Im-Pesaran-Shin (IPS) Panel Unit-Root 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.

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.

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.