For example some of the variables in the model are stationary at level and others are not. how do we deal with that.
When dealing with stationarity on case of unbalanced panel data where N>T, you can use the first difference transformation to make the data stationary. Stationarity tests for panel data are designed for panels where T>N, so when they are more similar to time series than cross-sectional data.
In the case of unbalanced panel data where N>T, stationarity can be dealt with by using the first-difference transformation. This transformation involves subtracting each observation from the previous observation in the same time series. The resulting series will have one less observation than the original series. Another approach is to use fixed effects, regression models. These models control for unobserved heterogeneity across individuals by including individual-specific intercepts.
In case of unbalanced panel data where N>T, one can use the first difference method to deal with stationarity. This method involves taking the difference between consecutive observations of each variable in the panel data. This method is useful when the panel data is not stationary and has a trend or unit root. Another method is to use fixed effects models which can help control for unobserved heterogeneity in the panel data1.
There are different methods to deal with stationarity in unbalanced panel data where N>T. One of the most commonly used methods is the mean group estimator, which assumes that the slope coefficients are different across individuals but the coefficients are constant over time. Another method is the pooled mean group estimator, which allows for individual-specific coefficients and time-varying coefficients. However, it is important to note that these methods have their own assumptions and limitations.
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