Title: Dynamic Simulation and Testing for Single-Equation ARDL Models
Version: 0.1.12
Maintainer: Soren Jordan <sorenjordanpols@gmail.com>
Description: While autoregressive distributed lag (ARDL) models allow for extremely flexible dynamics, interpreting substantive significance of complex lag structures remains difficult. This package is designed to assist users in dynamically simulating and plotting the results of various ARDL models. It also contains post-estimation diagnostics, including a test for cointegration when estimating the error-correction variant of the autoregressive distributed lag model (Pesaran, Shin, and Smith 2001 <doi:10.1002/jae.616>).
URL: https://github.com/andyphilips/dynamac/
BugReports: https://github.com/andyphilips/dynamac/issues
Imports: MASS, lmtest
Suggests: urca, knitr, rmarkdown, testthat
Depends: R (≥ 3.0.1)
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding: UTF-8
LazyData: true
BuildManual: yes
RoxygenNote: 7.2.2
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2022-11-17 01:55:47 UTC; scj0014
Author: Soren Jordan [aut, cre, cph], Andrew Q. Philips [aut]
Repository: CRAN
Date/Publication: 2022-11-17 18:20:06 UTC

Take first difference of a series

Description

Take first difference of a series

Usage

dshift(x)

Arguments

x

a series to be differenced

Details

dshift assumes that the series are ordered, that there is no missing data, and that the time intervals are even

Value

the differenced series

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

x.var <- seq(0, 50, 5)
d.x.var <- dshift(x.var)
head(x.var)
head(d.x.var)

Deprecated functions in package dynamac

Description

The functions listed below are deprecated and will be defunct in the near future. When possible, functions with similar functionality are mentioned. Help pages for deprecated functions are available at help-("deprecated").

Estimate and simulate ARDL model

Description

Estimate autoregressive distributed lag models and simulate interesting values (if desired)

Usage

dynardl(
  formula,
  data = list(),
  lags = list(),
  diffs = c(),
  lagdiffs = list(),
  levels = c(),
  ec = FALSE,
  trend = FALSE,
  constant = TRUE,
  modelout = FALSE,
  noLDV = FALSE,
  simulate = FALSE,
  shockvar = list(),
  shockval = sd(data[[shockvar]], na.rm = T),
  time = 10,
  qoi = "mean",
  forceset = NULL,
  range = 20,
  burnin = 20,
  sims = 1000,
  sig = 95,
  expectedval = FALSE,
  fullsims = FALSE
)

Arguments

formula

a symbolic description of the model to be estimated. ARDL models are estimated using linear regression

data

an optional data frame or list containing the the variables in the model

lags

a list of variables and their corresponding lags to be estimated

diffs

a vector of variables to be differenced. Only first differences are supported

lagdiffs

a list of variables to be included in lagged differences

levels

a vector of variables to be included in levels

ec

estimate model in error-correction form, (i.e., y appears in first-differences). By default, ec is set to FALSE, meaning y will appear in levels.

trend

include a linear time trend. The default is FALSE

constant

include a constant. The default is TRUE

modelout

print the regression estimates in the console

noLDV

do not add a lagged dependent variable (LDV) to ARDL models when omitted in formula (special thanks to Hannes Datta). This is not recommended

simulate

simulate the reponse. Otherwise, just the regression model will be estimated. If simulate = FALSE, options shockvar, shockval, time, qoi, forceset, range, burnin, sims, sig, expectedval, and fullsims are ignored. The default is FALSE so that users can build models without needing to simulate the results each time. When simulate = TRUE, users are highly encouraged to set a seed before simulation, as with any stochastic exercise

shockvar

the variable to be shocked in the counterfactual simulation. There is no default

shockval

the amount by which the shockvar should be shocked. The default is one standard deviation of the shocked variable

time

the time period in the simulation for the variable to be shocked

qoi

summarize the response of the dependent variable with the mean or the median. Although the default is mean, if there is underlying skew in the distribution, it might be better summarized by median

