## Friday, December 14, 2018

### Housing: Part 338 - Price/Rent ratios

One of the key ideas that fuels conventional wisdom about the financial crisis and the housing boom is that Price/Rent ratios (or, relatedly real home prices) shot way up outside the norm during the boom.  This seemed to be proof that credit markets were fueling an unsustainable price boom.

One of the key discoveries I made was that, oddly, even though rent is in the denominator of price/rent, it has such a strong effect on price that when rents rise, the price/rent ratio rises even more, and likewise, real home prices would rise even more.

 idiosyncraticwhisk.com   2018   (income on log scale)
I think I have posted some version of this graph before.  But, before, I have just shown r-squared values.  This version of the graph shows 1991, 2007, and 2018.  And, in addition to the r-squared values, I looked at the p-values.  I was surprised at how small the p-values are.  And, these are not weighted by MSA size, which I suspect would lead to even higher r-squared and lower p-values, because very large MSAs populate the far end of the regression.

The p-values are:

1991: .162 (not significant)
2007: 5.5 x 10-16(nearly zero)
2018: 2.5 x 10-35 (nearly zero)

And confidence levels are pretty tight.  The coefficient, at the 95% confidence level is (these are on a natural log scale, so this is the expected change in Price/Rent for each doubling of rent):

1991: -0.7 to 2.0
2007: 6.5 to 10.4
2018:  5.6 to 7.3

Interestingly, if I regress Price/Rent against the median income of each MSA, or against the median price, the relationship is very strong for every year.  I have written previously about how, within MSAs, there is a strong systematic relationship between Price/Rent and all three measures (rent, price, and income).  Within MSAs, each doubling in price is associated with a Price/Rent increase of about 3.  Between MSAs, each doubling of price is associated with an increase of 4 1/2 to 6 1/2.  Possibly, similar influences are at work, and the steeper relationship between MSAs is created because between MSAs, there could be an added systematic factor - expected rent inflation.

For each doubling of MSA median income, the 95% confidence range of the coefficient for Price/Rent is:

1991: 5.4 to 8.8
2007: 9.3 to 14.4
2018:  6.9 to 9.8

 idiosyncraticwhisk.com   2018   (income on log scale)
Those coefficients are huge.  The median US Price/Rent in those years was 10.7, 14.7, and 12.3.  So, doubling the median MSA income is associated with a change in Price/Rent that is nearly as high as the national median Price/Rent.  A log-linear relationship would mean that the median home price in a city with a median household income of about \$20,000 would be \$0.  Actually, look around some cities today, like Cleveland, and it isn't too far off that.

 idiosyncraticwhisk.com   2018   (income on log scale)
So, there has always been a strong relationship between income and Price/Rent both within and between MSAs, probably for similar reasons, such as that higher priced homes make better tax shelters, are more likely to be owner-occupied, have less credit constrained buyers, etc.  Incidentally, this is one reason why it has been really bad to block households from mortgage access because of low incomes, etc.  Homes in low-income neighborhoods are cheap.  It's the rare asset class where investors of lesser means have a natural advantage for getting higher yields.

But, the most interesting thing about this is the difference between the income effect and the rent effect.  I have concentrated previously on how during the boom (and since) rent has become more and more a factor in home prices at the MSA level, not less important.  So that rising Price/Rent levels were not actually a good signal of a bubble.

But, here, we can see that the reason that rent did become a more important signal was because rent and expected increases in rent, started to correlate with income, because of the Closed Access problem.  So, yes, rent has become increasingly important, but here, we can confirm that rent has become increasingly important only as a side effect of MSA income becoming more important and becoming rationed through rent.

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