Did this in Housing seem an obvious bubble?

I don’t think I’m going to be continuing yesterday’s post from just where I left off, but hopefully over the course of the next few posts it should become clear why I hold such bizarre beliefs. In this post I’m updating one from last year, in which I argued two points:

1. It is still reasonable to believe that the housing boom was not a bubble; and
   
   
2. Even if one believes that, one can still be ultra-bearish on housing today.

The argument, essentially, is that the fundamental value of housing depends inversely on real interest rates, which fell dramatically between 2000 and 2005 and then rose in 2006. Since the peak of interest rates in 2006, nominal interest rates have fallen, but most of the fall appears to be the result of a fall in inflation expectations; real long-term interest rates, as represented by TIPS yields, have fallen only slightly since their 2006 peak.

In this chart (an update of the earlier one), I plot an index of actual housing prices (the OFHEO Index, standardized to 1997Q2=100) and a crude estimate of the fundamental value of houses (CPI owner’s equivalent rent, capitalized at the 10-year TIPS yield plus a 2% risk premium, and expressed as an index standardized to 1997Q2=100).



My valuation method is crude, but it is not contrived. That is, I used what I considered the most obvious set of numbers, not some cherry-picked set designed to generate a certain result: I used the 10-year TIPS yield because it’s the most liquid market-determined long-term real interest rate for the US; I used 1997 as the base year because that is first year for which those yields are available; I added 2% because it’s an integer, and 1% was clearly too little, and 3% was clearly too much (at least prior to the last two weeks), and I used CPI-OER and OFHEO because those are first relevant indexes that I found for rents and house prices.

If you are willing to accept my crude approximation of the fundamental and my implicit (arbitrary but, I think, reasonable) assumption that prices in 1997Q2 were close to the fundamental, my results imply that there was no bubble this decade, but that housing prices now have to make a large downward adjustment due to a change in the fundamental. Actually, it is a conservative (that is, on the low side) estimate of how much adjustment prices have to make, because the relevant risk premium has clearly risen very recently, which would drive the fundamental values of houses down even further.

Some people have pointed out that, historically, interest rates do not explain most of the changes in aggregate housing prices, and that, in fact, if you model housing prices empirically using interest rates as one of the predictors, the results show that prices in late 2005 (where my two lines cross) were already far above the predicted value. People interpret this empirical finding to mean that housing prices must have been in a bubble. I see several problems with this argument:

1. This is one of those situations in economics where theory matters. If you want to argue that prices have moved far above the fundamental, you need a theory of what the fundamental value is; you can’t simply fit a bunch of possibly relevant variables empirically in a linear model and assume that the fitted value is the fundamental value. For example, if housing markets have become more efficient over time, then housing prices could have been deviating from the fundamental in all those past years and only now following the fundamental. And even if prices in the past did follow the fundamental, you would need to choose the exact right set of variables in order to get the correct fit, and you would need to choose the right functional form; otherwise, the coefficients on your variables will be biased, and, in particular, you may be underestimating the importance of interest rates.
   
   
2. If real interest rates are the most important variable, how do you represent them prior to 1997? There is no available series: you have to start with nominal rates and make some assumption about what expected inflation rate is applicable.
   
   
3. In an empirical fit, how do you account for the price adjustment process? Everyone knows that housing prices adjust slowly, so to make a meaningful empirical fit, you need a theory (explicit or implicit) about the adjustment process. If you ignore the adjustment process, you’re implicitly assuming that adjustment is instantaneous, which is obviously wrong. In particular, you will run into problems when there are dramatic changes in the fundamental, as for example, with the very low real interest rates in the late 1970s followed by the very high real interest rates in the early 1980s.

My approach avoids these problems because it doesn’t attempt to use historical data to ascertain fundamental values; it just asks whether the recent pattern of price changes is consistent with a theory of the fundamental. And it is. And if interest rates remain where they are, a lot of pain in the housing market over the next few years will be consistent with that same theory of the fundamental.