Edward L. Glaeser is an economics professor at Harvard and the author of “Triumph of the City.”

One of the biggest surprises from last week’s release of Census data was that New York City’s population appears to have grown by only 2.1 percent in the last decade, or about 167,000 people. The city’s overall population, 8.175 million, is 200,000 less than the Census Bureau had estimated for 2009.

Unsurprisingly, Mayor Bloomberg is challenging the Census figure and demanding a recount.

The crucial question is whether the Census missed significant numbers of immigrants in Brooklyn and Queens. If the Census total were left unchanged, New York’s population growth rate would have fallen significantly between the 1990s and the 2000s.

At first blush, this decline would seem quite surprising. After all, the city has continued to surge economically. Between 2000 and 2008 (the latest year available from County Business Patterns) payroll per worker in Manhattan increased by 35 percent (7.8 percent in real terms — that is, after adjusting for inflation) to $102,000. Over the same period, national payroll per worker increased by 25 percent (for no real gain) to $42,000.

You might have thought that robust increases in earnings in the economic heart of the city would have pulled in plenty of people.

Moreover, the high prices that persist in New York City suggest that the demand for city living isn’t falling. Case-Shiller data, which captures the metropolitan area rather than the city, shows that the New York area’s prices have risen by 67 percent since 2000 (32 percent in real terms), more than any metropolitan area in the sample except Los Angeles.

We don’t have comparably reliable figures for the city itself, but most data seems to show increases over the decade, as well.

In national perspective, New York’s limited growth is also somewhat surprising. A new policy brief of mine shows that people are moving disproportionately back to areas close to our old ports and to areas that had high wages as of 2000.

But the combination of economic strength and high prices need not lead to population growth if an area doesn’t build many more units. In that case, high housing demand leads only to higher prices — not more people.

The Bloomberg administration has long pushed for more building permits, and there were years during the middle of the last decade when the city was permitting construction of more than 30,000 units annually.

I had thought that all that building activity would lead to a significant increase in the housing stock of the city, but the city ended up adding only 170,000 units over the decade, a 5.3 percent increase.

Typically, population increases by a few percentage points less than the housing stock increases because of shrinking household size, so perhaps we shouldn’t be shocked that New York City’s population grew by only 2.1 percent.

For example, Boston’s population growth of 4.8 percent, the first time the city had grown more quickly than the state since the 1870s, was made possible by an 8.2 percent increase in the housing stock.

The growth of New York’s housing stock in the 2000s was not greatly lower than in the 1990s, when the city added about 200,000 housing units. But during that decade, the population increased far more quickly, in large part because of increased crowding in the outer boroughs.

During the 1990s, New York City’s population increased by 690,000, while Manhattan’s population rose by 50,000. The population of Queens increased by more than 10 percent during that decade, 280,000 people, although the number of occupied housing units increased only by 60,000.

The current 2010 Census doesn’t show a similar surge in the population of the boroughs outside Manhattan, and New York’s growth during the 2000s seems to have been more closely in line with what we should expect from the growth in the amount of housing.

Moreover, the city’s measured vacancy rate increased to 7.8 percent in 2010 from 5.6 percent in 2000, which means 80,000 fewer units being occupied. Increased vacancies meant that the number of occupied units grew less than 90,000, or under 3 percent, which makes 2.1 percent population growth completely understandable.

But this vacancy rate is far higher than the 2.7 percent vacancy rate reported by the 2008 New York Housing and Vacancy Survey, which is one reason why it will surely be part of the dispute between the city and the Census. One question is whether the Census takers made sure that seemingly empty units were actually empty.

One hypothesis is that the immigration-led growth of the 1990s was much slower during the 2000s. The other hypothesis is that the Census managed to miss large numbers of immigrants in the outer boroughs. If there is a recount, we may see which hypothesis is correct.

In either case, the Census count of the number of total housing units is likely to be correct, and that count shows relatively modest growth. Those boom years during the middle 2000s did not expand the city’s housing enough to make the city much more affordable and inclusive, especially in its most attractive neighborhoods.

The Bloomberg administration has worked hard to allow more building, but the recent Census numbers seem to suggest that a combination of slow growth and continuing high prices implies that New York’s barriers to building, such as a complex zoning code and ever more Historic Preservation Districts, are still shutting out families that would like to move to the city.

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