Package 'RGAP' reference manual

Title:	Production Function Output Gap Estimation
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.
Authors:	Sina Streicher [aut, cre]
Maintainer:	Sina Streicher <[email protected]>
License:	GPL-3
Version:	0.1.1
Built:	2025-02-13 05:59:32 UTC
Source:	https://github.com/sinast3000/rgap

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)
amecoData2input(tslAmeco, alpha = 0.65)

Arguments

`tslAmeco`	A time series list or a multiple time series object containing AMECO data.
`alpha`	A number between `0` and `1` indicating the labor share. The default is `alpha = 0.65`.

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:

`gdpdefl`	Gross domestic product deflator
`tfp`	Total factor productivity
`lfnd`	Labor force non-domestic (unit: 1000 persons)
`parts`	Participation rate
`ahours`	Average hours worked (unit: hours)
`prod`	Labor productivity (unit: real output in millions per person)
`tot`	Terms of trade (pconcp / gdpdefl)
`ws`	Wage share (unit: compensation per unit of nominal output)
`winfl`	Wage inflation
`rulc`	Real unit labor costs

Examples

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

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"
)
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

`tsl`	A list of time series objects, see details.
`type`	The variance restriction type. Possible options are `"basic"`, `"hp"`, see `initializeRestr`. The default is `type = "hp"`.
`q`	Quantile for the Inverse Gamma distribution (only used if `type = "hp"`), see `initializeRestr`. The default is `q = 0.01`.
`method`	The estimation method. Options are maximum likelihood estimation `"MLE"` and bayesian estimation `"bayesian"`. If `method = c("MLE", "bayesian")` the NAWRU is fitted by MLE and the TFP trend by Bayesian methods. The default is `method = "MLE"`.
`criterion`	Model selection criterion. Options are the Bayesian information criterion `"BIC"` and the root mean squared error `"RMSE"`, both computed for the second observation equation. The default is `criterion = "BIC"`. For Bayesian estimation and `criterion = "RMSE"`, the mean RMSE is used.
`fast`	Boolean, indicating whether a "fast" procedure should be used, see details.
`nModels`	Integer, the maximum number of models for each unobserved component model.
`nawruPoss`	List with possible model specifications for the NAWRU, see details.
`tfpPoss`	List with possible model specifications for the NAWRU, see details.
`auto`	If `auto = "NAWRU"` or `auto = "TFP"`, the function only finds the most suitable NAWRU or TFP model, respectively. The default is `auto = "gap"`.

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

`loglik`	log-likelihood function at optimum
`AIC`	Akaike information criterion
`BIC`	Bayesian information criterion
`HQC`	Hannan-Quinn information criterion
`RMSE`	Root mean squared error
`R2`	Coefficient of determination (R squared)
`signal-to-noise`	Signal-to-noise ratio
`LjungBox`	p-value of Ljung-Box test for autocorrelation (H0 = no autocorrelation)
`convergence`	0 indicates convergence of the optimization
`rrange`	relative range of trend series w.r.t original series
`neg`	1 indicates that negative values are present in the trend series
`rev`	relative excess volatility w.r.t. original series (stationary series)
`rsd`	relative standard deviation w.r.t. original series (stationary series)
`cor`	correlation between trend and original series (stationary series)
`msdtg`	mean standardized deviation (stationary trend)
`magtg`	mean absolute growth of trend (stationaty trend)
`drop`	1 indicates the model should be dropped

CUBS indicator

Description

Computes the capacity utilization economic sentiment (CUBS) indicator.

Usage

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

Arguments

`tsCU`	A multiple time series containing three survey time series, the first element needs to be capacity utilization in industry, see details. Alternatively, a list of time series can be supplied.
`tsVA`	A multiple time series containing three value added series that correspond to `tsCU`. Alternatively, a list of time series can be supplied.
`frequency`	The frequency of the computed cubs indicator. Possible entries are `frequency = 1` (annual), `frequency = 4` (quarterly). The default is `frequency = 1`.
`lambda`	The smoothing parameter for the application of the HP filter (see details). If not supplied, `lambda = 6.25` is used for yearly data and `lambda = 1600` for quarterly data.

