Type:	Package
Title:	Production Function Output Gap Estimation
Version:	0.1.1
Depends:	R (≥ 3.1.0)
Description:	The output gap indicates the percentage difference between the actual output of an economy and its potential. Since potential output is a latent process, the estimation of the output gap poses a challenge and numerous filtering techniques have been proposed. 'RGAP' facilitates the estimation of a Cobb-Douglas production function type output gap, as suggested by the European Commission (Havik et al. 2014) https://ideas.repec.org/p/euf/ecopap/0535.html. To that end, the non-accelerating wage rate of unemployment (NAWRU) and the trend of total factor productivity (TFP) can be estimated in two bivariate unobserved component models by means of Kalman filtering and smoothing. 'RGAP' features a flexible modeling framework for the appropriate state-space models and offers frequentist as well as Bayesian estimation techniques. Additional functionalities include direct access to the 'AMECO' https://economy-finance.ec.europa.eu/economic-research-and-databases/economic-databases/ameco-database_en database and automated model selection procedures. See the paper by Streicher (2022) http://hdl.handle.net/20.500.11850/552089 for details.
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.3
Imports:	stats, KFAS, zoo, dlm, openxlsx, ggplot2, gridExtra
Suggests:	testthat (≥ 3.0.0), R.rsp
VignetteBuilder:	R.rsp
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2023-11-02 07:56:36 UTC; sinast
Author:	Sina Streicher [aut, cre]
Maintainer:	Sina Streicher <streicher@kof.ethz.ch>
Repository:	CRAN
Date/Publication:	2023-11-02 09:00:02 UTC

Estimates the parameters and states of a two-dimensional state-space model by Bayesian methods to obtain the nawru.

Description

Estimates the parameters and states of a two-dimensional state-space model by Bayesian methods to obtain the nawru.

Usage

.BayesFitNAWRU(
  model,
  prior = initializePrior(model),
  R = 10000,
  burnin = ceiling(R/10),
  thin = 1,
  HPDIprob = 0.85,
  FUN = mean,
  MLEfit = NULL
)

Arguments

Estimates the parameters and states of a two-dimensional state-space model by Bayesian methods to obtain the tfp trend.

Description

Estimates the parameters and states of a two-dimensional state-space model by Bayesian methods to obtain the tfp trend.

Usage

.BayesFitTFP(
  model,
  prior = initializePrior(model),
  R = 10000,
  burnin = ceiling(R/10),
  thin = 1,
  HPDIprob = 0.85,
  FUN = mean,
  MLEfit = NULL
)

Arguments

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the nawru.

Description

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the nawru.

Usage

.MLEfitNAWRU(
  model,
  parRestr = initializeRestr(model = model),
  signalToNoise = NULL,
  control = NULL
)

Arguments

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the tfp trend.

Description

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the tfp trend.

Usage

.MLEfitTFP(
  model,
  parRestr = initializeRestr(model),
  signalToNoise = NULL,
  control = NULL
)

Arguments

Transforms the parameters of an AR(2) process to its re-parametrized version RAR(2) and vice versa.

Description

Transforms the parameters of an AR(2) process to its re-parametrized version RAR(2) and vice versa.

Usage

.RAR2transform(par, phi2Atau = TRUE)

Arguments

Value

A vector with the transformed parameters

Prepares state space model system matrices to create an object of type NAWRUmodel or TFPmodel.

Description

Prepares state space model system matrices to create an object of type NAWRUmodel or TFPmodel.

Usage

.SSSystem(tsl, cycle, trend, cycleLag, type = NULL, errorARMA)

Arguments

Computes figures regarding the model fit of the maximum likelihood estimation.

Description

Computes figures regarding the model fit of the maximum likelihood estimation.

Usage

.SSmodelfit(out, nPar)

Arguments

Computes additional results of the Kalman filter and smoother.

Description

Computes additional results of the Kalman filter and smoother.

Usage

.SSresults(out, model, prediction = FALSE)

Arguments

Computes additional results of the Kalman filter and smoother for Bayesian output.

Description

Computes additional results of the Kalman filter and smoother for Bayesian output.

Usage

.SSresultsBayesian(model, HPDIprob, state, obsFitted, FUN)

Arguments

Accesses the internal data frame dfSystem which contains data on the parameters to be estimated.

Description

Accesses the internal data frame dfSystem which contains data on the parameters to be estimated.

Usage

.accessDfSystem(model)

Arguments

Value

A data frame containing information on each involved parameter, for instance its corresponding system matrix, variable names, and parameter restrictions.

Temporally Aggregates time series.

Description

Temporally Aggregates time series.

Usage

.aggregate(x, freqLow, FUN)

Arguments

Assigns the appropriate function and its input variables for the Gibbs procedure.

Description

Assigns the appropriate function and its input variables for the Gibbs procedure.

Usage

.assignGibbsFUN(
  loc,
  type,
  trend,
  cycle,
  cubsAR,
  cycleLag,
  errorARMA,
  exoNames = NULL
)

Arguments

Checks the input parameters of .BayesFitTFP and .BayesFitNAWRU for consistency.

Description

Checks the input parameters of .BayesFitTFP and .BayesFitNAWRU for consistency.

Usage

.checkBayesInput(
  model,
  type,
  prior = NULL,
  R = NULL,
  burnin = NULL,
  thin = NULL,
  HPDIprob = NULL,
  FUN = NULL,
  MLEfit = NULL
)

Arguments

Checks whether estimated parameters lie on boundaries.

Description

Checks whether estimated parameters lie on boundaries.

Usage

.checkBoundaries(fit, loc)

Arguments

Checks the covariance matrix for invertibility and negative entries on the diagonal.

Description

Checks the covariance matrix for invertibility and negative entries on the diagonal.

Usage

.checkCV(fit, loc)

Arguments

Checks the input variables for the procedure cubs for consistency and validity.

Description

Checks the input variables for the procedure cubs for consistency and validity.

Usage

.checkCubs(tsCU, tsVA, lambda, frequency)

Arguments

Checks the input variables for the procedure KuttnerModel for consistency and validity.

Description

Checks the input variables for the procedure KuttnerModel for consistency and validity.

Usage

.checkKuttner(
  tsl,
  trend,
  cycle,
  cycleLag,
  errorARMA,
  start,
  end,
  anchor,
  anchor.h
)

Arguments

Checks whether model, prior and MLE fit match.

Description

Checks whether model, prior and MLE fit match.

Usage

.checkModelMLEfit(model, MLEfit)

Arguments

Checks whether model and prior match.

Description

Checks whether model and prior match.

Usage

.checkModelPrior(model, prior)

Arguments

Checks the input variables for the procedure NAWRUmodel for consistency and validity.

Description

Checks the input variables for the procedure NAWRUmodel for consistency and validity.

Usage

.checkNawru(
  tsl,
  trend,
  cycle,
  type,
  cycleLag,
  errorARMA,
  exoNames,
  exoType,
  start,
  end,
  anchor,
  anchor.h
)

Arguments

Checks the given variance restrictions for consistency.

Description

Checks the given variance restrictions for consistency.

Usage

.checkParRestr(model, parRestr)

Arguments

Checks the given prior information for consistency and applicability.

Description

Checks the given prior information for consistency and applicability.

Usage

.checkPrior(model, prior)

Arguments

Checks the input variables for the procedure TFPmodel for consistency and validity.

Description

Checks the input variables for the procedure TFPmodel for consistency and validity.

Usage

.checkTfp(
  tsl,
  trend,
  cycle,
  cycleLag,
  cubsAR,
  errorARMA,
  start,
  end,
  anchor,
  anchor.h
)

Arguments

Computes the covariance of an AR(q) process.

Description

Computes the covariance of an AR(q) process.

