Transform the GDRF formulae to fitted value formulae

Usage

yhat.calculator(
  formulae,
  d.y,
  model,
  the.coef,
  y.vrbl = NULL,
  inferences.y = NULL,
  prediction.values = NULL,
  baseline.y = NULL,
  shock.size = 1
)

Arguments

formulae: the list of formulae from general.calculator
d.y: an integer for the order of differencing of the y variable in the ADL model
model: the lm model containing the model estimates
the.coef: the coefficient vector from the estimated model
y.vrbl: a named vector of the (lagged) y variables and corresponding lag orders in the ADL model
inferences.y: whether the inferences for the dependent variable are in levels or differences. Must be one of levels or differences
prediction.values: a named list of values for non-y variables in the model, used to calculate a steady-state baseline when d.y = 0 and baseline.y is not supplied. If any differenced variables are included in the model, they should be set to 0. Ignored when d.y > 0
baseline.y: a user-supplied baseline value of y in levels. For d.y = 0, this overrides the steady-state calculation from prediction.values. For d.y > 0 with inferences.y = "levels", this is required. Optional uncertainty around this baseline can be supplied through baseline.y.se in the calling function
shock.size: the size of the shock to x in the units of x. Defaults to 1 (the marginal effect)

Value

a list of limit + 1 formula strings containing the fitted value formula in each period, for evaluation by deltaMethod in the calling function

Details

yhat.calculator does no calculation. It transforms the formulae from general.calculator into fitted value formulae by prepending a baseline value of y. For d.y = 0, the baseline is either a user-supplied value or a model-implied steady-state prediction, the latter of which incorporates model-based uncertainty. For d.y > 0, the baseline must be user-supplied through baseline.y, as the model in differences contains no information about the level of y. Optional uncertainty around a user-supplied baseline can be added through baseline.y.se, it is added as a post-processing step in the calling function

Author

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

Examples

# ADL model with y in levels
model.levels <- lm(y ~ x + l_1_x + l_1_y, data = toy.ts.interaction.data)

# set up formulae
pulses.levels <- pulse.calculator(x.vrbl = c("x" = 0, "l_1_x" = 1),
  y.vrbl = c("l_1_y" = 1), limit = 5)
general.levels <- general.calculator(d.x = 0, d.y = 0, h = -1,
  limit = 5, pulses = pulses.levels)

# I(0) y: steady state from means (warns about differenced variables)
#  Note this would mean different values for x and l_1_x, which might be undesirable
yhat.calculator(formulae = general.levels$formulae, d.y = 0,
  model = model.levels, the.coef = coef(model.levels),
  y.vrbl = c("l_1_y" = 1), inferences.y = "levels",
  prediction.values = NULL, baseline.y = 0, shock.size = 1)
#> [[1]]
#> [1] "0"
#> 
#> [[2]]
#> [1] "0 + 1 * (x )"
#> 
#> [[3]]
#> [1] "0 + 1 * (l_1_x  +  l_1_y * x )"
#> 
#> [[4]]
#> [1] "0 + 1 * (l_1_y * l_1_x  +  l_1_y**2 * x )"
#> 
#> [[5]]
#> [1] "0 + 1 * (l_1_y**2 * l_1_x  +  l_1_y**3 * x )"
#> 
#> [[6]]
#> [1] "0 + 1 * (l_1_y**3 * l_1_x  +  l_1_y**4 * x )"
#> 
#> [[7]]
#> [1] "0 + 1 * (l_1_y**4 * l_1_x  +  l_1_y**5 * x )"
#> 

# I(0) y: steady state from supplied prediction.values (same values for both x/l_1_x)
yhat.calculator(formulae = general.levels$formulae, d.y = 0,
  model = model.levels, the.coef = coef(model.levels),
  y.vrbl = c("l_1_y" = 1), inferences.y = "levels",
  prediction.values = list("x" = 1, "l_1_x" = 1),
  baseline.y = NULL, shock.size = 1)
#> [[1]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y))"
#> 
#> [[2]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y)) + 1 * (x )"
#> 
#> [[3]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y)) + 1 * (l_1_x  +  l_1_y * x )"
#> 
#> [[4]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y)) + 1 * (l_1_y * l_1_x  +  l_1_y**2 * x )"
#> 
#> [[5]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y)) + 1 * (l_1_y**2 * l_1_x  +  l_1_y**3 * x )"
#> 
#> [[6]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y)) + 1 * (l_1_y**3 * l_1_x  +  l_1_y**4 * x )"
#> 
#> [[7]]
#> [1] "((Intercept) + 1 * x + 1 * l_1_x) / (1 - (l_1_y)) + 1 * (l_1_y**4 * l_1_x  +  l_1_y**5 * x )"
#> 

