# Unit-root test for unbalanced panel data

I have data on 146 institutions for 15 years. All of them have not data for all time points so that I have unbalanced panel data. How can I calculate a unit-root test in Stata or EViews for this unbalanced panel dataset?

It depends on the type of unbalancedness. Is your unbalancedness such that your time series are of different lengths, but do not have missing values in between (often the case in macro panels)? Then, there is no need for interpolation within one time series.

As you basically want to pool evidence against a unit root from different time series in a panel unit root test, it is enough to combine test statistics or $p$-values, which need not have been computed from time series of identical lengths.

You should then for instance consider $p$-value combination tests such as Fisher's test as explored here, viz. $\sum_{i=1}^N-2\ln(p_i)$, which, under independence of the units (a strong assumption!), follows a $\chi^2$-distribution.

An alternative would be Simes' test, i.e. reject if there exists an ordered $p$-value $p_{(i)}$ such that $p_{(i)}<\alpha\cdot i/N$. It is also valid under certain types of dependence and has been investigated as a panel unit root test by, um, me.

• That is the same, unless I misunderstand your question. – Christoph Hanck Sep 26 '17 at 7:15

The Hadri Lagrange test for unit root is implemented within Stata, but, as you undoubtedly know already, requires strongly balanced data. You might wish to explore using multiple imputation appropriate to cross-sectional time series in multiple populations along the lines of King and Honaker's R software Amelia II: A Program for Missing Data. You can produce multiple data sets (say, 10) using a multiple imputation technique appropriate for your kind of data, calculate Hadri's z test statistic for each, and determine whether each imputated data set comes to the same conclusion.

Agreement (either rejection or failure to reject) might be reasonable support for evidence of/lack of evidence of unit root. Lack of agreement across the data, would suggest that stationarity your data may depend strongly on the values of the missing observations.

Honaker, J. and King, G. (2010). What to do about missing values in time-series cross-section data. American Journal of Political Science, 54(2):561–581.