Usage

.covAR(k, phi, sigma)

Arguments

Value

A k x k covariance matrix.

computes the unconditional variance of the cubs equation with p lags of cubs and k additional lags of the cycle. The cycle follows an AR process of order l.

Description

computes the unconditional variance of the cubs equation with p lags of cubs and k additional lags of the cycle. The cycle follows an AR process of order l.

Usage

.covCUBS(mu, phi, beta, sigma, phiC, sigmaC)

Arguments

Value

A list with a two covariance matrices; the first one depicts the covariance between the cycle and cubs and the second onf the covariance of cubs.

Adjusts the frequency of cubs input series.

Description

Adjusts the frequency of cubs input series.

Usage

.cubsTa(tsObj, conversion, frequency)

Arguments

Details

If frequency == 1, then the values for the latest and the first year are averaged over the existing months/quarters. However, for the latest year, this is only done if the third quarter is available.

Computes standard errors of the observation equation using the delta method (for forecast).

Description

Computes standard errors of the observation equation using the delta method (for forecast).

Usage

.deltaMethodObs(out, nameObs, model, constant = 1)

Arguments

Computes standard errors of the state using the delta method.

Description

Computes standard errors of the state using the delta method.

Usage

.deltaMethodState(out, nameState, constant = 1)

Arguments

defines Y and X in the CUBS equation.

Description

defines Y and X in the CUBS equation.

Usage

.getXYcubs(stateSmoothed, model, cycleLag, cubsAR, names, trim = FALSE)

Arguments

defines Y and X for the Phillips curve.

Description

defines Y and X for the Phillips curve.

Usage

.getXYpcInd(stateSmoothed, model, cycleLag, pcIndAR, names, trim = FALSE)

Arguments

Draws from the posterior of the parameters of the cubs equation, conditional on the states.

Description

Draws from the posterior of the parameters of the cubs equation, conditional on the states.

Usage

.gibbsStep2Eq(
  Y,
  X,
  p,
  pk,
  pa,
  betaLast,
  sigmaLast,
  betaDistr,
  sigmaDistr,
  phiLast = NULL,
  phiDistr = NULL,
  phiC,
  sigmaC
)

Arguments

Details

The parameter vector beta and the innovation variance are Normal-inverse Gamma distributed. A draw from their posterior is obtained by conjugacy.

If there are additional lags of the cycle or cubs, conjugacy does not apply since the starting values are not given. In this case, a Metropolis-Hasting step is implemented.

If the error term is an AR(1) or AR(2) process, an additional Gibbs step draws from the posterior of the autoregressive parameter, given all other parameters.

Draws from the posterior of the parameters of the AR(p), p = 1,2 cycle equation, conditional on the states.

Description

Draws from the posterior of the parameters of the AR(p), p = 1,2 cycle equation, conditional on the states.

Usage

.gibbsStepAR(Y, parLast, parDistr, varNames)

Arguments

Details

The autoregressive parameter and the innovation variance are drawn sequentially.

If the cycle is AR(1) process, the posterior is obtained by conjugacy. If it is an AR(2) process, a Metropolis-Hastings step is implemented.

Conditional on the autoregressive parameters, the innovation variance is drawn from the Inverse Gamma posterior which is obtained by conjugacy.

Draws from the posterior of the parameters of the damped trend equation, conditional on the states.

Description

Draws from the posterior of the parameters of the damped trend equation, conditional on the states.

Usage

.gibbsStepDT(Y, par, distr, varName)

Arguments

Details

The three parameters are drawn sequentially in a Gibbs procedure. (conditional on the two other parameters).

The parameter \omega is drawn from a normal posterior which is obtained by conjugancy.

The autoregressive parameter \phi is drawn via a Metropolis-Hastings step.

The innovation variance is drwan from the Inverse-Gamma distribution which obtained by conjugacy.

Draws from the posterior of the parameters of the RAR2 cycle equation, conditional on the states.

Description

Draws from the posterior of the parameters of the RAR2 cycle equation, conditional on the states.

Usage

.gibbsStepRAR2(Y, parLast, parDistr, varNames)

Arguments

Details

The parameters A and \tau are Beta distributed and the variance \sigma^2 is Gamma distributed.

The posterior is not available in closed form, instead it is obtained via an ARMS step.

Value

A list with the draws.

Initializes the location file containing default parameter constraints, among other things.

Description

Initializes the location file containing default parameter constraints, among other things.

Usage

.initializeLoc(model)

Arguments

Value

A data frame containing information on each involved parameter, for instance its corresponding system matrix, variable names, and parameter restrictions.

Initializes variance restrictions.

Description

Initializes variance restrictions.

Usage

.initializeVar(
  model,
  type = NULL,
  lambda = NULL,
  prior = FALSE,
  errorARMA = c(0, 0),
  q = 0.05
)

Arguments

Computes confidence interval of Inverse Gamma distributed variable with given mean and standard deviation.

Description

Computes confidence interval of Inverse Gamma distributed variable with given mean and standard deviation.

Usage

.intervalIGamma(mu, sd, qlower = 0.025, qupper = 1 - qlower)

Arguments

Value

A 2 x k matrix containing the lower and upper bounds of the intervals.

Converts the mean and standard deviation of a (possibly scaled) Beta-distributed variable into the two shape parameters \alpha and \beta.

Description

Converts the mean and standard deviation of a (possibly scaled) Beta-distributed variable into the two shape parameters \alpha and \beta.

Usage

.meanStd2Beta(m, std, lb = 0, ub = 1)

Arguments

Value

A vector with shape parameters \alpha and \beta.

Converts the mean and standard deviation of a Gamma-distributed variable into the parameters s and \nu.

Description

Converts the mean and standard deviation of a Gamma-distributed variable into the parameters s and \nu.

Usage

.meanStd2GammasNu(m, std)

Arguments

Details

The parameters s and nu are related to the regular shape \alpha and rate \beta parametrization in the following way: \alpha = \nu / 2 \beta = s / 2

Value

A vector with parameters s and \nu.

Modifies a an object of type NAWRUmodel or TFPmodel in case the variance constraint for the trend is set to zero or in case a signal-to-noise ratio is specified.

Description

Modifies a an object of type NAWRUmodel or TFPmodel in case the variance constraint for the trend is set to zero or in case a signal-to-noise ratio is specified.

Usage

.modifySSSystem(model, signalToNoise)

Arguments

Draws from the multivariate normal distribution.

Description

Draws from the multivariate normal distribution.

Usage

.mvrnorm(mu, sigma)

Arguments

Normalizes a time series / vector.

Description

Normalizes a time series / vector.

Usage

.normalize(x)

Arguments

Draws from the posterior the autoregressive parameter of a stationary AR(1) process without starting values.

Description

Draws from the posterior the autoregressive parameter of a stationary AR(1) process without starting values.

Usage

.postAR1(Y, phi, phi0, Q0, sigma, lb = -Inf, ub = Inf)

Arguments

Details

The corresponding model is given by Y_t = \phi Y_{t-1} + e_t, where e_t ~ N(0, \sigma) with prior distribution p(\phi) = N(\phi_0, 1/Q_0 ).

Conditional on the variance \sigma, the posterior is normal and known.

Stationarity and box constraints are enforced. If the stationarity constraint is not fulfilled, the last draw is returned.

Draws from the posterior of the autoregressive paramteres of a stationary AR(p), p > 1 process without starting values.

Description

Draws from the posterior of the autoregressive paramteres of a stationary AR(p), p > 1 process without starting values.

Usage

.postARp(Y, phi, phi0, Q0, sigma, lb = -Inf, ub = Inf)

Arguments

Details

The corresponding model is given by Y_t = \phi_1 Y_{t-1} + ... + \phi_p Y_{t-p} + e_t, where e_t ~ N(0, \sigma) with prior distribution p(\phi) = N(\phi_0, 1/Q_0 ).

