Thursday, October 25, 2018

Housing: Part 327 - More on Adam Ozimek's regressions and the wrong presumptions

I looked at some more data regarding the previous post that I think might help fill out my point.

To review, Ozimek finds that cities that have the strongest recoveries in building are the places where prices are also rising the most. So, he concludes that supply constraints aren't the cause of rising prices.  And, furthermore, the places with less building are places that had bigger bubbles.  He writes:
Instead of being correlated with rapid price growth, weak permitting is correlated with how big the housing bubble was in a metro area. This is clear in the data, where the permitting recovery is higher in areas that had smaller peak-to-trough declines in house prices during the bubble bursting.

My counternarrative is that we didn't have a bubble in housing supply.  The lack of urban supply has always been the problem, and was the core cause of the housing bubble.  And, I argue, that the main factor driving housing markets since 2007 has been extreme credit tightening that was imposed because of the incorrect presumptions about what caused the bubble.

Note that both narratives could explain the fact that cities with the deepest price collapses also have seen weaker supply recovery.  That could happen because they had oversupply or because the credit bust hit them harder.  Ozimek's finding only seems conclusive because my counternarrative is currently considered inconceivable and so nobody feels required to disprove it.

Ozimek follows the convention here when he says "weak permitting is correlated with how big the housing bubble was in a metro area".  This presumption is so deeply and broadly held, he can be forgiven.  But, he hasn't shown that at all.  He has shown that weak permitting is correlated with how big the housing bust was, and he is assuming that the bust was inevitable.  This is question begging, and it is universally practiced on this topic.  In fact, it is the reason we had a crisis in the first place, because as the crisis developed, the universal reaction was, "Well, this was inevitable."  But, it wasn't inevitable.  And, we can review the data to test the assumption.  Nobody else has done that because the assumption was canonized before the crisis even happened!

Here, I am using data that doesn't exactly match Ozimek's.  I am using some data I have previously downloaded on the largest 20 MSAs, going up to 2015.  But, it gives the same basic results as Ozimek's does, so I hope you will forgive me for having saved myself the time of gathering more extensive data.

As I mentioned in the previous post, supply constraints are still central, because the cities with the most recovery in permits, by Ozimek's measure, are the cities with the weakest building markets.  They have recovered to pre-crisis levels because their pre-crisis levels were extremely low.  Here is a scatterplot comparing the long-term annual permitting rate (permits/capita) to the ratio of the permitting rate in 2014-2015 / 2002-2003.  (In the previous post there is a similar graph with MSA income on the y-axis. It looks very similar, because building has recovered in cities with high incomes and constrained housing.)

Among the top 20 MSAs, there are two groups.  The Closed Access cities are the cities where economic potential is sharply limited by housing access, so they are building at rates similar to boom levels, and slightly higher than the 2002-2003 building levels.

Among other cities, there is no pattern.  Basically, building rates everywhere else have been cut in half (with variance) whether they built 0.005 homes per capita annually before the bust or 0.015 homes.

This is because a credit shock was imposed on the country, and it doesn't affect the Closed Access cities so much because they still permit fewer homes than any other city, and money is flowing into those markets in a desperate bidding war for access to prosperity.  That was our problem in 2000, 2005, 2015, and today.

But, let's back up a step.  What about Ozimek's comment that price declines during the bust are a signal of the size of the housing bubble?  We can test that with this data.  There is some relationship between rising prices during the boom and declining prices during the bust because of the brief price spike in the Contagion cities.  But that's about it.

I have created a measure of housing permits issued in 2004-2005 compared to 2002-2003.  This is a measure of how much extra building happened during the peak bubble years.  A regression between that measure and the MSA price change from 2005 to 2012 shows an insignificant relationship.

What about longer-term building?  A regression between the price change from 2005 and 2012 also has an insignificant relationship with building rates from 1996 to 2005.

We can also compare the decline in permits and the decline in prices.  The decline in permits from 2005 to 2012 is highly correlated with the decline in prices over that period.  Both quantities and prices declined together.  But, there is no relationship between declining permits from 2005 to the 2012 trough or to 2015 and price increases from 1999 to 2005.

The only way Ozimek can connect the price collapse to the bubble is by assuming it.  But, we don't have to assume it.  We can directly measure it.  And there is no evidence in this data that either high prices or high quantities before the crisis are associated with declining permitting rates.

Looking at all of these measures, the regression model that provides the best correlation with permitting rates in 2014-2015 compared to 2004-2005 has three variables that are all statistically significant.  In order of significance (t-stat in parentheses).

