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

Usage

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

Arguments

d.x: the order of differencing of the x variable in the ADL model. (Generally, this is the same x variable used in pulse.calculator)
d.y: the order of differencing of the y variable in the ADL model. (Generally, this is the same y variable used in pulse.calculator)
h: an integer for the shock/treatment history. h determines the counterfactual series that will be applied to the independent variable. -1 represents a pulse. 0 represents a step. 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 of pulse effect formulae used to construct the generalized effect formulae. We expect this will be provided by 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 treatment
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 treatment
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
#> 
#>