The posterior draw is obtained via a Metropolis Hastings step with proposal density q = \prod_{t=p+1}^Tn p(Y_t, \phi, \sigma, Y_{t-1}, ..., Y_{t-p} ) which is known due to conjugacy. The acceptance probability is given by \alpha = \min{1, p(Y_1, ... Y_p | \phi_r, \sigma) / p(Y_1, ... Y_p | \phi_{r-1}, \sigma)} where the subscript r denotes the r-th draw. p(Y_1, ... Y_p | \phi_r, \sigma) is itself normal.

Stationarity and box constraints are enforced. If the constraints are not fulfilled, the last draw is returned.

Draws from the posterior of parameters of a normal model with normal inverse gamma prior.

Description

Draws from the posterior of parameters of a normal model with normal inverse gamma prior.

Usage

.postNIG(Y, X, betaLast, betaDistr, sigmaDistr)

Arguments

Details

Draws from the posterior are obtained by conjugacy of the Normal-Inverse-Gamma distribution.

Value

A list with a draws for beta and the innovation variance.

Draws from the posterior of the variance parameter of a random walk or a random walk with constant or stochastic drift.

Description

Draws from the posterior of the variance parameter of a random walk or a random walk with constant or stochastic drift.

Usage

.postRW(Y, sigmaDistr, sigmaLast = NULL, muDistr = NULL)

Arguments

Details

If the process follows a random walk with constant drift, the two parameters are drawn sequentially (conditional on the other parameter). The constant is drawn from a normal posterior given by conjugacy.

The innovation variance is drawn from a Inverse-Gamma posterior given by conjugacy.

Prints the results of the Geweke test for the states and the parameters.

Description

Prints the results of the Geweke test for the states and the parameters.

Usage

.printGeweke(tsl, df, alpha = 0.05)

Arguments

Prints the model specifications.

Description

Prints the model specifications.

Usage

.printSSModel(x, call = TRUE, check = TRUE)

Arguments

Prints the model fit and possibly specifications.

Description

Prints the model fit and possibly specifications.

Usage

.printSSModelFit(x, call = TRUE, check = TRUE, print.model = TRUE)

Arguments

Transforms the prior distribution defined by mean and standard deviation to the appropriate input parameters.

Description

Transforms the prior distribution defined by mean and standard deviation to the appropriate input parameters.

Usage

.priorMSd2Parameter(
  prior,
  restr,
  namesInvGammaDistr,
  namesNormalDistr,
  namesBetaDistr
)

Arguments

Updates the parameter constraints for on object of class NAWRUmodel or TFPmodel.

Description

Updates the parameter constraints for on object of class NAWRUmodel or TFPmodel.

Usage

.updateParConstraints(model, parRestr)

Arguments

Value

The same model with updated list item loc.

Updates the system matrices of an object of class NAWRUmodel or TFPmodel during optimization or during a Bayesian Gibbs procedure.

Description

Updates the system matrices of an object of class NAWRUmodel or TFPmodel during optimization or during a Bayesian Gibbs procedure.

Usage

.updateSSSystem(
  pars,
  SSModel,
  loc,
  cycle,
  trend,
  errorARMA,
  signalToNoise = NULL,
  type = NULL,
  bayes = FALSE
)

Arguments

Extracts the derivative of the applied restriction function.

Description

Extracts the derivative of the applied restriction function.

Usage

Dconstraint(par, type = NA)

Arguments

Computes mean and variance of the part of the posterior distribution that relies on starting values. It then computes the density of the first p observations of Y.

Description

Computes mean and variance of the part of the posterior distribution that relies on starting values. It then computes the density of the first p observations of Y.

Usage

FUNcov(Xcubs, Xc, Y, mu, phi, beta, sigma, phiC, sigmaC)

Arguments

Computes the approximate highest posterior density interval (HPDI).

Description

Computes the approximate highest posterior density interval (HPDI).

Usage

HPDinterval(x, prob = 0.95)

Arguments

Kuttner model

Description

Creates a state space object object of class KuttnerModel which can be fitted using fit.

Usage

KuttnerModel(
  tsl,
  cycle = "AR2",
  cycleLag = 1,
  trend = "RW1",
  inflErrorARMA = c(0, 3),
  start = NULL,
  end = NULL,
  anchor = NULL,
  anchor.h = NULL
)

Arguments

Details

The list of time series tsl needs to have the following components:

gdp

Real gross domestic product.

infl

Inflation.

A cycleLag equal to 0 implies that only the contemporaneous cycle is included in the inflation equation. A cycleLag equal to 0:1 implies that the contemporaneous as well as the lagged cycle are included.

A inflErrorARMA equal to c(0, 0) implies that the error term in the inflation equation is white noise. inflErrorARMA = c(1, 0) implies that the error is an AR(1) process and for inflErrorARMA = c(1, 2) the error follows an ARMA(1, 2) process.

Value

Object of class KuttnerModel, which is a list with the following components:

In addition, the object contains the following attributes:

Examples

# load data for the Netherlands
data("gap")
country <- "Netherlands"
tsList <- as.list(gap[[country]][, c("cpih", "gdp")])
tsList$infl <- diff(tsList$cpih)
model <- KuttnerModel(tsl = tsList, trend = "RW2", start = 1980)

NAWRU model

Description

Creates a state space object object of class NAWRUmodel which can be fitted using fit.

Usage

NAWRUmodel(
  tsl,
  trend = "RW2",
  cycle = "AR2",
  type = "TKP",
  cycleLag = 0,
  pcErrorARMA = c(0, 0),
  exoType = NULL,
  start = NULL,
  end = NULL,
  anchor = NULL,
  anchor.h = NULL
)

Arguments

Details

The list of time series tsl needs to have the following components:

ur

Unemployment rate.

nulc

Nominal Unit labor costs, if type = "TKP".

rulc

Real unit labor costs, if type = "NKP".

and optionally other variables included in exoType.

A cycleLag equal to 0 implies that only the contemporaneous cycle is included in the Phillip's curve. A cycleLag equal to 0:1 implies that the contemporaneous as well as the lagged cycle are included.

A pcErrorARMA equal to c(0, 0) implies that the error term in the Phillip's curve is white noise. pcErrorARMA = c(1, 0) implies that the error is an AR(1) process and for pcErrorARMA = c(1, 2) the error follows an ARMA(1, 2) process.

For the New Keynesian Phillip's curve, the cycleLag cannot be chosen. cycleLag will be set to 0 if cycle = "AR1" and to 1 if cycle = "AR2". In the latter case, the forward solution of the Phillip's curve implies parameter restrictions for the lagged cycle on the Phillip's curve. Moreover, exogenous variables will be ignored in the case of the New Keynesian Phillip's curve.

The array exoType consists of non-negative integers or NAs. exoType[, , 1] = c(NA,1) and exoType[, , 2] = c(NA,2) implies that the first variable is not included in the Phillip's curve whereas the second lag of the first difference of the second variable is included.

Value

Object of class NAWRUmodel, which is a list with the following components:

In addition, the object contains the following attributes:

Examples

# load data for France
data("gap")
tsList <- amecoData2input(gap$France, alpha = 0.65)
# Traditional phillips curve
model <- NAWRUmodel(tsl = tsList, trend = "RW2", cycle = "AR2", type = "TKP", cycleLag = 0)

# New-Keynesian Phillips curve
model <- NAWRUmodel(tsl = tsList, trend = "RW2", cycle = "AR2", type = "NKP", cycleLag = 0:1)

# Traditional Phillips curve with 6 exogenous variables
# specify exogenous variable transformations
D <- matrix(c(2, 2, 2, 1, 1, 1), 2, 3, byrow = TRUE)
L <- matrix(c(0, 0, 0, 1, 1, 1), 2, 3, byrow = TRUE)
exoType <- initializeExo(varNames = c("tot", "prod","ws"), D = D, L = L)
model <- NAWRUmodel(tsl = tsList, cycleLag = 0:1, exoType = exoType)

TFP trend model

Description

Creates a state space object object of class TFPmodel which can be fitted using fit.

