Multipliers estimation
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.
multipliers(object, type = "lr", vcov_matrix = NULL) ## S3 method for class 'ardl' multipliers(object, type = "lr", vcov_matrix = NULL) ## S3 method for class 'uecm' multipliers(object, type = "lr", vcov_matrix = NULL)
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 100 for 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
|
Note that type = 0
is equivalent to type = "sr"
. Also,
type = s
will produce the same estimates as type = "lr"
for
those particular variable for which s >= from their ARDL order.
The delta method is used for approximating the standard errors (and thus the t-statistics and p-values) of the estimated multipliers.
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.
Constant and Linear Trend:
μ = \frac{c_{0}}{1-∑_{i=1}^{p}b_{y,i}}
δ = \frac{c_{1}}{1-∑_{i=1}^{p}b_{y,i}}
μ = \frac{c_{0}}{-π_{y}}
δ = \frac{c_{1}}{-π_{y}}
Short-Run Multipliers:
\frac{\partial y_{t}}{\partial x_{j,t}} = \frac{b_{j,0}}{1-∑_{i=1}^{p}b_{y,i}} \;\;\;\;\; \forall j=1,…,k
\frac{\partial y_{t}}{\partial x_{j,t}} = \frac{ω_{j}}{-π_{y}} \;\;\;\;\; \forall j=1,…,k
Interim Multipliers:
\frac{\partial y_{t+s}}{\partial x_{j,t}} = \frac{∑_{l=1}^{s}b_{j,l}}{1-∑_{i=1}^{p}b_{y,i}} \;\;\;\;\; \forall j=1,…,k \;\;\;\;\; s \in \{0,…,q_{j}\}
\frac{\partial y_{t+s}}{\partial x_{j,t}} = \frac{π_{j} + ψ_{j,s}}{-π_{y}} \;\;\;\;\; \forall j=1,…,k \;\;\;\;\; s \in \{1,…,q_{j}-1\}
Long-Run Multipliers:
\frac{\partial y_{t+∞}}{\partial x_{j,t}} = θ_{j} = \frac{∑_{l=0}^{q_{j}}b_{j,l}}{1-∑_{i=1}^{p}b_{y,i}} \;\;\;\;\; \forall j=1,…,k
\frac{\partial y_{t+∞}}{\partial x_{j,t}} = θ_{j} = \frac{π_{j}}{-π_{y}} \;\;\;\;\; \forall j=1,…,k
Kleanthis Natsiopoulos, klnatsio@gmail.com
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 interim multipliers of an ARDL(3,1,3,2) model ---------- # Note that the estimated interim multipliers match the long-run multipliers # for those variables that their ARDL order equals or exceeds the interim step mult_lr <- multipliers(uecm_3132, type = "lr") mult_1 <- multipliers(uecm_3132, type = 1) mult_2 <- multipliers(uecm_3132, type = 2) uecm_3132$order mult_lr mult_1 mult_2
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