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]
)
# 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]
)

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)
fetchAmecoData(country = NULL, cubs = TRUE)

Arguments

`country`	The country name. If left unspecified, data for all countries will be returned.
`cubs`	A logical indicating whether the CUBS indicator should be computed if possible (see details).

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:

`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 constant prices: manufacturing industry (unit: bn National currency, code: OVGM)
`vaserv`	Gross value added at constant prices: services (unit: bn National currency, code: OVG5)
`vabuil`	Gross value added at constant prices: building and construction (unit: bn National currency, code: OVG4)
`pconsp`	Price deflator private final consumption expenditure (unit: National currency reference year = 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 constant prices (unit: bn National currency, code: OVGD)
`gdpdefl`	Price deflator gross domestic product (unit: National currency reference year = 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 reference year = 100, code: PLCD)
`k`	Net capital stock at constant 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

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

Fit Method

Description

Defines the fit method.

Usage

fit(model, ...)
fit(model, ...)

Arguments

`model`	Some model.
`...`	Some stuff passed on to methods.

Value

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

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

Arguments

`model`	An object of class KuttnerModel.
`parRestr`	A list of matrices containing the parameter restrictions for the cycle, trend, and the inflation equation. Each matrix contains the lower and upper bound of the involved parameters. `NA` implies that no restriction is present. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. By default, `parRestr` is intitialized by the function `initializeRestr(model)`.
`signalToNoise`	(Optional) signal to noise ratio.
`control`	(Optional) A list of control arguments to be passed on to `optim`.
`...`	additional arguments to be passed to the methods functions.

Value

An object of class KuttnerFit containing the following components:

`model`	The input object of class `KuttnerModel`.
`SSMfit`	The estimation output from the funtcion `fitSSM` from `KFAS`.
`SSMout`	The filtering and smoothing output from the funtcion `KFS` from `KFAS`.
`parameters`	A data frame containing the estimated parameters, including standard errors, t-statistics, and p-values.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`loglik`	Log-likelihood function value.
`AIC`	Akaike information criterion.
`BIC`	Bayesian information criterion.
`AIC`	Hannan-Quinn information criterion.
`RMSE`	Root mean squared error of the inflation equation.
`R2`	R squared of the inflation equation.
`LjungBox`	Ljung-Box test output of the inflation equation.

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)

# 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,
  ...
)
## 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

`model`	An object of class NAWRUmodel.
`parRestr`	A list of matrices containing the parameter restrictions for the cycle, trend, and the Phillip's curve. Each matrix contains the lower and upper bound of the involved parameters. `NA` implies that no restriction is present. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. By default, `parRestr` is initialized by the function `initializeRestr(model)`. Only used if `method = "MLE"`.
`signalToNoise`	(Optional) signal to noise ratio. Only used if `method = "MLE"`.
`method`	The estimation method. Options are maximum likelihood estimation `"MLE"` and bayesian estimation `"bayesian"`. The default is `method = "MLE"`.
`control`	(Optional) A list of control arguments to be passed on to `optim`.
`prior`	A list of matrices with parameters for the prior distribution and box constraints. By default, `prior` is initialized by `initializePrior(model)`. See details. Only used if `method = "bayesian"`.
`R`	An integer specifying the number of MCMC draws. The default is `R = 10000`. Only used if `method = "bayesian"`.
`burnin`	An integer specifying the burn-in phase of the MCMC chain. The default is `burnin = ceiling(R / 10)`. Only used if `method = "bayesian"`.
`thin`	An integer specifying the thinning interval between consecutive draws. The default is `thin = 1`, implying that no draws are dopped. For `thin = 2`, every second draw is dropped and so on. Only used if `method = "bayesian"`.
`HPDIprob`	A numeric in the interval `(0,1)` specifying the target probability of the highest posterior density intervals. The default is `HPDIprob = 0.9`. Only used if `method = "bayesian"`.
`pointEstimate`	Posterior distribution's statistic of central tendency. Possible options are `"mean"` and `"median"`. The default is `pointEstimate = "mean"`. Only used if `method = "bayesian"`.
`MLEfit`	(Optional) An object of class `NAWRUfit` which is used for initialization. Only used if `method = "bayesian"`.
`...`	additional arguments to be passed to the methods functions.