Usage

TFPmodel(
  tsl,
  trend = "DT",
  cycle = "AR2",
  cycleLag = 0,
  cubsAR = 0,
  cubsErrorARMA = c(0, 0),
  start = NULL,
  end = NULL,
  anchor = NULL,
  anchor.h = NULL
)

Arguments

Details

The list of time series tsl needs to have the following components:

tfp

Total factor productivity.

cubs

Capacity utilization economic sentiment indicator.

A cycleLag equal to 0 implies that only the contemporaneous cycle is included in the CUBS equation. A cycleLag equal to 0:1 implies that the contemporaneous as well as the lagged cycle are included.

A cubsAR equal to 0 implies that no autoregressive term is included in the CUBS equation. cubsAR = 1 implies that a lagged term is included, cubsAR = 2 implies that a two lags are included, and so on.

A cubsErrorARMA equal to c(0, 0) implies that the error term in the CUBS equation is white noise. cubsErrorARMA = c(1, 0) implies that the error is an AR(1) process and for cubsErrorARMA = c(1, 2) the error follows an ARMA(1, 2) process.

Value

Object of class TFPmodel, which is a list with the following components:

In addition, the object contains the following attributes:

Examples

# load data for Germany
data("gap")
data("indicator")
country <- "Germany"
tsList <- amecoData2input(gap[[country]], alpha = 0.65)

# compute cubs indicator
namesCubs <- c("indu", "serv", "buil")
namesVACubs <- paste0("va", namesCubs)
tscubs <- cubs(
  tsCU = gap[[country]][, namesCubs],
  tsVA = gap[[country]][, namesVACubs]
)
tsList <- c(tsList, tscubs)

# define tfp model
model <- TFPmodel(tsl = tsList, cycle = "RAR2", cubsErrorARMA = c(1,0))

Data for estimation

Description

Computes the necessary input data for the EC output gap estimation on the basis of AMECO data.

Usage

amecoData2input(tslAmeco, alpha = 0.65)

Arguments

Details

The list of time series tslAmeco needs to have the following components:

popw

Population: 15 to 64 years (unit: 1000 persons, code: NPAN)

ur

Unemployment rate, total; Member States: definition EUROSTAT (unit: Percentage of civilian labor force, code: ZUTN)

etd

Employment, persons: total economy (National accounts) (unit: 1000 persons, code: NETN)

et

Employment, persons: all domestic industries (National accounts) (unit: 1000 persons, code: NETD)

eet

Employees, persons: all domestic industries (National accounts) (unit: 1000 persons, code: NWTD)

pconsp

Price deflator private final consumption expenditure (unit: National currency reference year = 100, code: PCPH)

ngdp

Gross domestic product at current prices (unit: bn National currency, code: UVGD)

gdp

Gross domestic product at constant prices (unit: bn National currency, code: OVGD)

l

Total annual hours worked: total economy (unit: millions, code: NLHT)

wtotal

Compensation of employees: total economy (unit: bn National currency, code: UWCD)

nulc

Nominal unit labour costs: total economy (Ratio of compensation per employee to real GDP per person employed.) (unit: National currency reference year = 100, code: PLCD)

k

Net capital stock at constant prices: total economy (unit: bn National currency, code: OKND)

Value

A list of time series containing the same components as the input list tslAmeco and the following additional components:

Examples

# load data for Germany
data("gap")
country <- "Germany"
tsListRaw <- gap[[country]]
tsListInput <- amecoData2input(tslAmeco = tsListRaw)

Applies suitable contraining functions to parameters.

Description

Applies suitable contraining functions to parameters.

Usage

assignConstraints(par, loc)

Arguments

Fit best production function model

Description

Finds the most suitable model for the NAWRU and the TFP trend according to the BIC or the RMSE. The function computes the output gap based on the chosen models.

Usage

autoGapProd(
  tsl,
  type = "hp",
  q = 0.01,
  method = "MLE",
  criterion = "BIC",
  fast = TRUE,
  nModels = 5,
  nawruPoss = list(maxCycleLag = 2, trend = c("RW2", "DT"), cycle = c("AR1", "AR2"),
    errorARmax = 1, errorMAmax = 0, type = c("TKP", "NKP"), exoNames = c("ws", "prod",
    "tot"), signalToNoise = NULL),
  tfpPoss = list(maxCycleLag = 2, trend = c("RW2", "DT"), cycle = c("AR1", "AR2",
    "RAR2"), cubsARmax = 0, errorARmax = 1, errorMAmax = 0, signalToNoise = NULL),
  auto = "gap"
)

Arguments

Details

For fast = TRUE, the function pre-selects suitable models by applying the following procedure: A HP-filtered trend is computed based on which the best trend and cycle models are chosen according to the BIC. Also based on the HP trend, a variety of different specifications for the second observation equation are estimated in a univariate regression and the best models are selected via the BIC. The nModels best models are subsequently estimated in the usual bivariate unobserved component model. For fast = FALSE, a variety of models is estimated in the usual bivariate unobserved component framework.

The input component nawruPoss is a list containing a (sub-) set of the following components:

maxCycleLag

Maximum cycle lag included in the second observation equation.

trend

Trend model specification.

cycle

Cycle model specification.

errorARmax

Maximum autoregressive order of the error term in the second observation equation.

errorMAmax

Maximum moving average order of the error term in the second observation equation.

type

Type of Phillip's curve.

exoNames

Names of the exogenous variables potentially included in the Phillip's curve (need to be included in the list of time series tsl).

signal-to-noise

Signal-to-noise ratio.

The input component tfpPoss is a list containing a (sub-) set of the following components:

maxCycleLag

Maximum cycle lag included in the second observation equation.

trend

Trend model specification.

cycle

Cycle model specification.

cubsARmax

Maximum CUBS autoregressive order.

errorARmax

Maximum autoregressive order of the error term in the second observation equation.

errorMAmax

Maximum moving average order of the error term in the second observation equation.

signal-to-noise

Signal-to-noise ratio.

The list of time series tsl needs to have the following components (plus those series included in the list component exoNames in nawruPoss):

ur

Unemployment rate.

nulc

Nominal Unit labor costs, if type = "TKP".

rulc

Real unit labor costs, if type = "NKP".

tfp

Total factor productivity.

cubs

Capacity utilization economic sentiment indicator.

lfnd

Labor force non-domestic (unit: 1000 persons).

parts

Participation rate.

ahours

Average hours worked (unit: hours).

gdp

Gross domestic product at constant prices (unit: bn National currency, code: OVGD).

k

Net capital stock at constant prices: total economy (unit: bn National currency, code: OKND).

popw

Population: 15 to 64 years (unit: 1000 persons, code: NPAN).

The set of tested models is extensive but not exhaustive. The best model is solely based on convergence and the chosen criterion (RMSE or BIC). A manual check of the results is highly recommended.

In some cases, more than nModels are checked. For instance, if a re-parametrized and regular AR(2) process are options for the cycle.

Value

A list containing three components: gap (the best model of class "gap"), tfp (a nested list of TFP models, fitted objects and model fit criteria), nawru (a nested list of NAWRU models, fitted objects and model fit criteria). The lists nawru and tfp contain a list of models, a list of fitted objects and a dataframe info, which contains

NAWRU model suggestion

Description

Finds the most suitable NAWRU models.

