| multipliers {ARDL} | R Documentation |
Multipliers estimation
Description
multipliers is a generic function used to estimate short-run (impact),
delay, interim and long-run (total) multipliers, accompanied by their
corresponding standard errors, t-statistics and p-values.
Usage
multipliers(object, type = "lr", vcov_matrix = NULL, se = FALSE)
## S3 method for class 'ardl'
multipliers(object, type = "lr", vcov_matrix = NULL, se = FALSE)
## S3 method for class 'uecm'
multipliers(object, type = "lr", vcov_matrix = NULL, se = FALSE)
Arguments
object |
An object of |
type |
A character string describing the type of multipliers. Use "lr" for long-run (total) multipliers (default), "sr" or 0 for short-run (impact) multipliers or an integer between 1 and 200 for delay and interim multipliers. |
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
|
se |
A logical indicating whether you want standard errors for delay
multipliers to be provided. The default is FALSE. Note that this parameter
does not refer to the standard errors for the long-run and short-run
multipliers, for which are always calculated. IMPORTANT: Calculating standard
errors for long periods of delays may cause your computer to run out of
memory and terminate your R session, losing important unsaved work. As a rule
of thumb, try not to exceed |
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.
type = 0 is equivalent to type = "sr".
Note that the interim multipliers are the cumulative sum of the delays, and that the sum of the interim multipliers (for long enough periods) and thus a distant enough interim multiplier match the long-run multipliers.
The delay (interim) multiplier can be interpreted as the effect on the dependent variable in period t+s, resulting from an instant (sustained) shock to an independent variable in period t.
The delta method is used for approximating the standard errors (and thus the t-statistics and p-values) of the estimated long-run and delay multipliers.
Value
multipliers returns (for long and short run multipliers) 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. For delay and
interim multipliers it returns a list with a data.frame for each variable,
containing the delay and interim multipliers for each period.
Mathematical Formula
Short-Run Multipliers:
- As derived from an ARDL:
\frac{\partial y_{t}}{\partial x_{j,t}} = b_{j,0} \;\;\;\;\; j \in \{1,\dots,k\}
- As derived from an Unrestricted ECM:
\frac{\partial y_{t}}{\partial x_{j,t}} = \omega_{j} \;\;\;\;\; j \in \{1,\dots,k\}
- Constant and Linear Trend:
c_{0}
c_{1}
Delay & Interim Multipliers:
- As derived from an ARDL:
Delay_{x_{j},s} = \frac{\partial y_{t+s}}{\partial x_{j,t}} = b_{j,s} + \sum_{i=1}^{min\{p,s\}} b_{y,i} \frac{\partial y_{t+(s-i)}}{\partial x_{j,t}} \;\;\;\;\; b_{j,s} = 0 \;\; \forall \;\; s > q
Interim_{x_{j},s} = \sum_{i=0}^{s} Delay_{x_{j},s}
- Constant and Linear Trend:
Delay_{intercept,s} = c_{0} + \sum_{i=1}^{min\{p,s\}} b_{y,i} Delay_{intercept,s-i} \;\;\;\;\; c_{0} = 0 \;\; \forall \;\; s \neq 0
Interim_{intercept,s} = \sum_{i=0}^{s} Delay_{intercept,s}
Delay_{trend,s} = c_{1} + \sum_{i=1}^{min\{p,s\}} b_{y,i} Delay_{trend,s-i} \;\;\;\;\; c_{1} = 0 \;\; \forall \;\; s \neq 0
Interim_{trend,s} = \sum_{i=0}^{s} Delay_{trend,s}
Long-Run Multipliers:
- As derived from an ARDL:
\frac{\partial y_{t+\infty}}{\partial x_{j,t}} = \theta_{j} = \frac{\sum_{l=0}^{q_{j}}b_{j,l}}{1-\sum_{i=1}^{p}b_{y,i}} \;\;\;\;\; j \in \{1,\dots,k\}
- Constant and Linear Trend:
\mu = \frac{c_{0}}{1-\sum_{i=1}^{p}b_{y,i}}
\delta = \frac{c_{1}}{1-\sum_{i=1}^{p}b_{y,i}}
- As derived from an Unrestricted ECM:
\frac{\partial y_{t+\infty}}{\partial x_{j,t}} = \theta_{j} = \frac{\pi_{j}}{-\pi_{y}} \;\;\;\;\; j \in \{1,\dots,k\}
- Constant and Linear Trend:
\mu = \frac{c_{0}}{-\pi_{y}}
\delta = \frac{c_{1}}{-\pi_{y}}
Author(s)
Kleanthis Natsiopoulos, klnatsio@gmail.com
See Also
Examples
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)
## Estimate the short-run multipliers of an ARDL(3,1,3,2) model --------
mult_sr <- multipliers(uecm_3132, type = "sr")
mult_0 <- multipliers(uecm_3132, type = 0)
all.equal(mult_sr, mult_0)
## Estimate the delay & interim multipliers of an ARDL(3,1,3,2) model --
mult_lr <- multipliers(uecm_3132, type = "lr")
mult_inter80 <- multipliers(uecm_3132, type = 80)
mult_lr
sum(mult_inter80$`(Intercept)`$Delay)
mult_inter80$`(Intercept)`$Interim[nrow(mult_inter80$`(Intercept)`)]
sum(mult_inter80$LRY$Delay)
mult_inter80$LRY$Interim[nrow(mult_inter80$LRY)]
sum(mult_inter80$IBO$Delay)
mult_inter80$IBO$Interim[nrow(mult_inter80$IBO)]
sum(mult_inter80$IDE$Delay)
mult_inter80$IDE$Interim[nrow(mult_inter80$IDE)]
plot(mult_inter80$LRY$Delay, type='l')
plot(mult_inter80$LRY$Interim, type='l')
mult_inter12 <- multipliers(uecm_3132, type = 12, se = TRUE)
plot_delay(mult_inter12, interval = 0.95)