# Maximum lag selection for panel unit root tests

I am interested in conducting panel unit root tests on a panel of subregional annual data where N>100 and T<10 (more specifically, depending on the independent variables included in each regression, T varies between 6 and 9). I want to implement the Maddala and Wu (1999) as well as the Pesaran (2007) panel unit root tests using multipurt command in Stata.

My question: what should my maximum lags be? I understand this often depends on the frequency of data i.e. 12 lags for monthly and 4 for quarterly data. Does it follow that annual data should have a max lag of 1? Given the shortness of my panel with T<10, I have concerns over specifying more lags than necessary.

## 1 Answer

Neither test is going to be very reliable no matter how you choose the lag length.

Both tests combine time series unit root test statistics, whose null distributions are derived under the assumption that $T\to\infty$. While that assumption is, of course, never literally satisfied, $T=6$ is going to give you time series test statstics, and hence panel statistics, whose properties are anybody's guess.

For example, Maddala and Wu's test sums up $-\ln(p_i)$ over $i$, where $p_i$ are the $p$-values of time series unit root test statistics like that of Dickey-Fuller's, and where the $p$-values are typically computed from asymptotic null distributions. (There are so-called response surface regressions that try to come up with better approximations to finite-sample distributions, but whether these are implemented in Stata, and if so, if these are reliable for $T$ so small is something I would not dare to say.)