Solved – Extracting long run coefficient in vector error correction model in R

rtime seriesvector-error-correction-model

I used the urca package in R to estimate an error correction model. I used the ca.jo and cajorls functions for estimation. The results report the coefficients of the model showing bellow:

Call:
lm(formula = substitute(form1), data = data.mat)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.24141 -0.07255  0.01178  0.08593  0.23220 

Coefficients:
          Estimate Std. Error t value Pr(>|t|)    
ect1      -0.28598    0.04589  -6.232 2.91e-08 ***
dem.dl1    0.46455    0.08292   5.603 3.76e-07 ***
compp.dl1 -0.45926    0.19675  -2.334   0.0224 *  
gdp.dl1   -4.30191    4.82234  -0.892   0.3754    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1202 on 71 degrees of freedom
Multiple R-squared:  0.5842,    Adjusted R-squared:  0.5608 
F-statistic: 24.94 on 4 and 71 DF,  p-value: 6.43e-13

I understand the coefficient associated with the ect1 is the adjustment coefficient to the long-run equilibrium. However, I have two questions about this estimations.

  1. Is there a way to recover the coefficient "inside" the ect1 term, the long-run equilibrium coefficient? Or do I have to estimate it using OLS?
  2. Is there a way to calculate the derivative of the dependent variable (dem) with respect to the variable compp? Or is it just the coefficient for compp.dl1?

Best Answer

Regarding question 1, let the output of ca.jo be x, then you can get the cointegration vectors as x@V. This will contain the coefficients "inside" the ect1 term.

Regarding question 2, the coefficient on compp.dl1 will the be effect of lagged (rather than contemporaneous) compp on dem. Keep in mind that compp might be affected by dem at the same time as it is affecting dem (that is, compp might be endogenous w.r.t. dem), although it need not necessarily be the case.

See the vignette of package "vars" and/or Pfaff "Analysis of Integrated and Cointegrated Time Series with R" for more details.

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