Example of GMM estimation (Arellano-Bond) using ox DPD (fmrisc /res5/ox21/packages/dpd) documented at http://fmwww.bc.edu/EC/Ec_Res_Info.html ======================================================================================= $ pwd /res5/ox21/packages/dpd $ cat abest1.ox #include #import main() { decl dpd = new DPD(), time = timer(), x; dpd.Load("abdata.in7"); // load data dpd.SetYear("YEAR"); // specify columns with years dpd.Select(Y_VAR, {"n", 0, 2}); // formulate model dpd.Select(X_VAR, {"w", 0, 1, "k", 0, 0, "ys", 0, 1}); dpd.Select(I_VAR, {"w", 0, 1, "k", 0, 0, "ys", 0, 1}); dpd.Gmm("n", 2, 99); // GMM-type instrument dpd.SetDummies(D_CONSTANT + D_TIME);// specify dummies dpd.SetTest(1, 2);// specification,Sargan,AR 1-2 tests dpd.Estimate(); // 1-step estimation print("\n\n***** Arellano & Bond (1991), Table 4 (b)"); dpd.SetMethod(M_2STEP); dpd.Estimate(); // 2-step estimation // this gives table 4, column (b) print("\ntime: ", timespan(time), "\n"); delete dpd; // finished with object } ======================================================================================= $ ox abest1.ox Ox version 2.10 (AIX) (C) J.A. Doornik, 1994-99 DPD package version 1.0, object created on 11-11-1999 ------------- One-step estimation using DPD ------------- Dependent variable: n Transformation used: first differences Transformed instruments: w w(-1) k ys ys(-1) Level instruments: Dummies Gmm(n,2,99) Coefficient Std.Error t-value t-prob Dn(-1) 0.534614 0.1274 4.20 0.000 Dn(-2) -0.0750692 0.04344 1.73 0.084 Dw -0.591573 0.06191 9.56 0.000 Dw(-1) 0.291510 0.09556 3.05 0.002 Dk 0.358502 0.03487 10.3 0.000 Dys 0.597199 0.1273 4.69 0.000 Dys(-1) -0.611705 0.1679 3.64 0.000 Constant 0.00542720 0.01281 0.424 0.672 T1980 0.00560768 0.02008 0.279 0.780 T1981 -0.0383049 0.01763 2.17 0.030 T1982 -0.0277852 0.01852 1.50 0.134 T1983 -0.00685022 0.01902 0.360 0.719 T1984 0.00631375 0.02375 0.266 0.790 no. of observations 611 no. of parameters 13 RSS 8.2193799364 TSS 12.599978399 ESE 0.1172381 ESE^2 0.01374478 ESE levels 0.08289989 constant: yes time dummies: 5 number of individuals 140 (derived from year) longest time series 6 [1979 - 1984] shortest time series 4 (unbalanced panel) Wald (joint): Chi^2(7) = 352.6 [0.000] ** Wald (dummy): Chi^2(6) = 11.25 [0.081] Wald (time): Chi^2(6) = 11.25 [0.081] Sargan test: Chi^2(25) = 73.86 [0.000] ** AR(1) test: N(0,1) = -3.409 [0.001] ** AR(2) test: N(0,1) = -0.3695 [0.712] ***** Arellano & Bond (1991), Table 4 (b) ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: first differences Transformed instruments: w w(-1) k ys ys(-1) Level instruments: Dummies Gmm(n,2,99) Coefficient Std.Error t-value t-prob Dn(-1) 0.534614 0.1664 3.21 0.001 Dn(-2) -0.0750692 0.06798 1.10 0.270 Dw -0.591573 0.1679 3.52 0.000 Dw(-1) 0.291510 0.1411 2.07 0.039 Dk 0.358502 0.05383 6.66 0.000 Dys 0.597199 0.1719 3.47 0.001 Dys(-1) -0.611705 0.2118 2.89 0.004 Constant 0.00542720 0.009714 0.559 0.577 T1980 0.00560768 0.01538 0.365 0.715 T1981 -0.0383049 0.01745 2.20 0.028 T1982 -0.0277852 0.01791 1.55 0.121 T1983 -0.00685022 0.02206 0.311 0.756 T1984 0.00631375 0.01971 0.320 0.749 no. of observations 611 no. of parameters 13 RSS 8.2193799364 TSS 12.599978399 