# Interpretation of coefficient of dummy variable in regression

I have a regression where the dependent variable is the difference in income between towns i and j. The independent variable is a dummy variable which takes value 0 if both towns have the same ruling party and takes value 1 if they are ruled by different parties. There are two political parties A and B in all. How do I interpret the coefficient of the dummy variable. Say it is -10 and significant. On average the income gap between the two town is lesser when they are ruled by different parties. Is this interpretation right? But this cannot be attributed to any one party. Say the income is lower when party A is ruling? I would like to use the difference in income in place of income itself to overcome an endogeneity problem. So I would like some help with interpreting the dummy variable.

Yes, your interpretation is mostly correct. If the coefficient of the dummy variable is -10 and significant, it suggests that, on average, the income gap between two towns is less when they are ruled by different parties compared to when they are ruled by the same party. In other words, there is a smaller income gap when towns have different ruling parties.

However, you are right in noting that this interpretation does not attribute the effect to any specific party. The current model cannot differentiate whether the income is lower when Party A or Party B is ruling. If you want to explore the effect of each party on the income gap more directly, you could include additional independent variables to capture the specific party effects.

One possible approach is to create two new dummy variables:

• A dummy variable for Town i being ruled by Party A (1 if ruled by Party A, 0 otherwise).
• A dummy variable for Town j being ruled by Party A (1 if ruled by Party A, 0 otherwise).

By including these two dummy variables in your regression, you can capture the separate effects of Party A ruling Town i and Party A ruling Town j on the income gap. The coefficients for these variables will indicate the average change in income gap when Party A is ruling one town compared to when Party B is ruling that town. By comparing the coefficients, you can explore the relative impacts of each party on the income gap.

• Thanks for the answer. I had a follow up question about how to arrive at this data. right now I have separate rows of data for each town and the party ruling. while producing the difference I am to consider pairs of adjacent towns. So should the differencing be done directionally? As in, in a pair of towns always subtract income of town ruled by A by town ruled by B... May 1, 2023 at 3:28
• That's correct, you should do the differencing directionally. May 1, 2023 at 18:38