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:

`model`	The input object of class `NAWRUmodel`.
`SSMfit`	The estimation output from the function `fitSSM` from `KFAS`.
`SSMout`	The filtering and smoothing output from the function `KFS` from `KFAS`.
`parameters`	A data frame containing the estimated parameters, including standard errors, t-statistics, and p-values.
`parRestr`	A list of matrices containing the enforced parameter constraints.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`loglik`	Log-likelihood function values.
`AIC`	Akaike information criterion.
`BIC`	Bayesian information criterion.
`AIC`	Hannan-Quinn information criterion.
`RMSE`	root mean squared error of the Phillip's curve equation.
`R2`	R squared of the Phillip's curve equation.
`LjungBox`	Ljung-Box test output of the Phillip's curve equation.
`signal-to-noise`	Signal-to-noise ratio.

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

`model`	The input object of class `NAWRUmodel`.
`tsl`	A list of time series containing the estimated states.
`parameters`	A data frame containing the estimated parameters, including standard errors, highest posterior density credible sets.
`prior`	A list of matrices containing the used prior distributions.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`R2`	R squared of the phillips curve equation,
`signal-to-noise`	Signal-to-noise ratio.

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)

# 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,
  ...
)
## 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

`model`	An object of class TFPmodel.
`parRestr`	A list of matrices containing the parameter restrictions for the cycle, trend, and the CUBS equation. Each matrix contains the lower and upper bound of the involved parameters. `NA` implies that no restriction is present. Autoregressive parameters are automatically restricted to the stationary region unless box constraints are specified. By default, `parRestr` is initialized by the function `initializeRestr(model)`. Only used if `method = "MLE"`.
`signalToNoise`	(Optional) signal to noise ratio. Only used if `method = "MLE"`.
`method`	The estimation method. Options are maximum likelihood estimation `"MLE"` and bayesian estimation `"bayesian"`. The default is `method = "MLE"`.
`control`	(Optional) A list of control arguments to be passed on to `optim`.
`prior`	A list of matrices with parameters for the prior distribution and box constraints. By default, `prior` is initialized by `initializePrior(model)`. See details. Only used if `method = "bayesian"`.
`R`	An integer specifying the number of MCMC draws. The default is `R = 10000`. Only used if `method = "bayesian"`.
`burnin`	An integer specifying the burn-in phase of the MCMC chain. The default is `burnin = ceiling(R / 10)`. Only used if `method = "bayesian"`.
`thin`	An integer specifying the thinning interval between consecutive draws. The default is `thin = 1`, implying that no draws are dopped. For `thin = 2`, every second draw is dropped and so on. Only used if `method = "bayesian"`.
`HPDIprob`	A numeric in the interval `(0,1)` specifying the target probability of the highest posterior density intervals. The default is `HPDIprob = 0.9`. Only used if `method = "bayesian"`.
`pointEstimate`	Posterior distribution's statistic of central tendency. Possible options are `"mean"` and `"median"`. The default is `pointEstimate = "mean"`. Only used if `method = "bayesian"`.
`MLEfit`	(Optional) An object of class `TFPfit` which is used for initialization. Only used if `method = "bayesian"`.
`...`	additional arguments to be passed to the methods functions.

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:

`model`	The input object of class `TFPmodel`.
`SSMfit`	The estimation output from the funtcion `fitSSM` from `KFAS`.
`SSMout`	The filtering and smoothing output from the funtcion `KFS` from `KFAS`.
`parameters`	A data frame containing the estimated parameters, including standard errors, t-statistic, and p-values.
`parRestr`	A list of matrices containing the enforced parameter constraints.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`loglik`	Log-likelihood function values.
`AIC`	Akaike information criterion.
`BIC`	Bayesian information criterion.
`AIC`	Hannan-Quinn information criterion.
`RMSE`	root mean squared error of the CUBS equation.
`R2`	R squared of the CUBS equation.
`LjungBox`	Ljung-Box test output of the CUBS equation.
`signal-to-noise`	Signal-to-noise ratio.

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

`model`	The input object of class `TFPmodel`.
`tsl`	A list of time series containing the estimated states.
`parameters`	A data frame containing the estimated parameters, including standard errors, highest posterior density credible sets.
`prior`	A list of matrices containing the used prior distributions.
`fit`	A list of model fit criteria (see below).
`call`	Original call to the function.

The list component fit contains the following model fit criteria:

`R2`	R squared of the CUBS equation.
`signal-to-noise`	Signal-to-noise ratio.