Usage

autoNAWRUmodel(tsl, poss, nModels = 10)

Arguments

Value

A nested list with one model specification per list entry.

TFP model suggestion

Description

Finds the most suitable TFP models.

Usage

autoTFPmodel(tsl, poss, nModels = 10)

Arguments

Value

A nested list with one model specification per list entry.

Computes the covariance of the estimated parameters given restrictions.

Description

Computes the covariance of the estimated parameters given restrictions.

Usage

computeCovar(par, loc, CV)

Arguments

Applies contraints to parameters.

Description

Applies contraints to parameters.

Usage

constraint(par, type = NA)

Arguments

CUBS indicator

Description

Computes the capacity utilization economic sentiment (CUBS) indicator.

Usage

cubs(tsCU, tsVA, frequency = 1, lambda = NULL)

Arguments

Details

The list tslCU contains capacity utilization in industry, and the relevant survey outcomes of the construction and service sector. The first list object needs to contain capacity utilization in industry.

The list tslVA contains the real value added series for the industry, construction and service sector in the same order as tslCU.

The computed CUBS indicator consists exclusively of capacity utilization in industry until both other series become available.

Value

A list containing the two time series capacity utilization in industry cu and the CUBS indicator cubs.

Examples

# load data for Germany
data("gap")
country <- "Germany"

# compute cubs indicator
namesCubs <- c("indu", "serv", "buil")
namesVACubs <- paste0("va", namesCubs)
tscubs <- cubs(
  tsCU = gap[[country]][, namesCubs],
  tsVA = gap[[country]][, namesVACubs]
)

Find suitable cycle specification

Description

Finds the most suitable cycle model according to the BIC.

Usage

cycleOptim(x, opt = c("AR1", "AR2", "RAR2"))

Arguments

Value

A character string with the chosen cycle model.

Finds first/last starting/end date in list of time series deepening on the input functions.

Description

Finds first/last starting/end date in list of time series deepening on the input functions.

Usage

dateTsList(x, FUN1 = start, FUN2 = max)

Arguments

Extracts the relevant 'AMECO' data

Description

Extracts the relevant 'AMECO' data

Usage

extract_ameco_data(df)

Arguments

Extracts the relevant 'AMECO' indicator data.

Description

Extracts the relevant 'AMECO' indicator data.

Usage

extract_indicator_data(folder)

Arguments

Current 'AMECO' data vintage

Description

Fetches the 'AMECO' data for the EC output gap estimation from the current vintage.

Usage

fetchAmecoData(country = NULL, cubs = TRUE)

Arguments

Details

For the computation of CUBS, the following three seasonally adjusted series are used: the utilization indicators in the service industry, the building and construction industry, and capacity utilization in manufacturing/industry.

The confidence indicator in the service industry is composed of question 1, 2, and 3 of the monthly service sector survey ((Q1 + Q2 + Q3)/3). The underlying survey questions are as follows:

• Q1 Business situation development over the past 3 months

• Q2 Evolution of the demand over the past 3 months

• Q3 Expectation of the demand over the next 3 months

The confidence indicator in the building and construction industry is composed of question 3 and 4 of the monthly building and construction sector survey ((Q3 and Q4)/2). The underlying survey questions are as follows:

• Q3 Evolution of your current overall order books

• Q4 Employment expectations over the next 3 months

The indicator for capacity utilization in manufacturing/industry is based on question 13 of the quarterly industry sector survey. The underlying survey question is as follows:

• Q3 Current level of capacity utilization

Value

A list with multiple time series objects for each country. If country is specified, a multiple time series object is returned. For each country, the following series are included:

Additionally, if cubs = TRUE, the capacity utilization economic sentiment indicator cubs will be returned.

Source

https://economy-finance.ec.europa.eu/economic-research-and-databases/economic-databases/ameco-database/download-annual-data-set-macro-economic-database-ameco_en

https://economy-finance.ec.europa.eu/economic-forecast-and-surveys/business-and-consumer-surveys_en

Capitalizes the first letter of a string.

Description

Capitalizes the first letter of a string.

Usage

firstLetterUp(x)

Arguments

Fit Method

Description

Defines the fit method.

Usage

fit(model, ...)

Arguments

Value

Depends on the model object, see documentation of specific methods.

See Also

Other fitting methods: fit.KuttnerModel(), fit.NAWRUmodel(), fit.TFPmodel()

Maximum likelihood estimation of a KuttnerModel

Description

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the output gap.

Usage

## S3 method for class 'KuttnerModel'
fit(
  model,
  parRestr = initializeRestr(model),
  signalToNoise = NULL,
  control = NULL,
  ...
)

Arguments

Value

An object of class KuttnerFit containing the following components:

The list component fit contains the following model fit criteria:

See Also

Other fitting methods: fit.NAWRUmodel(), fit.TFPmodel(), fit()

Examples

# load data for the Netherlands
data("gap")
country <- "Netherlands"
tsList <- as.list(gap[[country]][, c("cpih", "gdp")])
tsList$infl <- diff(tsList$cpih)
model <- KuttnerModel(tsl = tsList, trend = "RW2", cycleLag = 1, cycle = "AR2", start = 1980)

# estimate Kutter's model
parRestr <- initializeRestr(model = model, type = "hp")

gapKuttner <- fit(model, parRestr, signalToNoise = 1 / 10)

Estimation of a NAWRUmodel

Description

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the NAWRU using either maximum likelihood estimation or bayesian methods.

Usage

## S3 method for class 'NAWRUmodel'
fit(
  model,
  parRestr = initializeRestr(model = model),
  signalToNoise = NULL,
  method = "MLE",
  control = NULL,
  prior = initializePrior(model),
  R = 10000,
  burnin = ceiling(R/10),
  thin = 1,
  HPDIprob = 0.85,
  pointEstimate = "mean",
  MLEfit = NULL,
  ...
)

Arguments

Details

The list object prior contains three list elements cycle, trend, and pcInd. Each list element is a 4 x n matrix where n denotes the number of parameters involved in the respective equation. The upper two elements specify the distribution, the lower two parameters specify box constraints. NA denotes no constraints. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. For instance, prior$cycle[, 1] contains the mean, standard deviation, lower and upper bound for the first variable, in that respective order.

The respective prior distributions are defined through their mean and standard deviation.

The Gibbs sampling procedure is as follows. For each r = 1, ..., R

• The states are sampled by running the Kalman filter and smoother conditional on the parameters of the previous step, \theta_{r-1}

• Trend equation parameters \theta_{trend}: Conditional on the states \alpha_r, a draw \theta_{trend,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, or by conjugacy, depending on the trend model specification.

• Cycle equation parameters \theta_{cycle}: Conditional on the states \alpha_r, a draw \theta_{cycle,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, or by conjugacy, depending on the cycle model specification.

• Phillip's curve equation parameters \theta_{pcInd}: Conditional on the states \alpha_r, a draw \theta_{pcInd,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, a combination thereof, or by conjugacy, depending on the Phillip's curve equation specification.

Value

For maximum likelihood estimation, an object of class NAWRUfit containing the following components:

The list component fit contains the following model fit criteria:

For bayesian estimation, an object of class NAWRUfit containing the following components:

The list component fit contains the following model fit criteria:

See Also

Other fitting methods: fit.KuttnerModel(), fit.TFPmodel(), fit()

Examples

# define nawru model for France
data("gap")
country <- "France"
tsList <- amecoData2input(gap[[country]])
model <- NAWRUmodel(tsl = tsList)
# estimate nawru model via MLE
parRestr <- initializeRestr(model = model, type = "hp")

f <- fit(model = model, parRestr = parRestr)

# initialize priors and estimate model via Bayesian methods
prior <- initializePrior(model = model)

f <- fit(model = model, method = "bayesian", prior = prior, R = 5000, thin = 2)

Estimation of a TFPmodel

Description

Estimates a two-dimensional state-space model and performs filtering and smoothing to obtain the TFP trend using either maximum likelihood estimation or bayesian methods.

