The Trouble With Bubbles (Warning: Wonkish Post)

How can you tell you’re in an asset bubble? How can anyone not look at this graph and say that we’re not (index numbers; 2000=100):

But I couldn’t and still can’t, at least not by any objective measure. Here’s a look at why.

Consider the overall Malaysian House Price Index (MHPI index numbers; 2000=100):

If I were to draw a trend line for the MHPI for the period 2002-2008, it would look something like this:

Anybody seeing this would declare, without reservations, that we have a housing bubble. The price differential between actual prices and my trend line is currently about 20% (log difference):

But if I were to model it out (using working population and GDP as explanatory variables):

The line fits the actual increase in prices much more closely, and our “bubble” becomes more of a pimple (log difference):

From 20%, the differential is now just 7.5%. It’s a little higher than it should be, but not “bubbly”. Of course, the overall MHPI aggregates prices across a whole range of markets – house prices in Johore for instance are only 30% above 2000 levels, compared to 128% for KL, 106% for Penang, and 81% for Selangor. And even within states, there are significant differences between districts and by property type (e.g. high rises in KL are up 92%, but bungalows are up 180%).

Nevertheless, two different approaches, two substantially different conclusions. Which one’s right? I don’t know; I can argue for and against both.

The trend line approach provides an immediate sense of the increase in house prices, and one that fits well with the experience of the man on the street. But it also implicitly assumes that the historical movement of prices pre-2009 was “fundamentally” correct, which is an untested and potentially unwarranted assumption, especially given price movements before 2000 – note the steeper slope of the index from 1990-1997 (index numbers; 2000=100):

The econometric model provides a closer fit between explanatory data and actual realisation – but that’s potentially a weakness in itself, as it presumes that the model is correctly specified and because OLS estimation by construction minimises the variance. Most of the models for housing demand used in the literature start from microeconomic foundations and build from there, but the same criticism applies – a closely fit model doesn’t give you a full sense of fundamental misalignments.

[For statistics wonks, the model I’m using for the charts above isn’t correctly specified, as the sign for income is wrong. Adding a AR(1) variable corrects the problem (essentially fixing autocorrelated error terms), but as ARIMA models tend to give very close fits, any price variance from “fundamentals” are even further minimised. Check the end of the post for estimation results]

I could add further arguments: the pattern of house price increases mirrors that of internal migration. Selangor for instance saw a huge influx of workers after 2009 (quadratic-averaged interpolation; ‘000):

Population pressure explains part of the increase in house prices in particular areas.

Another part of the puzzle is this one:

Developers are completing just between 20k-40k homes a quarter over the past three years – that’s half to one third down from the level 10 years ago.

So we have a confluence of “fundamental reasons” that could be driving house price increases, at least within certain segments and certain locations. Higher than normal demand coupled with inadequate supply results in higher prices to ration the existing supply relative to demand. It’s not just a credit-driven, speculative frenzy pushing prices up.

So, what about credit? Mortgage loan growth is rising, but well off previous peaks (log annual changes):

The absolute levels are certainly increasing however (RM millions):

Just to be sure, I put prices and changes in mortgage loans outstanding in a VAR, concentrating on the post-recession period of 2009-2013 (again, see results at the end of the post). The estimates show that house prices and mortgage loans granted are certainly related, but causality tests are mixed depending on which sample period is tested. Before the recession, house prices were leading (granger-causing) mortgage loans; after the recession, loans were granger causing prices but the confidence level is smaller than I’d like to see (cannot reject null hypothesis at 95%, but rejects null at 90%). So there’s certainly an element of expansive credit driving up house prices after the last few years, but its not wholly the answer.

Having said that, let’s relook at the first chart above on prices of high rises in Selangor:

That’s my two best guesses at forecasting where prices should be – at the end of 2012, market prices were somewhere between 15%-10% too high. If we extrapolate that forward into 2013, the price differential is probably double that.

The same criticisms apply of course – high rise prices were almost flat from 2002-2008, which is highly unusual for property. We could thus be seeing a price catch-up in a sense (e.g. the KL example I quoted above). And neither can I tell if I’m over- or under-fitting the models to the data, or completely misspecifying them. The two model estimates suggest neither income nor population growth are good explanatory variables – which certainly suggests a bubble. Price rises are essentially feeding on themselves.

In simple English, estimating a statistical relationship from historical data makes the implicit assumption that there is a relationship between fundamentals and prices, and that this relationship is stable across time. But by definition, asset bubbles occur when prices deviate substantially from those suggested by fundamentals. If you fit a model to historical data that includes bubble periods, your estimates will be totally wrong and will tell you you are not in a bubble even if you actually are.

To make a long story short, you can’t identify a bubble through statistical means when its actually happening. It only becomes clear after the fact, when of course its far too late.

So the bottom line is: I think we have a property bubble, but I also think it’s not too frothy. And I can’t substantiate either of those two opinions.

Technical Notes:

1. MHPI data from the National Property Information Centre
2. Population and labour force data from the Department of Statistics
3. GDP data from Bank Negara Malaysia

Model estimates:

Trend OLS:

Uncorrected MHPI OLS [note negative sign on RGDP. Yes, I know I should use nominal per capita income, but the results are functionally the same. The point estimates are very close, although the standard errors are a little smaller]:

MHPI ARIMA [as above, point estimates for RGDP and NGDP per capita are close, though this time standard errors using NGDP per capita are larger]:

MHPI Selangor High Rise Model 1 [note: per capita NGDP is not statistically significant]:

MHPI Selangor High Rise Model 2 [note: neither income nor labour force numbers are statistically significant]:

VAR for MHPI and Mortgage loans [lag length of 1 quarter selected based on information criteria]: