OLS regression of VECM
cajools.RdThis function returns the OLS regressions of an unrestricted VECM,
i.e. it returns an object of class lm. The user can provide a
certain number of which equation in the VECM should be estimated and
reported, or if "reg.number=NULL" each equation in the VECM
will be estimated and its results are reported.
References
Johansen, S. (1988), Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, 12, 231–254.
Johansen, S. and Juselius, K. (1990), Maximum Likelihood Estimation and Inference on Cointegration – with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 2, 169–210.
Johansen, S. (1991), Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models, Econometrica, Vol. 59, No. 6, 1551–1580.
See also
ca.jo, cajorls, lm,
ca.jo-class and urca-class.
Examples
data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.vecm1 <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
season=4)
sjd.vecm2 <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="transitory",
season=4)
sjd.vecm.ols1 <- cajools(sjd.vecm1)
sjd.vecm.ols2 <- cajools(sjd.vecm2)
summary(sjd.vecm.ols1)
#> Response LRM.d :
#>
#> Call:
#> lm(formula = LRM.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l2 + LRY.l2 + IBO.l2 + IDE.l2 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.039482 -0.014437 -0.005498 0.013169 0.051973
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.055917 0.010563 -5.294 4.34e-06 ***
#> sd2 -0.016458 0.009426 -1.746 0.08831 .
#> sd3 -0.039480 0.008961 -4.406 7.40e-05 ***
#> LRM.dl1 0.014228 0.201655 0.071 0.94409
#> LRY.dl1 0.013753 0.166549 0.083 0.93459
#> IBO.dl1 -1.180148 0.393173 -3.002 0.00456 **
#> IDE.dl1 0.176409 0.598347 0.295 0.76961
#> LRM.l2 -0.180730 0.088757 -2.036 0.04822 *
#> LRY.l2 0.109768 0.120060 0.914 0.36592
#> IBO.l2 -1.041659 0.353320 -2.948 0.00526 **
#> IDE.l2 0.638122 0.434247 1.469 0.14933
#> constant 1.582925 0.547678 2.890 0.00613 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.02165 on 41 degrees of freedom
#> Multiple R-squared: 0.6804, Adjusted R-squared: 0.5868
#> F-statistic: 7.273 on 12 and 41 DF, p-value: 6.759e-07
#>
#>
#> Response LRY.d :
#>
#> Call:
#> lm(formula = LRY.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l2 + LRY.l2 + IBO.l2 + IDE.l2 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.03448 -0.01507 -0.00100 0.01115 0.05666
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.025121 0.010825 -2.321 0.0254 *
#> sd2 0.007339 0.009660 0.760 0.4518
#> sd3 -0.011369 0.009183 -1.238 0.2228
#> LRM.dl1 0.689838 0.206656 3.338 0.0018 **
#> LRY.dl1 -0.353616 0.170679 -2.072 0.0446 *
#> IBO.dl1 0.280519 0.402923 0.696 0.4902
#> IDE.dl1 -0.587402 0.613185 -0.958 0.3437
#> LRM.l2 0.185819 0.090958 2.043 0.0475 *
#> LRY.l2 -0.309055 0.123038 -2.512 0.0160 *
#> IBO.l2 0.657641 0.362082 1.816 0.0766 .
#> IDE.l2 -0.647679 0.445015 -1.455 0.1532
#> constant -0.389553 0.561260 -0.694 0.4916
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.02218 on 41 degrees of freedom
#> Multiple R-squared: 0.4015, Adjusted R-squared: 0.2264
#> F-statistic: 2.292 on 12 and 41 DF, p-value: 0.02421
#>
#>
#> Response IBO.d :
#>
#> Call:
#> lm(formula = IBO.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l2 + LRY.l2 + IBO.l2 + IDE.l2 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.0232722 -0.0044453 -0.0000303 0.0048527 0.0176373
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.0000689 0.0042027 -0.016 0.9870
#> sd2 0.0073995 0.0037503 1.973 0.0553 .