Usage

## S3 method for class 'TFPmodel'
fit(
  model,
  parRestr = initializeRestr(model = model),
  signalToNoise = NULL,
  method = "MLE",
  control = NULL,
  prior = initializePrior(model),
  R = 10000,
  burnin = ceiling(R/10),
  thin = 1,
  HPDIprob = 0.85,
  pointEstimate = "mean",
  MLEfit = NULL,
  ...
)

Arguments

Details

The list object prior contains three list elements cycle, trend, and cubs. Each list element is a 4 x n matrix where n denotes the number of parameters involved in the respective equation. The upper two elements specify the distribution, the lower two parameters specify box constraints. NA denotes no constraints. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. For instance, prior$cycle[, 1] contains the mean, standard deviation, lower and upper bound for the first variable, in that respective order.

The respective prior distributions are defined through their mean and standard deviation.

The Gibbs sampling procedure is as follows. For each r = 1, ..., R

• The states are sampled by running the Kalman filter and smoother conditional on the parameters of the previous step, \theta_{r-1}

• Trend equation parameters \theta_{trend}: Conditional on the states \alpha_r, a draw \theta_{trend,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, or by conjugacy, depending on the trend model specification.

• Cycle equation parameters \theta_{cycle}: Conditional on the states \alpha_r, a draw \theta_{cycle,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, or by conjugacy, depending on the cycle model specification.

• CUBS equation parameters \theta_{cubs}: Conditional on the states \alpha_r, a draw \theta_{cubs,k} is obtained either by a sequential Gibbs step, a Metropolis Hasting step, a combination thereof, or by conjugacy, depending on the CUBS equation specification.

Value

For maximum likelihood estimation, an object of class TFPit containing the following components:

The list component fit contains the following model fit criteria:

For bayesian estimation, an object of class TFPfit containing the following components:

The list component fit contains the following model fit criteria:

See Also

Other fitting methods: fit.KuttnerModel(), fit.NAWRUmodel(), fit()

Examples

# load data for Italy
data("gap")
country <- "Italy"
tsList <- amecoData2input(gap[[country]])
# define tfp model
model <- TFPmodel(tsl = tsList, cycle = "RAR2")
# initialize parameter restrictions and estimate model
parRestr <- initializeRestr(model = model, type = "hp")

f <- fit(model = model, parRestr = parRestr)

# Bayesian estimation
prior <- initializePrior(model = model)

f <- fit(model = model, method = "bayesian", prior = prior, R = 5000, thin = 2)

gap data set

Description

A dataset containing economic data on various countries from the 'AMECO' 2018 autumn vintage.

Usage

gap

Format

A list object with 53 country time series objects. Each time series object contains 14 variables:

popw

Population: 15 to 64 years (unit: 1000 persons, code: NPAN)

ur

Unemployment rate, total; Member States: definition EUROSTAT (unit: Percentage of civilian labor force, code: ZUTN)

etd

Employment, persons: total economy (National accounts) (unit: 1000 persons, code: NETN)

et

Employment, persons: all domestic industries (National accounts) (unit: 1000 persons, code: NETD)

eet

Employees, persons: all domestic industries (National accounts) (unit: 1000 persons, code: NWTD)

vaind

Gross value added at 2010 prices: manufacturing industry (unit: bn National currency, code: OVGM)

vaserv

Gross value added at 2010 prices: services (unit: bn National currency, code: OVG5)

vabuil

Gross value added at 2010 prices: building and construction (unit: bn National currency, code: OVG4)

pconsp

Price deflator private final consumption expenditure (unit: National currency 2010 = 100, code: PCPH)

cpih

Harmonised consumer price index (All-items, 2015 = 100, code: ZCPIH)

cpin

National consumer price index (All-items, 2015 = 100, code: ZCPIN)

ngdp

Gross domestic product at current prices (unit: bn National currency, code: UVGD)

gdp

Gross domestic product at 2010 reference levels (unit: bn National currency, code: OVGD)

gdpdefl

Price deflator gross domestic product (unit: National currency 2010 = 100, code: PVGD)

ahours

Average annual hours worked per person employed (unit: Hours, code: NLHA)

l

Total annual hours worked: total economy (unit: millions, code: NLHT)

wtotal

Compensation of employees: total economy (unit: bn National currency, code: UWCD)

nulc

Nominal unit labour costs: total economy (Ratio of compensation per employee to real GDP per person employed.) (unit: National currency 2010 = 100, code: PLCD)

k

Net capital stock at 2010 prices: total economy (unit: bn National currency, code: OKND)

serv

Confidence indicator in the service industry

buil

Confidence indicator in the bulding and construction industry

indu

Capacity utilization in manufacturing/industry

Source

https://economy-finance.ec.europa.eu/economic-research-and-databases/economic-databases/ameco-database_en

HP-filter output gap

Description

Computes a HP filtered output gap.

Usage

gapHP(x, lambda = NULL, end = NULL, start = NULL)

Arguments

Value

Object of class gap, which is a list containing the two elements potential and gap and additionally the original time series.

Production function output gap

Description

Computes potential output and the output gap based on a production function methodology.

Usage

gapProd(
  tsl,
  NAWRUfit,
  TFPfit,
  alpha = 0.65,
  start = NULL,
  end = NULL,
  lambda = NULL
)

Arguments

Details

The list of time series tsl needs to have the following components:

lfnd

Labor force non-domestic (unit: 1000 persons). (Set to zero if left unspecified).

parts

Participation rate.

ahours

Average hours worked (unit: hours).

gdp

Gross domestic product at constant prices (unit: bn National currency, code: OVGD).

k

Net capital stock at constant prices: total economy (unit: bn National currency, code: OKND).

popw

Population: 15 to 64 years (unit: 1000 persons, code: NPAN).

The trend of the list components parts, ahours and lfnd (if available) is computed using the Hodrick-Prescott filter with the smoothing constant lambda, unless the supplied time series list tsl contains their trend (for instance, denoted by partsTrend).

Value

Object of class gap, which is a list with the following components:

Examples

# compute the output gap given the previously obtained nawru and trend tfp
data("gap")
country <- "Belgium"
tsList <- amecoData2input(gap[[country]])
modelNAWRU <- NAWRUmodel(tsl = tsList)
modelTFP <- TFPmodel(tsl = tsList, cycle = "RAR2")


fittedNAWRU <- fit(model = modelNAWRU)
fittedTFP <- fit(model = modelTFP)

gapProd(tsl = tsList, NAWRUfit = fittedNAWRU, TFPfit = fittedTFP)

Conducts a Geweke test for convergence of the draws.

Description

Conducts a Geweke test for convergence of the draws.

Usage

gewekeTest(x, frac1 = 0.1, frac2 = 0.5, alpha = 0.05)

Arguments

Details

Under the H0 of convergence, the test statistic is standard normally distributed.

Naturally, frac1 + frac2 is between zero and one.

Value

A list with the following items

h

Test decision.

CD

Convergence Diagnostic (test statistic)

pvalue

The p-value.

alpha

The applied signifcicance level.

frac1

The fraction of data contained in the first interval.

frac2

The fraction of data contained in the second interval.

Growth rate

Description

Computes growth rates for time series.

