﻿VAR system, lag order 4
OLS estimates, observations 1960:2-2014:4 (T = 219)
Log-likelihood = 4542.8239
Determinant of covariance matrix = 6.6078992e-025
AIC = -40.5281
BIC = -38.9032
HQC = -39.8718
Portmanteau test: LB(48) = 1139.44, df = 1100 [0.1990]

Equation 1: d_J
Heteroskedasticity-robust standard errors, variant HC1

             coefficient   std. error   t-ratio    p-value
  --------------------------------------------------------
  const      −0.00398512   0.00112818   −3.532     0.0005  ***
  d_J_1       0.253486     0.117191      2.163     0.0317  **
  d_J_2      −0.426909     0.154901     −2.756     0.0064  ***
  d_J_3       0.309478     0.0989298     3.128     0.0020  ***
  d_J_4       0.0122494    0.131710      0.09300   0.9260 
  ld_M1_1     0.00784719   0.0549128     0.1429    0.8865 
  ld_M1_2     0.0357174    0.0665437     0.5368    0.5920 
  ld_M1_3     0.137736     0.0603912     2.281     0.0236  **
  ld_M1_4    −0.120318     0.0479997    −2.507     0.0130  **
  ld_P1_1     0.331213     0.205479      1.612     0.1086 
  ld_P1_2     0.362514     0.186790      1.941     0.0537  *
  ld_P1_3    −0.308619     0.197697     −1.561     0.1201 
  ld_P1_4    −0.318031     0.234116     −1.358     0.1759 
  ld_Y_1      0.141661     0.0591094     2.397     0.0175  **
  ld_Y_2      0.153985     0.0732111     2.103     0.0367  **
  ld_Y_3     −0.0396250    0.0551539    −0.7184    0.4733 
  ld_Y_4     −0.0209936    0.0536777    −0.3911    0.6961 
  ld_K_1      0.187932     0.220161      0.8536    0.3944 
  ld_K_2      0.137875     0.350156      0.3938    0.6942 
  ld_K_3     −0.275305     0.272559     −1.010     0.3137 
  ld_K_4      0.0330166    0.184525      0.1789    0.8582 

Mean dependent var  −0.000172   S.D. dependent var   0.006771
Sum squared resid    0.006617   S.E. of regression   0.005781
R-squared            0.338077   Adjusted R-squared   0.271216
F(20, 198)           3.275197   P-value(F)           9.89e-06
rho                  0.020676   Durbin-Watson        1.952145

F-tests of zero restrictions:

All lags of d_J             F(4, 198) =   3.5068 [0.0086]
All lags of ld_M1           F(4, 198) =   3.3088 [0.0119]
All lags of ld_P1           F(4, 198) =   1.5805 [0.1809]
All lags of ld_Y            F(4, 198) =   3.7595 [0.0057]
All lags of ld_K            F(4, 198) =   3.4895 [0.0089]
All vars, lag 4             F(5, 198) =   1.4514 [0.2075]

Equation 2: ld_M1
Heteroskedasticity-robust standard errors, variant HC1

             coefficient    std. error    t-ratio    p-value 
  -----------------------------------------------------------
  const       0.00367246    0.00286232    1.283      0.2010  
  d_J_1      −0.649126      0.104906     −6.188      3.44e-09 ***
  d_J_2      −0.0373789     0.105138     −0.3555     0.7226  
  d_J_3      −0.249588      0.127851     −1.952      0.0523   *
  d_J_4      −0.108965      0.104033     −1.047      0.2962  
  ld_M1_1     0.454239      0.0832767     5.455      1.45e-07 ***
  ld_M1_2     0.146591      0.0739913     1.981      0.0490   **
  ld_M1_3     0.0316559     0.0887668     0.3566     0.7218  
  ld_M1_4     0.0549386     0.0826871     0.6644     0.5072  
  ld_P1_1     0.469914      0.242591      1.937      0.0542   *
  ld_P1_2    −0.000755599   0.251605     −0.003003   0.9976  
  ld_P1_3    −0.00513231    0.226547     −0.02265    0.9819  
  ld_P1_4    −0.232341      0.229194     −1.014      0.3119  
  ld_Y_1     −0.0193594     0.0890161    −0.2175     0.8281  
  ld_Y_2      0.0181404     0.0770717     0.2354     0.8142  
  ld_Y_3      0.0908628     0.0698883     1.300      0.1951  
  ld_Y_4      0.0949581     0.0764055     1.243      0.2154  
  ld_K_1     −0.320978      0.385134     −0.8334     0.4056  
  ld_K_2     −0.273050      0.576487     −0.4736     0.6363  
  ld_K_3      1.19361       0.561718      2.125      0.0348   **
  ld_K_4     −0.957188      0.368566     −2.597      0.0101   **

