Package 'tseffects'

Title: Dynamic Inferences from Time Series (with Interactions)
Description: Autoregressive distributed lag (A[R]DL) models (and their reparameterized equivalent, the Generalized Error-Correction Model [GECM]) are the workhorse models in uncovering dynamic inferences. ADL models are simple to estimate; this is what makes them attractive. Once these models are estimated, what is less clear is how to uncover a rich set of dynamic inferences from these models. We provide tools for recovering those inferences. These tools apply to traditional time-series quantities of interest: especially instantaneous effects for any period and cumulative effects for any period (including the long-run effect). They also allow for a variety of shock histories to be applied to the independent variable (beyond just a one-time, one-unit increase) as well as the recovery of inferences in levels for shocks applies to (in)dependent variables in differences (what we call the Generalized Dynamic Response Function). These effects are also available for the general conditional dynamic model advocated by Warner, Vande Kamp, and Jordan (2026 <doi:10.1017/psrm.2026.10087>). We also provide the actual formulae for these effects.
Authors: Soren Jordan [aut, cre, cph] (ORCID: <https://orcid.org/0000-0003-4201-1085>), Garrett N. Vande Kamp [aut], Reshi Rajan [aut]
Maintainer: Soren Jordan <[email protected]>
License: GPL (>=2)
Version: 0.2.1
Built: 2026-06-05 07:10:26 UTC
Source: https://github.com/sorenjordan/tseffects

Help Index

Data on US Presidential Approval

Description

A dataset from: Cavari, Amnon. 2019. "Evaluating the President on Your Priorities: Issue Priorities, Policy Performance, and Presidential Approval, 1981–2016." Presidential Studies Quarterly 49(4): 798-826.

Usage

data(approval)

Format

A data frame with 140 rows and 14 variables:

APPROVE

Presidential approval

APPROVE_ECONOMY

Presidential approval: economy

APPROVE_FOREIGN

Presidential approval: foreign affairs

MIP_MACROECONOMICS

Salience (Most Important Problem): economy

MIP_FOREIGN

Salience (Most Important Problem): foreign affairs

PARTY_IN

Macropartisanship (in-party)

PARTY_OUT

Macropartisanship (out-party)

PRESIDENT

Numeric indicator for president

DIVIDEDGOV

Dummy variable for divided government

ELECTION

Dummy variable for election years

HONEYMOON

Dummy variable for honeymoon period

UMCSENT

Consumer sentiment

UNRATE

Unemployment rate

APPROVE_L1

Lagged presidential approval

Source

doi:10.1111/psq.12594

Evaluate (and possibly plot) the General Dynamic Response Function (GDRF) for an autoregressive distributed lag (ADL) model

Description

Evaluate (and possibly plot) the General Dynamic Response Function (GDRF) for an autoregressive distributed lag (ADL) model

Usage

GDRF.adl.plot(
  model = NULL,
  x.vrbl = NULL,
  y.vrbl = NULL,
  d.x = NULL,
  d.y = NULL,
  shock.history = "pulse",
  inferences.y = "levels",
  inferences.x = "levels",
  dM.level = 0.95,
  s.limit = 20,
  se.type = "const",
  return.data = FALSE,
  return.plot = TRUE,
  return.formulae = FALSE,
  ...
)

Arguments

model

the lm model containing the ADL estimates
x.vrbl

named vector of the x variables and corresponding lag orders in the ADL model
y.vrbl

named vector of the (lagged) y variables and corresponding lag orders in the ADL model
d.x

the order of differencing of the x variable in the ADL model
d.y

the order of differencing of the y variable in the ADL model
shock.history

the desired shock history. shock.history determines the shock history (h) that will be applied to the independent variable. -1 represents a pulse. 0 represents a step. These can also be specified via pulse and step. For others, see Vande Kamp, Jordan, and Rajan. The default is pulse
inferences.y

does the user want resulting inferences about the dependent variable in levels or in differences? (For y variables where d.y is 0, this is automatically levels.) The default is levels
inferences.x

does the user want to apply the shock history to the independent variable in levels or in differences? (For x variables where d.x is 0, this is automatically levels.) The default is levels
dM.level

significance level of the GDRF, calculated by the delta method. The default is 0.95
s.limit

an integer for the number of periods to determine the GDRF (beginning at s = 0)
se.type

the type of standard error to extract from the model. The default is const, but any argument to vcovHC from the sandwich package is accepted
return.data

return the raw calculated GDRFs as a list element under estimates. The default is FALSE
return.plot

return the visualized GDRFs as a list element under plot. The default is TRUE
return.formulae

return the formulae for the GDRFs as a list element under formulae (for the GDRFs) and binomials (for the shock history). The default is FALSE
...

