Bryan Caplan  

Mean Reversion and the Permanent Income Hypothesis: Suggested Answer

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Yesterday I asked:

Suppose you - and you alone - discover that the stock market is mean-reverting.  

True, False, and Explain:  If you are rational, you will NOT obey the permanent income hypothesis.
To review:

If the stock market is mean-reverting, low returns now predict high returns in the future, and high returns now predict low returns in the future. 

If you obey the permanent income hypothesis, your current consumption depends solely on your total wealth (including future labor income, of course), not current income.

My answer: TRUE. As long as there are no binding credit constraints, mean reversion implies that after periods of exceptionally low or high returns, the market valuation of your wealth is temporarily misleading.  When returns have been low, you can expect your wealth to grow unusually quickly in the future; when returns have been high, you can expect your wealth to grow unusually slowly in the future.  The researcher who correlates the market valuation of your total wealth with your current consumption will therefore find that you are less responsive to stock market changes than the PIH implies. 

Intuitively, imagine that the stock market fell 50% today, but you (and you alone) knew for sure it would return to its initial price tomorrow morning.  You'd have near-zero reason to revise your consumption this evening, because you're only poorer "on paper" - and you can readily borrow to resolve today's cash flow problems.

What if there are binding credit constraints?  Then there's another effect in the opposite direction.  Key idea: Mean reversion implies unusually good investment opportunities after stock market falls.  If you can't borrow unlimited amounts at the market rate, you will have to partially "self-finance" to take advantage of these temporarily good opportunities.  As a result, your current consumption tends to be more responsive to stock market crashes than the PIH implies.  During bad times, you'll want to really "tighten your belt" to take advantage of the situation.
 
In the real world, the relative size of these two effects is unclear - at least to me.  But it would be a miracle if they exactly cancelled, leaving the PIH unscathed.


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COMMENTS (5 to date)
Don Dale writes:

I think your solution needs to make a distinction between the PV of my lifetime wealth as observed by the researcher and the PV of my lifetime wealth as observed by me. With my insight into the future of asset prices, those two things will be different.

Of course, with my insight into the future of asset prices, I can make appropriately leveraged investments to earn unlimited amounts of profit both now and in the future, so I'm not sure how to even think about the PV of my lifetime wealth in that case. It's a pleasant thought, though.

MikeP writes:

How can this be correct? By betting both ways, I get to make as much money as I care to as long as there is variability in the market. I wouldn't actually own any of the market: All my wealth is in making bets on the reversion of the market.

That engineered income stream doesn't vary by whether the market goes up or down, so long as it goes up or down. A conservative estimate of future variability yields my expected income, and I will hew to that estimate to determine my consumption even though I'll probably make more than that.

So my answer is "false".

William B writes:

Yeesh. With this answer, as Don Dale suggested, it would be much better to have written "you will APPEAR NOT to obey the permanent income hypothesis". Specifically, it will appear to some observer who mis-estimates your true lifetime wealth that you do not obey the PIH, whereas in reality your will have adjusted your consumption to match your own correct estimate of your wealth.

In general, this is a very difficult question to answer because mean reversion, like all sufficiently strong rejections of the Efficient Markets Hypothesis, flirts with logical incoherence, so it is very hard to say what would happen if a borderline logically incoherent situation became a persistent state of the world.

Dangerman writes:

This answer appears to conflate "the stock market" and "your wealth"... as if there wasn't other places to put "your wealth."

Scheppers writes:

I did not compose my own answer before reading the others, but I had thought the "false" answer was very convincing. I agree with Don Dale, MikeP, William B and Dangerman why "false" is very reasonable.

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