Two variable Panel model - stationarity issue. Help!
I am writing a paper on the elasticity of substitution between capital and labor. The model is derived from the CES production function, and is just a fixed effects panel models between the labor share, and the capital/output ratio, variables that in economic theory are know as "naturally stationary" i.e. close to constant over a long time.
Its a macropanel with T>N, so i know non-stationarity is a potential issue. I have done CIPS and pescadf (Peseran CADF) to account for cross-sectional dependence (which the model also has), but also the first generation panel unitroot tests; LLC, breitung, fisher type and Hadri, with cross-sectional means removed. The results are mixed, the first two tests shows mixed order of integration (I(1) and I(0)), the latter four is mixed, some say both are I(1), others say mixed.
If they are of mixed order of integration, how do i resolve the stationarity issue? I assume cointegration is not possible since for a two variable model we need both to be atleast I(1). I am not confident that i can add lags or new variables, to potentially lean into cointegration, since the model is derived from economic theory, and the posited relationship exactly defines the substitution parameter, used to compute the elasticity of substitution through nlcom. I need to be able to extract this meaning from the model. Can i lean into the "naturally stationary" part? I assume not, since spurious regression could still be an issue. The only solution i have come up with is differencing, since it keeps the model "intact", but i am afraid this is not valid if 1 variable is I(0) such that it becomes overintegrated.
This problem has been nagging me for close to a year! Could i simulate the model with the present issues to see how it affect estimates? What about inference?
What should i do? In general how would one approach this issue in any context i.e. a two variable model, with mixed order of integration. Any help is much appreciated!
Regards Mathias
Its a macropanel with T>N, so i know non-stationarity is a potential issue. I have done CIPS and pescadf (Peseran CADF) to account for cross-sectional dependence (which the model also has), but also the first generation panel unitroot tests; LLC, breitung, fisher type and Hadri, with cross-sectional means removed. The results are mixed, the first two tests shows mixed order of integration (I(1) and I(0)), the latter four is mixed, some say both are I(1), others say mixed.
If they are of mixed order of integration, how do i resolve the stationarity issue? I assume cointegration is not possible since for a two variable model we need both to be atleast I(1). I am not confident that i can add lags or new variables, to potentially lean into cointegration, since the model is derived from economic theory, and the posited relationship exactly defines the substitution parameter, used to compute the elasticity of substitution through nlcom. I need to be able to extract this meaning from the model. Can i lean into the "naturally stationary" part? I assume not, since spurious regression could still be an issue. The only solution i have come up with is differencing, since it keeps the model "intact", but i am afraid this is not valid if 1 variable is I(0) such that it becomes overintegrated.
This problem has been nagging me for close to a year! Could i simulate the model with the present issues to see how it affect estimates? What about inference?
What should i do? In general how would one approach this issue in any context i.e. a two variable model, with mixed order of integration. Any help is much appreciated!
Regards Mathias
