Translate the coefficients from the General Error Correction Model (GECM) to the autoregressive distributed lag (ADL) model

Usage

gecm.to.adl(x.vrbl, y.vrbl, x.d.vrbl, y.d.vrbl)

Arguments

x.vrbl: a named numeric vector in which the names correspond to an independent variable (of the lower level of differencing, usually in levels d = 0) and its lags and the numbers correspond to the specific lag order of each variable in the GECM model
y.vrbl: a named numeric vector in which the names correspond to lags of the dependent variable (of the lower level of differencing, usually in levels d = 0) and the numbers correspond to the specific lag order of each variable in the GECM model
x.d.vrbl: a named numeric vector in which the names correspond to an independent variable (of the higher level of differencing, usually in first differences d = 1) and its lags and the numbers correspond to the specific lag order of each variable in the GECM model
y.d.vrbl: a named numeric vector in which the names correspond to lags of the dependent variable (of the higher level of differencing, usually in first differences d = 1) and the numbers correspond to the specific lag order of each variable in the GECM model

Value

a list of named vectors of translated ADL coefficients for the x and y variables of interest

Details

gecm.to.adl utilizes the mathematical equivalence between the GECM and ADL models to translate the coefficients from one to the other. This way, we can apply a single function using the ADL math to calculate effects

Author

Soren Jordan, Garrett N. Vande Kamp, and Reshi Rajan

Examples

# GECM(1,1)
the.x.vrbl <- c("l_1_x" = 1) 
the.y.vrbl <- c("l_1_y" = 1) 
the.x.d.vrbl <- c("d_x" = 0, "l_1_d_x" = 1) 
the.y.d.vrbl <- c("l_1_d_y" = 1) 
adl.coef <- gecm.to.adl(x.vrbl = the.x.vrbl, y.vrbl = the.y.vrbl, 
      x.d.vrbl = the.x.d.vrbl, y.d.vrbl = the.y.d.vrbl)
adl.coef$x.vrbl.adl
#>               d_x l_1_x+l_1_d_x-d_x      (-1)*l_1_d_x 
#>                 0                 1                 2 
adl.coef$y.vrbl.adl
#> l_1_y+l_1_d_y+1    (-1)*l_1_d_y 
#>               1               2