Calculating change in confidence intervals

[Scott Rick]

I apologize for asking a pure statistical question, and not stata question on here, but I'm incredibly lost with this.

My instrumental variable study looks at the effect of child health outcomes with an instrument of the number of community heath worker visits. I have the point estimate of the outcome and the corresponding confidence interval. I also have the mean of the instrument and the range (number of health worker visits in a year in a given population). I have to calculate how the confidence interval would change given a change in average of the number of health worker visits, i.e. the mean of the instrument. That is, how the confidence interval of the health outcome would change if the number of visits by the health worker changed. Can someone please guide me on how I can calculate this?

[George Ford]

The width of the confidence interval is proportional to the standard error. I believe if you change the mean of the instrument, the standard error would change proportionally to √(1/n), where n is the sample size.

But check on that.

sysuse auto, clear

summ displacement

ivreg2 mpg weight (displacement = turn)
nlcom _b[displacement]

local scale = 300/197.2973

nlcom (_b[displacement])*`scale'

Or does the SE change by the scale?