Panel Stationarity Tests: CADF and CIPS Explained

 When dealing with panel data, testing for stationarity (i.e., whether variables have a constant mean and variance over time) is crucial before estimation—especially in macroeconomic and financial studies.

Two advanced second-generation panel unit root tests used to check for stationarity while accounting for cross-sectional dependence are:

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🔹 1. CADF (Cross-sectionally Augmented Dickey-Fuller) Test

📌 Developed by: Pesaran (2007)

CADF is an extension of the Augmented Dickey-Fuller (ADF) test that augments each ADF regression with cross-sectional averages to account for cross-sectional dependence.

🔍 Model Form:

For each unit $i$, the CADF regression is:

$$\Delta y_{it} = a_i + b_i y_{i,t-1} + c_i \bar{y}_{t-1} + d_i \Delta \bar{y}_{t} + \sum_{j=1}^{p} \phi_{ij} \Delta y_{i,t-j} + \varepsilon_{it}$$

Where:

• $\bar{y}_t$ is the cross-sectional average of all $y_{it}$,

• $b_i$ tests for the unit root (null: $b_i = 0$).

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🔹 2. CIPS (Cross-sectionally Augmented IPS) Test

📌 Also Developed by: Pesaran (2007)

CIPS is the panel version of the CADF test. It aggregates the individual CADF statistics into one panel test statistic.

📊 Formula:

$$CIPS = \frac{1}{N} \sum_{i=1}^{N} t_i^{CADF}$$

Where:

• $t_i^{CADF}$ is the t-statistic from the CADF regression for unit $i$,

• The null hypothesis is: all series have a unit root (non-stationary),

• The alternative is: at least some cross-sections are stationary.

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🧪 CIPS vs First-Generation Tests

Feature	First-Generation (e.g., IPS, LLC)	Second-Generation (CIPS, CADF)
Assumes Cross-Section Independence	✅ Yes	❌ No
Handles Common Shocks	❌	✅ Yes
Suitable for Financial Panels	❌	✅ Highly Suitable
Example	Levin-Lin-Chu, Im-Pesaran-Shin	Pesaran’s CADF & CIPS

✅ When to Use CADF/CIPS:

• In macro or financial panel datasets where cross-sectional correlation is present (e.g., bank performance, regional inflation, country-level interest rates).

• When standard IPS or LLC tests give inconclusive results due to cross-sectional dependence.

🔎 Interpreting Results:

·         If CIPS statistic < critical value → Reject null → Stationarity.

·         If CIPS statistic > critical value → Do not reject null → Non-stationary.

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📝 Summary Table:

Test	Accounts for Cross-Section Dependence	Based On	Output	Null Hypothesis
CADF	✅ Yes	ADF	Individual t-stats	Unit root for each unit
CIPS	✅ Yes	CADF average	Panel stat	All units have unit root