Consumption discount factors in MimiGIVE

[sleepguyjin]

Hello,

Thank you for helpful discussions in this forum. We are calculating country-level SCCs from MimiGIVE 1k MCS results on country-level marginal damage with the compute_disaggregated_values flag.

Somehow our calculations do not feel right in terms of the order of the magnitude, as country-level SCC do not add up to USD 185 in the base case. I suspect that something is wrong with how we calculate consumption discount factors, as the global SCC output from MimiGIVE seems okay with an expected_scc = 144.67 (before price level adjustment).

I was wondering if separate consumption discount factors are used for each MCS draw (using global post-damage net cpc), or some sort of aggregate (e.g. average or median) consumption discount factors across 10k draws are used. I am assuming that the former could be the way that is taken in the model, but a clarification would be appreciated.

The related code in scc.jl is:

            #-------------------------------------------------------------------
            # Option 1. no equity weighting
            #-------------------------------------------------------------------

            if isnothing(dr.ew)
                df = [((cpc[year_index]/cpc[i])^dr.eta * 1/(1+dr.prtp)^(t-year) for (i,t) in enumerate(_model_years) if year<=t<=last_year)...]
                scc = sum(df .* marginal_damages[year_index:last_year_index])

Any other tips that might correct common mistakes/ misconceptions in regional disaggregation or consumption discount factors would also be appreciated!

[lrennels]

You're intuition is correct, each run of GIVE uses a different time-series of discount factors, computed based on that run's net consumption.

If you are computing country-level SCCs from the intermediate outputs of GIVE, and using country-specific Ramsey discount rates, they are not guaranteed to add up to the global SCC. If you use the Ramsey formula to get discount rates for each country separately, based on that country's consumption per capita time series, then the discount factors will all begin at 1 but then decline at different rates depending on the consumption growth of that country. The sum at the end will not necessarily match the global SCC from Rennert et al. 2021.

I would also briefly note that the rho and eta parameters from Mueller, Stock, and Watson are calibrated to global growth rates, so using them in this context (not sure if you are) isn't a perfect application -- though might be fine as a proxy for your case

• This is probably the most well-known paper using country-level SCCs -- https://www.nature.com/articles/s41558-018-0282-y
• A recent NCEE working paper discussed a US-specific SCC and the appendix has some details on my last point -- https://www.epa.gov/environmental-economics/economic-damages-climate-change-us-populations-integrating-evidence-recent

Lastly you mention order of magnitude. If the description above doesn't intuitively solve how off you think your values are, I would double check units, but I think we discussed that here #56 and you got that working.

[sleepguyjin]

Thank you so much @lrennels for this clarification on different time-series of consumption discount rates, and for the additional inputs.

Yes, I am computing country-level SCCs from the intermediate outputs of GIVE 1k run, but using globally common Ramsey discount factors (using global cpc). I think this is also justified by the theoretical simplification of free capital mobility, under which globally equalised interest rates arise.

If I were to use country-specific consumption discount factors, I would run into the inconsistency you suggest, unless we assume growth convergence across countries.

And thank you for the reference to these two papers:

This is probably the most well-known paper using country-level SCCs -- https://www.nature.com/articles/s41558-018-0282-y

This is indeed well known, along with RICE, and Tol (2019). In fact, we have used Ricke et al. results in our working paper.

A recent NCEE working paper discussed a US-specific SCC and the appendix has some details on my last point -- https://www.epa.gov/environmental-economics/economic-damages-climate-change-us-populations-integrating-evidence-recent

Thanks also for pointing out this paper, I will definitely look into it.

Something like 20 to 30 draws from my 1k run (2-3%) experience consumption discount factors >1 in 100 years, and 15 to 20 runs even in 2300. I understand that consumption discount factors greater than unity (or negative consumption discount rates) are not a problem on their own. However, perhaps as a result of outlier-ish large consumption discount factors, the mean SCC might have exploded in my run (the mean is four digits, while the median is two digits).

I was wondering if you had come across a similar problem in developing the model? Or perhaps I should try a 10k run to remove extreme cases..

Slightly related (but perhaps not directly relevant), you have already discussed an interesting problem of complex numbers when taking square roots of negative growth rates.

And yes, I think I got the #56 unit problem right, although I have not explicitly written pulse_size = 1.