ARDL (version 0.1.0)

multipliers: Multipliers estimation

Description

multipliers is a generic function used to estimate short-run (impact), interim and long-run (total) multipliers, along with their corresponding standard errors, t-statistics and p-values.

Usage

multipliers(object, type = "lr", vcov_matrix = NULL)
# S3 method for ardl
multipliers(object, type = "lr", vcov_matrix = NULL)
# S3 method for uecm
multipliers(object, type = "lr", vcov_matrix = NULL)

Arguments

object

An object of class 'ardl' or 'uecm'.

type

A character string describing the type of multipliers. The default is "lr" for long-run (total) multipliers (see 'Details').

vcov_matrix

The estimated covariance matrix of the random variable that the transformation function uses to estimate the standard errors (and so the t-statistics and p-values) of the multipliers. The default is vcov(object) (when vcov_matrix = NULL), but other estimations of the covariance matrix of the regression's estimated coefficients can also be used (e.g., using vcovHC or vcovHAC).

Value

multipliers returns a data.frame containing the independent variables (including possibly existing intercept or trend and excluding the fixed variables) and their corresponding standard errors, t-statistics and p-values.

Mathematical Formula

Long-Run Multipliers:

As derived from an ARDL:

$$\mu = \frac{c_{0}}{1-\sum_{i=1}^{p}}$$ $$\delta = \frac{c_{1}}{1-\sum_{i=1}^{p}}$$ $$\theta_{j} = \frac{\sum_{l=0}^{q_{j}}b_{j,l}}{1-\sum_{i=1}^{p}} \;\;\;\;\; \forall j=1,\dots,k$$

As derived from an Unrestricted ECM:

$$\mu = \frac{c_{0}}{-\pi_{y}}$$ $$\delta = \frac{c_{1}}{-\pi_{y}}$$ $$\theta_{j} = \frac{\pi_{j}}{-\pi_{y}} \;\;\;\;\; \forall j=1,\dots,k$$

Details

The function invokes two different methods, one for objects of class 'ardl' and one for objects of class 'uecm'. This is because of the different (but equivalent) transformation functions that are used for each class/model ('ardl' and 'uecm') to estimate the multipliers.

Currently only the long-run (total) multipliers are supported (type = "lr"). Other choices, including short-run (impact) and interim multipliers are going to be available in future versions.

The delta method is used for approximating the standard errors (and thus the t-statistics and p-values) of the estimated multipliers.

See Also

ardl, uecm

Examples

# NOT RUN {
data(denmark)

## Estimate the long-run multipliers of an ARDL(3,1,3,2) model ---------

# From an ARDL model
ardl_3132 <- ardl(LRM ~ LRY + IBO + IDE, data = denmark, order = c(3,1,3,2))
mult_ardl <- multipliers(ardl_3132)
mult_ardl

# From an UECM
uecm_3132 <- uecm(ardl_3132)
mult_uecm <- multipliers(uecm_3132)
mult_uecm

all.equal(mult_ardl, mult_uecm)
# }