I think for us to say it's "beginning to have a significant impact on the economy", there needs to be an actual measurable increase in productivity due to AI-enabled automation, which so far has been elusive. It might be impacting employment in some specific jobs, but the mix of jobs in the economy is always constantly changing.
Just because something is difficult to measure does not mean it doesn't exist. People who have automated their jobs are unlikely to report that, since they like having a paycheck. But that doesn't mean it isn't happening.
It's not difficult to measure though - we've been tracking total factor productivity of our economy for decades. Steam power, electrification, computers - all of these things had huge, measurable impacts on the amount of economic output vs input. No self-reporting (of what?) necessary. If AI means that companies are getting the same or more output from less input of labor and capital, productivity should be soaring right now.
@gitfan86 - You would measure that the same way productivity is always measured - The company's overall economic output would be unchanged, and their labor inputs would have decreased, so the total factor productivity would have increased by virtue of automating the DEI group (just the same as when companies used 'mail-merge' to automate large groups of people doing that work manually, for instance).
Electrical output, number of units shipped can be measured.
How do you measure the output of a DEI department? Now assume those people automated their jobs with Chat GPT. How would you measure the change in productivity?