Im-Pesaran-Shin (IPS) Panel Unit-Root Test
Also known as: IPS Test, IPS Panel Unit-Root Test, Heterogeneous Panel Unit-Root Test, Im-Pesaran-Shin Birim Kök Testi
The Im-Pesaran-Shin (IPS) test, introduced by Im, Pesaran, and Shin in 2003, is a panel unit-root test designed for heterogeneous panels where the autoregressive coefficient is allowed to differ across cross-sectional units. It averages individual Augmented Dickey-Fuller (ADF) t-statistics and constructs a standardized statistic with a standard normal limiting distribution, making it one of the most widely applied first-generation panel unit-root tests in applied econometrics.
Key highlights
- Allows heterogeneous autoregressive coefficients across cross-sectional units, relaxing the restrictive homogeneity assumption of the Levin-Lin-Chu test
- The W-statistic has a well-established standard normal limiting distribution, enabling straightforward inference
- More powerful than univariate ADF tests by exploiting the cross-sectional dimension of the panel
- Accommodates different lag lengths across units via individual ADF specifications
Intuition
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How it works
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When to use it
Use the IPS test when working with macro or micro panels where heterogeneity across units is expected—for instance, different countries, firms, or regions may exhibit different speeds of adjustment. The test requires a balanced or nearly balanced panel with moderate T (at least 10–25 observations per unit). It assumes cross-sectional independence; if cross-sectional dependence is present, second-generation tests such as the CIPS test (Pesaran, 2007) should be preferred. The test is appropriate as a first step before applying panel cointegration or panel regression methods.
Strengths & limitations
- Allows heterogeneous autoregressive coefficients across cross-sectional units, relaxing the restrictive homogeneity assumption of the Levin-Lin-Chu test
- The W-statistic has a well-established standard normal limiting distribution, enabling straightforward inference
- More powerful than univariate ADF tests by exploiting the cross-sectional dimension of the panel
- Accommodates different lag lengths across units via individual ADF specifications
- Assumes cross-sectional independence; spurious rejections can occur under cross-sectional dependence
- The alternative hypothesis is composite—stationary for some units but not necessarily all—so rejection does not indicate which units are I(0)
- Requires sufficiently large T for individual ADF regressions to be well-specified; performs poorly in very short panels
- The tabulated mean and variance corrections are derived under specific distributional assumptions that may not hold in finite samples
Common pitfalls
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Applications
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Frequently asked
How does the IPS test differ from the Levin-Lin-Chu (LLC) test?
The LLC test imposes a common autoregressive coefficient rho across all panel units under both the null and the alternative, making it a homogeneous test. The IPS test relaxes this assumption, allowing rho_i to differ across units. As a result, the IPS alternative is composite—only some units need to be stationary—whereas the LLC alternative requires all units to be stationary simultaneously.
What should I do if my panel exhibits cross-sectional dependence?
The IPS test is a first-generation test that assumes cross-sectional independence. When dependence is present—common in macro panels subject to global shocks—size distortions can be severe. In this case, use second-generation tests such as the CIPS test of Pesaran (2007), which augments individual ADF regressions with cross-sectional averages to filter out common factors.
How do I select the lag length for the individual ADF regressions?
Lag lengths p_i may be chosen separately for each unit using information criteria such as the Akaike Information Criterion (AIC) or Schwarz Bayesian Criterion (BIC), or by sequential testing of residual autocorrelation. The IPS framework explicitly accommodates unit-specific lag lengths, so there is no requirement to impose a common p across all cross-sections.
Sources
- 1.Im, K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels. Journal of Econometrics, 115(1), 53–74.
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ScholarGate. (2026, June 2). Im-Pesaran-Shin Test. ScholarGate. https://scholargate.app/econometrics/im-pesaran-shin-test