Time Dummies and Time trends --revisited

[svetlana zvyagintseva]

Dear StataList Users,

I have already done my search on the topic in the list of questions: Time dummies and time trends are not for using together, one makes the other redundant-- my question here would be different:

I have a panel data (of 38 countries and 20 years); my dependent variable is the number of conflict events, and independent variables are price level and volatility.

On top of these, I include country and year dummies, linear time trend and country specific time trends (1 for only one country year point and 0 for others) to control for fixed effects and test for robustness of the results.

My method of estimation is OLS (xtreg). Below is the list of my estimations:

1) C_it = a₀ + a₁ (P_it) + a_2i D_i + a_3t D_t +u_it

2) C_it = a₀ + a₁ (P_it) + a_2i D_i + a_3t D_t + a₄ T +u_it (trend+year effects)

3) C_it = a₀ + a₁ (P_it) + a_{5i t} (D_i D_t) + a₄ T +u_it (trend + country specific year effects)

To my surprise, the coefficients a₁ -- along with standard errors and test statistics, do not vary among models 1-2 or 3.

The only change is in the coefficients of time fixed effects, which are not to be reported, and which do not affect the coefficient of interest, i.e., a₁

I am attaching a table of results for your review. The issue is not the correlation among trend and time fixed effects, neither becomes redundant and drops in Stata.

Many thanks for your feedback!

[Carlo Lazzaro]

Svetlana:
without further details about what you exactly typed in Stata, my wild guess is that you probably used -xtreg, fe- and -fe- has done its job (i.e. cancelled out all time-invariant predictors) in the first three models.
Another interesting detail to know is whether some predictor where omitted due to collinearity.
For the future, please take advantage of CODE delimiters to post what you typed and what Stata gave you back (as per FAQ #12). Thanks.

[svetlana zvyagintseva]

Dear Carlo, Many thanks for your reply and sorry for the insufficient information.

I listed the codes I ve run below:

1 (also #1 in the table attached) .
My original model with time and country dummies :

xtreg number price cv i.year , fe vce(cluster id)

OR

xtreg number price cv  i.year i.id, robust

(gives same coefficient estimations)

2. (#2 in the table), trend added on top of year and country dummies:

xtreg number price cv i.year i.id trend, robust

Coefficients do not change between #1 and #2


3.

xtreg  number  price   cv  t_interact trend, robust

where

gen interaction = year*country
bys country: gen t_interact = _n

Again, coefficient estimations remain the same (column 3 in the table attached)

[Carlo Lazzaro]

svetlana:
thanks for providing further details.
However, it's difficult (for me, at least) to comment any further without seeing your data (posting an example via -dataex- may be the way to go).
That said, I will provide some more general remarks:
in 1, you've seemingly used -fe- (first code) and -re- (second code);
-re- seems the chosen specification in #2 and #3, too;
#3: interactions are better created via -fvvarlist-.

[William Lisowski]

I agree with Carlo's assessment.

I think if you were to examine your xtreg outout (which you don't show us) you would find that all three of your models are the same. I expect that in model 2 either an additional year indicator is dropped, or the trend variable is dropped. Similarlhy, the random effects default of models 2 and 3 adds nothing to the country fixed effects.

in your first post you write "Time dummies and time trends are not for using together, one makes the other redundant-- my question here would be different" but I don't see how it is different - you have used time trends and time dummies, and you have simiarly used country fixed effects together with country random effects.

We can better help you if we know not only what commands you have tried but also what Stata provided as results. It's particularly helpful to copy the commands and the output followig from your Stata Results window and paste this into your Statalist post using CODE delimiters, as you did for your commands in post #3 above.

[Clyde Schechter]

Time dummies and time trends are not for using together, one makes the other redundant

Tangential to the issue under discussion in this thread, I would like to point out that the above quote is incorrect. While there probably aren't many real world situations where it makes sense to use both time trends and time indicators ("dummies"), there is nothing wrong with it in principle, and they are not redundant. It would make sense to use them together if there is a long-term linear trend of the outcome in time, but it is also subject to periodic shocks that are large enough to matter in the situation at hand. (I have no idea if that is the case here.)

On the other hand, using country fixed effects and country random effects in the same model does not make sense to me.

[William Lisowski]

Clyde Schechter posits that using both time trends and time indicators can be sensible. It seems to me though that in doing so, some side conditions need to be imposed, since an arbitrary change in the coefficient on the trend could be offset by an appropriate change in the coefficients on the indicators.

That is, if you postulate that for data beginning in 2000,

y = a + bx + c1{year==2001} + c2{year==2002} + ... + d{year-2000}

then the following produces identical results

y = a + bx + (c1-k){year==2001} + (c2-2k){year==2002} + ... + (d+k){year-2000}

I'm not sure what happens in Stata if you try this; i suspect another year indicator is dropped. That is why I encourage posting both the commands and the results.

[Rich Goldstein]

as a historical aside, I note that for many decades the use of both a linear trend and dummies was considered a good way to test for linearity: I think there are better ways now, but some people might still use this

[Clyde Schechter]

William Lisowski Yes, you do get an extra indicator dropped in this case in order to identify the model. Actually, I wasn't all that clear in what I said. While, is Rich Goldstein notes, this approach of all the time indicators plus time trend can be used as a (somewhat outdated) test for linearity, what I really had in mind was the use of a time trend in conjunction with what would usually be a small number of selected indicators for specific time periods. For example, one might want to model some economic outcome with a linear time trend over a period of decades but also put in indicators for years in which there was a recession, or something like that. I can imagine there might be a circumstance where every year in the range had some special shock-like feature that warranted separately modeling it, and one still might want to estimate a linear overall trend. Such a situation would be possible and the model would, after identifying it by removing one of the year indicators beyond the base year, be a sensible model--but I would think situations like that are rare in practice.