other arguments to be passed to the call to plot

Author(s)

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

Examples

# ADL(1,1)
# Use the toy data to run an ADL. No argument is made this is well specified; it is just expository 
model.toydata <- lm(y ~ l_1_y + x + l_1_x, data = toy.ts.interaction.data)

# Pulse effect of x
GDRF.adl.plot(model = model.toydata, 
				x.vrbl = c("x" = 0, "l_1_x" = 1), 
				y.vrbl = c("l_1_y" = 1),
				d.x = 0,
				d.y = 0,
				shock.history = "pulse", 
				inferences.y = "levels",
				inferences.x = "levels",
				s.limit = 20)

# Step effect of x. You can store the data to draw your own plot,
#  if you prefer
test.cumulative <- GDRF.adl.plot(model = model.toydata, 
				x.vrbl = c("x" = 0, "l_1_x" = 1), 
				y.vrbl = c("l_1_y" = 1),
				d.x = 0,
				d.y = 0,
				shock.history = "step", 
				inferences.y = "levels",
				inferences.x = "levels",
				s.limit = 20)
test.cumulative$plot

Evaluate (and possibly plot) the General Dynamic Treatment Effect (GDRF) for a Generalized Error Correction Model (GECM)

Description

Evaluate (and possibly plot) the General Dynamic Treatment Effect (GDRF) for a Generalized Error Correction Model (GECM)

Usage

GDRF.gecm.plot(
  model = NULL,
  x.vrbl = NULL,
  y.vrbl = NULL,
  x.vrbl.d.x = NULL,
  y.vrbl.d.y = NULL,
  x.d.vrbl = NULL,
  y.d.vrbl = NULL,
  x.d.vrbl.d.x = NULL,
  y.d.vrbl.d.y = NULL,
  shock.history = "pulse",
  inferences.y = "levels",
  inferences.x = "levels",
  dM.level = 0.95,
  s.limit = 20,
  se.type = "const",
  return.data = FALSE,
  return.plot = TRUE,
  return.formulae = FALSE,
  ...
)

Arguments

model

the lm model containing the GECM estimates
x.vrbl

a named vector of the x variables (of the lower level of differencing, usually in levels d = 0) and corresponding lag orders in the GECM model
y.vrbl

a named vector of the (lagged) y variables (of the lower level of differencing, usually in levels d = 0) and corresponding lag orders in the GECM model
x.vrbl.d.x

the order of differencing of the x variable (of the lower level of differencing, usually in levels d = 0) in the GECM model
y.vrbl.d.y

the order of differencing of the y variable (of the lower level of differencing, usually in levels d = 0) in the GECM model
x.d.vrbl

a named vector of the x variables (of the higher level of differencing, usually first differences d = 1) and corresponding lag orders in the GECM model
y.d.vrbl

a named vector of the y variables (of the higher level of differencing, usually first differences d = 1) and corresponding lag orders in the GECM model
x.d.vrbl.d.x

the order of differencing of the x variable (of the higher level of differencing, usually first differences d = 1) in the GECM model
y.d.vrbl.d.y

the order of differencing of the y variable (of the higher level of differencing, usually first differences d = 1) in the GECM model
shock.history

the desired shock history. shock.history determines the shock history (h) that will be applied to the independent variable. -1 represents a pulse. 0 represents a step. These can also be specified via pulse and step. For others, see Vande Kamp, Jordan, and Rajan. The default is pulse
inferences.y

does the user want resulting inferences about the dependent variable in levels or in differences? The default is levels
inferences.x

does the user want to apply the shock history to the independent variable in levels or in differences? The default is levels
dM.level

level of significance of the GDRF, calculated by the delta method. The default is 0.95
s.limit

an integer for the number of periods to determine the GDRF (beginning at s = 0)
se.type

the type of standard error to extract from the GECM model. The default is const, but any argument to vcovHC from the sandwich package is accepted
return.data

return the raw calculated GDRFs as a list element under estimates. The default is FALSE
return.plot

return the visualized GDRFs as a list element under plot. The default is TRUE
return.formulae

return the formulae for the GDRFs as a list element under formulae (for the GDRFs) and binomials (for the shock history). The default is FALSE
...