#> sd3 0.0048269 0.0035652 1.354 0.1832
#> LRM.dl1 0.0654218 0.0802292 0.815 0.4195
#> LRY.dl1 0.1179269 0.0662622 1.780 0.0825 .
#> IBO.dl1 0.3825684 0.1564254 2.446 0.0188 *
#> IDE.dl1 0.0858928 0.2380548 0.361 0.7201
#> LRM.l2 0.0144878 0.0353122 0.410 0.6837
#> LRY.l2 -0.0177100 0.0477665 -0.371 0.7127
#> IBO.l2 0.0815823 0.1405700 0.580 0.5648
#> IDE.l2 -0.1673547 0.1727669 -0.969 0.3384
#> constant -0.0641545 0.2178960 -0.294 0.7699
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.008613 on 41 degrees of freedom
#> Multiple R-squared: 0.3992, Adjusted R-squared: 0.2234
#> F-statistic: 2.27 on 12 and 41 DF, p-value: 0.02555
#>
#>
#> Response IDE.d :
#>
#> Call:
#> lm(formula = IDE.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l2 + LRY.l2 + IBO.l2 + IDE.l2 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.0091249 -0.0028761 -0.0000153 0.0024579 0.0148999
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.004189 0.002665 -1.572 0.123709
#> sd2 -0.001087 0.002378 -0.457 0.650085
#> sd3 -0.002730 0.002261 -1.208 0.234120
#> LRM.dl1 0.065001 0.050881 1.278 0.208607
#> LRY.dl1 -0.001606 0.042023 -0.038 0.969697
#> IBO.dl1 0.370309 0.099203 3.733 0.000576 ***
#> IDE.dl1 -0.049376 0.150972 -0.327 0.745292
#> LRM.l2 -0.003677 0.022395 -0.164 0.870378
#> LRY.l2 0.020138 0.030293 0.665 0.509916
#> IBO.l2 0.143119 0.089148 1.605 0.116079
#> IDE.l2 -0.314235 0.109567 -2.868 0.006498 **
#> constant -0.071218 0.138187 -0.515 0.609062
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.005462 on 41 degrees of freedom
#> Multiple R-squared: 0.507, Adjusted R-squared: 0.3627
#> F-statistic: 3.514 on 12 and 41 DF, p-value: 0.001273
#>
#>
summary(sjd.vecm.ols2)
#> Response LRM.d :
#>
#> Call:
#> lm(formula = LRM.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l1 + LRY.l1 + IBO.l1 + IDE.l1 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.039482 -0.014437 -0.005498 0.013169 0.051973
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.055917 0.010563 -5.294 4.34e-06 ***
#> sd2 -0.016458 0.009426 -1.746 0.08831 .
#> sd3 -0.039480 0.008961 -4.406 7.40e-05 ***
#> LRM.dl1 0.194958 0.176615 1.104 0.27609
#> LRY.dl1 -0.096016 0.157827 -0.608 0.54630
#> IBO.dl1 -0.138489 0.436917 -0.317 0.75288
#> IDE.dl1 -0.461713 0.576711 -0.801 0.42798
#> LRM.l1 -0.180730 0.088757 -2.036 0.04822 *
#> LRY.l1 0.109768 0.120060 0.914 0.36592
#> IBO.l1 -1.041659 0.353320 -2.948 0.00526 **
#> IDE.l1 0.638122 0.434247 1.469 0.14933
#> constant 1.582925 0.547678 2.890 0.00613 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.02165 on 41 degrees of freedom
#> Multiple R-squared: 0.6804, Adjusted R-squared: 0.5868
#> F-statistic: 7.273 on 12 and 41 DF, p-value: 6.759e-07
#>
#>
#> Response LRY.d :
#>
#> Call:
#> lm(formula = LRY.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l1 + LRY.l1 + IBO.l1 + IDE.l1 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.03448 -0.01507 -0.00100 0.01115 0.05666
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.025121 0.010825 -2.321 0.02536 *
#> sd2 0.007339 0.009660 0.760 0.45179
#> sd3 -0.011369 0.009183 -1.238 0.22276
#> LRM.dl1 0.504019 0.180994 2.785 0.00807 **
#> LRY.dl1 -0.044561 0.161741 -0.276 0.78431
#> IBO.dl1 -0.377122 0.447752 -0.842 0.40453
#> IDE.dl1 0.060277 0.591012 0.102 0.91926
#> LRM.l1 0.185819 0.090958 2.043 0.04752 *
#> LRY.l1 -0.309055 0.123038 -2.512 0.01604 *
#> IBO.l1 0.657641 0.362082 1.816 0.07664 .