forceset

by default, in the simulations, variables in levels will be set to their means; variables in differences will be set to 0. Alternatively, users can set any variable in the model to a different value using a list in forceset. These values can be any user-defined value, including means, medians, percentiles, or other values of interest

range

the range of the simulation to be conducted

burnin

the number of time periods to disregard before recording the values. These do not include the range; in other words, they take place before the range specified above. Users can increase the number of burnin periods, but probably should not decrease them. The default is 20

sims

the number of simulations to use in creating the quantities of interest (the response of the dependent variable). The default is 1000

sig

the significance level (1 - p) that the user wants for the simulations. The default level is 95% significance (sig = 95)

expectedval

if this is TRUE, the simulation will record the expected values of across the sims by averaging errors. The default is FALSE, since expected values do not account for stochastic error present in the model itself

fullsims

whether all of the raw simulations should be stored in the model object. These are required for some of the more advanced plotting functions, especially those that use the simulations to derive confidence intervals about the size of the period-over-period differences. The default is FALSE

Details

Estimate an auto-regressive distributed lag model. Moreover, enable a graphical interpretation of the results (through dynardl.simulation.plot) by simulating the response of the dependent variable to shocks in one of the regressors, and enable the Pesaran, Shin, and Smith (2001) test for cointegration for error-correction models (through pssbounds)

Value

dynardl should always return an estimated model. It may or may not be simulated, according to the user. But the relevant regression output, model residuals (which can be tested for autocorrelation), and simulated response (if created) are stored in a list if the model is assigned to an object

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

# Using the inequality data from dynamac
ardl.model <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       diffs = c("incshare10", "urate"), 
       ec = TRUE, simulate = FALSE)
summary(ardl.model)

# Adding a lagged difference of the dependent variable
ardl.model.2 <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       diffs = c("incshare10", "urate"), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = FALSE)
summary(ardl.model.2)

# Does not work: levels and diffs must appear as a vector
## Not run: 
ardl.model.3 <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       levels = list("urate" = 1),
       diffs = list("incshare10" = 1, "urate" = 1), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = FALSE)

## End(Not run)

ardl.model.3 <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       levels = c("urate"),
       diffs = c("incshare10", "urate"), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = FALSE)

Combine all of the potential plots of a simulated response in a dynardl model

Description

Combine all of the potential plots of a simulated response in a dynardl model

Usage

dynardl.all.plots(
  x,
  type = "area",
  bw = FALSE,
  last.period = NULL,
  start.period = 1,
  tol = (abs(x$model$ymean) * 0.01),
  abs.errors = "none",
  ylim = NULL,
  xlab = NULL,
  ylab = NULL,
  ...
)

Arguments

x

a dynardl model with a simulation to be plotted. Since all plots includes absolute cumulative differences, fullsims must be TRUE in the dynardl simulation

type

whether the plot should be an area plot (area) or a spike plot (spike)

bw

should the colors be in black and white (for publication)? The default is FALSE

last.period

when deciding when to stop calculating the absolute value of the shocks to the dependent variable, you can specify a specific period in which to stop calculating absolute cumulative differences. Specify a tol or a last.period. If both are specified, last.period overrides tol

start.period

which period of the simulation to begin the plot with. You can view the equilibriating behavior of the dependent variable, or you can skip forward in time (maybe to just before the shock). The default is 1 (the first period of the simulation)

tol

when deciding when to stop calculating the absolute value of the shocks to the dependent variable, you can specify the minimum amount of movement required to qualify as a non-noise change over time periods (for calculating absolute cumulative differences). The default is 0.1 percent of the mean of the dependent variable. Specify a tol or a last.period. If both are specified, last.period overrides tol

abs.errors

when calculating confidence for the absolute cumulative effect, should differences accumulate in each time time period (cumulate, which could be explosive if the error in the model is large), should differences be observed at each time (within.period, which will have smaller values in equilibrium than when changing), or should only the values be plotted (none)

ylim

a user-defined y-limit to be used instead of the default (for instance, for shared axes. Use caution, as it will be passed to all plots)

xlab

a user-defined x-label to be used instead of the default (use caution, as it will be passed to all plots)

ylab

a user-defined y-label to be used instead of the default (use caution, as it will be passed to all plots)

