# Regression with two dummy variables: city and state in which one is implicitly included in the other: multicollinearity?

I am new to statistics and am really struggling with something that is probably easy for a statistics expert to answer.

I am currently working on my dissertation in which I am trying to see whether there is an effect between location of a company and firm value? I am looking at both cities and states. The city variable is a dummy variable which equals one if the firm is in any of five specific cities in the US, which I have chosen.The states variable is also a dummy which equals one if the state contains the any one of the five respective cities (e.g. it is also five states). Thus, the number of observations in the sample which only contains the cities is a lot smaller than the sample which contains states. Of course all firms located in the specific cities are also in the states but there are many more firms located in other cities in those states.

I have set up one regression in which city is the independent variable, one in which state is the independent variable and once I include both city and state. I tested whether I have a multicollinearity problem in Stata and supposedly I don't. However, I don't really understand how to interpret the coefficients. To the regression results:

If I only include city, the coefficient is 0.011 (being located in any of the specific cities leads to an increase in firm value of 1.1%). For the one in which I only include state, the coefficient is 0.051. Now if I include both the coefficient of city is: -0.024 and the coefficient of state is 0.055. So if I interpret that as being located in any of the five states leads to an increase of 5.5%. However, if the firm is specifically in one of the five cities this premium decreased by 2.4%. That would still mean that being in one of these cities leads to a premium of 3.1% but in the first regression I only found 1.1%. I really don't get it!!!! Do I need to disregard the last regression due to multicollinearity? How could I see a combined effect of which of the two (state or city) is actually driving the difference in value? Please help me!

Thank you very much. Gloria

• are the firms independent from each other. Ie is there a state effect? – mandata Aug 14 '15 at 23:59
• Thanks so much for responding!Yes the firms are independent & yes there is a state effect which includes the effect of the city. There can be firms which have headquarters in cities in the particular state but not in the so-called financial center/city. i.e. there is an overlap between firms with HQ in financial city and in the state. My problem is that all the firms which are located in financial city are coded 1 for the city dummy variable but these are of course also coded 1 for the state dummy variable, since they are in both. And my goal is to see which effect is driving the premium! – Gloria Little Aug 15 '15 at 0:53
• PS: lets say one city is NYC and one is Boston, the states are obviously NY and MA. When I do code "state = 1 if in NY or MA but not in NYC or BOS" I get totally different results from the 5.1% I mentioned above. – Gloria Little Aug 15 '15 at 0:58
• If the cities are nested within the states and there is a statistically significant state effect then you should consider MLM. – mandata Aug 15 '15 at 1:06
• Yes, that sounds like what I need. However, when I use the xtmixed function on Stata, how can I interpret which of the two (state or city) is driving the effect? My parameter for state is larger than for city but I think that just means standard deviation! I would be grateful for advice! – Gloria Little Aug 15 '15 at 2:22