WIP support for DualNumbers SCC calculations

[corakingdon]

I think DualNumbers magically works, just like you anticipated! (pending on the one small change in Mimi here: mimiframework/Mimi.jl#544)

I started trying to do this with the welfare component for FUND that you started here #21, but I wasn't sure about the units or why the welfare values were negative, so instead I branched off master and added a Discounting component. This component calculates discounted loss in each year, and sums the discounted values in the final timestep for total discounted damages (to use for SCC calcualtion).

Using DualNumbers, the "pulse" component (currently defined in "new_marginaldamages.jl") now just adds a Dual(0, pulse_size) in the desired year to emissions.

Not yet implemented:

• equity weighting (should be added to the Discounting component)
• non-zero eta values (should be added to the Discounting component)
• support for other gases (just needed to modify the functions for adding the pulse)

Design questions:

• right now I just added a number_type keyword to get_model where the user has to specify the actual DataType, such as Dual{Float64}. Alternatively, we could have get_model support various symbol type keywords for returning different types of MimiFUND models, such as type = :default or type = :dual
• right now I just added separate compute_scco2_dual and add_marginal_emissions_dual! functions, but these could be incorporated into the existing functions where we could do more sophisticated type checking
• is there a way to add the pulse without having to add a whole component like I did here?

[codecov-io]

Codecov Report

Merging #31 into master will decrease coverage by 2.09%.
The diff coverage is 6.06%.

@@            Coverage Diff            @@
##           master      #31     +/-   ##
=========================================
- Coverage   78.58%   76.48%   -2.1%     
=========================================
  Files          39       39             
  Lines         892      923     +31     
=========================================
+ Hits          701      706      +5     
- Misses        191      217     +26

Impacted Files	Coverage Δ
src/new_marginaldamages.jl	65.51% <0%> (-23.9%)	⬇️
src/MimiFUND.jl	100% <100%> (ø)	⬆️
src/components/ImpactSeaLevelRiseComponent.jl	86.9% <0%> (+5.95%)	⬆️

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[davidanthoff]

but I wasn't sure about the units or why the welfare values were negative

The negative numbers are correct (higher consumption still increases welfare). The trick is to normalize the marginal SCC estimate you get from the DualNumber with marginal welfare of consumption in the present, and at that point you should have a nice positive SCC. I do think it would be nicer if we can use the welfare component for this instead of a separate discounting component...

Dual(0, pulse_size)

I believe we want to make this Dual(0., 1.), and then after we computed the derivative adjust for pulse size.

is there a way to add the pulse without having to add a whole component like I did here

Maybe just set the parameter to a vector of Dual, and only in one year is the dual component of Dual set to 1?

[corakingdon]

but I wasn't sure about the units or why the welfare values were negative

The negative numbers are correct (higher consumption still increases welfare). The trick is to normalize the marginal SCC estimate you get from the DualNumber with marginal welfare of consumption in the present, and at that point you should have a nice positive SCC. I do think it would be nicer if we can use the welfare component for this instead of a separate discounting component...

So would it be:

scc = m[:welfare, :cum_welfare][end].epsilon / m[:welfare, marginal_welfare][present].value

Dual(0, pulse_size)

I believe we want to make this Dual(0., 1.), and then after we computed the derivative adjust for pulse size.

I have to admit I don't understand why, but we can discuss later!

is there a way to add the pulse without having to add a whole component like I did here

Maybe just set the parameter to a vector of Dual, and only in one year is the dual component of Dual set to 1?

The problem is that the emissions vector is calculated endogenously in the emissions component, and that gets passed to the co2 cycle component, so the pulse has to be added in between.

[davidanthoff]

So would it be:

I think yes.

The problem is that the emissions vector is calculated endogenously in the emissions component, and that gets passed to the co2 cycle component, so the pulse has to be added in between.

Can't we use the adder component from Mimi for that?