Mean dependent var   0.013838   S.D. dependent var   0.012923
Sum squared resid    0.016144   S.E. of regression   0.009030
R-squared            0.556549   Adjusted R-squared   0.511756
F(20, 198)           15.46887   P-value(F)           1.68e-30
rho                 −0.017816   Durbin-Watson        2.030406

F-tests of zero restrictions:

All lags of d_J             F(4, 198) =   10.877 [0.0000]
All lags of ld_M1           F(4, 198) =   28.400 [0.0000]
All lags of ld_P1           F(4, 198) =   2.2821 [0.0619]
All lags of ld_Y            F(4, 198) =   1.1258 [0.3455]
All lags of ld_K            F(4, 198) =   1.7445 [0.1417]
All vars, lag 4             F(5, 198) =   1.8938 [0.0970]

Equation 3: ld_P1
Heteroskedasticity-robust standard errors, variant HC1

             coefficient    std. error     t-ratio    p-value 
  ------------------------------------------------------------
  const      −0.000637194   0.000593179   −1.074      0.2840  
  d_J_1       0.0515316     0.0373335      1.380      0.1690  
  d_J_2       0.0222629     0.0437817      0.5085     0.6117  
  d_J_3      −0.00623999    0.0428322     −0.1457     0.8843  
  d_J_4       0.0383528     0.0423740      0.9051     0.3665  
  ld_M1_1     0.000166377   0.0207603      0.008014   0.9936  
  ld_M1_2    −0.0125042     0.0247911     −0.5044     0.6146  
  ld_M1_3     0.0298694     0.0207479      1.440      0.1515  
  ld_M1_4     0.00647990    0.0187536      0.3455     0.7301  
  ld_P1_1     0.519322      0.0942165      5.512      1.10e-07 ***
  ld_P1_2     0.130268      0.0895735      1.454      0.1474  
  ld_P1_3     0.139167      0.0765366      1.818      0.0705   *
  ld_P1_4     0.137942      0.0766372      1.800      0.0734   *
  ld_Y_1     −0.0187771     0.0249893     −0.7514     0.4533  
  ld_Y_2      0.00689375    0.0276696      0.2491     0.8035  
  ld_Y_3      0.0250232     0.0272368      0.9187     0.3594  
  ld_Y_4      0.0284304     0.0317720      0.8948     0.3720  
  ld_K_1      0.0769823     0.0853346      0.9021     0.3681  
  ld_K_2     −0.140869      0.137448      −1.025      0.3067  
  ld_K_3      0.210090      0.154651       1.358      0.1759  
  ld_K_4     −0.0641136     0.102973      −0.6226     0.5342  

Mean dependent var   0.008394   S.D. dependent var   0.005831
Sum squared resid    0.001237   S.E. of regression   0.002500
R-squared            0.833076   Adjusted R-squared   0.816215
F(20, 198)           39.07544   P-value(F)           9.54e-58
rho                 −0.003216   Durbin-Watson        1.996429

F-tests of zero restrictions:

All lags of d_J             F(4, 198) =   1.3923 [0.2380]
All lags of ld_M1           F(4, 198) =   1.3570 [0.2503]
All lags of ld_P1           F(4, 198) =   105.55 [0.0000]
All lags of ld_Y            F(4, 198) =  0.63958 [0.6349]
All lags of ld_K            F(4, 198) =   1.7318 [0.1444]
All vars, lag 4             F(5, 198) =   1.2980 [0.2662]

Equation 4: ld_Y
Heteroskedasticity-robust standard errors, variant HC1

             coefficient    std. error   t-ratio    p-value 
  ----------------------------------------------------------
  const       0.000279635   0.00185185    0.1510    0.8801  
  d_J_1       0.163759      0.100167      1.635     0.1037  
  d_J_2      −0.447222      0.111335     −4.017     8.37e-05 ***
  d_J_3       0.154424      0.102144      1.512     0.1322  
  d_J_4      −0.287321      0.101612     −2.828     0.0052   ***
  ld_M1_1    −0.0617168     0.0591424    −1.044     0.2980  
  ld_M1_2     0.156114      0.0643871     2.425     0.0162   **
  ld_M1_3    −0.124237      0.0574695    −2.162     0.0318   **
  ld_M1_4     0.0690787     0.0472550     1.462     0.1454  
  ld_P1_1     0.0100028     0.254585      0.03929   0.9687  
  ld_P1_2     0.0651184     0.350874      0.1856    0.8530  
  ld_P1_3    −0.304941      0.268472     −1.136     0.2574  
  ld_P1_4     0.189823      0.228931      0.8292    0.4080  
  ld_Y_1      0.255403      0.0772425     3.307     0.0011   ***
  ld_Y_2      0.141070      0.0826552     1.707     0.0894   *
  ld_Y_3     −0.0178239     0.0646401    −0.2757    0.7830  
  ld_Y_4      0.127254      0.0773508     1.645     0.1015  
  ld_K_1      0.550850      0.335019      1.644     0.1017  
  ld_K_2     −0.982975      0.552702     −1.778     0.0769   *
  ld_K_3      1.70805       0.710522      2.404     0.0171   **
  ld_K_4     −0.860279      0.401889     −2.141     0.0335   **

