Common mistake 1 with Panel unit-root tests

Ignoring cross-sectional dependence, which makes first-generation tests over-reject badly. Use Pesaran CIPS when CD rejects.

Common mistake 2 with Panel unit-root tests

Reading rejection as "the panel is stationary". It means at least some of it is.

Common mistake 3 with Panel unit-root tests

Running these on a panel with only three or four periods per entity.

Common mistake 4 with Panel unit-root tests

Applying a first-generation test after the Pesaran CD test has rejected. The module reports CD for exactly this reason: once cross-sectional dependence is established, the earlier tests over-reject badly and a second-generation test is the only defensible choice.

EconStatsCraft › Panel unit-root tests

Panel unit-root tests

The panel version of the ADF test. Pools evidence across entities, so it has far more power than testing one short series at a time - which is exactly why panel macro work uses it.

What it needs

Entity identifier
Time identifier
Series to test

The intuition

A single unit-root test on forty years of one country has very little power - it usually cannot reject a random walk even when the series is stationary. Pool twenty countries and you have twenty times the information about the same question. That is the whole appeal of panel unit-root tests, and also where the trouble starts, because pooling requires deciding what exactly is being assumed common across countries.

When to use it

Before any panel regression in levels on macro data, and before testing for panel cointegration.

Where the estimator comes from

All these tests run \Delta y_{it}=\rho_i y_{i,t-1}+\sum_j\gamma_{ij}\Delta y_{i,t-j}+\alpha_i+\delta_i t+\varepsilon_{it} and differ in what they impose. Levin-Lin-Chu assumes a COMMON \rho_i=\rho and tests \rho=0 against \rho<0, so the alternative is that every series is stationary. Im-Pesaran-Shin allows \rho_i to differ and averages the individual t statistics, \bar{t}=\frac{1}{N}\sum_i t_i, standardised to a normal; its alternative is that SOME fraction is stationary. Fisher-type tests combine the individual p-values, -2\sum_i\ln p_i\sim\chi^2_{2N}, which needs no balanced panel. Hadri inverts the null entirely and tests stationarity against a unit root, in the manner of KPSS.

The model

\bar{t}=\frac{1}{N}\sum_{i=1}^{N}t_i,\qquad Z_{\bar{t}}=\frac{\sqrt{N}\left(\bar{t}-E[t]\right)}{\sqrt{\operatorname{Var}[t]}},\qquad P=-2\sum_{i=1}^{N}\ln p_i\sim\chi^2_{2N}

What it assumes

Cross-sectional independence. This is the big one, and it usually fails on macro panels - check with Pesaran CD first.
Enough periods per entity for each individual ADF to mean anything.
The lag length is adequate for each series.
The panel is roughly balanced, or the test handles the imbalance explicitly. Entities with very different lengths contribute very different amounts of information, and the pooled statistic weights them in ways that are rarely what the analyst intends.

Statistical properties

The null and the alternative are not symmetric across these tests. Rejecting IPS means at least one series is stationary, not that all are - a conclusion far weaker than most write-ups claim.
All of the first-generation tests assume independence across units. Cross-sectional dependence, which is the norm in country panels, causes massive over-rejection: they find stationarity that is not there.
Second-generation tests - Pesaran's CIPS, Bai and Ng's PANIC - allow common factors and should be the default for macro panels. Run Pesaran's CD first to decide.
Power rises with N much faster than with T, which is the reason to pool at all. But bias also rises with N when the independence assumption fails, so more countries is not unambiguously better.
The deterministic terms matter as much as in the univariate case. Including a trend when there is none costs power; omitting one that exists guarantees failure to reject.
Structural breaks look like unit roots to every one of these tests, exactly as in the single-series case, and a break common to all units is the worst case.

How to read the output

The null is that EVERY series has a unit root.
IPS and Fisher have a heterogeneous alternative: rejecting means SOME series are stationary, not all.
The pooled (Levin–Lin–Chu style) test assumes a COMMON root across entities - a much stronger assumption.
Take the majority verdict across the three tests rather than the one you like.

A worked reading

Twenty countries, forty years each. Individually, the ADF test rejects for three of the twenty - the usual outcome, and not evidence that seventeen have unit roots, only that forty observations cannot tell. Pooled, IPS rejects at p = 0.003. But Pesaran CD also rejects strongly, which means the twenty series share common shocks and the IPS p-value is not to be believed: under dependence these tests reject far too readily. CIPS, which allows a common factor, gives p = 0.14. The honest conclusion is the cautious one, and it is the opposite of what the naive pooled test said.

Symptom → diagnosis → what to do

If you see this	It means	Do this
LLC rejects but IPS does not	The homogeneity assumption is doing the work	Trust IPS; LLC's common-rho alternative is implausible
Everything rejecting decisively	Check cross-sectional dependence first	First-generation tests over-reject badly under dependence
Pesaran CD strongly significant	Common factors present	Use CIPS rather than LLC or IPS
Unbalanced panel	LLC and IPS need balance	Use a Fisher-type test
Hadri rejecting as well as IPS	Contradictory only in appearance	Hadri over-rejects under dependence; both cannot be trusted
Results flipping with the lag length	Sensitive to the augmentation	Select lags by an information criterion per unit and report it

Common mistakes

Ignoring cross-sectional dependence, which makes first-generation tests over-reject badly. Use Pesaran CIPS when CD rejects.
Reading rejection as "the panel is stationary". It means at least some of it is.
Running these on a panel with only three or four periods per entity.
Applying a first-generation test after the Pesaran CD test has rejected. The module reports CD for exactly this reason: once cross-sectional dependence is established, the earlier tests over-reject badly and a second-generation test is the only defensible choice.

Where to read this properly

Levin, Lin and Chu (2002), Journal of Econometrics 108(1); Im, Pesaran and Shin (2003), Journal of Econometrics 115(1).
Pesaran (2007), "A Simple Panel Unit Root Test in the Presence of Cross-Section Dependence", Journal of Applied Econometrics 22(2).
Bai and Ng (2004), "A PANIC Attack on Unit Roots and Cointegration", Econometrica 72(4).
Baltagi, Econometric Analysis of Panel Data (2021), ch. 12.

Related Panel data

Panel regression · Panel cointegration tests · Heterogeneous panel: Mean Group & PMG · Gravity model of trade · Dynamic panel GMM · Panel diagnostics

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Panel unit-root tests

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

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