recm {ARDL} R Documentation

## Restricted ECM regression

### Description

Creates the Restricted Error Correction Model (RECM). This is the conditional RECM, which is the RECM of the underlying ARDL.

### Usage

recm(object, case)


### Arguments

 object An object of class 'ardl' or 'uecm'. case An integer from 1-5 or a character string specifying whether the 'intercept' and/or the 'trend' have to participate in the short-run or the long-run relationship (cointegrating equation) (see section 'Cases' below).

### Details

Note that the statistical significance of 'ect' in a RECM should not be tested using the corresponding t-statistic (or the p-value) because it doesn't follow a standard t-distribution. Instead, the bounds_t_test should be used.

### Value

recm returns an object of class c("dynlm", "lm", "recm"). In addition, attributes 'order', 'data', 'parsed_formula' and 'full_formula' are provided.

### Mathematical Formula

The formula of a Restricted ECM conditional to an ARDL(p,q_{1},\dots,q_{k}) is:

\Delta y_{t} = c_{0} + c_{1}t + \sum_{i=1}^{p-1}\psi_{y,i}\Delta y_{t-i} + \sum_{j=1}^{k}\sum_{l=1}^{q_{j}-1} \psi_{j,l}\Delta x_{j,t-l} + \sum_{j=1}^{k}\omega_{j}\Delta x_{j,t} + \pi_{y}ECT_{t} + \epsilon_{t}

\psi_{j,l} = 0 \;\; \forall \;\; q_{j} = 1, \psi_{j,l} = \omega_{j} = 0 \;\; \forall \;\; q_{j} = 0

Under Case 1:
• c_{0}=c_{1}=0

• ECT = y_{t-1} - (\sum_{j=1}^{k} \theta_{j} x_{j,t-1})

Under Case 2:
• c_{0}=c_{1}=0

• ECT = y_{t-1} - (\mu + \sum_{j=1}^{k}\theta_{j} x_{j,t-1})

Under Case 3:
• c_{1}=0

• ECT = y_{t-1} - (\sum_{j=1}^{k} \theta_{j} x_{j,t-1})

Under Case 4:
• c_{1}=0

• ECT = y_{t-1} - (\delta(t-1)+ \sum_{j=1}^{k} \theta_{j} x_{j,t-1})

Under Case 5:
• ECT = y_{t-1} - (\sum_{j=1}^{k} \theta_{j} x_{j,t-1})

In all cases, x_{j,t-1} in ECT is replaced by x_{j,t} \;\;\;\;\; \forall \;\; q_{j} = 0

### Cases

According to Pesaran et al. (2001), we distinguish the long-run relationship (cointegrating equation) (and thus the bounds-test 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 long-run relationship or they are unrestricted and so they participate in the short-run 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), 289-326

### Author(s)

Kleanthis Natsiopoulos, klnatsio@gmail.com

ardl uecm

### Examples

data(denmark)

## Estimate the RECM, conditional to it's underlying ARDL(3,1,3,2) -----

# Indirectly from an ARDL
ardl_3132 <- ardl(LRM ~ LRY + IBO + IDE, data = denmark, order = c(3,1,3,2))
recm_3132 <- recm(ardl_3132, case = 2)

# Indirectly from an UECM
uecm_3132 <- uecm(ardl_3132)
recm_3132_ <- recm(uecm_3132, case = 2)
identical(recm_3132, recm_3132_)
summary(recm_3132)

## Error Correction Term (ect) & Speed of Adjustment -------------------

# The coefficient of the ect,
# shows the Speed of Adjustment towards equilibrium.
# Note that this can be also be obtained from an UECM,
# through the coefficient of the term L(y, 1) (where y is the dependent variable).
tail(recm_3132$coefficients, 1) uecm_3132$coefficients[2]

## Post-estimation testing ---------------------------------------------

# See examples in the help file of the uecm() function



[Package ARDL version 0.2.4 Index]