The correct way for log wage and long difference of wage

Good afternoon, I'm starting to study econometrics and I have a doubt: I want to study the relationship between ICT exposure and changes in wages over the period of 2003 to 2021 $$\Delta y_{o} =\alpha + \beta ICT_{o}+ \gamma Z_0 + \epsilon_{o}$$ Y for wage, ICT for exposure to information and communication technology, and Z is a vector control for education. $$o = occupation$$. I aim to do a cross-section. $$\Delta y$$ would be a long difference from 2003 to 2021 for wages

When analyzing the change in wage for two years, 2003 and 2021, whereas the wage of 2003 has already been deflated. Should I ln the wage for 2003 and ln the wage for 2021 and then do the subtraction or do the subtraction of those two wages first and then log this difference between the two salaries? would this be a long difference for wage? I already deflated the wage and have a score for ICT exposure

• You should give more details about the econometric question you have. The first thing you should do is deflate wage in a manner that wage is comparable in both years. Typically this would be deflating each to some baseline year (e.g. 2015). If you are doing a diff-in-diff, then parallel trends in levels and parallel trends in logs are completely different assumptions, and you need to evaluate them in context. I encourage you to update your question with more details about what you are trying to estimate. This will help us in answering your question. Jun 3 at 10:07

My suggestion is motivated by practicality rather than theory however. I would suggest, $$\ln(y_{2021})-\ln(y_{2003})$$
Because you may have some observations for which $$y_{2021}-y_{2003}\le 0$$, in which case, $$\ln(y_{2021}-y_{2003})$$ is undefined.