ESE 0.1172381 ESE^2 0.01374478 ESE levels 0.08289989 constant: yes time dummies: 5 number of individuals 140 (derived from year) longest time series 6 [1979 - 1984] shortest time series 4 (unbalanced panel) Wald (joint): Chi^2(7) = 219.6 [0.000] ** Wald (dummy): Chi^2(6) = 11.45 [0.075] Wald (time): Chi^2(6) = 11.45 [0.075] AR(1) test: N(0,1) = -2.493 [0.013] * AR(2) test: N(0,1) = -0.3594 [0.719] ------------- Two-step estimation using DPD ------------- Coefficient Std.Error t-value t-prob Dn(-1) 0.474151 0.08530 5.56 0.000 Dn(-2) -0.0529675 0.02728 1.94 0.053 Dw -0.513205 0.04935 10.4 0.000 Dw(-1) 0.224640 0.08006 2.81 0.005 Dk 0.292723 0.03946 7.42 0.000 Dys 0.609775 0.1085 5.62 0.000 Dys(-1) -0.446373 0.1248 3.58 0.000 Constant 0.0105090 0.007251 1.45 0.148 T1980 0.00363321 0.01273 0.285 0.775 T1981 -0.0509621 0.01371 3.72 0.000 T1982 -0.0321490 0.01399 2.30 0.022 T1983 -0.0123558 0.01284 0.962 0.336 T1984 -0.0207295 0.01368 1.52 0.130 no. of observations 611 no. of parameters 13 RSS 8.0804358435 TSS 12.599978399 ESE 0.116243 ESE^2 0.01351243 ESE levels 0.08219621 Standard errors for 2-step estimates are not reliable. Wald (joint): Chi^2(7) = 372.0 [0.000] ** Wald (dummy): Chi^2(6) = 26.90 [0.000] ** Wald (time): Chi^2(6) = 26.90 [0.000] ** Sargan test: Chi^2(25) = 30.11 [0.220] AR(1) test: N(0,1) = -2.428 [0.015] * AR(2) test: N(0,1) = -0.3325 [0.739] time: 2.38 ======================================================================================= $ cat abest2.ox #include #import main() { decl dpd = new DPD(), time = timer(), x; dpd.Load("abdata.in7"); // load data dpd.SetYear("YEAR"); // specify columns with years dpd.SetGroup("IND"); // and with groups dpd.Select(Y_VAR, {"n", 0, 0}); // formulate model dpd.Select(X_VAR, {"n", 1, 2, "w", 0, 1, "k", 0, 2, "ys", 0, 2}); dpd.SetDummies(D_CONSTANT + D_TIME); // time, constant dpd.SetOptions(TRUE); // use robust standard errors dpd.SetTest(1, 2); // specification,Sargan,AR 1-2 tests //----------------- column (g) ------------------------ print("\n***** Arellano & Bond (1991), Table 5 (g)\n"); dpd.SetTransform(T_NONE); // estimate in levels dpd.Estimate(); // 1-step estimation //------------ column (h) using within ---------------- print("\n***** Arellano & Bond (1991), Table 5 (within)\n"); dpd.SetTransform(T_WITHIN); // proper within estimation dpd.Estimate(); // 1-step estimation //----------------- column (h) ------------------------ print("\n***** Arellano & Bond (1991), Table 5 (h)\n"); dpd.SetTransform(T_DEVIATIONS); // estimate within dpd.Estimate(); // 1-step estimation //----------------- column (e) ------------------------ print("\n***** Arellano & Bond (1991), Table 5 (e)\n"); dpd.Select(I_VAR, {"n", 2, 3, "w", 0, 1, "k", 0, 2, "ys", 0, 2}); dpd.SetTransform(T_DIFFERENCES); // estimate 1st diff dpd.Estimate(); // 1-step estimation //------------------- column (f) ------------------------ print("\n***** Arellano & Bond (1991), Table 5 (f)\n"); dpd.DeSelect(); dpd.SetYear("YEAR"); // specify columns with years dpd.Select(Y_VAR, {"n", 0, 0}); // formulate model dpd.Select(X_VAR, {"n", 1, 2, "w", 0, 1, "k", 0, 2, "ys", 0, 2}); dpd.Select(I_VAR, {"n", 2, 2, "w", 0, 1, "k", 0, 2, "ys", 0, 