Usage

growth(ts, k = 1)

Arguments

model selection fit comparison helper function

Description

Defines and fits models given the input parameters

Usage

helper_fit_comparison(fit, E1name, E1Trendname, E1trans = identity, fitBayes)

Arguments

Value

A data frame with information criteria, other goodness-of-fit measures, convergence status, trend volatility measures.

model comparison helper function

Description

Gets model attributes

Usage

helper_model_comparison(models)

Arguments

Value

A data frame with model attributes

model selection helper function

Description

Defines and fits models given the input parameters

Usage

helper_model_fit(FUNmodel, FUNfit, tsl, comb, poss, method, type, q, modelName)

Arguments

Value

A nested list with the models and fitted objects.

HP filter

Description

Applies the Hodrick Prescott Filter.

Usage

hpfilter(x, lambda)

Arguments

Value

A univariate time series object containing the trend of the original time series.

Examples

# get data for France
data("gap")
country <- "France"
tsList <- amecoData2input(gap[[country]], alpha = 0.65)
hp <- hpfilter(x = tsList$gdp, lambda = 6.25)

Indicators fo CUBS

Description

A dataset containing the service sector confidence indicator, the construction sector confidence indicator and the capacity utilization in manufacturing/industry.

Usage

indicator

Format

A list with 53 nested country lists with time series objects. Each country list contains 3 time series variables:

serv

Confidence indicator in the service industry.

buil

Confidence indicator in the bulding and construction industry.

indu

Capacity utilization in manufacturing/industry.

Details

A dataset containing the seasonally adjusted utilization indicators in the service industry, the building and construction industry, and capacity utilization in manufacturing/industry for all EU countries and some neighboring countries at different frequencies.

The confidence indicator in the service industry is composed of question 1, 2, and 3 of the monthly service sector survey ((Q1 + Q2 + Q3)/3). The underlying survey questions are as follows:

• Q1 Business situation development over the past 3 months

• Q2 Evolution of the demand over the past 3 months

• Q3 Expectation of the demand over the next 3 months

The confidence indicator in the building and construction industry is composed of question 3 and 4 of the monthly building and construction sector survey ((Q3 and Q4)/2). The underlying survey questions are as follows:

• Q3 Evolution of your current overall order books

• Q4 Employment expectations over the next 3 months

The indicator for capacity utilization in manufacturing/industry is based on question 13 of the quarterly industry sector survey. The underlying survey question is as follows:

• Q3 Current level of capacity utilization

Source

https://economy-finance.ec.europa.eu/economic-forecast-and-surveys/business-and-consumer-surveys_en

Computes standard errors, t-statistics, and p-values for the estimated state space parameters using the delta method.

Description

Computes standard errors, t-statistics, and p-values for the estimated state space parameters using the delta method.

Usage

inference(parOptim, hessian, loc)

Arguments

Initialization of exogenous variables

Description

Initializes the transformations applied to exogenous variables.

Usage

initializeExo(varNames, D = NULL, L = NULL)

Arguments

Details

For the matrices D and L, the rows denote different transformations to each of the variables in the columns. NA indicates no transformation.

Value

An array of size (n, k, 2). The [, , 1] specifies the difference order and [, , 2] the lag order.

Initialization of prior distributions

Description

Initializes the prior distributions for a model of class TFPmodel or NAWRUmodel.

Usage

initializePrior(model, MLE = !is.null(MLEfit), MLEfit = NULL)

Arguments

Value

A list of three matrices with parameters for the prior distribution and box constraints. Each list item refers to an equation, namely the cycle, trend, and second observation equation. Each list element is a 4 x n matrix where n denotes the number of parameters involved in the respective equation. The upper two elements specify the distribution, the lower two parameters specify box constraints. NA denotes no constraints. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. The respective prior distributions are defined through their mean and standard deviation. For instance, prior$cycle[, 1] contains the mean, standard deviation, lower and upper bound for the first variable, in that respective order.

Initialization of parameter restrictions

Description

Initializes parameter restrictions for objects of class NAWRUmodel, TFPmodel, or KuttnerModel.

Usage

initializeRestr(model, type = "basic", lambda = NULL, q = 0.01)

Arguments

Details

For type = "hp", the HP filter is applied to the appropriately differences first observation series to obtain its trend and cycle. Subsequently, the specified trend and cycle models are fitted to obtain its innovation variance. Moreover, the second observation series (according to its specification) is fitted to obtain its innovation variance. Lastly, the obtained innovations variances are used to get lower and upper bounds. To that end, the q and 1-q quantiles of the inverse gamma distribution are used, with mean and standard deviation set to the estimated variances.

Value

A list of three matrices containing the parameter restrictions for the cycle, trend, and the second observation equation. Each matrix contains the lower and upper bound of the involved parameters. NA implies that no restriction is present.

KuttnerFit object check

Description

Tests whether the input object is a valid object of class KuttnerFit.

Usage

is.KuttnerFit(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

KuttnerModel object check

Description

Tests whether the input object is a valid object of class KuttnerModel.

Usage

is.KuttnerModel(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

NAWRUfit object check

Description

Tests whether the input object is a valid object of class NAWRUfit.

Usage

is.NAWRUfit(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

NAWRUodel object check

Description

Tests whether the input object is a valid object of class NAWRUmodel.

Usage

is.NAWRUmodel(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

Examples

# load data for France
data("gap")
tsList <- amecoData2input(gap$France, alpha = 0.65)

# Traditional phillips curve
model <- NAWRUmodel(tsl = tsList, trend = "RW2", cycle = "AR2", type = "NKP", cycleLag = 0:1)
is.NAWRUmodel(model, return.logical = TRUE)
attr(model, "phillips curve")$cycleLag <- 0
is.NAWRUmodel(model, return.logical = TRUE)

TFPfit object check

Description

Tests whether the input object is a valid object of class TFPfit.

Usage

is.TFPfit(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

TFPmodel object check

Description

Tests whether the input object is a valid object of class TFPmodel.

Usage

is.TFPmodel(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

Examples

# load data for Germany
data("gap")
data("indicator")
country <- "Germany"
tsList <- amecoData2input(gap[[country]], alpha = 0.65)

# compute cubs indicator
namesCubs <- c("indu", "serv", "buil")
namesVACubs <- paste0("va", namesCubs)
tscubs <- cubs(
  tsCU = gap[[country]][, namesCubs],
  tsVA = gap[[country]][, namesVACubs]
)
tsList <- c(tsList, tscubs)

# define tfp model
model <- TFPmodel(
  tsl = tsList, trend = "DT", cycle = "RAR2",
  cycleLag = 2, cubsErrorARMA = c(1, 0)
)
is.TFPmodel(model, return.logical = TRUE)
attr(model, "cubs")$cycleLag <- 1
is.TFPmodel(model, return.logical = TRUE)

gap object check

Description

Tests whether the input object is a valid object of class gap.

Usage

is.gap(object, return.logical = FALSE)

Arguments

Value

A logical value or nothing, depending on the value of return.logical.

Capitalizes the first letter of a string.

Description

Capitalizes the first letter of a string.

Usage

matmult3d(a, b)

Arguments

Computes MCMC summary statistics.

Description

Computes MCMC summary statistics.

Usage

mcmcSummary(x, HPDIprob, frac1 = 0.1, frac2 = 0.5)

Arguments

Details

Naturally, frac1 + frac2 is between zero and one.

Value

A data frame with the following columns

Mean

The posterior mean.

Median

The posterior median.

SD

Standard deviation.

HPDI-LB

Highest posterior density credible interval lower bound

HPDI-UB

Highest posterior density credible interval upper bound

Naive SE

Naive Standard error of the mean (ignoring chain autocorrelation.

Time-series SE

Time-series standard error (based on spectral density at 0).

Geweke statistic

The Geweke test statistic.

frac1

The fraction of data contained in the first interval.

frac2

The fraction of data contained in the second interval.

