The Curve is Almost Certainly Flattening

Almost all chess events have been cancelled due to the coronavirus, so instead we use our statistical tools to analyze the epidemic. To flatten the curve, the US has shut down much of the economy. Are these efforts succeeding? At first glance, it looks like we haven't made any progress.

Confirmed cases in the US

(Source: CDC)

However, the trend is exponential, so it can be hard to spot changes in the growth rate. That's why we take logarithms:

Log of confirmed cases in the US

Now there does appear to be a recent slowdown in the growth rate. I checked this with a simple model. New York State announced a lockdown on 3/20. Within a few days, other states with big outbreaks made similar announcements. It can take a week or two for an infected person to show symptoms. Thus, even if the social distancing is working, you might not see results until the end of March or early April. So does the curve flatten starting in late March/early April? Yes, it does. In the picture below, "time73" is for the curve after the first week of April. "Time" is for the whole curve. You can see that the number next to "time73" is substantially smaller - this means that the curve started to flatten in early April.

The next part of this post is more technical. If you haven't studied a lot of stats, this is a good time to stop reading. The bottom part of the screenshot shows that the slowdown in the growth rate is statistically significant. However, this test presumes that we had already known the exact date of the structural break. We didn't. It could have been anywhere from 1 week to 2 weeks after the lockdown.  Andrews (1993) showed how to test for an unknown structural break (see Table 1 in this paper). However, the slowdown remains statistically significant after making these adjustments. Thus, I conclude that the curve really is flattening.

Though I looked for a structural break based on when the social distancing started, the test does not prove that the lockdown caused the curve to flatten. It seems likely to be true, but showing that is more complicated. I guess I would start by comparing the results for different states that began the lockdown at different times (while being aware of the endogeneity). I don't have time to explore that, but hopefully one of my readers does. Write a comment with your results. My analysis also does not show if the shutdown was worth it. That would be a separate project. 

That's all for today. Stay safe, everyone!