Generate the generalized effect formulae for an autoregressive distributed lag (ADL) model, given pulse effects and shock history

Usage

general.calculator(d.x, d.y, h, limit, pulses)

Arguments

d.x: an integer determining the order of differencing of the x variable before a shock is applied when parametrized as an ADL model. (Generally, this is the same x variable used in pulse.calculator)
d.y: an integer determining the order of differencing of the y variable when parametrized as an ADL model. (Generally, this is the same y variable used in pulse.calculator)
h: an integer determining the shock history applied to the independent variable in levels. -1 represents the Impulse Response Function. 0 represents a Step Response Function. For others, see Vande Kamp, Jordan, and Rajan
limit: an integer for the number of periods (s) to determine the generalized effect (beginning at 0)
pulses: a list comprising the formulae for Impulse Response Functions, typically generated using pulse.calculator

Value

a list of limit + 1 mpoly formulae containing the generalized effect formula in each period

Details

general.calculator does no calculation. It generates a list of mpoly formulae that contain variable names that represent the generalized effect in each period. The expectation is that these will be evaluated using coefficients from an object containing an ADL model with corresponding variables. Note: mpoly does not allow variable names with a .; variables passed to general.calculator should not include this character

Author

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

Examples

# ADL(1,1)
x.lags <- c("x" = 0, "l_1_x" = 1) # lags of x
y.lags <- c("l_1_y" = 1)
s <- 5
pulse.effects <- pulse.calculator(x.vrbl = x.lags, y.vrbl = y.lags, limit = s)
# Assume that both x and y are in levels and we want a pulse shock history
general.pulse.effects <- general.calculator(d.x = 0, d.y = 0, 
              h = -1, limit = s, pulses = pulse.effects)
general.pulse.effects
#> $formulae
#> $formulae[[1]]
#> [1] "x "
#> 
#> $formulae[[2]]
#> [1] "l_1_x  +  l_1_y * x "
#> 
#> $formulae[[3]]
#> [1] "l_1_y * l_1_x  +  l_1_y**2 * x "
#> 
#> $formulae[[4]]
#> [1] "l_1_y**2 * l_1_x  +  l_1_y**3 * x "
#> 
#> $formulae[[5]]
#> [1] "l_1_y**3 * l_1_x  +  l_1_y**4 * x "
#> 
#> $formulae[[6]]
#> [1] "l_1_y**4 * l_1_x  +  l_1_y**5 * x "
#> 
#> 
#> $binomials
#> $binomials[[1]]
#> [1] 1
#> 
#> $binomials[[2]]
#> [1] 1 0
#> 
#> $binomials[[3]]
#> [1] 1 0 0
#> 
#> $binomials[[4]]
#> [1] 1 0 0 0
#> 
#> $binomials[[5]]
#> [1] 1 0 0 0 0
#> 
#> $binomials[[6]]
#> [1] 1 0 0 0 0 0
#> 
#> 
# Apply a step shock response function
general.step.effects <- general.calculator(d.x = 0, d.y = 0, 
              h = 0, limit = s, pulses = pulse.effects)
general.step.effects
#> $formulae
#> $formulae[[1]]
#> [1] "x "
#> 
#> $formulae[[2]]
#> [1] "l_1_x  +  l_1_y * x  +  x "
#> 
#> $formulae[[3]]
#> [1] "l_1_y * l_1_x  +  l_1_y**2 * x  +  l_1_x  +  l_1_y * x  +  x "
#> 
#> $formulae[[4]]
#> [1] "l_1_y**2 * l_1_x  +  l_1_y**3 * x  +  l_1_y * l_1_x  +  l_1_y**2 * x  +  l_1_x  +  l_1_y * x  +  x "
#> 
#> $formulae[[5]]
#> [1] "l_1_y**3 * l_1_x  +  l_1_y**4 * x  +  l_1_y**2 * l_1_x  +  l_1_y**3 * x  +  l_1_y * l_1_x  +  l_1_y**2 * x  +  l_1_x  +  l_1_y * x  +  x "
#> 
#> $formulae[[6]]
#> [1] "l_1_y**4 * l_1_x  +  l_1_y**5 * x  +  l_1_y**3 * l_1_x  +  l_1_y**4 * x  +  l_1_y**2 * l_1_x  +  l_1_y**3 * x  +  l_1_y * l_1_x  +  l_1_y**2 * x  +  l_1_x  +  l_1_y * x  +  x "
#> 
#> 
#> $binomials
#> $binomials[[1]]
#> [1] 1
#> 
#> $binomials[[2]]
#> [1] 1 1
#> 
#> $binomials[[3]]
#> [1] 1 1 1
#> 
#> $binomials[[4]]
#> [1] 1 1 1 1
#> 
#> $binomials[[5]]
#> [1] 1 1 1 1 1
#> 
#> $binomials[[6]]
#> [1] 1 1 1 1 1 1
#> 
#>