Mean dependent var   0.007522   S.D. dependent var   0.008400
Sum squared resid    0.010265   S.E. of regression   0.007200
R-squared            0.332610   Adjusted R-squared   0.265197
F(20, 198)           4.771312   P-value(F)           2.38e-09
rho                 −0.011453   Durbin-Watson        2.015237

F-tests of zero restrictions:

All lags of d_J             F(4, 198) =   5.2510 [0.0005]
All lags of ld_M1           F(4, 198) =   2.2512 [0.0650]
All lags of ld_P1           F(4, 198) =  0.44151 [0.7785]
All lags of ld_Y            F(4, 198) =   6.1884 [0.0001]
All lags of ld_K            F(4, 198) =   5.5493 [0.0003]
All vars, lag 4             F(5, 198) =   2.4134 [0.0376]

Equation 5: ld_K
Heteroskedasticity-robust standard errors, variant HC1

             coefficient    std. error     t-ratio     p-value 
  -------------------------------------------------------------
  const       0.000981174   0.000493955    1.986      0.0484    **
  d_J_1      −0.00717982    0.00976732    −0.7351     0.4632   
  d_J_2      −0.0155997     0.0130499     −1.195      0.2334   
  d_J_3       0.00107188    0.00921689     0.1163     0.9075   
  d_J_4      −0.00105706    0.0117781     −0.08975    0.9286   
  ld_M1_1    −0.00793239    0.00610769    −1.299      0.1955   
  ld_M1_2     0.00501110    0.0100322      0.4995     0.6180   
  ld_M1_3    −0.0128443     0.00614950    −2.089      0.0380    **
  ld_M1_4     2.20890e-05   0.00498311     0.004433   0.9965   
  ld_P1_1    −0.00415762    0.0187683     −0.2215     0.8249   
  ld_P1_2     0.0200290     0.0253474      0.7902     0.4304   
  ld_P1_3    −0.0189672     0.0234605     −0.8085     0.4198   
  ld_P1_4     0.00784560    0.0196059      0.4002     0.6895   
  ld_Y_1      0.0122237     0.0183228      0.6671     0.5055   
  ld_Y_2      0.0231741     0.0185029      1.252      0.2119   
  ld_Y_3     −0.00438663    0.0158254     −0.2772     0.7819   
  ld_Y_4      0.0302114     0.0196748      1.536      0.1262   
  ld_K_1      1.46447       0.201004       7.286      7.43e-012 ***
  ld_K_2     −0.548518      0.238665      −2.298      0.0226    **
  ld_K_3     −0.290527      0.245687      −1.183      0.2384   
  ld_K_4      0.208680      0.156250       1.336      0.1832   

Mean dependent var   0.007644   S.D. dependent var   0.003783
Sum squared resid    0.000280   S.E. of regression   0.001188
R-squared            0.910355   Adjusted R-squared   0.901300
F(20, 198)           118.3352   P-value(F)           1.43e-98
rho                 −0.061438   Durbin-Watson        1.870055

F-tests of zero restrictions:

All lags of d_J             F(4, 198) =  0.80825 [0.5212]
All lags of ld_M1           F(4, 198) =   1.5191 [0.1980]
All lags of ld_P1           F(4, 198) =  0.21046 [0.9324]
All lags of ld_Y            F(4, 198) =   1.1713 [0.3247]
All lags of ld_K            F(4, 198) =   24.743 [0.0000]
All vars, lag 4             F(5, 198) =   1.3100 [0.2612]

For the system as a whole:

  Null hypothesis: the longest lag is 3
  Alternative hypothesis: the longest lag is 4
  Likelihood ratio test: Chi-square(25) = 72.3065 [0.0000]

  Comparison of information criteria:
  Lag order 4: AIC = -40.5281, BIC = -38.9032, HQC = -39.8718
  Lag order 3: AIC = -40.4262, BIC = -39.1882, HQC = -39.9262