2}); dpd.Select(IL_VAR, {"n", 3, 3}); dpd.SetTransform(T_DIFFERENCES); // estimate 1st diff dpd.Estimate(); // 1-step estimation delete dpd; // finished with object print("\ntime: ", timespan(time), "\n"); } ======================================================================================= $ ox abest2.ox Ox version 2.10 (AIX) (C) J.A. Doornik, 1994-99 DPD package version 1.0, object created on 11-11-1999 ***** Arellano & Bond (1991), Table 5 (g) ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: none Coefficient Std.Error t-value t-prob n(-1) 1.04464 0.05106 20.5 0.000 n(-2) -0.0765427 0.04811 1.59 0.112 w -0.523673 0.1716 3.05 0.002 w(-1) 0.476754 0.1693 2.82 0.005 k 0.343395 0.04796 7.16 0.000 k(-1) -0.201899 0.06411 3.15 0.002 k(-2) -0.115647 0.03538 3.27 0.001 ys 0.432874 0.1764 2.45 0.014 ys(-1) -0.767912 0.2478 3.10 0.002 ys(-2) 0.312472 0.1304 2.40 0.017 Constant 0.274727 0.3149 0.872 0.383 T1979 0.0158888 0.008912 1.78 0.075 T1980 0.0219932 0.01478 1.49 0.137 T1981 -0.0221533 0.02389 0.927 0.354 T1982 -0.0150344 0.02112 0.712 0.477 T1983 0.00739307 0.01935 0.382 0.703 T1984 0.0153955 0.02014 0.765 0.445 R^2 0.9943935 no. of observations 751 no. of parameters 17 RSS 7.5737817162 TSS 1350.8917476 ESE 0.10158 ESE^2 0.0103185 constant: yes time dummies: 6 number of individuals 140 (derived from year) longest time series 7 [1978 - 1984] shortest time series 5 (unbalanced panel) Wald (joint): Chi^2(10) = 2.199e+05 [0.000] ** Wald (dummy): Chi^2(7) = 14.02 [0.051] Wald (time): Chi^2(6) = 14.02 [0.029] * AR(1) test: N(0,1) = 1.468 [0.142] AR(2) test: N(0,1) = -1.029 [0.304] ***** Arellano & Bond (1991), Table 5 (within) ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: within groups (deviation from individual means) Coefficient Std.Error t-value t-prob n(-1) 0.734583 0.05927 12.4 0.000 n(-2) -0.138069 0.07737 1.78 0.075 w -0.566515 0.1568 3.61 0.000 w(-1) 0.308888 0.1410 2.19 0.029 k 0.391713 0.05523 7.09 0.000 k(-1) -0.0827196 0.05229 1.58 0.114 k(-2) -0.0294126 0.04271 0.689 0.491 ys 0.507163 0.1403 3.62 0.000 ys(-1) -0.614259 0.2030 3.03 0.003 ys(-2) 0.0370549 0.1263 0.293 0.769 T1979 0.0114337 0.008019 1.43 0.154 T1980 0.0210796 0.008389 2.51 0.012 T1981 -0.0108935 0.01086 1.00 0.316 T1982 -0.0185528 0.008625 2.15 0.032 T1983 -0.0111981 0.01422 0.788 0.431 T1984 0.00236981 0.01602 0.148 0.882 R^2 0.7970538 no. of observations 751 no. of parameters 156 RSS 5.2591612193 TSS 25.914063478 ESE 0.09401556 ESE^2 0.008838926 constant: no time dummies: 6 (dummies imply constant) number of individuals 140 (derived from year) longest time series 7 [1978 - 1984] shortest time series 5 (unbalanced panel) Wald (joint): Chi^2(10) = 1715. [0.000] ** Wald (dummy): Chi^2(6) = 9.425 [0.151] Wald (time): Chi^2(6) = 9.425 [0.151] AR(1) test: N(0,1) = -3.894 [0.000] ** AR(2) test: N(0,1) = -4.673 [0.000] ** ***** Arellano & Bond (1991), Table 5 (h) ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: orthogonal deviations Coefficient Std.Error t-value t-prob On(-1) 0.734465 0.05821 12.6 0.000 On(-2) -0.141171 0.07658 1.84 0.066 Ow -0.556846 0.1555 3.58 0.000 Ow(-1) 0.326033 0.1426 2.29 0.023 Ok 0.384878 0.05551 6.93 0.000 Ok(-1) -0.0837814 0.05266 1.59 0.112 Ok(-2) -0.0254546 