My title is a littel bit ambiguous. I'm working on a project on measure the degree of sorting in housing market,put it simple, sorting refers to people with similar characteristics tend to live in the same community, so in extreme case (prefectly sorting),correlation coefficient of some attributes like income,education should be 1 for people live in the same community. But there are always some unobervable characteristics that we cannot observe,like attitude, so in a hedonic regression they fall into the error terms.
What I want to do is ,given a list of characteristics like income,education as dependent variables, run SUR on its average value in the community(average edu attainment) and control several other household background attributes. the model specification can be written like:
where Y(it) denotes characteristics vector, y(n(t)) denotes average value, z denote control variable
After that I check two things: (I)the estimated coefficient of average value (II) the correlation coefficent in the estimation error, denoted by rho. If there is two predetermined groups in each community, and I find there are significant difference of estimated coefficient and correlation coefficient between two groups, then we can say the sorting degree is different for these two groups
My questions are ,firstly ,statistically speaking, is there any obvious flaw of my above statement? Secondly, we can put some cross-equation t test of the estimated coefficient using statistic package like stata, how about the correlation coefficient in the error term, any suitable test?