Determine location of structural break in cross-section data

[phantomcow2]

I'm trying to run a simple regression for a data set (n=165). I've determined via a Chow Test that there exists a structural break somewhere; the same least squares estimate cannot be accurately used to represent the entire range of values the explanatory variable takes on. I've found two very different (.08 and .2) estimates if I break the data down into two catagories: whenexplanatory variable takes values of less than 70000, and where it takes values above 70,000.

However I only took an educated guess to arrive at the 70,000 figure. Is there a more precise, mathematical method available that allows me to determine where the structural break begins to occur?

 

[SW VandeCarr]

However I only took an educated guess to arrive at the 70,000 figure. Is there a more precise, mathematical method available that allows me to determine where the structural break begins to occur?

Cluster analysis or discriminant analysis may be useful here. The latter is primarily for anticipated or predetermined subsets in the data.http://faculty.chass.ncsu.edu/garson/PA765/cluster.htm

 

[EnumaElish]

There is no hard and fast rule -- a rule of thumb is to rank-order the data and try 5%, 10%, 25% and 50%.