0.04206 0.605 0.545 Oys 0.520666 0.1934 2.69 0.007 Oys(-1) -0.659444 0.2083 3.17 0.002 Oys(-2) 0.00136125 0.1393 0.00977 0.992 Constant 0.00879628 0.01539 0.572 0.568 T1980 0.0104788 0.008829 1.19 0.236 T1981 0.0296796 0.01428 2.08 0.038 T1982 0.00475290 0.02516 0.189 0.850 T1983 -0.00478264 0.02751 0.174 0.862 T1984 -0.0147255 0.02185 0.674 0.501 R^2 0.6885331 no. of observations 611 no. of parameters 16 RSS 5.238389296 TSS 16.818448096 ESE 0.09382972 ESE^2 0.008804016 constant: yes time dummies: 5 number of individuals 140 (derived from year) longest time series 6 [1979 - 1984] shortest time series 4 (unbalanced panel) Wald (joint): Chi^2(10) = 1423. [0.000] ** Wald (dummy): Chi^2(6) = 10.91 [0.091] Wald (time): Chi^2(6) = 10.91 [0.091] AR(1) test: N(0,1) = -5.514 [0.000] ** AR(2) test: N(0,1) = 0.3408 [0.733] ***** Arellano & Bond (1991), Table 5 (e) ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: first differences Transformed instruments: n(-2) n(-3) w w(-1) k k(-1) k(-2) ys ys(-1) ys(-2) Level instruments: Dummies Coefficient Std.Error t-value t-prob Dn(-1) 1.42277 1.001 1.42 0.156 Dn(-2) -0.164552 0.1276 1.29 0.198 Dw -0.752467 0.2298 3.27 0.001 Dw(-1) 0.962763 0.7683 1.25 0.211 Dk 0.322168 0.1047 3.08 0.002 Dk(-1) -0.324879 0.3861 0.842 0.400 Dk(-2) -0.0953951 0.1234 0.773 0.440 Dys 0.766087 0.3114 2.46 0.014 Dys(-1) -1.36188 0.8814 1.55 0.123 Dys(-2) 0.321300 0.4156 0.773 0.440 Constant 0.0161201 0.02491 0.647 0.518 T1981 -0.0574197 0.03174 1.81 0.071 T1982 -0.0308750 0.03871 0.798 0.425 T1983 -0.0180198 0.04164 0.433 0.665 T1984 -0.0108950 0.03812 0.286 0.775 no. of observations 471 no. of parameters 15 RSS 16.213037205 TSS 10.637399173 ESE 0.1885601 ESE^2 0.03555491 ESE levels 0.1333321 constant: yes time dummies: 4 number of individuals 140 (derived from year) longest time series 5 [1980 - 1984] shortest time series 3 (unbalanced panel) Wald (joint): Chi^2(10) = 199.3 [0.000] ** Wald (dummy): Chi^2(5) = 5.300 [0.380] Wald (time): Chi^2(5) = 5.300 [0.380] AR(1) test: N(0,1) = -1.237 [0.216] AR(2) test: N(0,1) = -0.7814 [0.435] ***** Arellano & Bond (1991), Table 5 (f) ------------- One-step estimation using DPD ------------- Dependent variable: n Transformation used: first differences Transformed instruments: n(-2) w w(-1) k k(-1) k(-2) ys ys(-1) ys(-2) Level instruments: Dummies n(-3) Coefficient Std.Error t-value t-prob Dn(-1) 2.30762 1.002 2.30 0.022 Dn(-2) -0.224027 0.1203 1.86 0.063 Dw -0.810362 0.1692 4.79 0.000 Dw(-1) 1.42224 0.6214 2.29 0.022 Dk 0.253097 0.09485 2.67 0.008 Dk(-1) -0.552461 0.3165 1.75 0.081 Dk(-2) -0.212636 0.1360 1.56 0.118 Dys 0.990576 0.3365 2.94 0.003 Dys(-1) -1.93791 0.7846 2.47 0.014 Dys(-2) 0.487084 0.3558 1.37 0.171 Constant 0.0626484 0.04096 1.53 0.127 T1980 -0.0172953 0.04471 0.387 0.699 T1981 -0.100226 0.05071 1.98 0.049 T1982 -0.0565573 0.04350 1.30 0.194 T1983 -0.0495875 0.05109 0.971 0.332 T1984 -0.0566218 0.06242 0.907 0.365 no. of observations 611 no. of parameters 16 RSS 37.276848257 TSS 12.599978399 ESE 0.2503002 ESE^2 0.06265017 ESE levels 0.1769889 constant: yes time dummies: 5 number of individuals 140 (derived from year) longest time series 6 [1979 - 1984] shortest time series 4 (unbalanced