Compute Dynamic Multipliers for kardl Models

Computes cumulative dynamic multipliers based on a model estimated using the kardl framework. The function supports different configurations of linearity and asymmetry in both short-run and long-run dynamics.

Usage

mplier(kmodel, horizon = 80, minProb = 0)

Arguments

kmodel: An object of class kardl_lm produced by the kardl function.
horizon: Integer. Number of periods ahead for which dynamic multipliers are computed.
minProb: Numeric. Minimum p-value threshold for including coefficients in the calculation. Coefficients with p-values above this threshold will be set to zero. Default is 0 (no threshold). This parameter allows users to control the inclusion of coefficients in the calculation based on their statistical significance. Setting a threshold can help focus the analysis on more relevant variables, but it may also exclude potentially important effects if set too stringently.

Value

A list of class kardl_mplier containing:

mpsi: Matrix of cumulative dynamic multipliers.
omega: Vector of omega coefficients (persistence structure).
lambda: Matrix of short-run dynamic coefficients.
horizon: Forecast horizon used.
vars: Extracted model variable structure.

Details

The asymmetry structure is determined internally:

Variables in extractedInfo$ASvars are treated as asymmetric in the short run.
Variables in extractedInfo$ALvars are treated as asymmetric in the long run.

This allows four possible configurations:

LL: Linear in both short-run and long-run
NN: Asymmetric in both short-run and long-run
SA: Short-run linear, long-run asymmetric
AS: Short-run asymmetric, long-run linear

When a component is linear, the same coefficient path is used for both positive and negative changes. When asymmetric, separate positive and negative effects are computed.

The mplier function computes dynamic multipliers based on the coefficients and lag structure of a model estimated using the kardl package. The function extracts necessary information from the model, such as coefficients, lag structure, and variable names, to compute the dynamic multipliers. It calculates the short-run coefficients, Lambda values, and omega values based on the model's parameters and lag structure. The output includes a matrix of dynamic multipliers (mpsi), which can be used for further analysis or visualization. The dynamic multipliers provide insight into how changes in the independent variables affect the dependent variable over time, allowing for a deeper understanding of the relationships captured by the model. The function also allows users to set a minimum p-value threshold for including coefficients in the calculation, providing flexibility in focusing on statistically significant effects.

The function constructs dynamic multipliers based on the recursive relationship:

$$ \psi_{h}^{+} = \sum_{i=0}^{h} \frac{\partial y_{t+i}}{\partial x_{t}^{+}}, \quad \psi_{h}^{-} = \sum_{i=0}^{h} \frac{\partial y_{t+i}}{\partial x_{t}^{-}} $$

where $\psi_h^{+}$ and $\psi_h^{-}$ represent cumulative responses to positive and negative shocks.

The recursion is defined as:

$$ \psi_h = \lambda_h + \sum_{j=1}^{p} \omega_j \psi_{h-j} $$

where $\lambda_h$ captures short-run effects and $\omega_j$ reflects persistence through lagged dependent variables.

When asymmetry is present, positive and negative shocks are propagated separately. Otherwise, the same dynamic path is used.

Examples


# This example demonstrates how to use the mplier function to calculate dynamic multipliers
# from a model estimated using the kardl package. The example includes fitting a model with
# the kardl function, calculating the multipliers, and visualizing the results using both
# base R plotting and ggplot2.

 # Calculating dynamic multipliers for a linear model in short and long run (NN)

 kardl_model<-kardl(imf_example_data, CPI~ER )
 m<-mplier(kardl_model,40)
 head(m$mpsi)
#>      h    ER_POS     ER_NEG ER_dif
#> [1,] 0 0.1011301 -0.1011301      0
#> [2,] 1 0.2430853 -0.2430853      0
#> [3,] 2 0.3149552 -0.3149552      0
#> [4,] 3 0.3564520 -0.3564520      0
#> [5,] 4 0.3891548 -0.3891548      0
#> [6,] 5 0.4154632 -0.4154632      0
 plot(m)


