Regression with change relative to base year

[Julia Raciniewska]

Hello!
I am sorry if this topic came up before, I tried searching for answers but without luck. I have panel data for N=11 over 2006-2017 and I am trying to estimate whether a greater share of "routine occupations" in the base year (2006) had led to greater computer adoption.
I was thinking of regression using re as that's was Hausman test suggested:

xtset industry time
xtreg computer_adoption L10.routine, re robust

My question is whether this specification is correct or would that give me an estimation for something different that I look for?

[Marcos Almeida]

You didn't tell much about "computer_adoption", is it continuous? That said, if I understood right, the sample is quite small, T = n, and the lag of 10 years (?) would encompass practically the whole follow up time,

[Julia Raciniewska]

Marcos Almeida Thank you for your response. Computer adoption is the % of employees using computer at work. Yes - my n=t and I do know it is a very short time period (t=11) but thats is the only data available. Do you have advice on any model I could use to measure whether industries with larger routine share (also variable in %) have experienced larger change in computer adoption?
Thank you very much in advance.

[Marcos Almeida]

I'm not sure what should be the best approach in such a case, under a small sample size. There is also the issue of DV being a percentage, which should be taken into consideration. Last but not least, potential autocorrelation. I wonder whether - xtgls - may tackle this situation. Hopefully you get a more insightful advice.