other arguments to be passed to the call to plot

Details

We assume that the GECM model estimated is well specified, free of residual autocorrelation, balanced, and meets other standard time-series qualities. Given that, to obtain inferences for the specified shock history, the user only needs a named vector of the x and y variables, as well as the order of the differencing. Internally, the GECM to ADL equivalences are used to calculate the GDRFs from the GECM

Value

depending on return.data, return.plot, and return.formulae, a list of elements relating to the GDTE

Author(s)

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

Examples

# GECM(1,1)
# Use the toy data to run a GECM. No argument is made this 
#  is well specified or even sensible; it is just expository
model <- lm(d_y ~ l_1_y + l_1_x + l_1_d_y + d_x + l_1_d_x, data = toy.ts.interaction.data)
test.pulse <- GDRF.gecm.plot(model = model,
                                  x.vrbl = c("l_1_x" = 1), 
                                  y.vrbl = c("l_1_y" = 1),
                                  x.vrbl.d.x = 0, 
                                  y.vrbl.d.y = 0,
                                  x.d.vrbl = c("d_x" = 0, "l_1_d_x" = 1),
                                  y.d.vrbl = c("l_1_d_y" = 1),
                                  x.d.vrbl.d.x = 1,
                                  y.d.vrbl.d.y = 1,
                                  shock.history = "pulse", 
                                  inferences.y = "levels", 
                                  inferences.x = "levels",
                                  s.limit = 10, 
                                  return.plot = TRUE, 
                                  return.formulae = TRUE)
names(test.pulse)

Evaluate (and possibly plot) the General Dynamic Treatment Effect (GDTE) for an autoregressive distributed lag (ADL) model

Description

Evaluate (and possibly plot) the General Dynamic Treatment Effect (GDTE) for an autoregressive distributed lag (ADL) model

Usage

GDTE.adl.plot(
  model = NULL,
  x.vrbl = NULL,
  y.vrbl = NULL,
  d.x = NULL,
  d.y = NULL,
  te.type = "pte",
  inferences.y = "levels",
  inferences.x = "levels",
  dM.level = 0.95,
  s.limit = 20,
  se.type = "const",
  return.data = FALSE,
  return.plot = TRUE,
  return.formulae = FALSE,
  ...
)

Arguments

model

the lm model containing the ADL estimates
x.vrbl

a named vector of the x variables and corresponding lag orders in the ADL model
y.vrbl

a named vector of the (lagged) y variables and corresponding lag orders in the ADL model
d.x

the order of differencing of the x variable in the ADL model
d.y

the order of differencing of the y variable in the ADL model
te.type

the desired treatment history. te.type determines the counterfactual series (h) that will be applied to the independent variable. -1 represents a Pulse Treatment Effect (PTE). 0 represents a Step Treatment Effect (STE). These can also be specified via pte, pulse, ste, and step. For others, see Vande Kamp, Jordan, and Rajan. The default is pte
inferences.y

does the user want resulting inferences about the dependent variable in levels or in differences? (For y variables where d.y is 0, this is automatically levels.) The default is levels
inferences.x

does the user want to apply the counterfactual treatment to the independent variable in levels or in differences? (For x variables where d.x is 0, this is automatically levels.) The default is levels
dM.level

level of significance of the GDTE, calculated by the delta method. The default is 0.95
s.limit

an integer for the number of periods to determine the GDTE (beginning at s = 0)
se.type

the type of standard error to extract from the ADL model. The default is const, but any argument to vcovHC from the sandwich package is accepted
return.data

return the raw calculated GDTEs as a list element under estimates. The default is FALSE
return.plot

return the visualized GDTEs as a list element under plot. The default is TRUE
return.formulae

return the formulae for the GDTEs as a list element under formulae (for the GDTEs) and binomials (for the treatment history). The default is FALSE
...

other arguments to be passed to the call to plot

Details

We assume that the ADL model estimated is well specified, free of residual autocorrelation, balanced, and meets other standard time-series qualities. Given that, to obtain causal inferences for the specified treatment history, the user only needs a named vector of the x and y variables, as well as the order of the differencing

Value

depending on return.data, return.plot, and return.formulae, a list of elements relating to the GDTE

Author(s)