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)

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

Arguments

`x`	A time series object containing gdp.
`lambda`	The smoothing parameter for the application of the HP filter. If not supplied, `lambda = 6.25` for yearly data, `lambda = 1600` for quarterly data, and `lambda = 129600` for monthly data.
`end`	(optional) A two element vector containing a year and a period specifying the end point for the filter application.
`start`	(optional) A two element vector containing a year and a period specifying the start point for the filter application.

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

Arguments

`tsl`	A list of time series objects, see details.
`NAWRUfit`	An object of class `NAWRUfit` obtained via the function `fit`.
`TFPfit`	An object of class `TFPfit` obtained via the function `fit`.
`alpha`	A scalar between zero and one depicting the labor share. The default is `alpha = 0.65`.
`start`	(optional) A two element vector containing a year and a period specifying the start point for the estimation.
`end`	(optional) A two element vector containing a year and a period specifying the end point for the estimation.
`lambda`	The smoothing parameter for the application of the HP filter (see details). If not supplied, `lambda = 6.25` for yearly data, `lambda = 1600` for quarterly data, and `lambda = 129600` for monthly data.

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:

`tsl`	List of time series including potential output `potential`, the output gap `gap`, all HP-filtered trend series, and all original series.
`NAWRUfit`	Provided `NAWRUfit` object.
`TFPfit`	Provided `TFPfit` object.
`call`	Original call to the function.

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)

# 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)

HP filter

Description

Applies the Hodrick Prescott Filter.

Usage

hpfilter(x, lambda)
hpfilter(x, lambda)

Arguments

`x`	A univariate time series object.
`lambda`	The smoothing parameter.

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

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

Initialization of exogenous variables

Description

Initializes the transformations applied to exogenous variables.

Usage

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

Arguments

`varNames`	A `(k x 1)` character vector containing the names of the exogenous variables.
`D`	A `(n x k)` matrix containing the difference transformations, see details.
`L`	A `(n x k)` matrix containing the lag transformations, see details.

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

Arguments

`model`	An object of class `TFPmodel` or `NAWRUmodel`.
`MLE`	(Optional) A logical indicating whether the MLE estimates should be used for the initialization. The default is `MLE = FALSE` if `MLEfit` is not provided and vice versa.
`MLEfit`	(Optional) An object of class `TFPfit` or `NAWRUfit` which is used if `MLE = TRUE`.

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

Arguments

`model`	An object of class `NAWRUmodel`, `TFPmodel`, or `KuttnerModel`.
`type`	The variance restriction type. Possible options are `"basic"`, `"hp"`, see details. The default is `type = "basic"`.
`lambda`	The smoothing constant for the HP-filter if `type = "hp"`.
`q`	Quantile for the Inverse Gamma distribution (only used if `type = "hp"`). The default is `q = 0.01`.

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.

`gap` object check

Description

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

Usage

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

Arguments

`object`	An object to be tested.
`return.logical`	If `return.logical = FALSE` (default), an error message is printed if the object is not of class `gap`. If `return.logical = TRUE`, a logical value is returned.

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

Arguments

`object`	An object to be tested.
`return.logical`	If `return.logical = FALSE` (default), an error message is printed if the object is not of class `KuttnerModel`. If `return.logical = TRUE`, a logical value is returned.

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

Arguments

`object`	An object to be tested.
`return.logical`	If `return.logical = FALSE` (default), an error message is printed if the object is not of class `NAWRUmodel`. If `return.logical = TRUE`, a logical value is returned.

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")$cycleLag <- 0
is.NAWRUmodel(model, return.logical = TRUE)
# load data for France
data("gap")
tsList <- amecoData2input(gap$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)

`TFPmodel` object check

Description

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

Usage

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

Arguments

`object`	An object to be tested.
`return.logical`	If `return.logical = FALSE` (default), an error message is printed if the object is not of class `TFPmodel`. If `return.logical = TRUE`, a logical value is returned.

