Time dummies and time trend simultaneously

[Marcos Gonzalez]

Hello everyone,

I would like to ask if it makes any sense to include time dummies and a time trend in the same specification model .

I am running a panel data regression with macro economic variables. Therefore I would like to include time dummies, but some variables show a clear linear trend in the long term. Therefore I would like to include a trend for de-trending my data. Therefore my data include something like this:

Panel identifier	year	trend
1	2001	1
1	2002	2
1	2003	3
1	2004	4
1	2005	5
2	2001	1
2	2002	2

and also the time dummies which take the value 1 or 0 as usual. I do not know if the model is sensible if I include both (time dummies and a time trend at the same time).

Thanks in advance.

Regards

[Clyde Schechter]

Well, of course, you can only include indicator variables for all but one of the years in the ordinary case. And if you also include a time trend, you will lose a second such indicator as well. (Don't worry about this: just use i.year and Stata will handle it for you automatically. See -help fvvarlist- if you are not familiar with factor variable notation.)

If you use both a time trend and year indicators, then you are saying that you thing there is some linear movement in your outcome variable over time (at least during the time periods in your study) and that, on top of that, there can be specific shocks to the outcome in each particular year. If that is a plausible model of how your outcome varies in reality, then, yes using trend and i.year together is sensible and will reflect that.

Be aware, however, that all of the same information about the effects of time on your outcome is captured by just using i.year. The difference between using trend and i.year vs i.year alone is that with the inclusion of trend you will get an estimate of the average annual linear movement in your outcome. If you use i.year alone, the effects of time will still be modeled correctly, but you won't have results that separately identify the linear component and the shocks: the linear component will be absorbed by, and hidden in, the shocks.

Since it's generally a good idea to use the simplest model that is reasonable, I would only include the trend variable if actually estimating that trend is one of the research goals. If it is, then, of course, you must include it. If it isn't, then including it serves no purpose and adds complexity.

[Marcos Gonzalez]

Thank you very much for your answer,

Of course what I am trying to take into account is, on one hand, that my outcome variable shows a linear trend in the long term and, on the other hand, that there are specific shocks (for instance the financial crisis in 2008). Therefore, I feel that including both makes sense.

Nevertheless, what you are telling me is that including the trend is not needed if I do not need to interpret its coefficient, since the linear trend would be taken into account indirectly in the time dummies which reflect the shocks, is that correct?

Regards

[Clyde Schechter]

Nevertheless, what you are telling me is that including the trend is not needed if I do not need to interpret its coefficient, since the linear trend would be taken into account indirectly in the time dummies which reflect the shocks, is that correct?

Yes, that is correct.

[Ji Ma]

Well, of course, you can only include indicator variables for all but one of the years in the ordinary case. And if you also include a time trend, you will lose a second such indicator as well. (Don't worry about this: just use i.year and Stata will handle it for you automatically. See -help fvvarlist- if you are not familiar with factor variable notation.)

If you use both a time trend and year indicators, then you are saying that you thing there is some linear movement in your outcome variable over time (at least during the time periods in your study) and that, on top of that, there can be specific shocks to the outcome in each particular year. If that is a plausible model of how your outcome varies in reality, then, yes using trend and i.year together is sensible and will reflect that.

Be aware, however, that all of the same information about the effects of time on your outcome is captured by just using i.year. The difference between using trend and i.year vs i.year alone is that with the inclusion of trend you will get an estimate of the average annual linear movement in your outcome. If you use i.year alone, the effects of time will still be modeled correctly, but you won't have results that separately identify the linear component and the shocks: the linear component will be absorbed by, and hidden in, the shocks.

Since it's generally a good idea to use the simplest model that is reasonable, I would only include the trend variable if actually estimating that trend is one of the research goals. If it is, then, of course, you must include it. If it isn't, then including it serves no purpose and adds complexity.

Hi Clyde, this comment is very clear and helpful. Can you provide more materials (e.g., textbook, Stata manual, etc.) on this point? I want to learn more about it. Thanks! BTW: have been reading many of your comments and they are all very helpful!

[高佳]

Hi Cylde, thanks so much for your clear response. A very relevant question here, in the case that I need to add both time trend and time dummies in the same regression, how can I obtain the coefficient of time trend?

[Joro Kolev]

I do not disagree with any of the mechanics that Clyde explains, but my conclusion based on the same mechanics is different.

It is mechanically impossible to include a linear trend on the top of full set of time dummies (without a constant), as Clyde explained this will result in a dummy being dropped. It makes no sense to want to include a linear trend on top of full set of dummies -- the full set of dummies already show nonparametrically and fully generally what is the trend. One can just plot the dummies against time, and see whether the trend is linear or any other.

[高佳]

I do not disagree with any of the mechanics that Clyde explains, but my conclusion based on the same mechanics is different.

It is mechanically impossible to include a linear trend on the top of full set of time dummies (without a constant), as Clyde explained this will result in a dummy being dropped. It makes no sense to want to include a linear trend on top of full set of dummies -- the full set of dummies already show nonparametrically and fully generally what is the trend. One can just plot the dummies against time, and see whether the trend is linear or any other.

This is true oftentimes, but in some cases, one may want to control from yea dummy and interact a linear trend with another variable of interest. In this case, both linear trend and year dummy will be added in the same equation.