# A Good Example of Metrics

The Jerusalem Post on Thursday 9 May 2013 had a simple op-ed on affordable housing in Israel. My interest here is not the political side of it - which is most of what the article addresses - but the good use of metrics the author, Ron Diller, uses to lead off on the article.

The author takes the average home sale price in Tel Aviv, average family income price, and relates the two.

- Average sale price of 3-4 bedroom apartment: $850,000 USD
- Average gross family income for Tel Aviv resident families: $52,038 USD

In the US, most long-term mortgages are 80% D/V (debt to value of the home), in Israel the most one can get is 75%, so he uses that number. 75% of the home value is $637,500. A 20-year mortgage at 4% therefore has a monthly payment of $3,863.12. By the way, this is different than in the article, where he gives $4,337. Clearly he made an error in APR calculation.

So, while his math may be off, and I have not had the opportunity to check his data sources, the net monthly payment, if his sources are correct is $3,683.12, for an annual payment of $46,357.50. For a family that has a total average gross income of $52,038, and "gross" means "before taxes", to pay $46,357.50 in annual mortgage payments is simply impossible. Put in other terms, the average mortgage payment for a reasonable long-term mortgage on average housing is 89% of gross income, which was the point of the article.

One more weakness is the use of mean instead of median for average. Mean is usually a good average, but is highly susceptible to a few extreme outliers. Since there are a few extremely valuable apartments in Tel Aviv, and very wealthy individuals may own more than one, and the extremely wealthy are less susceptible to price fluctuations, this keeping the high end far above the average, the median sale price might have been materially lower with better insight.

For counterpoint, here are the numbers in the US in general and New York City in particular.

In 2011, median (not mean) household income in the US was ~$50,000, with mean income around $63,000. New York City had a median of ~$57,000 and a mean of ~$76,000.

For home prices, Trulia puts the median home sales price as $1.1MM, but more interestingly $1,292 per square foot, or $13,907 per square metre. Since the average Tel Aviv home listed above was, according to the author 120-150 square metres, we will take the midpoint of 135 square metres. A similar apartment in NYC would cost $1.8MM.

Put in other terms, with a mean income level of 46% higher than Tel Aviv, real estate is approximately 112% more expensive than Tel Aviv. On an apples to apples basis, New York City is more expensive to buy real estate, as a percentage of income, than Tel Aviv. One could argue that New York City is as unsustainable as Tel Aviv, or that there is some data that is missing here, e.g. median vs mean.

The story is somewhat better across the US. The lowest median home sales price across all reported months in the United States was $240,ooo USD. With median family income across the US around the same as in Tel Aviv, the median home price is slightly more than a quarter of Tel Aviv prices. But the US is a vast country with many different types of cities, suburbia and rural areas.

Either New York and Tel Aviv are equally sustainable, and we are missing something in the numbers, or they are equally unsustainable, and the author's message is correct.

Either way, hats off to the author for using solid numbers to make his point. If only his math were a little better