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)
# 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)

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

Arguments

`tsl`	A list of time series objects, see details.
`cycle`	A character string specifying the cycle model. `cycle = "AR1"` denotes an AR(1) process, `cycle = "AR2"` an AR(2) process. The default is `cycle = "AR2"`.
`cycleLag`	A non-negative integer specifying the maximum cycle lag that is included in the inflation equation. The default is `cycleLag = 0`, see details.
`trend`	A character string specifying the trend model. `trend = "RW1"` denotes a first order random walk, `trend = "RW2"` a second order random walk (local linear trend) and `trend = "DT"` a damped trend model. The default is `trend = "RW1"`.
`inflErrorARMA`	A `2 x 1` vector with non-negative integers specifying the AR and MA degree of the error term in the inflation equation. The default is `inflErrorARMA = c(0, 3)`, see details.
`start`	(Optional) Start vector for the estimation, e.g. `c(1980, 1)`.
`end`	(Optional) End vector for the estimation, e.g. `c(2020, 1)`.
`anchor`	(Optional) Anchor value for the logarithm of trend gdp.
`anchor.h`	(Optional) Anchor horizon in the frequency of the given time series.

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:

`tsl`	A list of used time series.
`SSModel`	An object of class SSModel specifying the state-space model.
`loc`	A data frame containing information on each involved parameter, for instance its corresponding system matrix, variable names, and parameter restrictions.
`call`	Original call to the function.

In addition, the object contains the following attributes:

`cycle`	Cycle specification.
`trend`	Trend specification.
`inflation equation`	A list containing the components `cycleLag, errorARMA, exoVariables`.
`anchor`	A list containing the components `value, horizon`.
`period`	A list containing the components `start, end, frequency`.

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)
# 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
)
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

`tsl`	A list of time series objects, see details.
`trend`	A character string specifying the trend model. `trend = "RW1"` denotes a first order random walk, `trend = "RW2"` a second order random walk (local linear trend) and `trend = "DT"` a damped trend model. The default is `trend = "RW2"`.
`cycle`	A character string specifying the cycle model. `cycle = "AR1"` denotes an AR(1) process, `cycle = "AR2"` an `AR(2)` process. The default is `cycle = "AR2"`.
`type`	A character string specifying the type of the Phillip's curve. `type = "TKP"` denotes the traditional Keynesian Phillip's curve and `type = "NKP"` the New Keynesian Phillip's curve, see details. The default is `type = "TKP"`.
`cycleLag`	A vector specifying the cycle lags that are included in the Phillip's curve. The default is `cycleLag = 0`, see details.
`pcErrorARMA`	A `2 x 1` vector with non-negative integers specifying the AR and MA degree of the error term in the Phillip's curve equation. The default is `pcErrorARMA = c(0, 0)`, see details.
`exoType`	An optional `n x m x 2` array specifying the possible difference and lag transformation for the variables. `exoType` can be initialized using the function `inizializeExo`. The column names give the variable names. `exoType[, , 1]` contains the difference transformations and `exoType[, , 2]` the subsequent lag transformations, see details.
`start`	(Optional) Start vector for the estimation, e.g. `c(1980, 1)`.
`end`	(Optional) End vector for the estimation, e.g. `c(2020, 1)`.
`anchor`	(Optional) Anchor value for the unemployment rate.
`anchor.h`	(Optional) Anchor horizon in the frequency of the given time series.

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:

`tsl`	A list of used time series.
`SSModel`	An object of class SSModel specifying the state-space model.
`loc`	A data frame containing information on each involved parameter, for instance its corresponding system matrix, variable names, and parameter restrictions.
`call`	Original call to the function.

In addition, the object contains the following attributes:

`cycle`	Cycle specification.
`trend`	Trend specification.
`phillipsCurve`	A list containing the components `type, cycleLag, errorARMA, exoVariables`.
`anchor`	A list containing the components `value, horizon`.
`period`	A list containing the components `start, end, frequency`.

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)
# 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)

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

Arguments

`x`	An object of class `gap`.
`contribution`	A boolean indicating whether the contributions to potential output growth and the output gap should be plotted (only applicable for production function type output gaps).
`path`	An optional file path. If specified, the plots will be saved using the format in `device` under the given path.
`combine`	A logical indicating whether the plots should be combined or not, the default is `TRUE`.
`prefix`	An optional character string to be added to the names of the plots in case `path` is specified.
`device`	Device passed on to `ggplot` for plot saving. Options are `"eps", "ps", "tex"` (pictex), `"pdf", "jpeg", "tiff", "png", "bmp", "svg"` or `"wmf"`.
`width`	The plot width in case of printing.
`height`	The plot height in case of printing.
`...`	Ignored.

