How to deal with variables integrated of order 2 in panel data?

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Ma'Mon Abu Hammad

In panel data, if a variable is integrated of order 2 (also known as I(2)), it means that it needs to be differenced twice to become stationary. In other words, it has a quadratic trend that needs to be removed to achieve stationarity.

Dealing with I(2) variables in panel data can be challenging, but there are a few possible approaches that you could consider:

First-differencing the data: One approach to dealing with I(2) variables is to first-difference the data twice to make it stationary. However, this can lead to a loss of information and may not be appropriate if the I(2) variable is an important part of the research question.

Including a quadratic time trend: Another approach is to include a quadratic time trend in the model to account for the non-stationarity. This involves adding a time-squared variable as a regressor in the model, which captures the quadratic trend in the I(2) variable. This approach can be effective if the quadratic trend is the only source of nonstationarity in the variable.

Using a cointegration analysis: If the I(2) variable is related to other variables in the model, it may be appropriate to use cointegration analysis. Cointegration analysis involves testing for a long-term relationship between the I(2) variable and other stationary variables in the model. If cointegration is found, a vector error correction model (VECM) can be used to model the dynamic relationships between the variables.

Using an I(2) model: Finally, if the I(2) variable is the main focus of the research question, it may be appropriate to use an I(2) model. This involves modeling the I(2) variable explicitly using methods such as the I(2) autoregressive distributed lag (ARDL) model. This approach can be effective if the I(2) variable is a key component of the research question and is not related to other variables in the model.

Overall, the choice of method will depend on the specific research question and the characteristics of the data. It may be useful to consult with a statistician or econometrician to determine the best approach for your particular study.