Advice for FE or FD model for panel data

[Julia Raciniewska]

Hello,
I am looking for advice on the correct form of my model. I am planning to run a regression to measure the impact of a change in % of employees using a computer and expenditure on investment in technology on employment of higher-skilled vs routine occupations, while controlling for education.
Therefore my regressions are:

ln (high_skilled) = alpha + ln (technology_expenditure) + using_computers + lndegree
ln (routine) = alpha + ln (technology_expenditure) + using_computers + lndegree

My hypothesis is that beta 1 and beta 2 should be positive for first equation, and negative for the second.
I have panel data for 12 industries and 11 time periods (2006-2017).

I am very confused about which model would be better to choose. I want to look at the change in % using computer or change in expenditure on the change of number of people employed . I was thinking about first differences. But then someone suggested me, fixed effects could be better. However, in my data there are no time-invariant characteristics, investment of all of them changes, although some had smaller amount at the base year (2006) while others had higher.
I got very confused with which model would be best for my analysis. I would be enormously thankful for any advice.

[Phil Bromiley]

First difference is just a way to estimate a fixed effects model - read the xtreg documentation pdf carefully. You can find it through the Help then Pdf Documentation. They should give very similar results - indeed, for some data structures they give exactly the same results.