Thursday, August 09, 2012

Unabsorbed Detached Units in Vancouver CMA

An anomaly has presented itself in some CMHC data regarding matching the completed, absorbed, and unabsorbed datasets available through Statscan's CANSIM tables. First a bit of background on the data I'm using:

  • "Completed" is the number of units that have been registered as being completed in a given month.
  • A unit is "absorbed” is when a binding, non-conditional agreement is made to buy or rent the dwelling.
  • "Unabsorbed inventory" is the total number of units that have not been absorbed.
  • "Completed but unabsorbed" is the number of units that completed but were not absorbed in a given month.
"Unabsorbed inventory" (U) is theoretically derived from "completed" (C) and "absorbed" (A) as follows (where i is a given month and i-i is the previous month):
U[i] = U[i-1]+C[i]-A[i]

So taking the reported unabsorbed inventory and reconstructing it using completed and absorbed data should produce a match. CANSIM data are only available for single and semi detached properties so these are the data I have used. Alas they don't seem to track very well in absolute terms:
The reason for the divergence is unclear but a much more interesting thing arises upon visual inspection: the higher-frequency terms appear to track each other closely. To isolate this effect I added a first order highpass filter with 6 month time constant and yield the following result:
Indeed for most of the series over the past 24 years the higher frequency terms are similar, except in the past 18 months or so where the reported absorbed inventory has fallen markedly short of reported completions, but this is not showing up in the reported unabsosrbed inventory.

I'll leave it for CMHC to figure out what's going on before making any speculations, but for those tracking unabsorbed inventory when looking for potential distress in housing markets, this should be something that should be resolved. If I can find the multi-unit absorbed/unabsorbed datasets I'll add to the analysis to see if this effect carries over. (Multi-unit is a much more significant component of Vancouver CMA's construction activity; detached is about 25% in terms of dwelling completions in the past few years.)


Unknown said...

A comment regarding your calculation method here, the distortion in your analysis could be caused by variability of completed and absorbed values with respect to time. Allow me to explain:

you started off with the following fact:

U[i] = U[i-1]+C[i]-A[i] -- Eq (1)

Then, you have graphed what seems to be equivalent to the following:

Integral((U[i] - U[i-1])/Delta(T))


Integral((C[i]-A[i])/Delta(T)) -- Eq (2)

Then, you have applied the high pass filter that showed better match.

This seems to indicate that C[i], A[i] and U[i] could be variable with T (i.e., time) therefore you get a better match where time interval for integration is shorter; thus you get smaller distortion.

If for some reason (could be legal) the number of completed and absorbed changes after the end of the month then you may end up with C[i], A[i] and U[i] being time variable function in Eq 2 above, then you cannot treat them as constant in that integration, and hence is the deviation.

Your original assumption (i.e., Eq 1) is derivative of Eq 2 with respect to time, and then setting Delta(T) to 1 month that seems to be the smallest discrete time interval for the data.

jesse said...

Unknown, yes that is plausible. The thing I wanted to highlight was the stark deviation that has occurred in the past year or so. I'm not so concerned with the longer-term deviation because (as you mention) there are practical reasons the running inventory needs to be readjusted.

I'm curious as to which way the data are going to be adjusted to resolve the most recent deviation.

Unknown said...

Yes, I concur. The deviation is just too big in such short time.