In a panel regression, the dependent variable is decreasing over time, while some independent variables are increasing over time (e.g. school enrollment). But there are not any independent variables with similar decreasing trend as the dependent variable has.
I know that if dependent variable and some independent variables have similar direction of trend over time, then a time trend variable is needed to de-trend. But I am not certain if time trend variable should be included in my case.
Moreover, in some cases the role of time trend is very clear (e.g. exogenous technology advance), but in some other cases it may not be. For example, increase in schooling year is a common phenomenon worldwide. So if time trend is added into a regression that tries to explain increase in schooling year, what is its role? Just to account for the part that cannot be explained by other variables (a so-called exogenous trend?)?
thank you!
Do you have multiple regression analysis in mind? If yes, allow model to take care of the effect of trend. Please specify, your dependent and independent variables.
Since you have panel data, first you need to investigate whether or not the variables of interest exhibit a unit root as the presence of a unit root could render your estimates biased and inconsistent. You state that your dependent variable might be trended, so this brings the question of whether or not the variable is non-stationary, trend stationary, or non-stationary to the forefront.
Assuming that you are not discussing a bivariate panel data model, then you need to specify your dependent and independent variables. You would (after confirming that the dependent variable, for example, is stationary) then need to examine whether or not a fixed or random effects estimator is more appropriate (I'm assuming that you are estimating a static and not dynamic estimator) through, for example, a Hausman test. Let's assume that you find that the RE estimator is inconsitent and use the FE estimator. You would include, most likely, time and individual effects. It may be that these time and individual effects, in a multivariate analysis, capture the apparent 'trend' of the data, that would need to be seen (and tested whether the effects are jointly significant). You could include a time trend that increases in each period but you should think about what happens to this trend variable with regards to the Within transformation.
In short, make sure to also provide your model, variables, and so on. That'll help answers be more precise...hope this helps in general
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