Title

xtfaclm -- Factor-augmented panel LM unit-root test with two
structural breaks (PANIC + Lee-Strazicich)

Syntax

xtfaclm varname [if] [in] [, options]

The data must be xtset as a strongly balanced panel.

model(string) break specification: constant (level breaks,
default) or trend (level & trend breaks)

kmax(#) maximum number of common factors (default 5)

icfactor(#) factor-number criterion: 1=PCp, 2=ICp (default)

pmax(#) maximum augmentation lag (default 5)

iclag(#) lag selection: 1=AIC, 2=BIC (default), 3=t-stat

trim(#) break-location trimming fraction (default 0.3)

factors(#) fix the number of common factors instead of estimating

Description

xtfaclm implements the factor-augmented panel LM unit-root test with two
structural breaks of Payne, Lee, Islam and Nazlioglu (2022), developed for
testing greenhouse-gas emission convergence. The procedure iterates between (i)
estimating two structural breaks in each series by minimum residual sum of
squares, and (ii) extracting common factors by principal components (the PANIC
approach), until the idiosyncratic variance stabilises. Each de-factored series
is then tested with a Lee-Strazicich two-break LM regression that includes the
estimated common factors, and the resulting p-values are combined into the Fisher
panel statistics P and Pm.

Removing the common factors makes the test robust to strong cross-sectional
dependence, while the two breaks accommodate structural change of unknown timing.
xtfaclm is part of the xtpdroot library. See
help xtfaclm methods for the formulas.

Options

model(string): constant (breaks in the level, the default) or
trend (breaks in level and trend).

kmax(#), icfactor(#): the maximum number of common factors
(default 5) and the Bai-Ng (2002) criterion (1=PCp, 2=ICp, the default). The
number of factors is the ICp2 minimiser.

pmax(#), iclag(#): the maximum augmentation lag (default 5) and
the lag-selection rule. iclag(2) (BIC, the default) and iclag(1) (AIC)
select the lag from the regression sum of squares and reproduce the source GAUSS
routine to the last digit. iclag(3) reproduces the original
general-to-specific t-rule; because that rule keys off the t-statistic
of the last common factor — whose sign and rotation are not statistically
identified — its selected lag can depend on the eigenvector basis and is therefore
not reproducible across linear-algebra libraries. Use iclag(1) or the
default iclag(2) for exact reproducibility.

trim(#): the fraction trimmed at each end when searching for break
dates (default 0.3).

factors(#) fixes the number of common factors at # instead of
estimating it.

Examples

Level-break factor-augmented panel LM test:

. xtset country year

. xtfaclm lco2, model(constant)

Level & trend breaks, three common factors imposed:

. xtfaclm lco2, model(trend) factors(3)

Stored results

xtfaclm is rclass and stores:

Scalars

r(P), r(P_p) Fisher chi-square panel statistic and p-value

r(Pm), r(Pm_p) standardized panel statistic and p-value

r(nf) number of common factors

r(N), r(T) panel and time dimensions

Matrices

r(units) per-unit id, LM, p-value, break1, break2, lag

Interpreting the output

The null is a unit root in each panel. The per-unit LM statistic is a (negative)
t-ratio that rejects for large negative values; the panel P and Pm
reject for large values, in favour of (trend-)stationarity around the two breaks
once common factors are removed. The break columns report the estimated break
periods in the units of your time variable.

References

Payne, J. E., J. Lee, N. Islam, and S. Nazlioglu. 2022. Convergence of
per-capita greenhouse-gas emissions: LM unit-root tests with breaks and factors.
Energy Economics 115: 106360.

Lee, J., and M. C. Strazicich. 2003. Minimum Lagrange multiplier unit root
test with two structural breaks. Review of Economics and Statistics 85:
1082-1089.

Bai, J., and S. Ng. 2004. A PANIC attack on unit roots and cointegration.
Econometrica 72: 1127-1177.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane

Faithful Stata port of the GAUSS routine by S. Nazlioglu; validated
byte-for-byte against the GAUSS output on the CAIT greenhouse-gas panel (183
series, AIC/BIC lag selection: all per-unit LM statistics, breaks and lags exact).
Part of the xtpdroot library.