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

Examples

# ADL(1,1)
# Use the toy data to run an ADL. No argument is made this is well specified; it is just expository 
model <- lm(y ~ l_1_y + x + l_1_x, data = toy.ts.interaction.data)
test.pulse <- GDTE.adl.plot(model = model,
                                  x.vrbl = c("x" = 0, "l_1_x" = 1), 
                                  y.vrbl = c("l_1_y" = 1),
                                  d.x = 0, 
                                  d.y = 0,
                                  te.type = "pulse", 
                                  inferences.y = "levels", 
                                  inferences.x = "levels",
                                  s.limit = 20, 
                                  return.plot = TRUE, 
                                  return.formulae = TRUE)
names(test.pulse)

# Using Cavari's (2019) approval model (without interactions)
# Cavari's original model: APPROVE ~ APPROVE_ECONOMY + APPROVE_FOREIGN + 
#     APPROVE_L1 + PARTY_IN + PARTY_OUT + UNRATE + 
#	     MIP_MACROECONOMICS + MIP_FOREIGN + 
#     DIVIDEDGOV + ELECTION + HONEYMOON + as.factor(PRESIDENT)

cavari.model <- lm(APPROVE ~ APPROVE_ECONOMY + APPROVE_FOREIGN + MIP_MACROECONOMICS + MIP_FOREIGN +
     APPROVE_L1 + PARTY_IN + PARTY_OUT + UNRATE + 
     DIVIDEDGOV + ELECTION + HONEYMOON + as.factor(PRESIDENT), data = approval)

# What if there was a permanent, one-unit change in the salience of foreign affairs?
cavari.step <- GDTE.adl.plot(model = cavari.model,
                                  x.vrbl = c("MIP_FOREIGN" = 0), 
                                  y.vrbl = c("APPROVE_L1" = 1),
                                  d.x = 0,
                                  d.y = 0,
                                  te.type = "ste", 
                                  inferences.y = "levels", 
                                  inferences.x = "levels",
                                  s.limit = 10, 
                                  return.plot = TRUE, 
                                  return.formulae = TRUE)

Evaluate (and possibly plot) the General Dynamic Treatment Effect (GDTE) for a Generalized Error Correction Model (GECM)

Description

Evaluate (and possibly plot) the General Dynamic Treatment Effect (GDTE) for a Generalized Error Correction Model (GECM)

Usage

GDTE.gecm.plot(
  model = NULL,
  x.vrbl = NULL,
  y.vrbl = NULL,
  x.vrbl.d.x = NULL,
  y.vrbl.d.y = NULL,
  x.d.vrbl = NULL,
  y.d.vrbl = NULL,
  x.d.vrbl.d.x = NULL,
  y.d.vrbl.d.y = NULL,
  te.type = "pte",
  inferences.y = "levels",
  inferences.x = "levels",
  dM.level = 0.95,
  s.limit = 20,
  se.type = "const",
  return.data = FALSE,
  return.plot = TRUE,
  return.formulae = FALSE,
  ...
)

Arguments

model

the lm model containing the GECM estimates
x.vrbl

a named vector of the x variables (of the lower level of differencing, usually in levels d = 0) and corresponding lag orders in the GECM model
y.vrbl

a named vector of the (lagged) y variables (of the lower level of differencing, usually in levels d = 0) and corresponding lag orders in the GECM model
x.vrbl.d.x

the order of differencing of the x variable (of the lower level of differencing, usually in levels d = 0) in the GECM model
y.vrbl.d.y

the order of differencing of the y variable (of the lower level of differencing, usually in levels d = 0) in the GECM model
x.d.vrbl

a named vector of the x variables (of the higher level of differencing, usually first differences d = 1) and corresponding lag orders in the GECM model
y.d.vrbl

a named vector of the y variables (of the higher level of differencing, usually first differences d = 1) and corresponding lag orders in the GECM model
x.d.vrbl.d.x

the order of differencing of the x variable (of the higher level of differencing, usually first differences d = 1) in the GECM model
y.d.vrbl.d.y

the order of differencing of the y variable (of the higher level of differencing, usually first differences d = 1) in the GECM model
te.type

the desired treatment history. te.type determines the counterfactual series (h) that will be applied to the independent variable. -1 represents a Pulse Treatment Effect (PTE). 0 represents a Step Treatment Effect (STE). These can also be specified via pte, pulse, ste, and step. For others, see Vande Kamp, Jordan, and Rajan. The default is pte
inferences.y

does the user want resulting inferences about the dependent variable in levels or in differences? The default is levels
inferences.x

