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Everybody knows that you should read the fine print on a legal contract.  The same logic applies when interpreting data since many numerical “measures” or “indices” or “scales” or “ratios” have fancy sounding names which do not always mean what they say.  Today’s news discussed a report focusing on a methodological issues with implications for real estate markets.

For example, the Economist magazine has been claiming that Canada’s housing market is one of the most over-valued for a couple of years.  Two ratios are commonly used to measure the degree of over-valuation:

  • ratio of the selling price of a home to an apartment rent
  • ratio of the selling price of a home to consumer income.

The first ratio makes sense since a home and a rented residence are good substitutes.  The second ratio also makes sense as a measure of affordability.  The methodological problems appear when these sensible measures are implemented.

Since there is no theory which suggests the “right” value of a ratio, implementation involves comparing the current ratio to a historic average.  That comparison is often sensible but one should also always be aware of when the historic average is not relevant: did something else change which would make it inappropriate?  In Canada, today, the answer is Yes: current interest rates are very different from their historic average.  That is a relevant difference since it would be shocking if a change in the level of interest rates did not affect the “user cost” of owning a home and thus the relative price of substitute residences.

(With more work, the effect of this difference can be calculated.  That extra work should also account for covariation in the inflation rate, since the real interest rate is more important.)

These ratios are popular because they can be computed using commonly available data.  Specifically, they are based on data reported for the average price, the average income and average rent paid.  Again, this methodology is sensible and convenient but the data should not be used carelessly.  Specifically, nobody thinks of themselves as “average” and it is not the same averaging used for all of these measures.  Therefore, this measure is vaguely true but is specifically true for very few individuals.  (There is another puzzle involving “Jensen’s Inequality”  and non-linear functions, but it is mostly for advanced readers.)

The methodological quirk reported today is in how they measure the average price of a home or the average rent of an apartment. (The headline-grabbing stuff in the report is at the front but the important stuff is at the back.)  Again the problem is relative to history: as one example, houses built today are bigger than those built in the past.  Month-to-month variation in the types of houses sold contaminates the most common measures of the average price.  So, it is important to control for quality and, slowly, such measures are being reported: http://housepriceindex.ca/ (see also the methodology link).

If somebody taught how these measures were constructed, nobody would pay attention.  (Actually, they are taught in classes that many people dislike.)  But these methodological fine print can affect what appears to be true.  So, the real lesson is that people need to have the patience to read the fine print and the curiosity to wonder what it might mean.

PA

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