I would like to analyze income mixing in the neighbourhoods of a group of cities. One way to think of neighbourhood income mix is as the spread of incomes found in a neighbourhood. I have census variables for average income, median income, standard error of average income, and other sociodemographic characteristics. The data are aggregated at the neighbourhood level (I don't have access to microdata with information about individuals at this small scale). I would like to do OLS regression using the coefficient of variation (std.error of income divided by average income) as the dependent variable. I have three questions about this:
- If I wanted to see whether wealthier neighbourhoods, controlling for other characteristics, have more or less income mixing than less wealthy ones, does it make sense to use the CV of income as the dependent variable and median income as an independent variable?
- To use it as a dependent variable, I would be transforming the CV by taking its square root. How should I interpret the regression coefficients? For example, if a coefficient is significant and equal to 0.3, is it correct to say that 0.3 to the power of two, or 0.09, is the expected change in income CV for a one unit increase in X? What if the coefficient is negative?
- Are you aware of published studies that use CV as the dependent variable?