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Archive for August 30, 2022

Do Rents Really Actually Lead Home Prices?

The inflation thesis at this point has both a top-down and a bottom-up rationale (as all good theses do). The top-down rationale is that the extraordinary rise in the quantity of money over the last few years has yet to be fully reflected in the price level; ergo, inflation should continue for a while – even if money supply growth stops cold – because the price level has a lot of ‘catching up’ to do.

The bottom-up rationale depends a lot on what happens in the housing market. The first place that prices shot up was in the more flexible components of inflation, especially in goods. “Sticky” inflation followed, only turning north in 2021 and then accelerating in earnest especially as the eviction moratorium eventually ended and rents began to catch up. As the chart below (source: Atlanta Fed) illustrates, core “flexible” CPI (in white, right hand scale) is decelerating and is down to about 7% y/y…but core “sticky” CPI (red, left hand scale) is at 5.6% and shows no signs of even peaking.

An important part of the “sticky” basket is the weighting assigned to rents. Rents show up as both Rent of Primary Residence (you rent a place to live) and Owners’ Equivalent Rent of Residences (your opportunity cost is that you don’t have to pay for an apartment, so this is an imputed cost). Both rents move together, mostly because the Bureau of Labor Statistics reasons quite naturally that the best measure of the imputed rent a homeowner would pay is the market for rentals that he/she actually could pay. These two pieces of CPI are the biggest and the baddest, and they don’t even exercise. I always say that if you can forecast rents accurately, you will not be terribly wrong on overall inflation. Rents are the 800lb gorilla. Where they sit has a big influence on overall inflation.

Traditionally, observers of the inflation market have forecast rent based on a simple lag of home prices. There are reasons to suspect that’s not the whole story, but it has worked for a very long time. Here is a chart of the last 20 years or so, with the Case-Shiller index (lagged 18 months) in green and the Existing Home Sales Median Price y/y (lagged 15 months) in blue against Owners’ Equivalent Rent in red.

Even though inflation as a whole has been low and stable, home prices themselves have varied enough thanks to the housing implosion in the mid-2000s that you can see a reasonable outline of why inflation people tend to like this simple model. It’s at least suggestive.

Recently, that has been called into question by a researcher at the Mercatus Center at George Mason University. Kevin Erdmann wrote a paper published this year entitled “Rising Home Prices are Mostly from Rising Rents.” When the paper came out I tweeted it with the note “I need to read the whole paper.” If Erdmann is right, then the entire market is doing it wrong and (a) home price inflation should not be slowing down right now, since rents are not, and (b) the way the market models rents is just plain useless. So, this was definitely worth looking at from my perspective!

Well, I’ve read the paper. I am sorry to report that in my view, the author makes very strong claims but supports his argument with very weak statistics. That being said, I still think this is a paper worth reading – some might come to a different conclusion than I have.

It isn’t like I think the author is completely out of his gourd. It is absolutely reasonable to expect home prices and rents to be related since they are both ways to acquire shelter services. It isn’t as if Erdmann is saying that they aren’t related, and some of his cross-sectional data and findings are interesting. The problem is that he starts with a mental model of how things work, and then proceeds to show information which, given his assumptions, seem to support what he is saying. The mental model isn’t absurd: a home can be thought of as a way to purchase a whole stream of shelter services in one lump. When home prices rise, it could mean that buyers are evaluating this stream of services as being worth more than they previously were because they are observing rising rents, or because they were priced out of the rental market and chose to buy an asset with a shelter services component instead.

But it could also be the case that home buyers are reflecting rising expectations of long-term rent inflation, in which case spot rents needn’t change at all. It might be the case that home buyers are making totally stochastic decisions, and it just happens that when lots of people buy homes it pushes up home prices which then displaces people into the rental market.

All of these stories would result in time series that are highly correlated. And Erdmann has a number of illustrations and data points showing that there is a correlation. For example, he pointed out that in 2021, “the metropolitan areas with the highest rents also had the highest prices.” However, Erdmann’s real claim isn’t that home prices and rents are closely related, but that rents lead home prices. The point about the connection of rents and prices in various metropolitan areas is not evidence supporting his claim that rents cause prices, but it doesn’t refute it either. The problem is, he takes such data as support of his claim, when it isn’t. This turns out to be his modus operandi – start with a mental model of how it works, show data that demonstrates the two things are connected, and then assert causality.

In the paper, there is not a single test of causality. With time series, we can test whether one series statistically leads another in various ways; for example, with the Granger Causality Test (which doesn’t actually test causality but merely the lead-lag relationship). If the point of the paper is that (contrary to the usual assumption) movements in rents cause movements in home prices – which is a big claim – then at the very least I’d have expected to see a Granger test.

There is some evidence that statistical inference is not the author’s strong suit. He shows several clouds of data points where any reasonable person can see there is no clear trend, and then proceeds to run a regression line through them. The fact that we can calculate a regression slope – we can always calculate a regression slope – does not mean that it is statistically significant. And even if it is statistically significant, it may not be economically significant. Unfortunately, there are no such tests of significance in the paper and I suspect for several of the charts it would be impossible to reject the null hypothesis that there is no relationship at all between the variables despite a provocatively-drawn regression line.

He also has a figure (Figure 9 in the paper) which shows changes in prices and rents for a number of metro areas over time. Clearly, there is a positive relationship – but no one disputes that. The question is, does the relationship get better when you lag one of the variables? No such analysis is done.

In general, all the author “proves” is that there is a relationship between rents and home prices, which I think we already knew. The rest of it is storytelling, trying to persuade us that the causality makes sense his way. I don’t mean to suggest that the paper is a complete bust! The author does have some good ideas that I will borrow. He makes the point that discounting home prices by general inflation doesn’t really make sense because we don’t care about the general price level when we buy a home; we care about the price level of shelter. This is a simple point, but fairly profound in a way. It risks being somewhat circular if we aren’t careful, but it’s a good point.

And the funny thing is, despite the fact that I think the evidence is much stronger that the evidence for causality runs the other way, I agree with some of his policy conclusions. His main conclusion is that “…if rising rents are the more important factor [rather than temporary demand factors or monetary stimulus], then policies aimed at stimulating more construction may be more apt and may help increase real incomes for Americans in neighborhoods where rents have been rising.” I completely agree that, given the severe housing shortage that we seem to have in this country, that making it easier for builders to create homes and apartments would be good industrial policy.

But you don’t need to believe that rents lead home prices to think that is a good idea!

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