 # Calculating dynamic multipliers for a model with
 # Short-run linear, long-run asymmetric (SA)
 kardl_model<-kardl(imf_example_data, CPI~lasym(ER) )
 m<-mplier(kardl_model,40)
 head(m$mpsi)
#>      h    ER_POS     ER_NEG ER_dif
#> [1,] 0 0.1016347 -0.1016347      0
#> [2,] 1 0.2438260 -0.2438260      0
#> [3,] 2 0.3149033 -0.3149033      0
#> [4,] 3 0.3546481 -0.3546481      0
#> [5,] 4 0.3853433 -0.3853433      0
#> [6,] 5 0.4103829 -0.4103829      0
 plot(m)


 # Calculating dynamic multipliers for a model with
 # Short-run asymmetric, long-run linear (AS)
 kardl_model<-kardl(imf_example_data, CPI~sasym(ER) )
 m<-mplier(kardl_model,40)
 head(m$mpsi)
#>      h    ER_POS      ER_NEG     ER_dif
#> [1,] 0 0.1168062 -0.02760744 0.08919873
#> [2,] 1 0.2613810 -0.04554608 0.21583495
#> [3,] 2 0.3275027 -0.04989274 0.27760999
#> [4,] 3 0.3633209 -0.03618489 0.32713603
#> [5,] 4 0.3930679 -0.05739910 0.33566883
#> [6,] 5 0.4172614 -0.01462712 0.40263432
 plot(m)


 # Calculating dynamic multipliers for a model with
 # asymmetric effects in both short and long run (NN)
 kardl_model<-kardl(imf_example_data, CPI~asym(ER) )
 m<-mplier(kardl_model,40)
 head(m$mpsi)
#>      h    ER_POS      ER_NEG      ER_dif
#> [1,] 0 0.1148948 -0.03765414  0.07724068
#> [2,] 1 0.2574646 -0.13534259  0.12212202
#> [3,] 2 0.3218792 -0.24609073  0.07578847
#> [4,] 3 0.3553747 -0.34526280  0.01011187
#> [5,] 4 0.3828353 -0.48437435 -0.10153903
#> [6,] 5 0.4058231 -0.55248000 -0.14665691
 plot(m)


 # The mpsi matrix contains the cumulative dynamic multipliers for each variable and time horizon.
 # The omega vector contains the persistence structure of the model,
 # while the lambda matrix contains the short-run dynamic coefficients.
 # You can inspect these components to understand the dynamics captured by the model.
 kardl_model<-kardl(imf_example_data, CPI~PPI+asym(ER) )
 m<-mplier(kardl_model,40)
 head(m$mpsi)
#>      h    PPI_POS     PPI_NEG PPI_dif    ER_POS      ER_NEG     ER_dif
#> [1,] 0 0.02132813 -0.02132813       0 0.1063165 -0.03176480 0.07455172
#> [2,] 1 0.07315202 -0.07315202       0 0.2435925 -0.08346931 0.16012314
#> [3,] 2 0.11052625 -0.11052625       0 0.3036652 -0.13943921 0.16422600
#> [4,] 3 0.14464258 -0.14464258       0 0.3292762 -0.19429402 0.13498218
#> [5,] 4 0.20964369 -0.20964369       0 0.3467835 -0.24716862 0.09961483
#> [6,] 5 0.28576074 -0.28576074       0 0.3634339 -0.29819112 0.06524275
 head(m$omega)
#> [1]  1.37561845 -0.47712514  0.07968277
 head(m$lambda)
#>           PPI_POS      PPI_NEG       ER_POS      ER_NEG
#> [1,]  0.021328127  0.021328127  0.106316519 0.031764799
#> [2,]  0.022484531  0.022484531 -0.008975032 0.008008269
#> [3,] -0.023739497 -0.023739497 -0.078040265 0.000000000
#> [4,]  0.005730656  0.005730656  0.000000000 0.000000000
#> [5,]  0.031772768  0.031772768  0.000000000 0.000000000
#> [6,]  0.000000000  0.000000000  0.000000000 0.000000000

 # For plotting specific variables, you can specify them in the plot function. For example,
 # to plot the multipliers for the variable "PPI":

 plot(m, variable = "PPI")