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

Arguments

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.

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.

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

Constant and Linear Trend:

As derived from an ARDL:

μ = \frac{c_{0}}{1-∑_{i=1}^{p}b_{y,i}}

δ = \frac{c_{1}}{1-∑_{i=1}^{p}b_{y,i}}

As derived from an Unrestricted ECM:

μ = \frac{c_{0}}{-π_{y}}

δ = \frac{c_{1}}{-π_{y}}

Short-Run Multipliers:

As derived from an ARDL:

\frac{\partial y_{t}}{\partial x_{j,t}} = \frac{b_{j,0}}{1-∑_{i=1}^{p}b_{y,i}} \;\;\;\;\; \forall j=1,…,k

As derived from an Unrestricted ECM:

\frac{\partial y_{t}}{\partial x_{j,t}} = \frac{ω_{j}}{-π_{y}} \;\;\;\;\; \forall j=1,…,k

Interim Multipliers:

As derived from an ARDL:

\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}\}

As derived from an Unrestricted ECM:

\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:

As derived from an ARDL:

\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

As derived from an Unrestricted ECM:

\frac{\partial y_{t+∞}}{\partial x_{j,t}} = θ_{j} = \frac{π_{j}}{-π_{y}} \;\;\;\;\; \forall j=1,…,k

Author(s)

Kleanthis Natsiopoulos, klnatsio@gmail.com

See Also

ardl, uecm

Examples