help for madfuller                        (StataList distribution 16 July 2001)

Multivariate Augmented Dickey-Fuller panel unit root test

madfuller varname [if exp] [in range] ,lags(numlist)

madfuller is for use with panel data. You must tsset your data before using madfuller, using the panel form of tsset; see help tsset.

varname may contain time-series operators; see help varlist.


madfuller performs the multivariate augmented Dickey-Fuller (MADF) panel unit root test (Sarno and Taylor, 1998; Taylor and Sarno, 1998) on a variable that contains both cross-section and time-series components. The MADF test is a generalization of the test developed by Abuaf and Jorion (1990) in which a single autoregressive parameter is estimated over the panel. In contrast, Sarno and Taylor allow for higher order serial correlation in the series and allow the sum of autoregressive coefficients to vary across panel units under the alternative hypothesis. The authors claim that the MADF test is "very much more powerful than the univariate ADF test." (Taylor and Sarno, p. 298)

The test applies Zellner's seemingly unrelated equation estimator sureg to N equations, defined for the N units of the panel. Each equation is specified as a k-th order autoregression. The test involves testing the hypothesis, for each equation, that the sum of the coefficients of the autoregressive polynomial is unity. The null hypothesis consists of the joint test that this condition is satisfied over the N equations. Under the null hypothesis, all of the series under consideration are realizations of I(1), or nonstationary, stochastic processes. The distribution of the test statistic must be approximated because of the "theoretically infinite variance of the processes generating the ... series under the null hypothesis." Taylor and Sarno (1998, p. 299) provide response surface estimates of the 5% critical values, derived from Monte Carlo simulation. The response surface was estimated over sample sizes ranging from 25 to 500 observations per cross-sectional unit.

The test's null hypothesis should be carefully considered. It will be violated if even one of the series in the panel is stationary. A rejection should thus not be taken to indicate that each of the series is stationary. Johansen's likelihood ratio test (Sarno and Taylor, 1998) applies the opposite hypothesis: that at least one of the series in the panel is a nonstationary process.

The test may be compared with Levin and Lin's (1993) panel unit root test levinlin which imposes a single autoregressive parameter over all units in the panel but utilizes a variant of xtreg, fe for estimation. The Levin-Lin test may thus be employed for small-T, large-N panels. However, the caveats mentioned above apply to this test.


lags, which must be provided, specifies the lag orders to be used in augmenting the Dickey-Fuller regression. If multiple lag orders are given, the test is performed for each lag order.


. use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear

. madfuller rgdppc if country<11, lags(2(2)8)

. madfuller D.rgdppc if country<11, lags(4)


Abuaf, N. and P. Jorion. Purchasing power parity in the long run. Journal of Finance 45, 1990, 157-174.

Levin, Andrew and Lin, Chien-Fu. Unit Root Tests in Panel Data: New Results", University of California Discussion Paper No. 93-56, 1993.

Sarno, Lucio and Mark P. Taylor. Real exchange rates under the current float: unequivocal evidence of mean reversion. Economics Letters, 60, 1998, 131-137.

Taylor, Mark P. and Lucio Sarno. The behavior of real exchange rates during the post-Bretton Woods period. Journal of International Economics, 46, 1998, 281-312.


I thank Falko Juessen for suggesting improvements to the help file.


Christopher F Baum, Boston College, USA, baum@bc.edu

Also see

Manual: [R] dfuller

On-line: help for dfuller, time, tsset, sureg, dfgls (if installed), levinlin