Participation Rate Equals Unconditional Stock Share Early in Life: Why?

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In my research, which is based on your portfolio choice models, I study stock demand measured by the stock market participation rate and the unconditional stock share (i.e., stock holdings in the portfolios of both participants and nonparticipants).

I still use old no refine version where:

FnsToEvaluate.riskyshare=@(savings,riskyshare,a,z1,z2,e1,e2) riskyshare; 
FnsToEvaluate.stockmarketparticpation=@(savings,riskyshare,a,z1,z2,e1,e2)(savings>0)*(riskyshare>0);

My issue/question:

I am unable to understand why the participation rate corresponds exactly to the unconditional stock share for many years at the beginning of the life cycle. Is this a modelling artefact, or does this dynamic have some technical interpretation?

Figure:

ParticipationAndRiskyShare_Overlay_WordReady
ParticipationAndRiskyShare_Overlay_WordReady3392×2199 138 KB

Thank you!

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Can you please email me a copy of code that generates this graph so I can take a closer look?

(My guess, everyone who participates during those first few years puts a share of one in the risky asset. This would make participation and risky asset essentially the same. And this lasts just the first few periods. Obviously this is a comment about what is happening in code, not about economic intuition for it. Nor about whether this is ‘correct’)

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Sharp intuition, Robert.

This does actually seem to be the case. It makes sense both from a technical and economic perspective. Now the interplay between stock market participation, conditional and unconditional stock share is clear to me.

I don’t want to take any more of your time on this particular topic, so there’s no need to look into the code.

I have one or two more issues/questions, but they’re much less critical at this point, so there’s no need to resolve them right away.

See:

ParticipationAndStockShare_Overlay_WordReady
ParticipationAndStockShare_Overlay_WordReady3380×2199 138 KB

:slight_smile:

Thank you!

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From age 38+: participation rate=1, so the ‘stock share’ will be the same whether if is ‘of Participants and Nonparticipants’ or it is ‘of Participants’ since everyone is anyway a participant.

Pre age 38: same thing as previous post (0 stock share of all nonparticipants, together with 1 stock share of all participants; so stock share across all is just the participation rate).

PS. Rereading your post, I think the graph was a statement confirming/illustrating the ideas of previous post and not a question, but since I’ve already written an answer I am just going to post it anyway :smiley:

PPS. Less sharp intuition, more just have solved a lot of models over the years so there is little I haven’t seen before :wink:

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