# Adding trend does not impact coefficients

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) Cit = a0 + a1 (Pit) + a2i Di + a3t Dt +uit

2) Cit = a0 + a1 (Pit) + a2i Di + a3t Dt + a4 T +uit (trend+year effects)

3) Cit = a0 + a1 (Pit) + a5i t (Di Dt) + a4 T +uit (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.

Here are my codes in Stata:

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

Code:

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


OR

Code:

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


(gives same coefficient estimations)

1. (#2 in the table), trend added on top of year and country dummies:

Code:

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


Coefficients do not change between #1 and #2

3. Code:

xtreg  number  price   cv  t_interact trend, robust


where Code:

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


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