1919 LMACHINE -0.32733 0.1071 -3.057 0.004-0.444 -0.2728 -0.3273 LENERGY 0.18553 0.1340 1.385 0.174 0.219 0.0972 0.1855 LFERT -0.22199E-01 0.8257E-01 -0.2689 0.789-0.044 -0.0333 -0.0222 LSEEDFD 0.11664E-01 0.1501 0.7771E-01 0.938 0.013 0.0087 0.0117 LOTHERS 0.98230E-01 0.1121 0.8764 0.386 0.141 0.0558 0.0982 CONSTANT 2.5528 1.652 1.545 0.131 0.243 0.0000 2.5528 |_* Confirm with a Hildreth-Lu estimate. |_auto loutput llabor lland lmachine lenergy lfert lseedfd lothers /GS LOGLOG REQUIRED MEMORY IS PAR= 14 CURRENT PAR= 2000 DEPENDENT VARIABLE = LOUTPUT ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 46 OBSERVATIONS BY GRID SEARCH TO ACCURACY OF .01 ITERATION RHO LOG L.F. SSE 1 -0.90000 -131.462 0.13721 2 -0.80000 -128.805 0.12395 3 -0.70000 -126.275 0.11189 4 -0.60000 -123.808 0.10100 5 -0.50000 -121.406 0.91300E-01 6 -0.40000 -119.091 0.82761E-01 7 -0.30000 -116.900 0.75372E-01 8 -0.20000 -114.879 0.69113E-01 9 -0.10000 -113.081 0.63958E-01 10 0.00000 -111.560 0.59879E-01 11 0.10000 -110.370 0.56846E-01 12 0.20000 -109.556 0.54834E-01 13 0.30000 -109.153 0.53819E-01 14 0.40000 -109.176 0.53780E-01 15 0.50000 -109.622 0.54698E-01 16 0.60000 -110.467 0.56548E-01 17 0.70000 -111.664 0.59276E-01 18 0.80000 -113.141 0.62732E-01 19 0.90000 -114.754 0.66360E-01 ITERATION RHO LOG L.F. SSE 20 0.31000 -109.136 0.53771E-01 21 0.32000 -109.123 0.53734E-01 22 0.33000 -109.115 0.53706E-01 23 0.34000 -109.111 0.53687E-01 24 0.35000 -109.111 0.53679E-01 25 0.36000 -109.116 0.53680E-01 26 0.37000 -109.124 0.53690E-01 27 0.38000 -109.137 0.53711E-01 28 0.39000 -109.155 0.53741E-01 29 0.40000 -109.176 0.53780E-01 30 0.41000 -109.202 0.53829E-01 31 0.42000 -109.232 0.53888E-01 32 0.43000 -109.267 0.53956E-01 33 0.44000 -109.305 0.54034E-01 34 0.45000 -109.348 0.54121E-01 35 0.46000 -109.394 0.54218E-01 36 0.47000 -109.445 0.54324E-01 37 0.48000 -109.500 0.54439E-01 38 0.49000 -109.559 0.54564E-01 39 0.35000 -109.111 0.53679E-01 LOG L.F. = -109.111 AT RHO = 0.35000 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.35000 0.01908 0.13812 2.53410 R-SQUARE = 0.9802 R-SQUARE ADJUSTED = 0.9765 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.14126E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.37584E-01 SUM OF SQUARED ERRORS-SSE= 0.53679E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -109.111 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 38 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR -0.71057 0.9068E-01 -7.836 0.000-0.786 -1.1084 -0.7106 LLAND 1.1910 0.3974 2.997 0.005 0.437 0.1782 1.1910 LMACHINE -0.32720 0.1070 -3.058 0.004-0.444 -0.2727 -0.3272 LENERGY 0.18528 0.1339 1.384 0.175 0.219 0.0971 0.1853 LFERT -0.22198E-01 0.8253E-01 -0.2690 0.789-0.044 -0.0333 -0.0222 LSEEDFD 0.12108E-01 0.1501 0.8069E-01 0.936 0.013 0.0090 0.0121 LOTHERS 0.98071E-01 0.1120 0.8755 0.387 0.141 0.0557 0.0981 CONSTANT 2.5559 1.651 1.548 0.130 0.244 0.0000 2.5559 |_* Sequential model reduction removing insignificant variables results in the |_* following model. |_AUTO loutput llabor lland lmachine lenergy /LOGLOG RSTAT REQUIRED MEMORY IS PAR= 13 CURRENT PAR= 2000 DEPENDENT VARIABLE = LOUTPUT ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 46 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100 ITERATION RHO LOG L.F. SSE 1 0.00000 -112.718 0.62971E-01 2 0.34375 -109.739 0.55170E-01 3 0.36233 -109.736 0.55144E-01 4 0.36403 -109.736 0.55143E-01 5 0.36419 -109.736 0.55143E-01 LOG L.F. = -109.736 AT RHO = 0.36419 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.36419 0.01886 0.13732 2.65222 R-SQUARE = 0.9796 R-SQUARE ADJUSTED = 0.9776 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.13450E-02 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.36674E-01 SUM OF SQUARED ERRORS-SSE= 0.55143E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -109.736 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 41 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR -0.72052 0.4305E-01 -16.74 0.000-0.934 -1.1239 -0.7205 LLAND 1.2158 0.3626 3.353 0.002 0.464 0.1819 1.2158 LMACHINE -0.34665 0.9421E-01 -3.680 0.001-0.498 -0.2889 -0.3467 LENERGY 0.23165 0.1135 2.040 0.048 0.304 0.1214 