Unit root tests for panel data

purtest implements several testing procedures that have been proposed to test unit root hypotheses with panel data.

  data = NULL,
  index = NULL,
  test = c("levinlin", "ips", "madwu", "Pm", "invnormal", "logit", "hadri"),
  exo = c("none", "intercept", "trend"),
  lags = c("SIC", "AIC", "Hall"),
  pmax = 10,
  Hcons = TRUE,
  q = NULL,
  dfcor = FALSE,
  fixedT = TRUE,
  ips.stat = NULL,

# S3 method for purtest print(x, ...)

# S3 method for purtest summary(object, ...)

# S3 method for summary.purtest print(x, ...)

object, x

Either a "data.frame" or a matrix containing the time series (individuals as columns), a "pseries" object, a formula; a "purtest" object for the print and summary methods,


a "data.frame" or a "pdata.frame" object (required for formula interface, see Details and Examples),


the indexes,


the test to be computed: one of "levinlin" for LEVIN:LIN:CHU:02;textualplm, "ips" for IM:PESAR:SHIN:03;textualplm, "madwu" for MADDA:WU:99;textualplm, "Pm" , "invnormal", or "logit" for various tests as in CHOI:01;textualplm, or "hadri" for HADR:00;textualplm, see Details,


the exogenous variables to introduce in the augmented Dickey--Fuller (ADF) regressions, one of: no exogenous variables ("none"), individual intercepts ("intercept"), or individual intercepts and trends ("trend"), but see Details,


the number of lags to be used for the augmented Dickey-Fuller regressions: either an integer (the number of lags for all time series), a vector of integers (one for each time series), or a character string for an automatic computation of the number of lags, based on the AIC ("AIC"), the SIC ("SIC"), or on the method by HALL:94;textualplm ("Hall"); argument is irrelevant for test = "hadri",


maximum number of lags (irrelevant for test = "hadri"),


logical, only relevant for test = "hadri", indicating whether the heteroskedasticity-consistent test of HADR:00;textualplm should be computed,


the bandwidth for the estimation of the long-run variance (only relevant for test = "levinlin", the default (`q = NULL``) gives the value as suggested by the authors as round(3.21 * T^(1/3))),


logical, indicating whether the standard deviation of the regressions is to be computed using a degrees-of-freedom correction,


logical, indicating whether the individual ADF regressions are to be computed using the same number of observations (irrelevant for test = "hadri"),


NULL or character of length 1 to request a specific IPS statistic, one of "Wtbar" (also default if ips.stat = NULL), "Ztbar", "tbar",

further arguments (can set argument p.approx to be passed on to non-exported function padf to either "MacKinnon1994" or "MacKinnon1996" to force a specific method for p-value approximation, the latter only being possible if package 'urca' is installed).


All these tests except "hadri" are based on the estimation of augmented Dickey-Fuller (ADF) regressions for each time series. A statistic is then computed using the t-statistics associated with the lagged variable. The Hadri residual-based LM statistic is the cross-sectional average of the individual KPSS statistics KWIA:PHIL:SCHM:SHIN:92plm, standardized by their asymptotic mean and standard deviation.

Several Fisher-type tests that combine p-values from tests based on ADF regressions per individual are available:

  • "madwu" is the inverse chi-squared test MADDA:WU:99plm, also called P test by CHOI:01;textualplm.

  • "Pm" is the modified P test proposed by CHOI:01;textualplm for large N,

  • "invnormal" is the inverse normal test by CHOI:01plm, and

  • "logit" is the logit test by CHOI:01plm.

The individual p-values for the Fisher-type tests are approximated as described in MACK:96;textualplm if the package 'urca' (PFAFF:08;textualplm) is available, otherwise as described in MACK:94;textualplm.

For the test statistic tbar of the test of Im/Pesaran/Shin (2003) (ips.stat = "tbar), no p-value is given but 1%, 5%, and 10% critical values are interpolated from paper's tabulated values via inverse distance weighting (printed and contained in the returned value's element statistic$ips.tbar.crit).

Hadri's test, the test of Levin/Lin/Chu, and the tbar statistic of Im/Pesaran/Shin are not applicable to unbalanced panels; the tbar statistic is not applicable when lags > 0 is given.

The exogeneous instruments of the tests (where applicable) can be specified in several ways, depending on how the data is handed over to the function:

  • For the formula/data interface (if data is a data.frame, an additional index argument should be specified); the formula should be of the form: y ~ 0, y ~ 1, or y ~ trend for a test with no exogenous variables, with an intercept, or with individual intercepts and time trend, respectively. The exo argument is ignored in this case.

  • For the data.frame, matrix, and pseries interfaces: in these cases, the exogenous variables are specified using the exo argument.

With the associated summary and print methods, additional information can be extracted/displayed (see also Value).


For purtest: An object of class "purtest": a list with the elements "statistic" (a "htest" object), "call", "args", "idres" (containing results from the individual regressions), and "adjval" (containing the simulated means and variances needed to compute the statistic, for "test = levinlin" and "ips", otherwise NULL), "sigma2" (short-run and long-run variance for "test = levinlin", otherwise NULL).


See Also


  • purtest
  • print.purtest
  • summary.purtest
  • print.summary.purtest
data("Grunfeld", package = "plm")
y <- data.frame(split(Grunfeld$inv, Grunfeld$firm)) # individuals in columns

purtest(y, pmax = 4, exo = "intercept", test = "madwu")

## same via formula interface
purtest(inv ~ 1, data = Grunfeld, index = c("firm", "year"), pmax = 4, test = "madwu")

# }
Documentation reproduced from package plm, version 2.2-5, License: GPL (>= 2)

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