coint_eq {ARDL}  R Documentation 
Cointegrating equation (longrun level relationship)
Description
Creates the cointegrating equation (longrun level relationship) providing an 'ardl', 'uecm' or 'recm' model.
Usage
coint_eq(object, case)
## S3 method for class 'recm'
coint_eq(object, ...)
## Default S3 method:
coint_eq(object, case)
Arguments
object 
An object of 
case 
An integer from 15 or a character string specifying whether the
'intercept' and/or the 'trend' have to participate in the longrun level
relationship (cointegrating equation) (see section 'Cases' below). If the
input object is of class 'recm', 
... 
Currently unused argument. 
Value
coint_eq
returns an numeric vector containing the
cointegrating equation.
Cases
According to Pesaran et al. (2001), we distinguish the longrun relationship (cointegrating equation) (and thus the boundstest and the Restricted ECMs) between 5 different cases. These differ in terms of whether the 'intercept' and/or the 'trend' are restricted to participate in the longrun relationship or they are unrestricted and so they participate in the shortrun relationship.
 Case 1:

No intercept and no trend.

case
inputs: 1 or "n" where "n" stands for none.
 Case 2:

Restricted intercept and no trend.

case
inputs: 2 or "rc" where "rc" stands for restricted constant.
 Case 3:

Unrestricted intercept and no trend.

case
inputs: 3 or "uc" where "uc" stands for unrestricted constant.
 Case 4:

Unrestricted intercept and restricted trend.

case
inputs: 4 or "ucrt" where "ucrt" stands for unrestricted constant and restricted trend.
 Case 5:

Unrestricted intercept and unrestricted trend.

case
inputs: 5 or "ucut" where "ucut" stands for unrestricted constant and unrestricted trend.
Note that you can't restrict (or leave unrestricted) a parameter that doesn't
exist in the input model. For example, you can't compute recm(object,
case=3)
if the object is an ARDL (or UECM) model with no intercept. The same
way, you can't compute bounds_f_test(object, case=5)
if the object is
an ARDL (or UECM) model with no linear trend.
References
Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289326
Author(s)
Kleanthis Natsiopoulos, klnatsio@gmail.com
See Also
plot_lr
ardl
uecm
recm
bounds_f_test
bounds_t_test
Examples
data(denmark)
library(zoo) # for cbind.zoo()
## Estimate the Cointegrating Equation of an ARDL(3,1,3,2) model 
# From an ARDL model (under case 2, restricted constant)
ardl_3132 < ardl(LRM ~ LRY + IBO + IDE, data = denmark, order = c(3,1,3,2))
ce2_ardl < coint_eq(ardl_3132, case = 2)
# From an UECM (under case 2, restricted constant)
uecm_3132 < uecm(ardl_3132)
ce2_uecm < coint_eq(uecm_3132, case = 2)
# From a RECM (under case 2, restricted constant)
# Notice that if a RECM has already been estimated under a certain case,
# the 'coint_eq()' can't be under different case, so no 'case' argument needed.
recm_3132 < recm(uecm_3132, case = 2)
# The RECM is already under case 2, so the 'case' argument is no needed
ce2_recm < coint_eq(recm_3132)
identical(ce2_ardl, ce2_uecm, ce2_recm)
## Check for a degenerate level relationship 
# The bounds Ftest under both cases reject the Null Hypothesis of no level relationship.
bounds_f_test(ardl_3132, case = 2)
bounds_f_test(ardl_3132, case = 3)
# The bounds ttest also rejects the NUll Hypothesis of no level relationship.
bounds_t_test(ardl_3132, case = 3)
# But when the constant enters the longrun equation (case 3)
# this becomes a degenerate relationship.
ce3_ardl < coint_eq(ardl_3132, case = 3)
plot_lr(ardl_3132, coint_eq = ce2_ardl, show.legend = TRUE)
plot_lr(ardl_3132, coint_eq = ce3_ardl, show.legend = TRUE)
plot_lr(ardl_3132, coint_eq = ce3_ardl, facets = TRUE, show.legend = TRUE)