#> IDE.l1 -0.647679 0.445015 -1.455 0.15317
#> constant -0.389553 0.561260 -0.694 0.49155
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.02218 on 41 degrees of freedom
#> Multiple R-squared: 0.4015, Adjusted R-squared: 0.2264
#> F-statistic: 2.292 on 12 and 41 DF, p-value: 0.02421
#>
#>
#> Response IBO.d :
#>
#> Call:
#> lm(formula = IBO.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l1 + LRY.l1 + IBO.l1 + IDE.l1 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.0232722 -0.0044453 -0.0000303 0.0048527 0.0176373
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.0000689 0.0042027 -0.016 0.9870
#> sd2 0.0073995 0.0037503 1.973 0.0553 .
#> sd3 0.0048269 0.0035652 1.354 0.1832
#> LRM.dl1 0.0509340 0.0702669 0.725 0.4727
#> LRY.dl1 0.1356369 0.0627923 2.160 0.0367 *
#> IBO.dl1 0.3009861 0.1738292 1.732 0.0909 .
#> IDE.dl1 0.2532475 0.2294467 1.104 0.2761
#> LRM.l1 0.0144878 0.0353122 0.410 0.6837
#> LRY.l1 -0.0177100 0.0477665 -0.371 0.7127
#> IBO.l1 0.0815823 0.1405700 0.580 0.5648
#> IDE.l1 -0.1673547 0.1727669 -0.969 0.3384
#> constant -0.0641545 0.2178960 -0.294 0.7699
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.008613 on 41 degrees of freedom
#> Multiple R-squared: 0.3992, Adjusted R-squared: 0.2234
#> F-statistic: 2.27 on 12 and 41 DF, p-value: 0.02555
#>
#>
#> Response IDE.d :
#>
#> Call:
#> lm(formula = IDE.d ~ sd1 + sd2 + sd3 + LRM.dl1 + LRY.dl1 + IBO.dl1 +
#> IDE.dl1 + LRM.l1 + LRY.l1 + IBO.l1 + IDE.l1 + constant -
#> 1, data = data.mat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.0091249 -0.0028761 -0.0000153 0.0024579 0.0148999
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> sd1 -0.004189 0.002665 -1.572 0.1237
#> sd2 -0.001087 0.002378 -0.457 0.6501
#> sd3 -0.002730 0.002261 -1.208 0.2341
#> LRM.dl1 0.068678 0.044563 1.541 0.1310
#> LRY.dl1 -0.021744 0.039822 -0.546 0.5880
#> IBO.dl1 0.227189 0.110241 2.061 0.0457 *
#> IDE.dl1 0.264860 0.145513 1.820 0.0760 .
#> LRM.l1 -0.003677 0.022395 -0.164 0.8704
#> LRY.l1 0.020138 0.030293 0.665 0.5099
#> IBO.l1 0.143119 0.089148 1.605 0.1161
#> IDE.l1 -0.314235 0.109567 -2.868 0.0065 **
#> constant -0.071218 0.138187 -0.515 0.6091
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.005462 on 41 degrees of freedom
#> Multiple R-squared: 0.507, Adjusted R-squared: 0.3627
#> F-statistic: 3.514 on 12 and 41 DF, p-value: 0.001273
#>
#>