pvars (version 1.1.1)

pcoint: Panel cointegration rank tests

Description

Performs test procedures for the rank of cointegration in a panel of VAR models. First, the chosen individual procedure is applied over all \(N\) individual entities for \(r_{H0}=0,\ldots,K-1\). Then, the \(K \times N\) individual statistics and \(p\)-values are combined to panel test results on each \(r_{H0}\) using all combination approaches available for the chosen procedure.

Usage

pcoint.JO(
  L.data,
  lags,
  type = c("Case1", "Case2", "Case3", "Case4"),
  t_D1 = NULL,
  t_D2 = NULL,
  n.factors = FALSE
)
pcoint.BR(
  L.data,
  lags,
  type = c("Case1", "Case2", "Case3", "Case4"),
  t_D1 = NULL,
  t_D2 = NULL,
  n.iterations = FALSE
)
pcoint.SL(L.data, lags, type = "SL_trend", t_D = NULL, n.factors = FALSE)
pcoint.CAIN(L.data, lags, type = "SL_trend", t_D = NULL)

Value

A list of class 'pcoint' with elements:

panel

List for the panel test results, which contains one matrix for the test statistics and one for the \(p\)-values.

individual

List for the individual test results, which contains one matrix for the test statistics and one for the \(p\)-values.

CSD

List of measures for cross-sectional dependency. NULL if a first generation test has been used.

args_pcoint

List of characters and integers indicating the panel cointegration test and specifications that have been used.

beta_H0

List of matrices, which comprise the pooled cointegrating vectors for each rank \(r_{H0}\). NULL if any other test than BR has been used.

Arguments

L.data

List of 'data.frame' objects for each individual. The variables must have the same succession \(k = 1,\ldots,K\) in each individual 'data.frame'.

lags

Integer or vector of integers. Lag-order of the VAR models in levels, which is either a common \(p\) for all individuals or individual-specific \(p_i\) for each individual. In the vector, \(p_i\) must have the same succession \(i = 1,\ldots,N\) as argument L.data.

type

Character. The conventional case of the deterministic term.

t_D1

List of vectors. The activating break periods \(\tau\) for the period-specific deterministic regressors in \(d_{1,it}\), which are restricted to the cointegration relations. The accompanying lagged regressors are automatically included in \(d_{2,it}\). The \(p\)-values are calculated for up to two breaks resp. three sub-samples.

t_D2

List of vectors. The activating break periods \(\tau\) for the period-specific deterministic regressors in \(d_{2,it}\), which are unrestricted.

n.factors

Integer. Number of common factors to be subtracted for the PANIC by Arsova and Oersal (2017, 2018). Deactivated if FALSE (the default).

n.iterations

Integer. The (maximum) number of iterations for the pooled estimation of the cointegrating vectors.

t_D

List of vectors. The activating break periods \(\tau\) for the period-specific deterministic regressors in \(d_{it}\) of the SL-procedure. The accompanying lagged regressors are automatically included in \(d_{it}\). The \(p\)-values are calculated for up to two breaks resp. three sub-samples.

Functions

• pcoint.JO(): based on the Johansen procedure.

• pcoint.BR(): based on the pooled two-step estimation of the cointegrating vectors.

• pcoint.SL(): based on the Saikkonen-Luetkepohl procedure.

• pcoint.CAIN(): accounting for correlated probits between the individual SL-procedures.

References

Larsson, R., Lyhagen, J., and Lothgren, M. (2001): "Likelihood-based Cointegration Tests in Heterogeneous Panels", Econometrics Journal, 4, pp. 109-142.

Choi, I. (2001): "Unit Root Tests for Panel Data", Journal of International Money and Finance, 20, pp. 249-272.

Arsova, A., and Oersal, D. D. K. (2018): "Likelihood-based Panel Cointegration Test in the Presence of a Linear Time Trend and Cross-Sectional Dependence", Econometric Reviews, 37, pp. 1033-1050.

Breitung, J. (2005): "A Parametric Approach to the Estimation of Cointegration Vectors in Panel Data", Econometric Reviews, 24, pp. 151-173.

Oersal, D. D. K., and Droge, B. (2014): "Panel Cointegration Testing in the Presence of a Time Trend", Computational Statistics & Data Analysis, 76, pp. 377-390.

Oersal, D. D. K., and Arsova, A. (2017): "Meta-Analytic Cointegrating Rank Tests for Dependent Panels", Econometrics and Statistics, 2, pp. 61-72.

Arsova, A., and Oersal, D. D. K. (2018): "Likelihood-based Panel Cointegration Test in the Presence of a Linear Time Trend and Cross-Sectional Dependence", Econometric Reviews, 37, pp. 1033-1050.

Hartung, J. (1999): "A Note on Combining Dependent Tests of Significance", Biometrical Journal, 41, pp. 849-855.

Arsova, A., and Oersal, D. D. K. (2021): "A Panel Cointegrating Rank Test with Structural Breaks and Cross-Sectional Dependence", Econometrics and Statistics, 17, pp. 107-129.

Examples

### reproduce Oersal,Arsova 2017:67, Ch.5 ###
data("MERM")
names_k = colnames(MERM)[-(1:2)] # variable names
names_i = levels(MERM$id_i)      # country names
L.data  = sapply(names_i, FUN=function(i) 
   ts(MERM[MERM$id_i==i, names_k], start=c(1995, 1), frequency=12), 
   simplify=FALSE)

# Oersal,Arsova 2017:67, Tab.5 #
R.lags = c(2, 2, 2, 2, 1, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 1, 1, 2, 2)
names(R.lags) = names_i  # individual lags by AIC (lag_max=4)
n.factors = 8  # number of common factors by Onatski's (2010) criterion
R.pcsl = pcoint.SL(L.data, lags=R.lags, n.factors=n.factors, type="SL_trend")
R.pcjo = pcoint.JO(L.data, lags=R.lags, n.factors=n.factors, type="Case4")

# Oersal,Arsova 2017:67, Tab.6 #
R.Ftsl = coint.SL(y=R.pcsl$CSD$Ft, dim_p=2, type_SL="SL_trend")  # lag-order by AIC
R.Ftjo = coint.JO(y=R.pcsl$CSD$Ft, dim_p=2, type="Case4")

### reproduce Oersal,Arsova 2016:13, Ch.6 ###
data("ERPT")
names_k = c("lpm5", "lfp5", "llcusd")  # variable names for "Chemicals and related products"
names_i = levels(ERPT$id_i)[c(1,6,2,5,4,3,7)]  # ordered country names
L.data  = sapply(names_i, FUN=function(i) 
   ts(ERPT[ERPT$id_i==i, names_k], start=c(1995, 1), frequency=12), 
   simplify=FALSE)

# Oersal,Arsova 2016:21, Tab.6 (only for individual results) #
R.lags = c(3, 3, 3, 4, 3, 3, 3); names(R.lags)=names_i  # lags of VAR model by MAIC
R.cain = pcoint.CAIN(L.data, lags=R.lags, type="SL_trend")
R.pcsl = pcoint.SL(L.data,   lags=R.lags, type="SL_trend")

# Oersal,Arsova 2016:22, Tab.7/8 #
R.lags = c(3, 3, 3, 4, 4, 3, 4); names(R.lags)=names_i  # lags of VAR model by MAIC
R.t_D  = list(t_break=89)  # a level shift and trend break in 2002_May for all countries
R.cain = pcoint.CAIN(L.data, lags=R.lags, t_D=R.t_D, type="SL_trend")