panel) Wald (joint): Chi^2(10) = 116.2 [0.000] ** Wald (dummy): Chi^2(6) = 5.182 [0.521] Wald (time): Chi^2(6) = 5.182 [0.521] AR(1) test: N(0,1) = -2.165 [0.030] * AR(2) test: N(0,1) = -1.128 [0.259] time: 2.72 ======================================================================================= $ cat bbest1.ox #include #import main() { decl dpd = new DPD(), time = timer(), x; dpd.Load("abdata.in7"); // load data print("\n\n***** Blundell & Bond (1998), Table 4: 1976-86 GMM-DIF"); // decl year = dpd.GetVar("YEAR"), yearsub; // yearsub = year .< 1979 .? M_NAN .: year; // dpd.Append(yearsub, "yearsub"); // dpd.SetYear("yearsub"); // specify columns with years dpd.SetYear("YEAR"); // specify columns with years dpd.SetGroup("IND"); dpd.Select(Y_VAR, {"n", 0, 1}); // formulate model dpd.Select(X_VAR, {"w", 0, 1, "k", 0, 1}); dpd.SetDummies(D_CONSTANT + D_TIME); // specify dummies dpd.Gmm("n", 2, 99); // GMM-type instruments dpd.Gmm("w", 2, 99); dpd.Gmm("k", 2, 99); dpd.SetTest(1, 2); // specification,Sargan,AR 1-2 tests dpd.SetMethod(M_2STEP); dpd.Estimate(); // 2-step estimation print("\n\n***** Blundell & Bond (1998), Table 4: 1976-86 GMM-SYS"); dpd.GmmLevel("n", 1, 1); // GMM instruments for levels dpd.GmmLevel("w", 1, 1); dpd.GmmLevel("k", 1, 1); dpd.SetMethod(M_2STEP); dpd.Estimate(); // 2-step estimation // print("\n\n***** Blundell & Bond (1998), 1976-86 GMM-DEV-SYS"); // // dpd.SetTransform(T_DEVIATIONS); // orthog deviations // dpd.SetMethod(M_2STEP); // dpd.Estimate(); // 2-step estimation print("\ntime: ", timespan(time), "\n"); delete dpd; // finished with object } ======================================================================================= $ ox bbest1.ox Ox version 2.10 (AIX) (C) J.A. Doornik, 1994-99 DPD package version 1.0, object created on 11-11-1999 ***** Blundell & Bond (1998), Table 4: 1976-86 GMM-DIF ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: first differences Level instruments: Dummies Gmm(n,2,99) Gmm(w,2,99) Gmm(k,2,99) Coefficient Std.Error t-value t-prob Dn(-1) 0.707470 0.08418 8.40 0.000 Dw -0.708797 0.1171 6.05 0.000 Dw(-1) 0.500015 0.1113 4.49 0.000 Dk 0.465978 0.1010 4.61 0.000 Dk(-1) -0.215131 0.08585 2.51 0.012 Constant 0.00576354 0.01661 0.347 0.729 T1979 0.00210950 0.01775 0.119 0.905 T1980 -0.0265558 0.01946 1.36 0.173 T1981 -0.0326771 0.02329 1.40 0.161 T1982 0.0223883 0.02546 0.879 0.379 T1983 0.0188752 0.02359 0.800 0.424 T1984 0.0107431 0.02692 0.399 0.690 no. of observations 751 no. of parameters 12 RSS 12.589373919 TSS 13.736140817 ESE 0.1305208 ESE^2 0.01703569 ESE levels 0.09229217 constant: yes time dummies: 6 number of individuals 140 (derived from year) longest time series 7 [1978 - 1984] shortest time series 5 (unbalanced panel) Wald (joint): Chi^2(5) = 324.6 [0.000] ** Wald (dummy): Chi^2(7) = 14.76 [0.039] * Wald (time): Chi^2(7) = 14.76 [0.039] * AR(1) test: N(0,1) = -5.596 [0.000] ** AR(2) test: N(0,1) = -0.1367 [0.891] ------------- Two-step estimation using DPD ------------- Coefficient Std.Error t-value t-prob Dn(-1) 0.678787 0.01678 40.5 0.000 Dw -0.719830 0.01569 45.9 0.000 Dw(-1) 0.462691 0.03351 13.8 0.000 Dk 0.453905 0.02112 21.5 0.000 Dk(-1) -0.191492 0.02426 7.89 0.000 