# [R-SIG-Finance] [R-sig-finance] Normalization and Cointegrating Vectors from VECM analysis

Hammed hammeda at ffc.co.za
Thu Jul 9 19:14:40 CEST 2009

```On page 24 of Bernhard Pfaff's  "VAR, SVAR and SVEC Models: Implementation
Within R Package vars" the analysis noted the existence of one cointegration
relationship. Subsequently a VECM with the restriction that r=1 and a
normalization of the long-run relationship with respect to total wages was
re-estimated. This was done via

R>vecm <-cajo(Canada[, c("rw", "prod", "e", "U"], type="trace",
ecdet="trend", K=3, spec="transitory")
R> vecmR1 <-cajorls(vecm, r=1).

Here are the questions I have:

1. Does placing "rw" first signal that it is the variable on which the VECM
estimation will be normalized? If  not, how is normalization conducted?

2. How does one go about obtaining the t-statistics (and standard errors) of
the alpha and beta parameters as provided in Table 5? I have searched the
net and noted that other users have had similar issues in obtaining
something similar to Table 5 when one gets results such attached below

>Coefficients:
LY.d        LPVI.d      LGC.d       LPI.d

ect1      -1.281e-01   2.857e-01  -7.791e-01   1.412e+00

>

>constant   1.585e+02  -3.532e+02   9.635e+02  -1.746e+03

>

>LY.dl1     7.591e-01   3.701e-01   1.370e+00  -4.387e-01

>

>LPVI.dl1   8.272e-02   4.471e-01   2.071e-01   6.531e-02

>

>LGC.dl1    2.629e-02   2.016e-01  -6.392e-06   3.304e-02

>

>LPI.dl1   -6.621e-03  -1.903e-02   6.491e-03   3.498e-01

>

>

>

>\$beta

>

>                ect1

>

>LY.l1     1.00000000

>

>LPVI.l1  -0.29140737

>

>LGC.l1    0.20201033

>

>LPI.l1   -0.02771818

>

>trend.l1 -0.56077672

>

>

>

>> summary(vecm.r1\$rlm)

>

>Response LY.d :

>

>

>

>Call:

>

>lm(formula = substitute(LY.d), data = data.mat)

>

>

>

>Residuals:

>

>      Min        1Q    Median        3Q       Max

>

>-1.556232 -0.212279 -0.006118  0.281033  1.025720

>

>

>

>Coefficients:

>

>           Estimate Std. Error t value Pr(>|t|)

>

>ect1      -0.128062   0.082565  -1.551    0.127

>

>constant 158.511805 102.096882   1.553    0.127

>

>LY.dl1     0.759144   0.161426   4.703 1.93e-05 ***

>

>LPVI.dl1   0.082721   0.060251   1.373    0.176

>

>LGC.dl1    0.026292   0.047268   0.556    0.580

>

>LPI.dl1   -0.006621   0.013322  -0.497    0.621

>

>---

>

>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

>

>

>

>Residual standard error: 0.4673 on 52 degrees of freedom

>

>Multiple R-squared: 0.807,      Adjusted R-squared: 0.7847

>

>F-statistic: 36.23 on 6 and 52 DF,  p-value: < 2.2e-16

>

>

>

>Response LPVI.d :

>

>

>

>Call:

>

>lm(formula = substitute(LPVI.d), data = data.mat)

>

>

>

>Residuals:

>

>    Min      1Q  Median      3Q     Max

>

>-1.8874 -0.5372 -0.0947  0.4634  2.9403

>

>

>

>Coefficients:

>

>           Estimate Std. Error t value Pr(>|t|)

>

>ect1        0.28566    0.15822   1.806 0.076780 .

>

>constant -353.15002  195.64231  -1.805 0.076853 .

>

>LY.dl1      0.37008    0.30933   1.196 0.236966

>

>LPVI.dl1    0.44706    0.11546   3.872 0.000303 ***

>

>LGC.dl1     0.20157    0.09058   2.225 0.030415 *

>

>LPI.dl1    -0.01903    0.02553  -0.745 0.459427

>

>---

>

>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

>

>

>

>Residual standard error: 0.8955 on 52 degrees of freedom

>

>Multiple R-squared: 0.8414,     Adjusted R-squared: 0.8231

>

>F-statistic: 45.97 on 6 and 52 DF,  p-value: < 2.2e-16

>

>

>

>

>

>Response LGC.d :

>

>

>

>Call:

>

>lm(formula = substitute(LGC.d), data = data.mat)

>

>

>

>Residuals:

>

>    Min      1Q  Median      3Q     Max

>

>-2.4355 -0.8068 -0.1286  0.9971  2.3484

>

>

>

>Coefficients:

>

>           Estimate Std. Error   t value Pr(>|t|)

>

>ect1     -7.791e-01  2.163e-01    -3.601 0.000707 ***

>

>constant  9.635e+02  2.675e+02     3.602 0.000706 ***

>

>LY.dl1    1.370e+00  4.230e-01     3.240 0.002088 **

>

>LPVI.dl1  2.071e-01  1.579e-01     1.312 0.195284

>

>LGC.dl1  -6.392e-06  1.238e-01 -5.16e-05 0.999959

>

>LPI.dl1   6.491e-03  3.491e-02     0.186 0.853192

>

>---

>

>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

>

>

>

>Residual standard error: 1.224 on 52 degrees of freedom

>

>Multiple R-squared: 0.4406,     Adjusted R-squared: 0.3761

>

>F-statistic: 6.827 on 6 and 52 DF,  p-value: 2.219e-05

>

>

>

>

>

>Response LPI.d :

>

>

>

>Call:

>

>lm(formula = substitute(LPI.d), data = data.mat)

>

>

>

>Residuals:

>

>     Min       1Q   Median       3Q      Max

>

>-17.2248  -1.7118  -0.1967   2.2343   8.0607

>

>

>

>Coefficients:

>

>           Estimate Std. Error t value Pr(>|t|)

>

>ect1      1.412e+00  7.243e-01   1.950  0.05661 .

>

>constant -1.746e+03  8.956e+02  -1.950  0.05660 .

>

>LY.dl1   -4.386e-01  1.416e+00  -0.310  0.75798

>

>LPVI.dl1  6.531e-02  5.285e-01   0.124  0.90214

>

>LGC.dl1   3.304e-02  4.147e-01   0.080  0.93680

>

>LPI.dl1   3.498e-01  1.169e-01   2.993  0.00421 **

>

>---

>

>Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

>

>

>

>Residual standard error: 4.1 on 52 degrees of freedom

>

>Multiple R-squared: 0.3707,     Adjusted R-squared: 0.2981

>

>F-statistic: 5.105 on 6 and 52 DF,  p-value: 0.0003471

>
--
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