...

other arguments to be passed to the call to plot. Use caution, as they will be passed to all plots

Details

When running dynardl, simulate must be TRUE so that there is a simulation to plot. Also, fullsims must be TRUE as the plot will contain absolute cumulative differences. See dynardl.simulation.plot for arguments to the individual plotting types

Value

a 2 x 3 grid of the plots of the simulated dynardl model effects plots

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

# Using the ineq data in dynamac
# Shocking Income Top 10
# Not run: simulations are time-intensive to estimate as an example
## Not run: 
set.seed(1)
ardl.model <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       diffs = c("incshare10", "urate"), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = TRUE, range = 30,
       shockvar = "incshare10", fullsims = TRUE)

# Shows all of the potential responses
dynardl.all.plots(ardl.model)	
# Same plot, but with spikeplot
dynardl.all.plots(ardl.model, type = "spike")  
# Grayscale plots
dynardl.all.plots(ardl.model, bw = TRUE)	 

## End(Not run)

Run a variety of autocorrelation tests on the residuals from a dynardl model

Description

Run a variety of autocorrelation tests on the residuals from a dynardl model

Usage

dynardl.auto.correlated(
  x,
  bg.type = "Chisq",
  digits = 3,
  order = NULL,
  object.out = FALSE
)

Arguments

x

a dynardl model

bg.type

a character string for the type of Breusch-Godfrey test to run. The default is Chisq: the Chisq test statistic. The other option is F: the F-test statistic

digits

the number of digits to round to when showing output. The default is 3

order

the maximum order of serial autocorrelation to test when executing the Breusch-Godfrey test

object.out

if TRUE, and dynardl.auto.correlated is assigned to an object, the AIC, BIC, and results will be stored for the user's convenience

Details

This is a simple and convenient way to test whether the residuals from the dynardl model are white noise. As an aside, this is also why dynardl has a simulate = FALSE argument: users can ensure the model has white noise residuals before estimating a potentially time-intensive simulation. The output also reminds the user of the null hypotheses for the autocorrelation tests

Value

The results of autocorrelation tests

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

# Using the ineq data from dynamac
ardl.model <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       diffs = c("incshare10", "urate"), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = FALSE)
dynardl.auto.correlated(ardl.model)

Create a plot of a simulated response in a dynardl model

Description

Create a plot of a simulated response in a dynardl model

Usage

dynardl.simulation.plot(
  x,
  type = "area",
  response = "levels",
  bw = FALSE,
  last.period = NULL,
  tol = (abs(x$model$ymean) * 0.01),
  start.period = 1,
  abs.errors = "none",
  ylim = NULL,
  ylab = NULL,
  xlab = NULL,
  ...
)

Arguments

x

a dynardl model with a simulation to be plotted

type

whether the plot should be an area plot (area) or a spike plot (spike)

response

whether the plot of the response should be shown in levels of the dependent variable (levels), levels from the mean of the dependent variable (levels.from.mean), period-over-period changes in the dependent variable (diffs), the absolute value of the (decreasing) change in the dependent variable in each time period due to the shock (shock.effect.decay), the sum of the period-over-period changes (cumulative.diffs), or the absolute value of the cumulative differences (where negative effects are treated as positive) (cumulative.abs.diffs). The default is levels

bw

should the colors be in black and white (for publication)? The default is FALSE

last.period

when deciding when to stop calculating the absolute value of the shocks to the dependent variable, you can specify a specific period in which to stop calculating absolute cumulative differences. Specify a tol or a last.period. If both are specified, last.period overrides tol

tol

when deciding when to stop calculating the absolute value of the shocks to the dependent variable, you can specify the minimum amount of movement required to qualify as a non-noise change over time periods (for calculating absolute cumulative differences). The default is 0.1 percent of the mean of the dependent variable. Specify a tol or a last.period. If both are specified, last.period overrides tol

start.period

which period of the simulation to begin the plot with. You can view the equilibriating behavior of the dependent variable, or you can skip forward in time (maybe to just before the shock). The default is 1 (the first period of the simulation)

abs.errors

when calculating confidence for the absolute cumulative effect, should differences accumulate in each time time period (cumulate, which could be explosive if the error in the model is large), should differences be observed at each time (within.period, which will have smaller values in equilibrium than when changing), or should only the values be plotted (none). The default is none

ylim

a user-defined y-limit to be used instead of the default (for instance, for shared axes)

ylab

a user-defined y-label to be used instead of the default

xlab

a user-defined x-label to be used instead of the default

...