  • (4.80) The decline in MSA home prices from 2005 to 2012.  For each 1% (log) price decline, there was a decline of about 1.6% (log) of permits in 2014-2015 compared to 2002-2003.

  • (3.61) The increase in building permits in 2004-2005 compared to 2002-2003.  For each 1% (log) increase in the rate of permits during the boom, there has been a 1.3% (log) increase in permitting rates in 2014-2015.  That is not a typo.  The relationship is positive and significant.  This mirrors the construction numbers I recently reviewed.  MSAs that had increased rates of building at the peak of the boom are MSAs that have continued to have strong local markets.  (There is also a positive, but not significant relationship between permit growth in 2004-2005 and price appreciation from 2012-2015.)

  • (-2.60) The long term rate of building from 1996-2005.  For each additional permit/100 residents annually from 1996 to 2005 a city issued, the ratio of permits in 2014-2015/2002-2003 is 39% (log) lower.  But, as we see in the graph above, this really consists of the Closed Access cities, where permits have recovered, and the rest of the country, where permits are at half the 2002-2003 level and there isn't much relationship between previous building rates and the current rate.
There was no housing bubble.  There was a housing supply bust in the Closed Access cities that continues to this day.  In a misguided attempt to lower housing prices in the face of that housing supply bust, we have done nothing to change the dynamic of the Closed Access cities, where rates of building continue to peak at very low levels while prices rise.  And, the rest of the country is saddled with a credit bust that has decimated home prices, rates of building, and longstanding natural patterns of migration.  The cities that were harmed were not cities that were engaged in a random bout of speculation.  They were cities whose generous building and growth traditions were nonetheless overcome by a wave of housing refugees until we killed the market with macro-level bloodletting.

But, this account was assumed out of the story before the story was even written.  Practically every piece of analysis that has been written about the crisis has been based on a reading of the evidence that depends on assumptions that were wrong.

PS: MSA Income is an important factor I should have looked at before.  Income is related to the other variables in two important ways.  First, migration pre-crisis was strongly tilted toward cities with lower incomes.  That is the perversity at the heart of my research.  So, as I explained above, permitting rates are dominated by the Closed Access cities where few permits are issued in cities with high incomes, and that explains why the long term rate of building is a significant variable.  Once I add income, that variable becomes insignificant.

Income also relates to the decline of home prices after the crisis.  Since the credit bust was imposed based on borrower characteristics, buyers with low incomes were hardest hit, and thus, cities with low incomes were hardest hit.  This isn't as strong as the pre-crisis migration relationship, but it is strong enough that adding income to the regression with permit recovery also makes the 2005-2012 price decline insignificant.

A regression of permit recovery from 2003 to 2015 against just two variables - Income and the increase in building permits from 2002-2003 to 2004-2005 has an r-squared of 0.69.  Income is highly significant (t-stat = 5.68) and the level of MSA income 1% (log) higher is correlated with a log 2% increase in permit recovery.  For each 1% (log) increase in the rate of building in 2004-2005, permit recovery has been 1.0% stronger (t-stat = 2.77).  Again, this is the opposite sign of the bubble story.  More building in 2004-2005 is correlated with more building in 2015.

PPS: Oops.  Sorry.  I had an error in the excel worksheet.  (The error doesn't effect the regression described above, but the price collapse does have a correlation with building permit recovery.)  Income is actually highly correlated with the price collapse from 2005-2012.  An MSA with income 1% higher was correlated with 0.6% less of a price collapse.  Even with that relationship, the price collapse is correlated with permit recovery.  So, a regression with three variables - Income, the increase in permits from 2002-2003 to 2004-2005, and the price collapse residuals after accounting for the effect of income - has an r-squared of 0.79, and the significance of both income and permitting rates are increased compared to the two variable regression.  The coefficients are:
Income: 2.08
2004-2005 permitting rate: 1.32
Price Collapse: 1.02

So, stronger permit recovery is related to higher income, growth in the rate of building in 2004-2005, and less of a price collapse from 2005-2012.  All of this supports the conclusion that there was not a housing supply bubble but there was a credit bust imposed on low income borrowers after 2005.


  1. I have some more info on the housing crisis unfolding in Australia:
    - In spite of record house prices (they peaked in the second half of 2017), there are still some 120.000 EMPTY apartments/condos/houses (think: speculation/"Store of value").
    - There are still some 80.000 dwellings being build. And if all the building plans get approved then an additional 80.000 dwellings could be added to the stock of australian real estate in the next say 8 year.
    - And that proves your point that there wasn't a shortage of houses. But the rise in home prices gave the impression that there was more demand for houses, a shortage of houses.
    - A better way to gauge demand for housing is the development of rents.

