New York, Unequal New York

This morning, Felix Salmon of Reuters pointed out an “income barbell” on Manhatten and some of its boroughs. The post begins:

Did you know that there are more rich households (anything over $192,000 a year for a family of four) in Bay Ridge than there are on the East Side south of 14th Street?

Salmon’s post draws on a mapping application from Envisioning Development.

I’ve never been to Bay Ridge and my time in New York City is only cursory. I actually noted the post mostly because of the great work being done in that neighborhood by a Columbia J-School student.

But from the Envisioning Development data, I was able to test just how much of a barbell there is in any New York neighborhood. For the reasons above, I’ve picked Bay Ridge as a test case. The EV map provides a number of people in various income ranges for each neighborhood. For instance, the Bay Ride data says that 5,595 middle income families, who earn between $61,000 to $91,000, live in the neighborhood. The EV data also reports that the median income in the neighborhood is $65,800* or 85 percent of the citywide median. The distribution is called a “barbell” due to the large number of people near the bottom and the top.

Yet it turns out that the barbell in Bay Ridge is not really much different from the national average. I drew this conclusion by simulating the distribution of Bay Ridge’s income form the EV data. I created a random sample of families with income distributions the same as the EV data. Since the EV data only provides a range of incomes, I’ve assumed that any income value within a given range is equally likely. The other assumption used in my analysis is to top code the income distribution at $325,000.&

I’ve compared my analysis to a common metric of income inequality, the Gini Coefficient. Gini values close to zero indicate equal income across a population and Gini values close to one are more unequal.

According to the Census Bureau the national Gini index was .461 in 2007. I’ve produced a value of about .42, on average for multiple iterations, of the simulation.

Below is the Lorenz Curve, the graphical representation of Gini, for a single iteration of the sample.

*My simulated cohorts produce a similar value.& Public Use Micordata released by the Census Bureau typically top codes at $250,000. I’ve used a higher value to account for the smaller than usual sample size.