Time dummy is a variable which equals 1 for a given year and 0 for all other years. It allows to control for time-specific fixed effects i.e. shocks which impact is restricted to a given time-period, affects or panel units and are not controlled by other explanatory variables. Normally you should  include T-1 time dummies (for T being time dimension of a dataset) but it can be restricted if you have some strong prior as to where the time-fixed effects should occure (e.g. war years). Time trend is a variable which is equal to the time index in a given year (if your sample includes years 2000-2010 than time trend variable equals 1 for 2000, 2 for 2001 etc.). It allows to control for the exogenous increase in the dependent variable which is not explained by other variables. You may include both type of variables simultaneously as long as you have some solid explanation, however neither time-dummies nor time trend is a solution to nonstationarity (unit root) issue. I would recommend that you first check stationarity of your data with the use of panel unit root tests.

Dear Piotr, thank you for clear explanation. I haven't checked the stationary of the unit root yet. After receiving your comments, I include both time trends and dummies into the regression. There is no significant change in the results. At least I am confident that including both time trends and dummies at the same time is ok. First I thought that if I choose one, I have to exclude another.

I apply this control variable in non-linear model.

Thanks.

Time-trend is usually applied as a proxy for technical progress, whereas time-dummy is to control for a specific year, for example serious flood or natural disaster year. Not all panel data analysis need to go through stationarity tests. It depends on what your research question is. If you are trying any kind of co-integration analysis, then checking for stationarity is a must.  

Hi, I have a very related question so I write it here. I am working with panel data. If I have a non-stationary issue (having done panel unit root tests), Piotr said that adding time trend would not solve this issue.

Non-stationary data leads to problems of spurious correlations.

So, the way I understand it is that we add time trend (t=0,1,2..T) as an independent variable if we want to solve a spurious problem, controlling for exogenous increases in the independent and dependent variables.

And as Piotr said, our data is still non-stationary but we no longer have the spurious problem? Is it correct?

So what is the relevance of adding time trend to stationarity? I dont think I have a co-integration analysis, so do I need to worry about the non-stationary issue?Should we eliminate the problem of non-stationarity? Having made the time series stationary (by whatever means), what`s the point of the time trend? (It is not going to spurious because we have made it stationary, is that right?)

Can someone help me clarify?