other arguments to be passed to the call to plot

Details

When running dynardl, simulate must be TRUE so that there is a simulation to plot. For types cumulative.diffs and cumulative.abs.diffs, fullsims must be TRUE in the dynardl simulation

Value

a plot of the simulated dynardl model

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

# Using the ineq data in dynamac
# Shocking Income Top 10
# Not run: simulations are time-intensive to estimate as an example
## Not run: 
set.seed(1)
ardl.model <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       diffs = c("incshare10", "urate"), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = TRUE, range = 30,
       shockvar = "incshare10", fullsims = TRUE)

# Shows absolute levels
dynardl.simulation.plot(ardl.model)	
# Shows changes from mean level
dynardl.simulation.plot(ardl.model, response = "levels.from.mean")  
# Same plot, but with spikeplot
dynardl.simulation.plot(ardl.model, type = "spike", response = "levels.from.mean")  
# Grayscale plots
dynardl.simulation.plot(ardl.model, bw = TRUE)

## End(Not run)

Data on French Energy Consumption and GDP

Description

Data on GDP are from World Bank World Development Indicators. Data on energy consumption are from the PB Statistical Review of World Energy (June 2018).

Usage

data(france.data)

Format

A data frame with 53 rows and 4 variables:

country

Country

year

Year

lnGDP_cons2010USD

ln(GDP), constant 2010 US dollars

lnenergy

ln(energy consumption), millions tons oil equivalent

Data on public concern about economic inequality

Description

A dataset from: Wright, Graham. 2017. "The political implications of American concerns about economic inequality." Political Behavior 40(2): 321-346.

Usage

data(ineq)

Format

A data frame with 49 rows and 9 variables:

year

Year

mood

Public mood liberalism

urate

Unemployment rate

concern

Concern about economic inequality

demcontrol

Democratic control of congress

incshare10

Proportion of income of top 10 percent

csentiment

Consumer sentiment

incshare01

Proportion of income of top 1 percent

Source

doi: 10.7910/DVN/UYUU9G

Take the lagged first difference of a series

Description

Take the lagged first difference of a series

Usage

ldshift(x, l)

Arguments

x

a series to be differenced

l

the number of lags

Details

ldshift assumes that the series are ordered, that there is no missing data, and that the time intervals are even

Value

the lagged differenced series

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

x.var <- runif(50)
ld.1.x.var <- ldshift(x.var, 1)
ld.2.x.var <- ldshift(x.var, 2)
head(x.var)
head(ld.1.x.var)
head(ld.2.x.var)

Take lag transformation of a series

Description

Take lag transformation of a series

Usage

lshift(x, l)

Arguments

x

a series to be lagged

l

the number of lags

Details

lshift assumes that the series are ordered, that there is no missing data, and that the time intervals are even

Value

the lagged series

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

x.var <- runif(50)
l.1.x.var <- lshift(x.var, 1)
l.2.x.var <- lshift(x.var, 2)
head(x.var)
head(l.1.x.var)
head(l.2.x.var)

Perform Pesaran, Shin, and Smith (2001) cointegration test

Description

Perform Pesaran, Shin, and Smith (2001) cointegration test

Usage

pssbounds(
  data = list(),
  obs = NULL,
  fstat = NULL,
  tstat = NULL,
  case = NULL,
  k = NULL,
  restriction = FALSE,
  digits = 3,
  object.out = FALSE
)

