i am conducting research on urban sprawl with evidence to Karachi. i am interested to know the methods through which i could find the cause and effect relationship of urban sprawl on economic inequalities.
First, you need to identify both theoretically and empirically the relationship between urban sprawl and economic inquality. I think some people will object to the existence of this relationship while some others may be very interested in it. One possible mechanism behind it might be the spatial mismatch hypothesis. As to the (empirical) methods, I think you can find from the literature some measures of urban sprawl (which are usually based on satellite image or other remote sensing data) as well as measures of economic inequalities. Then, a simple way is to calculate their correlation coefficients and more complex ways include regression analysis. The most difficult task might be the analysis of theoretical causal relations between the two variables.
First, thanks for valuable suggestions. Please can you define the spatial mismatch hypothesis in simple words. Second if you have any studies related spatial mismatch hypothesis please share me I am very thankful to you.