Find suitable 2nd observation specification

Description

Finds the most suitable model for the second observation equation according to the BIC.

Usage

obs2Optim(
  x1,
  x2,
  xexo = NULL,
  errorARmax = 2,
  errorMAmax = 2,
  maxCycleLag = 2,
  maxAR = 2,
  nModels = 1
)

Arguments

Value

A list containing the chosen parameters: errorAR, errorMA, cycleLag, ar, exo.

Performs a mathematical operation to the ts elements of two lists with the same names

Description

Performs a mathematical operation to the ts elements of two lists with the same names

Usage

operTsLists(x, y, operator)

Arguments

Plots for a KuttnerFit object

Description

Plots potential growth and the output gap and gives diagnostic plots based on standardized residuals for objects of class KuttnerFit.

Usage

## S3 method for class 'KuttnerFit'
plot(
  x,
  alpha = 0.05,
  bounds = TRUE,
  path = NULL,
  combine = TRUE,
  prefix = NULL,
  device = "png",
  width = 10,
  height = 3,
  ...
)

Arguments

Value

No return value, plots are printed.

Plots for a NAWRUfit object

Description

Plots the NAWRU and the Phillip's curve and gives diagnostic plots based on standardized residuals for objects of class NAWRUfit.

Usage

## S3 method for class 'NAWRUfit'
plot(
  x,
  alpha = 0.05,
  bounds = TRUE,
  path = NULL,
  combine = TRUE,
  prefix = NULL,
  posterior = FALSE,
  device = "png",
  width = 10,
  height = 3,
  ...
)

Arguments

Value

No return value, plots are printed.

Plots for a TFPfit object

Description

Plots the TFP trend and the CUBS equation and gives diagnostic plots based on standardized residuals for objects of class TFPfit.

Usage

## S3 method for class 'TFPfit'
plot(
  x,
  alpha = 0.05,
  bounds = TRUE,
  path = NULL,
  combine = TRUE,
  prefix = NULL,
  posterior = FALSE,
  device = "png",
  width = 10,
  height = 3,
  ...
)

Arguments

Value

No return value, plots are printed.

Plots for a gap object

Description

Plots potential output growth and the output gap based on an objects of class gap.

Usage

## S3 method for class 'gap'
plot(
  x,
  contribution = FALSE,
  path = NULL,
  combine = TRUE,
  prefix = NULL,
  device = "png",
  width = 10,
  height = 3,
  ...
)

Arguments

Value

No return value, plots are printed.

Plots the trend series and the (fitted) second observation equation and gives diagnostic plots based on standardized residuals.

Description

Plots the trend series and the (fitted) second observation equation and gives diagnostic plots based on standardized residuals.

Usage

plotGap(
  tsl,
  legend,
  title,
  boundName,
  contribution,
  res = NULL,
  namesPrint,
  bounds,
  combine,
  path,
  device,
  width,
  height
)

Arguments

Plots the trend series and the (fitted) second observation equation and gives diagnostic plots based on standardized residuals.

Description

Plots the trend series and the (fitted) second observation equation and gives diagnostic plots based on standardized residuals.

Usage

plotSSprediction(
  tsl,
  legend,
  title,
  n.ahead,
  boundName,
  res = NULL,
  namesPrint,
  bounds,
  combine,
  path,
  device,
  width,
  height
)

Arguments

Plots the trend series and the (fitted) second observation equation and gives diagnostic plots based on standardized residuals.

Description

Plots the trend series and the (fitted) second observation equation and gives diagnostic plots based on standardized residuals.

Usage

plotSSresults(
  tsl,
  legend,
  title,
  boundName,
  res = NULL,
  namesPrint,
  bounds,
  combine,
  path,
  device,
  width,
  height
)

Arguments

Plots the diagnostic plots of the posterior distribution.

Description

Plots the diagnostic plots of the posterior distribution.

Usage

plot_gibbs_output(
  path = NULL,
  draws,
  parName,
  burnin,
  mu = NULL,
  prec = NULL,
  shape = NULL,
  scale = NULL,
  shape1 = NULL,
  shape2 = NULL,
  ub = NULL,
  lb = NULL,
  prefix = NULL,
  device,
  width,
  height
)

Arguments

Predictions

Description

Computes predictions for an object of class NAWRUfit, TFPfit, or KuttnerFit estimated via MLE or Bayesian methods (objects of class fit).

Usage

## S3 method for class 'fit'
predict(object, n.ahead = 10, exogenous = "mean", returnFit = TRUE, ...)

Arguments

Value

The fitted object with an updated time series list tsl. If returnFit = FALSE, only the updated time series list is returned.

Predictions for Bayesian estimation

Description

Computes predictions for an object of class NAWRUfit, TFPfit estimated via Bayesian methods.

Usage

predictBayes(fit, n.ahead = 10, exogenous = "mean", returnFit = TRUE)

Arguments

Predictions for MLE

Description

Computes predictions for an object of class NAWRUfit, TFPfit, KuttnerFit estimated via MLE.

Usage

predictMLE(fit, n.ahead = 10, exogenous = "mean", returnFit = TRUE)

Arguments

Print KuttnerFit object

Description

Prints the model specifications and the estimation results of an object of class KuttnerFit.

Usage

## S3 method for class 'KuttnerFit'
print(x, ...)

Arguments

Value

No return value, results are printed.

Print KuttnerModel object

Description

Prints the model specifications of an object of class KuttnerModel.

Usage

## S3 method for class 'KuttnerModel'
print(x, call = TRUE, check = TRUE, ...)

Arguments

Value

No return value, model information is printed.

Print NAWRUfit object

Description

Prints the model specifications and the estimation results of an object of class NAWRUfit.

Usage

## S3 method for class 'NAWRUfit'
print(x, ...)

Arguments

Value

No return value, results are printed.

Print NAWRUmodel object

Description

Prints the model specifications of an object of class NAWRUmodel.

Usage

## S3 method for class 'NAWRUmodel'
print(x, call = TRUE, check = TRUE, ...)

Arguments

Value

No return value, model information is printed.

Print TFPfit object

Description

Prints the model specifications and the estimation results of an object of class TFPfit.

Usage

## S3 method for class 'TFPfit'
print(x, ...)

Arguments

Value

No return value, results are printed.

Print TFPmodel object

Description

Prints the model specifications of an object of class TFPmodel.

Usage

## S3 method for class 'TFPmodel'
print(x, call = TRUE, check = TRUE, ...)

Arguments

Value

No return value, model information is printed.

Print gap object

Description

Prints the model specifications of an object of class gap.

Usage

## S3 method for class 'gap'
print(x, ...)

Arguments

Value

No return value, results are printed.

Trend anchor

Description

Computes the anchored trend given a fitted object of class NAWRUfit, TFPfit, or KuttnerFit.

Usage

trendAnchor(fit, anchor = NULL, h = NULL, returnFit = FALSE)

Arguments

Value

A fitted object if returnFit = TRUE or a time series with the anchored trend.

Examples

# define nawru model for France
data("gap")
tsList <- amecoData2input(gap$France)
model <- NAWRUmodel(tsl = tsList)

# estimate nawru model

f <- fit(model = model)

# compute anchored nawru
anchoredNawru <- trendAnchor(fit = f, anchor = 6.5, h = 10)

Find suitable trend specification

Description

Finds the most suitable trend model according to the BIC.

Usage

trendOptim(x, opt = c("RW1", "RW2", "DT"))

Arguments

Value

A character string with the chosen trend model.

Trend volatility measures

Description

Computes trend volatility measures.

Usage

trendVolaMeasures(tsOriginal, tsTrend, nDiff)

Arguments

Value

A list containing the different measures.