Can i have stationary and non-stationary variables together in a panel data model?

[Georgios Kolias]

I run a panel data model (N=5, T=17, unbalance). The depended variable is stationary while three of the six independent variables are non-stationary. These non-stationary variables are cointegrated. Are the regression results misleading?

[Phil Bromiley]

You didn't get a quick response. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata data, and sample data using dataex.

You obviously cannot have N of 5 and T of 17. N can never be less than T. Some fields worry about stationary variables and cointegration and others don't.

[Georgios Kolias]

Hi Phil,
Can you please become more clear? Do you mean that there is no way to estimate a model with T>N?
Best
Georgios

[Carlo Lazzaro]

Georgios:
not quite.
Stata allows estimating long panel data like yours (that is, panel data with a small cross-sectional dimension [N] and a large time-series dimension [T]): you can take a look at Stata built-in commands such as: -xtgls-; and -xtregar-.
I would be more concerned about the small number of your (5*17)=85 observations.
About conintegration, you may want to consider -xtunitroot-: unfortunately, from a theoretical standpoint, the topic of cointegration in panel data regression does not seem to be well covered in the panel data econometrics literature (as far as I know), possibly because most part of the analyses relates to microeconometrics, where short panels (large N, small T dimensions) are much more frequent.

[Georgios Kolias]

Thanks, Carlo
With all these problems (and hoping for the best results) I estimate the model using the xtgls command incorporating into independent variables, dummy-variable repressors to capture any cross-section effects. Moreover, I include a time variable in the model to deal with the linear trend.
Finally, I examine the residuals for unit roots using the - xtunitroot fisher- command.
Overall, I have
I(0) dependent variable,
I(1) of some independent variables,
I(0) residuals, and
estimations consistent with the theory

Best regards
Georgios

[Carlo Lazzaro]

Georgios:
as far as the linera trend is concerned, have you tested the presence of non-linear relationship between time and regressand via a squared term?:

c.time##c.time

[Georgios Kolias]

Thank you, Carlo

The time-squared variable is insignificant so i cannot accept the existence of a quadratic trend in time


Georgios

[Carlo Lazzaro]

Georgios:
go linear then.

[Georgios Kolias]

Thank you very much Carlo