does the user want to apply the counterfactual treatment to the independent variable in levels or in differences? The default is levels
dM.level

level of significance of the GDTE, calculated by the delta method. The default is 0.95
s.limit

an integer for the number of periods to determine the GDTE (beginning at s = 0)
se.type

the type of standard error to extract from the GECM model. The default is const, but any argument to vcovHC from the sandwich package is accepted
return.data

return the raw calculated GDTEs as a list element under estimates. The default is FALSE
return.plot

return the visualized GDTEs as a list element under plot. The default is TRUE
return.formulae

return the formulae for the GDTEs as a list element under formulae (for the GDTEs) and binomials (for the treatment history). The default is FALSE
...

other arguments to be passed to the call to plot

Details

We assume that the GECM model estimated is well specified, free of residual autocorrelation, balanced, and meets other standard time-series qualities. Given that, to obtain causal inferences for the specified treatment history, the user only needs a named vector of the x and y variables, as well as the order of the differencing. Internally, the GECM to ADL equivalences are used to calculate the GDTEs from the GECM

Value

depending on return.data, return.plot, and return.formulae, a list of elements relating to the GDTE

Author(s)

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

Examples

# GECM(1,1)
# Use the toy data to run a GECM. No argument is made this 
#  is well specified or even sensible; it is just expository
model <- lm(d_y ~ l_1_y + l_1_x + l_1_d_y + d_x + l_1_d_x, data = toy.ts.interaction.data)
test.pulse <- GDTE.gecm.plot(model = model,
                                  x.vrbl = c("l_1_x" = 1), 
                                  y.vrbl = c("l_1_y" = 1),
                                  x.vrbl.d.x = 0, 
                                  y.vrbl.d.y = 0,
                                  x.d.vrbl = c("d_x" = 0, "l_1_d_x" = 1),
                                  y.d.vrbl = c("l_1_d_y" = 1),
                                  x.d.vrbl.d.x = 1,
                                  y.d.vrbl.d.y = 1,
                                  te.type = "pulse", 
                                  inferences.y = "levels", 
                                  inferences.x = "levels",
                                  s.limit = 10, 
                                  return.plot = TRUE, 
                                  return.formulae = TRUE)
names(test.pulse)

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

Description

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 vector of the x variables (of the lower level of differencing, usually in levels d = 0) and corresponding lag orders in the GECM model
y.vrbl

a named vector of the (lagged) y variables (of the lower level of differencing, usually in levels d = 0) and corresponding lag orders in the GECM model
x.d.vrbl

a named vector of the x variables (of the higher level of differencing, usually first differences d = 1) and corresponding lag orders in the GECM model
y.d.vrbl

a named vector of the y variables (of the higher level of differencing, usually first differences d = 1) and corresponding lag orders in the GECM model

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

Value

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

Author(s)

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$x.vrbl.adl
adl.coef$y.vrbl.adl

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

Description

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

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

Value

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

Author(s)

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
# 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

Plot the interaction in a single-equation time series model estimated via lm. It is imperative that you double-check you have referenced all x, y, z, and interaction terms through x.vrbl, y.vrbl, z.vrbl, and x.z.vrbl. You must also have their orders correctly entered. interact.adl.plot has no way of determining, from the variable list, which correspond with which

Description

Plot the interaction in a single-equation time series model estimated via lm. It is imperative that you double-check you have referenced all x, y, z, and interaction terms through x.vrbl, y.vrbl, z.vrbl, and x.z.vrbl. You must also have their orders correctly entered. interact.adl.plot has no way of determining, from the variable list, which correspond with which

Usage

interact.adl.plot(
  model = NULL,
  x.vrbl = NULL,
  z.vrbl = NULL,
  x.z.vrbl = NULL,
  y.vrbl = NULL,
  effect.type = "impulse",
  plot.type = "lines",
  line.options = "z.lines",
  heatmap.options = "significant",
  line.colors = "okabe-ito",
  heatmap.colors = "Blue-Red",
  z.vals = NULL,
  s.vals = c(0, "LRM"),
  z.label.rounding = 3,
  z.vrbl.label = names(z.vrbl)[1],
  dM.level = 0.95,
  s.limit = 20,
  se.type = "const",
  return.data = FALSE,
  return.plot = TRUE,
  return.formulae = FALSE,
  ...
)

