Working with the ZRI Data
How chaotic is rent in New York?
Looking for a place to rent in New York shouldn't be like jumping into a dark hole. Finding a place to rent should provide at least a few months of comfort in knowing you have a place to call home — but what should be considered before choosing a place to rent?
This isn't a guide to renting in the city, but more a project of data exploration and analysis, again using Zillow's ZRI data. This time, New York City is the focus, and the key exploration is higher-order derivatives. Can higher-order derivatives be used in choosing a neighborhood to rent in New York City?
It turns out that a combination of first, second, and third-order derivatives may provide greater insight into trends in rent throughout different neighborhoods, and can help to make sense of chaotic changes in rent. This study borrows from Physics' application of derivatives — velocity, acceleration, and jerk refer to first, second, and third-order derivatives, respectively.
This study utilizes averages in rent, velocity, acceleration, and jerk — measured in $/month, $/month, $/month2, and $/month3, respectively. This is what the four look like over time in the Upper West Side:
Velocity measured in $/month, acceleration in $/month2, and jerk in $/month3.
Here it's pretty evident that rent fluctuates frequently. The higher-order derivatives seem chaotic, and frankly to the untrained eye — meaningless. "Rent goes up and down. Derivatives simply emphasize that." That was my initial sentiment. However, in physics, jerk refers to the change in acceleration — the change in change in change in position. I couldn't help but be convinced that a third-order derivative could provide at least some insight to trends in rent.
After some reading up and grappling with the concept of a "change in change in change", I gathered that average jerk can help to project property value in different areas. Theoretically, a neighborhood on pace to increase in property value is identified by a 0-jerk (low rent sensitivity), a close-to-zero acceleration (constant rate of change in rent), and a high velocity (constant increases in rent). Essentially, jerk is indicative of sensitivity to external variables — a neighborhood with close-to-0 jerk isn't easily affected by factors that more prominently affect rent in areas with greater average jerk.
For example, Little Italy has the highest average jerk in New York City. A plotting of average rent in that neighborhood shows that rent seems to be quite chaotic:
In comparison, rent in Park Slope — where average jerk is 0 — is quite consistent in trend, with only 4 peaks and valleys over time. Little Italy, on the other hand, is riddled with local minima and maxima.
It seems that in areas with a smaller absolute jerk value, one can rent without having to anticipate changes in property value as often as in other areas. It's important to keep in mind that jerk is not necessarily indicative of rent itself — a high average jerk could apply in both low-rent and high-rent areas alike. Jerk is indicative of rent sensitivity, and could allude to various factors: Is the area undergoing a serious fit of gentrification? Is the neighborhood bringing in an unusual influx of small/medium businesses? All three derivatives should be considered when assessing an area's rent volatility.