Value

No return value, plots are printed.

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,
  ...
)
## 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

`x`	An object of class `KuttnerFit`.
`alpha`	The significance level for the trend (`alpha in [0,1]`). Only used if `bounds = TRUE`.
`bounds`	A logical indicating whether significance intervals should be plotted around gdp. The default is `bounds = TRUE`.
`path`	An optional file path. If specified, the plots will be saved using the format in `device` under the given path.
`combine`	A logical indicating whether the diagnostic plots should be combined or not, the default is `TRUE`.
`prefix`	An optional character string to be added to the names of the plots in case `path` is specified.
`device`	Device passed on to `ggplot` for plot saving. Options are `"eps", "ps", "tex"` (pictex), `"pdf", "jpeg", "tiff", "png", "bmp", "svg"` or `"wmf"`.
`width`	The plot width in case of printing.
`height`	The plot height in case of printing.
`...`	Ignored.

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,
  ...
)
## 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

`x`	An object of class `NAWRUfit`.
`alpha`	The significance level for the NAWRU (`alpha in [0,1]`). Only used if `bounds = TRUE`.
`bounds`	A logical indicating whether significance intervals should be plotted around the nawru. The default is `bounds = TRUE`.
`path`	An optional file path. If specified, the plots will be saved using the format in `device` under the given path.
`combine`	A logical indicating whether the diagnostic plots should be combined or not, the default is `TRUE`.
`prefix`	An optional character string to be added to the names of the plots in case `path` is specified.
`posterior`	A logical indicating whether posterior diagnostics should be plotted. The default is `FALSE`. Only applied in the case of bayesian estimation.
`device`	Device passed on to `ggplot` for plot saving. Options are `"eps", "ps", "tex"` (pictex), `"pdf", "jpeg", "tiff", "png", "bmp", "svg"` or `"wmf"`.
`width`	The plot width in case of printing.
`height`	The plot height in case of printing.
`...`	Ignored.

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,
  ...
)
## 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

`x`	An object of class `TFPfit`.
`alpha`	The significance level for the TFP trend (`alpha in [0,1]`). Only used if `bounds = TRUE`.
`bounds`	A logical indicating whether significance intervals should be plotted around tfp growth. The default is `bounds = TRUE`.
`path`	An optional file path. If specified, the plots will be saved using the format in `device` under the given path.
`combine`	A logical indicating whether the diagnostic plots should be combined or not, the default is `TRUE`.
`prefix`	An optional character string to be added to the names of the plots in case `path` is specified.
`posterior`	A logical indicating whether posterior diagnostics should be plotted. The default is `FALSE`. Only applied in the case of bayesian estimation.
`device`	Device passed on to `ggplot` for plot saving. Options are `"eps", "ps", "tex"` (pictex), `"pdf", "jpeg", "tiff", "png", "bmp", "svg"` or `"wmf"`.
`width`	The plot width in case of printing.
`height`	The plot height in case of printing.
`...`	Ignored.

Value

No return value, plots are printed.

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

Arguments

`object`	An object of class `NAWRUfit`, `TFPfit`, or `KuttnerFit` (objects of class `fit`).
`n.ahead`	An integer specifying the prediction horizon.
`exogenous`	A character string specifying the computation of exogenous variables included in the model (if applicable). Valid options are `exogenous = "mean"` and `exogenous = "last".`
`returnFit`	A logical. If `TRUE`, an object of the same class as `fit` where the list entry `tsl` is replaced. If `FALSE`, only the new time series list is returned.
`...`	Ignored.

Value

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

Print `gap` object

Description

Prints the model specifications of an object of class gap.

Usage

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

Arguments

`x`	An object of class `gap`.
`...`	Ignored.

Value

No return value, results are printed.

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

Arguments

`x`	An object of class `KuttnerFit`.
`...`	Ignored.

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

Arguments

`x`	An object of class `KuttnerModel`.
`call`	A logical. If `TRUE`, the call will be printed.
`check`	A logical. If `TRUE`, the model class will be checked.
`...`	Ignored.

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

Arguments

`x`	An object of class `NAWRUfit`.
`...`	Ignored.

