Replace loop with vectorized calculation of optimal share

[alanlujan91]

There's long been a comment on ConsPortfolioModel that says:

This loop can probably be eliminated, but it's such a small step that it won't speed things up much.

This is my attempt at replacing the loop with vectorized calculations to test just how much faster this could be. Working out how to do this in vectorized form can provide insights into how to do it in higher dimensions, where loops might be much slower than in this instance.

• Update CHANGELOG.md with major/minor changes.

[alanlujan91]

alpha and other variables here can be saved and added to save_points.

[alanlujan91]

Good candidate for benchmark #1131

[codecov]

Codecov Report

Patch coverage: 100.00% and project coverage change: -0.01 ⚠️

Comparison is base (90178db) 72.56% compared to head (7815d06) 72.55%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1079      +/-   ##
==========================================
- Coverage   72.56%   72.55%   -0.01%     
==========================================
  Files          78       78              
  Lines       13012    13009       -3     
==========================================
- Hits         9442     9439       -3     
  Misses       3570     3570              

Impacted Files	Coverage Δ
HARK/ConsumptionSaving/ConsPortfolioModel.py	89.81% <100.00%> (-0.07%)	⬇️

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[Mv77]

Looks good.

This is not about this PR but I don't really like how the optimal share and consumption are found.

I think it'd be clearer (and maybe more accurate?) to do the stage thing where the optimal share associated with every a is found and then the a is decided later.

But that's for another day. Not what this PR is about.

Happy to have it merged.

[Mv77]

Here are some thoughts.

1. The share grid is kind of inefficient. We evaluate in, say, 11 places to find the pair of points at which the FOC crosses 0. Then we approximate the FOC linearly and find its 0. This uses 11 evaluations and in the end we are guaranteed to be within $0.1$ of the optimal share. If we instead used something like bisection, 11 evaluations would get us to a bound of $1/2^{9}$ if my math is correct.

2. We are finding optimal consumption as a convex combination of consumption at the share-interval endpoints. And the combination weights are the same as that of the estimated share. This might not be very accurate? It might be worth finding the exact consumption implied by the EoPdvda implicit in the estimated share.

[alanlujan91]

I agree. There are some shortcuts here that are meant to be "close enough" and maybe pedagogical. But maybe we should have the "best" portfolio choice solver we can come up with and the more pedagogical one as separate models.