Arguments

model

the lm model containing the ADL estimates
x.vrbl

named vector of the “main” x variables and corresponding lag orders in the ADL model
z.vrbl

named vector of the “moderating” z variables and corresponding lag orders in the ADL model
x.z.vrbl

named vector with the interaction variables and corresponding lag orders in the ADL model. IMPORTANT: enter the lag order that pertains to the “main” x variable. For instance, x_l_1_z (contemporaneous x times lagged z) would be 0 and l_1_x_z (lagged x times contemporaneous z) would be 1
y.vrbl

named vector of the (lagged) y variables and corresponding lag orders in the ADL model
effect.type

whether impulse or cumulative effects should be calculated. impulse generates impulse effects, or short-run/instantaneous effects specific to each period. cumulative generates the accumulated, or long-run/cumulative effects up to each period (including the long-run multiplier). The default is impulse
plot.type

whether to feature marginal effects at discrete values of s/z as lines, or across a range of values through a heatmap. The default is lines
line.options

if drawing lines, whether the moderator should be values of z (z.lines) or values of s (s.lines). The default is z.lines
heatmap.options

if drawing a heatmap, whether all marginal effects should be shown or just statistically significant ones. (Note: this just sets the insignificant effects to the numeric value of 0. If the middle value of your scale gradient is white, these will effectively “disappear.” If another gradient is used, they will take on the color assigned to 0 values.) The default is significant
line.colors

what color lines would you like for line plots? This defaults to the color-safe Okabe-Ito (okabe-ito) colors. There is also a grayscale option through bw. Users can also include whatever colors they like. The number of colors must match the number of lines drawn. This is passed to scale_color_discrete
heatmap.colors

what color scale would you like for the heatmap? The default is Blue-Red. Alternate colors must be one of hcl.pals(). For grayscale plots, use Grays. This is passed to scale_fill_gradientn
z.vals

values for the moderating variable. If plot.type = lines, these are treated as discrete levels of z. If plot.type = heatmap, these are treated as a lower and upper level of a range of values of z. If none are provided, interact.adl.plot will pick
s.vals

values for the time since the shock. This is only used if line.options = s.lines, meaning s is treated as the moderator. The default is 0 (short-run) and the LRM
z.label.rounding

number of digits to round to for the z labels in the legend (if those values are automatically calculated)
z.vrbl.label

the name of the moderating z variable, used in plotting
dM.level

significance level of the (cumulative) marginal effects, calculated by the delta method. The default is 0.95
s.limit

an integer for the number of periods to determine the (cumulative) marginal effects (beginning at s = 0)
se.type

the type of standard error to extract from the model. The default is const, but any argument to vcovHC from the sandwich package is accepted
return.data

return the raw calculated (cumulative) marginal effects as a list element under estimates. The default is FALSE
return.plot

return the visualized (cumulative) marginal effects as a list element under plot. The default is TRUE
return.formulae

return the formulae for the (cumulative) marginal effects as a list element under formulae (for the (cumulative) marginal effects) and binomials (for the shock history). The default is FALSE
...

other arguments to be passed to the call to plot

Author(s)

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

Examples

# Using Cavari's (2019) approval model
# Cavari's original model: APPROVE ~ APPROVE_ECONOMY + APPROVE_FOREIGN + MIP_MACROECONOMICS + 
#     MIP_FOREIGN + APPROVE_ECONOMY*MIP_MACROECONOMICS + APPROVE_FOREIGN*MIP_FOREIGN + 
#     APPROVE_L1 + PARTY_IN + PARTY_OUT + UNRATE + 
#     DIVIDEDGOV + ELECTION + HONEYMOON + as.factor(PRESIDENT)

approval$ECONAPP_ECONMIP <- approval$APPROVE_ECONOMY*approval$MIP_MACROECONOMICS
approval$FPAPP_ECONFP <- approval$APPROVE_FOREIGN*approval$MIP_FOREIGN

cavari.model <- lm(APPROVE ~ APPROVE_ECONOMY + APPROVE_FOREIGN + MIP_MACROECONOMICS + 
     MIP_FOREIGN + ECONAPP_ECONMIP + FPAPP_ECONFP + 
     APPROVE_L1 + PARTY_IN + PARTY_OUT + UNRATE + 
     DIVIDEDGOV + ELECTION + HONEYMOON + as.factor(PRESIDENT), data = approval)