0.2317 CONSTANT 2.7690 1.334 2.076 0.044 0.308 0.0000 2.7690 DURBIN-WATSON = 1.9855 VON NEUMANN RATIO = 2.0296 RHO = -0.00035 RESIDUAL SUM = -0.51836E-02 RESIDUAL VARIANCE = 0.13456E-02 SUM OF ABSOLUTE ERRORS= 1.2699 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9796 R-SQUARE BETWEEN ANTILOGS OBSERVED AND PREDICTED = 0.9753 RUNS TEST: 20 RUNS, 24 POS, 0 ZERO, 22 NEG NORMAL STATISTIC = -1.1822 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = -0.64673E-02 MODIFIED FOR AUTO ORDER=1 |_* These results are not reasonable. The output-elasticity values for labor and machinery |_* are significantly negative, which makes no sense. |_* |_* Some possible explanations: |_* (1) The specification assumes that technology remains unchanged over a 46-year interval, |_* which is improbable. LOUTPUT has a very strong positive trend, so the anomalous |_* results could be explained by a pattern of technological change which is labour- |_* and machinery-saving, and possibly land-using. A cross-section study would be |_* less vulnerable to this form of misspecification. |_* (2) The functional form is double-log, which implies a Cobb-Douglas technology with |_* unity elasticity of substitution among factors of production. This is improbable |_* when there are seven factors of production, some of which are probably complements |_* (e.g., machinery and energy) rather than subatitutes. A more complex functional |_* form (for example, the translog) would be appropriate. |_* (3) Some of the factors (for example, machinery and land) make no allowance for changes |_* in capacity utilization, and so may misstate the amount of productive services |_* that are being provided by the factor in question. |_* |_* Technoolgical change is sometimes factored in by including a time trend in the equation. |_* In effect, the detrended values of the variables are related to one another, so that |_* technological change becomes less of a factor. |_AUTO loutput llabor lland lmachine lenergy YEAR /LOGLOG RSTAT REQUIRED MEMORY IS PAR= 13 CURRENT PAR= 2000 DEPENDENT VARIABLE = LOUTPUT ..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS LEAST SQUARES ESTIMATION 46 OBSERVATIONS BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100 ITERATION RHO LOG L.F. SSE 1 0.00000 -99.8069 0.35921E-01 2 0.03798 -99.7683 0.35860E-01 3 0.04522 -99.7666 0.35857E-01 4 0.04666 -99.7665 0.35856E-01 5 0.04695 -99.7665 0.35856E-01 LOG L.F. = -99.7665 AT RHO = 0.04695 ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC ESTIMATE VARIANCE ST.ERROR T-RATIO RHO 0.04695 0.02169 0.14728 0.31876 R-SQUARE = 0.9868 R-SQUARE ADJUSTED = 0.9851 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.89641E-03 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.29940E-01 SUM OF SQUARED ERRORS-SSE= 0.35856E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -99.7665 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 40 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR 0.90036E-01 0.1558 0.5778 0.567 0.091 0.1404 0.0900 LLAND 0.73505 0.2913 2.523 0.016 0.371 0.1100 0.7351 LMACHINE -0.72437E-01 0.8115E-01 -0.8926 0.377-0.140 -0.0604 -0.0724 LENERGY 0.66652E-01 0.7881E-01 0.8458 0.403 0.133 0.0349 0.0667 YEAR 0.21598E-01 0.4072E-02 5.304 0.000 0.643 1.1818 0.0216 CONSTANT -42.025 8.609 -4.881 0.000-0.611 0.0000 -42.0247 DURBIN-WATSON = 1.9149 VON NEUMANN RATIO = 1.9574 RHO = 0.00003 RESIDUAL SUM = -0.18041E-02 RESIDUAL VARIANCE = 0.89649E-03 SUM OF ABSOLUTE ERRORS= 0.99183 R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.9868 R-SQUARE BETWEEN ANTILOGS OBSERVED AND PREDICTED = 0.9827 RUNS TEST: 22 RUNS, 24 POS, 0 ZERO, 22 NEG NORMAL STATISTIC = -0.5846 DURBIN H STATISTIC (ASYMPTOTIC NORMAL) = 0.37381E-02 MODIFIED FOR AUTO ORDER=1 |_* This looks more reasonable. The autocorrelation disappears, and the labour elasticity |_* at least becomes positive (although machinery remains negative). On the other hand, |_* of the original variables, only land is statistically significant. |_* Reestimating the original model by OLS, with thie trend included: |_OLS loutput llabor lland lmachine lenergy lfert lseedfd lothers year /LOGLOG DWPVALUE REQUIRED