autoGapProd {RGAP}

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

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