# Now: marginal effect of X at different levels of Z
interact.adl.plot(model = cavari.model, 
	x.vrbl = c("APPROVE_ECONOMY" = 0), y.vrbl = c("APPROVE_L1" = 1),
		z.vrbl = c("MIP_MACROECONOMICS" = 0), x.z.vrbl = c("ECONAPP_ECONMIP" = 0),
	effect.type = "impulse", plot.type = "lines", line.options = "z.lines")

# Use well-behaved simulated data (included) for even more examples, 
#  using the Warner, Vande Kamp, and Jordan general model
model.toydata <- lm(y ~ l_1_y + x + l_1_x + z + l_1_z +
	x_z + z_l_1_x +
	x_l_1_z + l_1_x_l_1_z, data = toy.ts.interaction.data)

# Marginal effect of z (not run: computational time)
# Be sure to specify x.z.vrbl orders with respect to x term
## Not run: interact.adl.plot(model = model.toydata, x.vrbl = c("x" = 0, "l_1_x" = 1), 
				y.vrbl = c("l_1_y" = 1), z.vrbl = c("z" = 0, "l_1_z" = 1),
				x.z.vrbl = c("x_z" = 0, "z_l_1_x" = 1, 
					"x_l_1_z" = 0, "l_1_x_l_1_z" = 1),
				z.vals = -2:2,
				effect.type = "impulse", 
				plot.type = "lines", 
				line.options = "z.lines",
				s.limit = 20)

## End(Not run)

# Heatmap of marginal effects, since X and Z are actually continuous
#  (not run: computational time)
## Not run: interact.adl.plot(model = model.toydata, x.vrbl = c("x" = 0, "l_1_x" = 1), 
				y.vrbl = c("l_1_y" = 1), z.vrbl = c("z" = 0, "l_1_z" = 1),
				x.z.vrbl = c("x_z" = 0, "z_l_1_x" = 1, 
					"x_l_1_z" = 0, "l_1_x_l_1_z" = 1),
				z.vals = c(-2,2),
				effect.type = "impulse", 
				plot.type = "heatmap", 
				heatmap.options = "all",
				s.limit = 20)

## End(Not run)

Generate pulse effect formulae for a given autoregressive distributed lag (ADL) model

Description

Generate pulse effect formulae for a given autoregressive distributed lag (ADL) model

Usage

pulse.calculator(x.vrbl, y.vrbl = NULL, limit)

Arguments

x.vrbl

a named vector of the x variables and corresponding lag orders in an ADL model
y.vrbl

a named vector of the (lagged) y variables and corresponding lag orders in an ADL model
limit

an integer for the number of periods (s) to determine the pulse effect (beginning at 0)

Details

pulse.calculator does no calculation. It generates a list of mpoly formulae that contain variable names that represent the pulse 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 pulse.calculator should not include this character

Value

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

Author(s)

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
pulses <- pulse.calculator(x.vrbl = x.lags, y.vrbl = y.lags, limit = s)
pulses
# Will also handle finite dynamics
x.lags <- c("x" = 0, "l_1_x" = 1) # lags of x
finite.pulses <- pulse.calculator(x.vrbl = x.lags, limit = s)

Simulated interactive time series data

Description

A simulated, well-behaved dataset of interactive time series data

Usage

data(toy.ts.interaction.data)

Format

A data frame with 50 rows and 23 variables:

time

Indicator for time period

x

Contemporaneous x

l_1_x

First lag of x

l_2_x

Second lag of x

l_3_x

Third lag of x

l_4_x

Fourth lag of x

l_5_x

Fifth lag of x

d_x

First difference of x

l_1_d_x

First lag of first difference of x

l_2_d_x

Second lag of first difference of x

l_3_d_x

Third lag of first difference of x

z

Contemporaneous z

l_1_z

First lag of z

l_2_z

Second lag of z

l_3_z

Third lag of z

l_4_z

Fourth lag of z

l_5_z

Fifth lag of z

y

Contemporaneous y

l_1_y

First lag of y

l_2_y

Second lag of y

l_3_y

Third lag of y

l_4_y

Fourth lag of y

l_5_y

Fifth lag of y

d_y

First difference of y

l_1_d_y

First lag of first difference of y

l_2_d_y

Second lag of first difference of y

d_2_y

Second difference of y

l_1_d_2_y

First lag of second difference of y

x_z

Interaction of contemporaneous x and z

x_l_1_z

Interaction of contemporaneous x and lagged z

z_l_1_x

Interaction of lagged x and contemporaneous z

l_1_x_l_1_z

Interaction of lagged x and lagged z