MEMORY IS PAR= 30 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= LOUTPUT ...NOTE..SAMPLE RANGE SET TO: 1, 46 DURBIN-WATSON STATISTIC = 2.07982 DURBIN-WATSON POSITIVE AUTOCORRELATION TEST P-VALUE = 0.237048 NEGATIVE AUTOCORRELATION TEST P-VALUE = 0.762952 R-SQUARE = 0.9876 R-SQUARE ADJUSTED = 0.9849 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.90649E-03 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.30108E-01 SUM OF SQUARED ERRORS-SSE= 0.33540E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -98.2296 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 37 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR 0.18503 0.1725 1.073 0.290 0.174 0.2886 0.1850 LLAND 0.58401 0.3099 1.885 0.067 0.296 0.0874 0.5840 LMACHINE -0.68673E-01 0.8771E-01 -0.7830 0.439-0.128 -0.0572 -0.0687 LENERGY 0.32326E-01 0.9548E-01 0.3386 0.737 0.056 0.0169 0.0323 LFERT 0.43123E-01 0.5930E-01 0.7272 0.472 0.119 0.0647 0.0431 LSEEDFD 0.84910E-01 0.1103 0.7700 0.446 0.126 0.0634 0.0849 LOTHERS 0.23769E-01 0.7950E-01 0.2990 0.767 0.049 0.0135 0.0238 YEAR 0.21964E-01 0.4075E-02 5.390 0.000 0.663 1.2018 0.0220 CONSTANT -43.049 8.626 -4.990 0.000-0.634 0.0000 -43.0490 |_* Unfortunately, the process of model reduction does not give stable results. |_* The results are highly sensitive to the specification. |_* For example, sequentially removing LOTHERS, LENERGY, LMACHINE, and LSEEDFD gives |_OLS loutput llabor lland lfert year /LOGLOG DWPVALUE REQUIRED MEMORY IS PAR= 29 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= LOUTPUT ...NOTE..SAMPLE RANGE SET TO: 1, 46 DURBIN-WATSON STATISTIC = 2.03325 DURBIN-WATSON POSITIVE AUTOCORRELATION TEST P-VALUE = 0.335497 NEGATIVE AUTOCORRELATION TEST P-VALUE = 0.664503 R-SQUARE = 0.9870 R-SQUARE ADJUSTED = 0.9858 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.85532E-03 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.29246E-01 SUM OF SQUARED ERRORS-SSE= 0.35068E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -99.2543 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 41 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR 0.25354 0.1247 2.033 0.049 0.303 0.3955 0.2535 LLAND 0.41586 0.1829 2.274 0.028 0.335 0.0622 0.4159 LFERT 0.66697E-01 0.4797E-01 1.390 0.172 0.212 0.1000 0.0667 YEAR 0.24072E-01 0.3181E-02 7.566 0.000 0.763 1.3172 0.0241 CONSTANT -46.546 7.130 -6.528 0.000-0.714 0.0000 -46.5456 |_* which looks almost reasonable. However, removing the insignificant LFERT gives |_OLS loutput llabor lland year /LOGLOG DWPVALUE REQUIRED MEMORY IS PAR= 28 CURRENT PAR= 2000 OLS ESTIMATION 46 OBSERVATIONS DEPENDENT VARIABLE= LOUTPUT ...NOTE..SAMPLE RANGE SET TO: 1, 46 DURBIN-WATSON STATISTIC = 1.87541 DURBIN-WATSON POSITIVE AUTOCORRELATION TEST P-VALUE = 0.196097 NEGATIVE AUTOCORRELATION TEST P-VALUE = 0.803903 R-SQUARE = 0.9864 R-SQUARE ADJUSTED = 0.9855 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.87433E-03 STANDARD ERROR OF THE ESTIMATE-SIGMA = 0.29569E-01 SUM OF SQUARED ERRORS-SSE= 0.36722E-01 MEAN OF DEPENDENT VARIABLE = 4.3283 LOG OF THE LIKELIHOOD FUNCTION(IF DEPVAR LOG) = -100.314 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 42 DF P-VALUE CORR. COEFFICIENT AT MEANS LLABOR 0.16726 0.1093 1.530 0.134 0.230 0.2609 0.1673 LLAND 0.57129 0.1464 3.903 0.000 0.516 0.0855 0.5713 YEAR 0.23478E-01 0.3187E-02 7.366 0.000 0.751 1.2847 0.0235 CONSTANT -45.372 7.158 -6.338 0.000-0.699 0.0000 -45.3720 |_* and LLABOUR is no longer significant! |_* It would have to be concluded that not much reliability should be placed on |_* these estimates. |_* |_* Further, to anticipate chapter 10, it appears (using the command |_* COINT loutput llabor lland lmachine lenergy lfert lseedfd lothers *) |_* that most of the variables have a unit root, but (from the command |_* COINT loutput llabor lland lmachine lenergy lfert lseedfd lothers/ TYPE=RESD *) |_* are not cointegrated. Therefore, what correlation does exist in the relationship |_* may well be spurious. The unstable results that appear in the process of |_* model reduction supports this possibility. |_* |_* Updated March 6, 2008. ..INPUT FILE COMPLETED..TYPE A NEW COMMAND OR TYPE: STOP