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

Arguments

`x`	An object of class `NAWRUmodel`.
`call`	A logical. If `TRUE`, the call will be printed.
`check`	A logical. If `TRUE`, the model class will be checked.
`...`	Ignored.

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

Arguments

`x`	An object of class `TFPfit`.
`...`	Ignored.

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

Arguments

`x`	An object of class `TFPmodel`.
`call`	A logical. If `TRUE`, the call will be printed.
`check`	A logical. If `TRUE`, the model class will be checked.
`...`	Ignored.

Value

No return value, model information is printed.

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

Arguments

`tsl`	A list of time series objects, see details.
`trend`	A character string specifying the trend model. `trend = "RW1"` denotes a first order random walk, `trend = "RW2"` a second order random walk (local linear trend) and `trend = "DT"` a damped trend model. The default is `trend = "DT"`.
`cycle`	A character string specifying the cycle model. `cycle = "AR1"` denotes an AR(1) process, `cycle = "AR2"` an AR(2) process, `cycle = "RAR2"` a reparametrized AR(2) process. The default is `cycle = "AR2"`.
`cycleLag`	A non-negative integer specifying the maximum cycle lag that is included in the CUBD equation. The default is `cycleLag = 0`, see details.
`cubsAR`	A non-negative integer specifying the maximum CUBS lag that is included in the CUBS equation. The default is `cubsAR = 0`, see details.
`cubsErrorARMA`	A vector with non-negative integers specifying the AR and MA degree of the error term in the CUBS equation. The default is `cubsErrorARMA = c(0, 0)`, see details.
`start`	(Optional) Start vector for the estimation, e.g. `c(1980, 1)`.
`end`	(Optional) End vector for the estimation, e.g. `c(2020, 1)`.
`anchor`	(Optional) Snchor value for the log of the TFP trend.
`anchor.h`	(Optional) Anchor horizon in the frequency of the given time series.

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:

`tsl`	A list of used time series.
`SSModel`	An object of class SSModel specifying the state-space model.
`loc`	A data frame containing information on each involved parameter, for instance its corresponding system matrix, variable names, and parameter restrictions.
`call`	Original call to the function.

In addition, the object contains the following attributes:

`cycle`	Cycle specification.
`trend`	Trend specification.
`cubs`	A list containing the components `cycleLag, cubsAR, errorARMA, exoVariables`.
`anchor`	A list containing the components `value, horizon`.
`period`	A list containing the components `start, end, frequency`.

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))
# 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))

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

Arguments

`fit`	An object of class `NAWRUfit`, `TFPfit`, or `KuttnerFit`.
`anchor`	A numeric specifying the anchor value. If unspecified, `anchor` is taken from the object `fit` (if specified).
`h`	An integer specifying the anchor horizon in the frequency of the underlying model. If unspecified, `h` is taken from the object `fit` (if specified).
`returnFit`	A logical. If `TRUE`, an object of the same class as `fit` including the anchored trend is returned. If `FALSE`, only the anchored trend time series is returned.

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)

# 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)

Package 'RGAP'

Help Index

Data for estimation

Description

Usage

Arguments

Details

Value

Examples

Fit best production function model

Description

Usage

Arguments

Details

Value

CUBS indicator

Description

Usage

Arguments

Details

Value

Examples

Current 'AMECO' data vintage

Description

Usage

Arguments

Details

Value

Source

Fit Method

Description

Usage

Arguments

Value

See Also

Maximum likelihood estimation of a KuttnerModel

Description

Usage

Arguments

Value

See Also

Examples

Estimation of a NAWRUmodel

Description

Usage

Arguments

Details

Value

See Also

Examples

Estimation of a TFPmodel

Description

Usage

Arguments

Details

Value

See Also

Examples

gap data set

Description

Usage

Format

Source

HP-filter output gap

Description

Usage

Arguments

Value

Production function output gap

Description

Usage

Arguments

Details

Value

Examples

HP filter

Description

Usage

Arguments

Value

Maximum likelihood estimation of a `KuttnerModel`

Estimation of a `NAWRUmodel`

Estimation of a `TFPmodel`

`gap` object check

`KuttnerModel` object check

`NAWRUodel` object check

`TFPmodel` object check

Plots for a `gap` object

Plots for a `KuttnerFit` object