    - This is the result of rising australian real estate prices in the last - at least - 20 years in combination with credit growth

    1. What a strange article. It's quite clear from the graphs in the article that Australia is much like the US. Prices across cities are jointly affected by credit, taxes, interest rates, etc. And the difference between cities is mostly about rent. Rent is clearly very important. That they conclude otherwise is odd.

  2. Bravo.
    But, Kevin Erdmann, macroeconomics is not about being right.

    It is about having the best narrative, given the agenda.

    Fables, hagiographies, and totems characterize the modern economic environment, parading behind is escutcheon-carriers,left-wing and right.

    Good luck, Kevin Erdmann.

  3. As someone with a background in the hard sciences (STEM), my view of these housing/construction boom/bust cycles looks at the system dynamics with feedback control (zoning/permit control systems with delays, coupled with physical finance/construction/marketing systems). The feedback instability is from the price system where developers start requesting more permits when the prices increase but the product only hits the market on the downside of the boom phase driving down the bust phase.

    Such a feedback control system is unstable when the natural frequency of the coupled systems are similar. This is shown in the complex mathematics describing these coupled systems, and everyone is familiar with this dynamic phenomenon in the context of feedback on microphones and speakers in an auditorium (microphones controlling speaker output).

    There is a natural frequency to real estate market driven by the business cycle and employment fluctuations measured in 5 to 10 year range. Actual construction time to build buildings is measured in a year or so (the Empire State Building took one year). With almost no regulations in the 40's through the 70's, I observed Los Angeles go through several boom/bust construction cycles with only minor price changes and some local overbuilding in a dramatically changing city.

    However, the political bureaucracies of zoning and development commissions evolved resulting in a dramatic slowing of development approvals. Five to ten year delays in obtaining permissions are the rule for major developments. Now the overall project timescales including regulatory control is similar to the natural timescales thereby creating a mathematically unstable system, where normal boom/bust small variations are driven (amplified) into the massive booms and busts in both prices Interestingly, Texas has not experienced these massive fluctuations due to its limited zoning regulations and fast permit times.

    I suggest you include dynamics in your thinking about this issue. There are people in fields of engineering like control theory and electrical engineering or acoustics who work with dynamic systems all the time and could help you understand how and why adding a time delay by zoning and environmental regulations can create a dynamic failure in real estate development under all conditions: both fast growing and slow growing markets with both high and low prices can go unstable, just as speaking quietly or loudly into a microphone similarly result in the same feedback instability.

    The control theory and EE professors working on this type of problem may require more mathematical ability than most economists remember to fully utilize the engineer's tools required for thinking on these subjects. Indeed, this requires more complex number math than I remember at my age. However, learning these methods, including the complex mathematics that goes with it will be worth it. < >

    If you want to really understand the world, having tools that can reasonably model our observation is the first step. The people over in the Engineering department have these dynamic tools, use them.

    If you could get information on the permission times (from proposal to sale) required in the various areas of the country along with the price variations of the boom/busts, you may show this instability with even a simple plot showing dramatic boom/bust variations at high permission/development times (more inspections and sub-permits slow actual construction). You could then do the math that would show that a price control feedback system is unstable when combined with a government regulatory system creating time delays.

    Demonstrating this instability could impact policy regarding the impacts of regulatory delay.

    1. Your explanation is reasonable and plausible, but I don't think it fits the facts in this case.

      The problem in the Closed Access cities is that there is never a boom. There isn't a wildly oscillating supply reaction. There is a stagnant supply, the price of which mostly reacts to demand. There weren't hundreds of thousands of units coming online in the Closed Access cities in 2007-2008. That's a problem I have with some explanations from people like Robert Shiller. Their model says that bubbles bust when a wave of delayed supply hits the market. It is a reasonable model to use in a number of contexts, and it seems like it should apply here, but it doesn't. If it did apply, home prices in the Closed Access cities would be much lower than they are.

      In cities like Phoenix, supply was very responsive to changing conditions. A big part of what happened there is that builders started on new homes that had qualified buyers with financing, and those buyers canceled their orders in 2006 and 2007 after the homes were finished. Certainly that lag time is important for that to happen, but even in Phoenix, the main issue wasn't builders still blindly putting up new spec homes in 2007 that caused the collapse. It was the whipsaw in demand.

  4. Yes, what you have essentially in closed access cities is not delayed supply due to controls but supply ceilings. The amount of new housing supplied is minuscule in relation to the size of the market and demand.