Constant 0.00525824 0.007063 0.745 0.457 T1979 -0.00238732 0.008580 0.278 0.781 T1980 -0.0258996 0.008907 2.91 0.004 T1981 -0.0317157 0.008056 3.94 0.000 T1982 0.0226916 0.01055 2.15 0.032 T1983 0.0246048 0.009343 2.63 0.009 T1984 0.0105050 0.007540 1.39 0.164 no. of observations 751 no. of parameters 12 RSS 12.168838065 TSS 13.736140817 ESE 0.1283224 ESE^2 0.01646663 ESE levels 0.09073761 Standard errors for 2-step estimates are not reliable. Wald (joint): Chi^2(5) = 8898. [0.000] ** Wald (dummy): Chi^2(7) = 103.2 [0.000] ** Wald (time): Chi^2(7) = 103.2 [0.000] ** Sargan test: Chi^2(79) = 88.80 [0.211] AR(1) test: N(0,1) = -5.626 [0.000] ** AR(2) test: N(0,1) = -0.1709 [0.864] ***** Blundell & Bond (1998), Table 4: 1976-86 GMM-SYS ------------- One-step estimation using DPD ------------- (Using robust variance-covariance matrix) Dependent variable: n Transformation used: first differences GMM-SYS estimation combines transformed and level equations Instruments for transformed equation: Level instruments: Gmm(n,2,99) Gmm(w,2,99) Gmm(k,2,99) Instruments for level equations: Level instruments: Dummies GmmLevel(n,1,1) GmmLevel(w,1,1) GmmLevel(k,1,1) Coefficient Std.Error t-value t-prob Dn(-1) 0.871414 0.04405 19.8 0.000 Dw -0.781090 0.1159 6.74 0.000 Dw(-1) 0.512074 0.1675 3.06 0.002 Dk 0.468830 0.07067 6.63 0.000 Dk(-1) -0.355981 0.07190 4.95 0.000 Constant 0.999429 0.3900 2.56 0.011 T1978 0.00472661 0.02076 0.228 0.820 T1979 0.0193132 0.02450 0.788 0.431 T1980 0.00146472 0.02472 0.0593 0.953 T1981 -0.0211725 0.02966 0.714 0.476 T1982 0.0148305 0.02742 0.541 0.589 T1983 0.0310377 0.02552 1.22 0.224 T1984 0.0201427 0.03149 0.640 0.523 no. of observations 891 no. of parameters 13 RSS 14.62396674 TSS 1601.0425015 ESE levels 0.1290581 ESE^2 levels 0.016656 constant: yes time dummies: 7 number of individuals 140 (derived from year) longest time series 7 [1978 - 1984] shortest time series 5 (unbalanced panel) Wald (joint): Chi^2(5) = 3439. [0.000] ** Wald (dummy): Chi^2(8) = 30.78 [0.000] ** Wald (time): Chi^2(7) = 16.42 [0.022] * AR(1) test: N(0,1) = -5.983 [0.000] ** AR(2) test: N(0,1) = -0.1670 [0.867] ------------- Two-step estimation using DPD ------------- Coefficient Std.Error t-value t-prob Dn(-1) 0.872881 0.006663 131. 0.000 Dw -0.779745 0.008676 89.9 0.000 Dw(-1) 0.526803 0.01439 36.6 0.000 Dk 0.470077 0.01433 32.8 0.000 Dk(-1) -0.357608 0.01401 25.5 0.000 Constant 0.948489 0.06204 15.3 0.000 T1978 0.00580177 0.005493 1.06 0.291 T1979 0.0188976 0.005414 3.49 0.001 T1980 0.00281961 0.005411 0.521 0.602 T1981 -0.0200226 0.006481 3.09 0.002 T1982 0.0152802 0.004690 3.26 0.001 T1983 0.0317310 0.005305 5.98 0.000 T1984 0.0224205 0.004914 4.56 0.000 no. of observations 891 no. of parameters 13 RSS 14.305523988 TSS 1601.0425015 ESE levels 0.1276452 ESE^2 levels 0.01629331 Standard errors for 2-step estimates are not reliable. Wald (joint): Chi^2(5) = 2.372e+05 [0.000] ** Wald (dummy): Chi^2(8) = 700.3 [0.000] ** Wald (time): Chi^2(7) = 319.7 [0.000] ** Sargan test: Chi^2(100) = 111.6 [0.201] AR(1) test: N(0,1) = -6.303 [0.000] ** AR(2) test: N(0,1) = -0.1497 [0.881] time: 13.37 =======================================================================================