That's a great question! I don't have any good answer, but I've looked online and found some interesting papers so I'll just post some stuff I've got so far.

It seems like there is recently a shift toward "societal-impact focused research", as opposed to "quality-focused", driven mostly by the need to calculate Return On Investment. I think that this biases the current metrics/evaluators to be more short-termed and focused on health/security/tech-innovations.

Here, the authors ask research evaluators how they think about assessing societal impact. They have identified 5 dimension -

1. The Importance of the Underpinning Research in Evaluating Impact.

For more quality-focused evaluators, the importance of underpinning research when evaluating impact was driven by an underlying value system depicting a strong link between scientific and societal impact.

2. The Value of the Impact Versus the Value of the “Right” Impact.

For some evaluators, the necessity for research of a high quality to underpin societal impact was guided by the assumption that impact referred to ‘good impact’, as opposed to ‘negative’ societal impact.

3. Impact as Linear, Controllable or Serendipitous

A major underpinning factor influencing evaluators’ opinions was related to whether to view impact as related to ‘outside factors’ separate to the research, or something that was viewed rationally, therefore related to the quality of the research.

Towards the quality-focused extreme, evaluators envisaged a ‘pipeline’ from high quality research to societal impact – “a sort of translational pipeline is the okay term that tends to get used for taking a scientific discovery and pushing it towards some sort of laboratory test, new drug, or whatever, which, I guess, many people would view as some sort of impact”(P1OutImp5). Thus, the relationship between scientific and societal impact hinged upon the idea that “impact requires that you generate the evidence and then that you, in turn you get into guidelines and the people start using that information to change their practice”

4. Push Factors and Assessing Impact

Towards the quality-focused evaluator extreme, the assessment of societal impact was influenced by a belief that a researcher’s role in ensuring societal impact was limited solely to providing high quality research, whereas it was the responsibility of other, non-researchers to use this as evidence to pursue societal impact.

5. Measurable Impact Outcomes Versus Unmeasurable Impact Journeys

The final factor which influenced the evaluation scale was whether evaluators valued societal impact as a single, measureable outcome, or as a process or journey that, in many cases, is impossible to be measured.

Some low-effort thoughts (I am not an economist so I might be embarrassing myself!):

• My first inclination is something like "find the average output of the field per unit time, then find the average growth rate of a field, and then calculate the 'extra' output you'd get with a higher growth rate." In other words: (1) what is the field currently doing of value? (2) how much more value would that field produce if they did whatever they're currently doing faster?
• It would be interesting to see someone do a quantitative analysis of the history of progress in some particular field. However, because so much intellectual progress has happened in the last ~300 years by so few people (relatively speaking), my guess is we might not have enough data in many cases.
• The more something like the "great man theory" applies to a field (i.e. the more stochastic progress is), the more of a problem you have with this model. [Had an example here, removed it because I no longer think it's appropriate.]
• With regard to that latter question (also your second set-up), I wonder how reliably we could apply heuristics for determining the EV of particular contributions (i.e. how much value do we usually get from papers in field Y with ~X citations?).

It's worth keeping in mind that it could actually be net negative if it pulls enough attention of other (potential) researchers away from better things to work on.

But how do we estimate the EV of estimating the EV of general intellectual progress?

On a less facetious note, it's about the average effect of intellectual progress on innovation right? What EV comes from general intellectual progress that is not a result of innovation?

So you try to causally estimate the effect of innovation on things you value (e.g. GDP), and you try to create measures of general intellectual progress to see how those causally impact innovation. That's obviously easier said than done.