# I(0) y: user-supplied baseline.y overrides prediction.values
yhat.calculator(formulae = general.levels$formulae, d.y = 0,
  model = model.levels, the.coef = coef(model.levels),
  y.vrbl = c("l_1_y" = 1), inferences.y = "levels",
  prediction.values = list("x" = 0, "l_1_x" = 1),
  baseline.y = 5, shock.size = 1)
#> [[1]]
#> [1] "5"
#> 
#> [[2]]
#> [1] "5 + 1 * (x )"
#> 
#> [[3]]
#> [1] "5 + 1 * (l_1_x  +  l_1_y * x )"
#> 
#> [[4]]
#> [1] "5 + 1 * (l_1_y * l_1_x  +  l_1_y**2 * x )"
#> 
#> [[5]]
#> [1] "5 + 1 * (l_1_y**2 * l_1_x  +  l_1_y**3 * x )"
#> 
#> [[6]]
#> [1] "5 + 1 * (l_1_y**3 * l_1_x  +  l_1_y**4 * x )"
#> 
#> [[7]]
#> [1] "5 + 1 * (l_1_y**4 * l_1_x  +  l_1_y**5 * x )"
#> 

# ADL model with differenced y
model.diffs <- lm(d_y ~ x + l_1_x + l_1_d_y, data = toy.ts.interaction.data)

# set up formulae
pulses.diffs <- pulse.calculator(x.vrbl = c("x" = 0, "l_1_x" = 1),
  y.vrbl = c("l_1_d_y" = 1), limit = 5)
general.diffs <- general.calculator(d.x = 0, d.y = 1, h = -1,
  limit = 5, pulses = pulses.diffs)

if (FALSE) { # \dontrun{
# inferences in differences, baseline.y != 0. warn that this makes no sense (implies the
#  model is always changing) and change baseline.y to 0
yhat.calculator(formulae = general.diffs$formulae, d.y = 1,
  model = model.diffs, the.coef = coef(model.diffs),
  y.vrbl = c("l_1_y" = 1), inferences.y = "differences",
  baseline.y = 3, shock.size = 1)
  
# inferences in differences, shock size of 1: identical to marginal effect (warns)
yhat.calculator(formulae = general.diffs$formulae, d.y = 1,
  model = model.diffs, the.coef = coef(model.diffs),
  y.vrbl = c("l_1_y" = 1), inferences.y = "differences",
  baseline.y = NULL, shock.size = 1)

# inferences in differences, shock size of 2: scales the marginal effect
#  Since we're asking for inferences.y in differences, the baseline will automatically be 0
yhat.calculator(formulae = general.diffs$formulae, d.y = 1,
  model = model.diffs, the.coef = coef(model.diffs),
  y.vrbl = c("l_1_y" = 1), inferences.y = "differences",
  baseline.y = NULL, shock.size = 2)

# inferences in levels with no baseline.y: stops with an error
yhat.calculator(formulae = general.diffs$formulae, d.y = 1,
  model = model.diffs, the.coef = coef(model.diffs),
  y.vrbl = c("l_1_y" = 1), inferences.y = "levels",
  baseline.y = NULL, shock.size = 2)

# inferences in levels with prediction.values but no baseline.y: warns and stops
yhat.calculator(formulae = general.diffs$formulae, d.y = 1,
  model = model.diffs, the.coef = coef(model.diffs),
  y.vrbl = c("l_1_y" = 1), inferences.y = "levels",
  prediction.values = list("x" = 1, "l_1_x" = 1),
  baseline.y = NULL, shock.size = 2)
} # }

# inferences in levels with a supplied baseline
yhat.calculator(formulae = general.diffs$formulae, d.y = 1,
  model = model.diffs, the.coef = coef(model.diffs),
  y.vrbl = c("l_1_y" = 1), inferences.y = "levels",
  prediction.values = list("x" = 1, "l_1_x" = 1),
  baseline.y = 5, shock.size = 2)
#> [[1]]
#> [1] "5"
#> 
#> [[2]]
#> [1] "5 + 2 * (x )"
#> 
#> [[3]]
#> [1] "5 + 2 * (l_1_x  +  l_1_d_y * x  +  x )"
#> 
#> [[4]]
#> [1] "5 + 2 * (l_1_d_y * l_1_x  +  l_1_d_y**2 * x  +  l_1_x  +  l_1_d_y * x  +  x )"
#> 
#> [[5]]
#> [1] "5 + 2 * (l_1_d_y**2 * l_1_x  +  l_1_d_y**3 * x  +  l_1_d_y * l_1_x  +  l_1_d_y**2 * x  +  l_1_x  +  l_1_d_y * x  +  x )"
#> 
#> [[6]]
#> [1] "5 + 2 * (l_1_d_y**3 * l_1_x  +  l_1_d_y**4 * x  +  l_1_d_y**2 * l_1_x  +  l_1_d_y**3 * x  +  l_1_d_y * l_1_x  +  l_1_d_y**2 * x  +  l_1_x  +  l_1_d_y * x  +  x )"
#> 
#> [[7]]
#> [1] "5 + 2 * (l_1_d_y**4 * l_1_x  +  l_1_d_y**5 * x  +  l_1_d_y**3 * l_1_x  +  l_1_d_y**4 * x  +  l_1_d_y**2 * l_1_x  +  l_1_d_y**3 * x  +  l_1_d_y * l_1_x  +  l_1_d_y**2 * x  +  l_1_x  +  l_1_d_y * x  +  x )"
#>