## Does bubble exist in Toronto’s Housing Market?

Everyone keeps talking about 33% year-over-year house price growth in March in Toronto….. Toronto’s housing market is definitely on fire! However, is there a bubble? Well, let us do some econometricks! 🙂

Data

Most of the data I will use for today’s study come from the Statistics Canada’s CANSIM database. Since city-level data are not available. I use Ontario’s monthly economic data ranging from 1997M1 to 2016M12 as a proxies for Toronto’s Economic variables. (Note that this may create some bias in our estimates but what else can we do? Canada has a huge lack of data! Even though Conference Board Canada has time series economic data for Toronto, I actually have some doubt in the accuracy of their data. Plus,  as a poor Econometrickster, I  don’t have money to buy the subscription data from Conference Board Canada)

For the house price data of Toronto, I use the MLS HPI from the CREA website: http://www.crea.ca/housing-market-stats/mls-home-price-index/hpi-tool/

Now what I will do is to replicate the method used in this paper written by 3 Chinese economists from: http://file.scirp.org/pdf/JSSM20090100006_39362604.pdf

Let’s run some regressions

The first regression we run is the following, here’s the eviews output below:

$ln(P_t) = \beta_0 +\beta_1ln(Income_t)+\beta_2ln(Rate_t)+\beta_3ln(P_{t-1})+\epsilon_t$

Where $Income_t$ denotes real disposable income er capita, which is not available. We gotta use monthly wage data from Statistics Canada, deflated by the CPI index. $Rate_t$ denotes the real interest rate. I use the bank rate (minus the inflation rate) to get the real interest rate… $P_t$ is the house price level, which I use the house price data from CREA. Below is the output from EViews:

Well….Results are not that great. All the variables are not significant except the AR(1) lag… This can be partially explained by the fact that all the economic variables I use are proxy variables, which introduces bias in the estimates. However, let us move on. The coefficient we are mostly interested in is the autoregressive coefficient, which is 0.986 in our case. Now we need to estimate the real growth momentum of house price $h_t$:

$h_t = (P_t/P_{t-1})^{0.986}-1$

Above shows the estimated pure real price growth

Then we run the following simple AR model of order 2 with constant intercept:

$h_t = \alpha_0+\alpha_1h_{t-1}+\alpha_2h_{t-2}+v_t$

The coefficient we are mostly interested in is $\alpha_1$. If $\alpha_1> 0.4$, it is said to be a huge warning sign of speculative bubble

Now, instead of using the whole sample size,  I am gonna use the rolling regression methods to compute the monthly growth speculative bubble index  $\alpha_1$ for each month in Eviews. I set the rolling window sample size to be 32 observations per roll.

Below shows the estimated bubble index I estimated using the rolling regressions :

(Note that estimates could be subject to upward bias because the proxies for fundamental economic variables fail to capture Toronto’s fundamentals. Also the size of the rolling window also plays a role in the estimates)

When the bubble does burst, it will be very nasty for sure.