Here’s a way of thinking about it.

First we work out the contribution of R&D to economic
growth. Grilliches,
(Griliches, Zvi, 1988. ">Productivity Puzzles and R&D: Another
Nonexplanation” Journal of Economic Perspectives, American Economic Association,
vol. 2(4), pages 9-21, Fall shows what to do.
As he says

Write a growth accounting expression

Second, we apply some numbers. Suppose the returns to R&D, private and
social, are 30%, an upper estimate. In the
UK, spending on research councils is about £3.5bn and spending on HEFCE, which is
university money related to research is £1.5bn.
Total GDP is £1.56tn. Then r(R/Y)=0.3*(5bn/1.56tn)=0.001,
which is the contribution of this public spend to growth. Multiplying that by GDP gives £1.56bn.

Suppose now that open access improves the ability of firms
to get information from the R&D stock and so raises spillovers to public
R&D. Suppose this raises the rate of
return to 0.31. Then the extra GDP from
open access is 0.01* £5bn = £50m. This
looks like a lot. Is it worth it?

The 2008 RAE had 52,400 staff submitting to it. Suppose they submitted 4 articles each which
is around 200,000 articles. If Gold open
access costs around £2,000 per article (taking a round number), this is therefore £400m. Over 5 years, this is £80m per year. So it all hangs on whether Open Access boosts
the rate of return to R&D, which it would have to do by more than 1percentage
point in this case. Will it?

- Of the 30% return to R&D, Griliches suggests that spillovers are 20% (private returns are 10%). So a rise of 1pp in spillovers is a 5% rise in the spillovers rate of return. That seems like a very large number.
- Many argue that quite a lot of research is open access already in which case the cost might be lower, but the rise in the rate of return will be tiny.
- Rates of return in economic sectors like airlines and airports are numbers 11% and 8%. So a 1% change is very large.
- Total TFP growth in an economy is a Domar-weighted average of TFP growth in the sectors of the economy. Suppose that one of the sectors is public R&D and that its Domar weight is the share of public R&D in value added. So to get a rise in the growth contribution of 1 percentage point is the equivalent of a rise in researcher TFP of 1 percentage point. This seems like a very large increase just from Open Access (set against most estimates of total TFP growth which are around 1%pa, though of course researcher TFP growth might be higher).

**Update**

My excellent colleague Torsten Reimer points me to this report by JISC on the economic benefits of OA. If I look here, it points me to a report by Houghton, Open Access – What are the economic benefits? A comparison of the United Kingdom, Netherlands and Denmark, where box 1 uses a similar logic, that is, returns to R&D would rise. In turn note 6 on p.9 points me to pp193-208of http://www.cfses.com/EI-ASPM, avaialable here. On p.197, we see return to R&D will increase by the same percentage increase as that in the accessibility and efficiency parameters." Their base case in table 5.2 is a rise of 5% on a rate of return of 20%, which, i think, takes their rate of return to 21%. Page 213 suggests the costs of doing this do not justify the benefits, but they dismiss this case as being where authors have to pay both for OA and libraries for journal subscriptions.

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