I don't think the two line segments actually create a model of best fit. It's an added parameter that just complicates the model--a single downsloping line would likely explain the data better.

Without access to his data I can't show this with code, but I'll say that the addition of a flat line segment seemed arbitrary to me (and misleading).

The way to confirm would be to:

* Fit a single linear regression to the data for a county. Get the Akaike Information Criterion for that line.

* Fit a POLYNOMIAL regression to the data for the county, with a degree of 2 (to allow for a kink in the curve). Collect the AIC for that.

If the extra degree of complexity is warranted by better predictivity, the AIC for the polynomial should be lower (a better model).

If you can point me to where I can find Ayyadurai's data, I'd be happy to do that.