Why I get the same standard error and big residuals after regressing a variable on a series of year dummies?

[Chenli You]

Dear Statalists,

I am running a regular OLS regression of "GDP growth rate" on a series of year dummies, but get exactly the same standard error for all the coefficients, which is puzzling. The details are as follows.

I have a panel data of "GDP growth rate" for a list of countries during 1981-2017. I run a simple regression of the "GDP growth rate" on all the year dummies. In the result table, all the coefficients of the year dummies are different, but they have exactly the same standard errors (no matter I include the constant term or not). My code and results are as below:

reg gdpgrowth i.year

gdpgrowth	Coef.	Std. Err.
year
1982	-1.779273	1.853554
1983	-1.418455	1.853554
1984	2.871273	1.853554
1985	1.883364	1.853554
1986	1.190636	1.853554
1987	0.8425455	1.853554
1988	2.321364	1.853554
1989	2.683545	1.853554

When I predict the residual from the above regression, the residuals are pretty big.

When I sum "GDP growth rate" by year as below, means and s.d. of gdpgrowth are both very different across years.
bysort year: sum gdpgrowth

May I know why I am getting the same s.e. for all the coefficients and why the residuals generated from the regression are very big?

Thanks a lot,
Chenli

[Clyde Schechter]

When I sum "GDP growth rate" by year as below, means and s.d. of gdpgrowth are both very different across years.
bysort year: sum gdpgrowth

May I know why I am getting the same s.e. for all the coefficients and why the residuals generated from the regression are very big?

The standard deviations of GDP growth rate and the standard errors of the coefficients of the year indicators have almost nothing to do with each other. The standard errors of the coefficients of the year indicators depend on the root mean square error of the regression as a whole, and the number of observations in each year. You are getting the same standard error for each coefficient because you have the same number of observations in each year (i.e. your panel is balanced). This is perfectly normal.

[Chenli You]

Dear Clyde,

Thank you very much for the reply. I understand s.d. and s.e. are not related, but just wanted to use s.d. to check if there is any problem with the data. Now the issue is clear.

Thanks a lot again,
Chenli