In a recent article, economist Andy Xie suggested we " Fear Empty Flats in China's Property Bubble ." In his attempt to make you "fear," Mr. Xie makes the silly claim that the vacancy rate in urban China is 25% - 30%. This subject arose in China out of what appears to be a false rumor about electricity usage, which Mr. Xie first cites. As a former analyst, long ago I learned to be wary of cited numbers and to look at the assumptions that go into them. The subject is important because China's housing market is repeatedly cited by shorts as one of the main reasons they believe equity markets will fall.

First, please keep in mind that recently China's Ministry of Urban Rural Development said more than half of China's total urban housing will be torn down in the next 20 years . Those who call China's housing market a "bubble" fail to mention that a huge percentage of China's existing housing stock is old and "pre-teardown." That should be good for housing-related issues like Ehouse China ( EJ) and Chinese developers as well as commodity players like Freeport-McMoran ( FCX), Southern Copper ( SCCO), Rio Tinto ( RTP) and BHP Billiton ( BHP) who produce the materials that go into China's housing.

The first trick Mr. Xie uses to get readers to "fear" is a fractions game. He tells us that if there were 32.5 million vacant "households" in urban China, it would amount to a 20% vacancy rate. Implied in this he's also telling us he believes there are only 129 million occupied households in urban China; it's simple math (occupied households would then have to be 4 times 32.5 million.) That's a pretty small number for the 625 million people living in urban China. It would be almost 4.9 people per household and is simply not credible. There may on average be 5-6 young, newly migrated workers living together in China's factory dormitories, but not all of urban China. Thus, we see Mr. Xie's fraction trick; he underestimates the real demand for China's housing.

(Note, even if we back out all of China's 200 million migrant workers who don't all live in factory dormitories, his numbers still imply 3.3 people per "household," very high for a relatively young, urban Chinese, mostly upper and middle class population with a low birth rate. In this case for every mostly upper or middle class single person living alone, there would have to be 6 people living together, or for every couple, 5. We already backed out China's newly migrated workers, and so some who live in "households.")

In the U.S. we have about 2.3 people her household, so 4.9 would be an eye opener. China's urban population growth is driven by migration from rural areas. Migrant workers tend to be young people who migrate at least initially without families. When they migrate they tend to live in crowded factory dormitories, but as incomes rise over time their first goal is to get a place of their own. In addition, China's natural population growth is only .6% meaning fewer children per household. And yet for every single person or couple living alone, there would have to be almost 8 or 9 people living together to reach an average at 4.9. Even including newly migrated workers the real average is much lower.

Mr. Xie's second suspect assumption is average housing size. Also using simple math we can know Mr. Xie believes there are approximately 173 million "households" in urban China. Using the middle of his inflated and speculative range for vacancy, we can know he's claiming there's about 44 million vacant households. Adding 44 million to 129 million occupied households gives us his estimate of 173 million total "households." Again all just simple math.

But here's where it gets interesting. Because he's telling us he thinks there's 17 billion square meters of total housing stock in urban China, that means with 173 million households, his numbers imply China's housing stock averages 98 square meters, or just more than 1,000 square feet. Simply not credible given what we know about China's history.

(Even if his numbers for "households" don't include factory dormitory units but his numbers for housing stock do, backing out a reasonable estimate for all dormitory housing stock from his total housing stock estimate only brings down this 98 square meter average for "households" by a small fraction. The assumption still doesn't hold.)

While it may be that housing in China built over the past 10 years averages 98 square meters, there is a huge stock of very old and very small units existing today that certainly bring the average down significantly. I was in Beijing in the late 90's and remember well. The average apartment was very small. Credible sources then argued there was as little as 7 square meters of housing stock per person in Shanghai in the mid 90's. Back then only a small percentage of Chinese urban residents could afford 70 square meters (let alone 98) and yet more than 400 million people lived in China's cities then. Mr. Xie seems to admit this in that he claims 1 billion square meters of old housing have been torn down, but then he says tear down housing averages a whopping 70 square meters.

China's economy has grown at 10% per year for 29 years. At a 10% growth rate, China's economy is almost 4 times the size it was 15 years ago. If the shorts believe Chinese residents can on average only afford 98 square meters per "household" today, how were they supposed to be able to afford on average 70 square meters 10-15 years ago when China's GDP was 25% to 35% of what it is today? No, that old housing stock is much smaller on average. The good news is they can now afford more housing.

The simple fact is that there are tens of millions of very small, very old apartments in urban China that are "pre-teardown," my guesstimate is somewhere between 40-80 million units between 25-50 square meters in size. We know it's a big number because Mr. Xie tells us only 1 billion square meters have been torn down in the past 10 years and yet there had to be several times that number of older tiny units to house the more than 400 million people who lived in urban China in the mid to late 90's. Where in many countries these units may have already been torn down, in China's cities that are flooded with as many as 15-20 million new migrant workers each year, the useful life of old, small apartments can be extended.

Between a realistic estimate for people per housing unit and in light of tens of millions of old, smaller apartments, clearly there are many, many more than 129 million occupied housing units in China's cities. If (when we include migrant workers) the real number was 50% higher, it still only implies 3.2 people per housing unit which would be almost 40% higher than in the U.S., even though they have fewer children per household. China's real need for "households" is much, much larger than Mr. Xie assumes, and as incomes grow demand rises quickly.

I don't doubt that China's urban vacancy rate is higher than most major countries; it needs to be to accommodate the huge migration of new residents moving from rural areas each year. There may be 32.5 million or more vacant units in urban China; it's speculation and it frankly doesn't matter much. There is a surplus of old and small housing in China that is in less demand than modern era housing. (Note, you often hear about the recent 12% increases in the price of China's new private housing which averages just slightly more than $100 per square foot, but rarely hear that for low income housing the price has just barely risen of late.)

That there is likely more of this very small, old and "pre-teardown" housing sitting vacant in urban China, well it shouldn't alarm anyone. That it needs to be torn down and replaced over the next 20 years is a great thing for China's housing sector as well as commodities in general. That some remains vacant today will have very little economic impact on China or the world. It is a reminder of China's housing past and the reality of an economy growing so quickly where incomes also grow quickly and were cities swell through urbanization. But, in attempting to make reader's "fear" China's urban vacancy, Mr. Xie has built an argument around assumptions that don't stand up to scrutiny.

At the time of writing, Fisher owned EJ.