Arguments

data

an optional dynardl model. This option is highly recommended. Users are welcome to supply their own case, k regressors, t-statistic, F-statistic, and observations, but it is easier to have the model determine these quantities. If a dynardl model is supplied, user-supplied arguments are ignored

obs

number of observations

fstat

F-statistic of the joint test that variables in first lags are equal to zero: the specific restriction tested is l.y + l.1.x1 + l.1.x2 + ... + l.1.xk = 0, except in cases II and IV (see restriction and case)

tstat

t-statistic of the lagged dependent variable

case

The case of the test, as per Pesaran, Shin, and Smith (2001). Case I: no intercept or trend; case II: restricted intercept, no trend; case III: unrestricted intercept with no trend; case IV: unrestricted intercept and restricted trend; case V: unrestricted intercept and trend. Case III is most frequently specified

k

number of regressors appearing in levels in the estimated model, not including the lagged dependent variable

restriction

if you design to test case II or IV of pssbounds, where it is assumed that the constant (case 2) or trend (case 4) are restricted in the resulting F-test, indicate that restriction = TRUE. If restriction = TRUE and there is no trend in the regression (trend = FALSE in dynardl), the F-test will include the constant in addition to the lagged dependent variable and lagged regressors in order to test for cointegration under the assumption of a restricted constant (see Pesaran, Shin and Smith [2001], case II). If restriction = TRUE and there is a trend in the regression (trend = TRUE in dynardl), the F-test will include the trend term in addition to the lagged dependent variable and lagged regressors in order to test for cointegration under the assumption of a restricted trend (see Pesaran, Shin and Smith [2001], case IV). If you are estimating the regular unrestricted ECM (this is more common), restriction = FALSE. The default is FALSE

digits

the number of digits to round to when showing output. The default is 3

object.out

if TRUE, and pssbounds is assigned to an object, the test quantities will be stored for the user's convenience

Details

pssbounds performs post-estimation cointegration testing using the bounds testing procedure from Pesaran, Shin, and Smith (2001). Since test statistics vary based on the number of k regressors, length of the series, these are required, in addition to F- and t-statistics

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

# Using the ineq data from dynamac
# We can get all the values by hand
ardl.model <- dynardl(concern ~ incshare10 + urate, data = ineq, 
        lags = list("concern" = 1, "incshare10" = 1),
        diffs = c("incshare10", "urate"), 
        lagdiffs = list("concern" = 1),
        ec = TRUE, simulate = FALSE)
summary(ardl.model)
pssbounds(obs = 47, fstat = 7.01578, tstat = -3.223, case = 3, k = 1)

# Or just pass a dynardl model.
pssbounds(ardl.model)

Enable summary calls to dynardl model objects

Description

Enable summary calls to dynardl model objects

Usage

## S3 method for class 'dynardl'
summary(object, ...)

Arguments

object

a dynardl model

...

additional arguments in the generic summary call

Details

dynardl, by default, stores regression results in foo$model. This calls those results directly with summary

Value

A summary of the fitted ARDL model.

Author(s)

Soren Jordan and Andrew Q. Philips

Examples

# Using the ineq data from dynamac
ardl.model <- dynardl(concern ~ incshare10 + urate, data = ineq, 
       lags = list("concern" = 1, "incshare10" = 1),
       diffs = c("incshare10", "urate"), 
       lagdiffs = list("concern" = 1),
       ec = TRUE, simulate = FALSE)
summary(ardl.model)

Data on US Supreme Court Approval

Description

A dataset from: Durr, Robert H., Andrew D. Martin, and Christina Wolbrecht. 2000. "Ideological divergence and public support for the Supreme Court." American Journal of Policial Science 44(4): 768-776.

Usage

data(supreme.sup)

Format

A data frame with 42 rows and 9 variables:

dcalc

Supreme Court support

l_dcalc

Lagged Supreme Court spport

iddiv

Ideological divergence

mooddev

Mean deviation of Mood

dirdev

Mean deviation of percent liberal decisions

sg

Rulings against Solicitor General's amicus briefs

laws

Laws declared unconstitutional

presapp

Approval of president

congapp

Approval of Congress

Source

doi: 10.2307/2669280

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