Dummy impact depending on the value of the dependent variable

[Fernando Martins]

Hi,

I have a sample of some municipalities that signed an investment contract in basic sanitation with a development bank. I want to see if the contract signature had any impact on the sewage coverage (0 to 1) of these cities. For that I'm using a dummy variable to capture the signature of the contract (0 prior to the signature and 1 from the year of the signature onward).

I noticed that there is a lot of heterogeneity on the impacts (large coefficient with large error). I interacted the contract dummy with some regional dummies and that helped quite a lot. But I noticed that the regions that have almost no impact of the contract are regions where the sewage coverage was already higher compared to others when the contract was signed. I mean, the impact of the contract on sewage coverage has a nonlinear relation with the dependent variable.

I tried dividing the sample in 4 (every 0.25), but the sample is already small and results were even worse.

Any other suggestions on how I can capture the decreasing effect of the contract dummy but using the whole sample?

I know that this is not the perfect analysis for policy impact, but I just want to have some rough insights on the data that is available.

[Clyde Schechter]

One possibility I would consider is including the pre-contract level of sewage coverage as a covariate and including both it and its interaction with the contract variable in the model. You would expect to see a negative coefficient for the interaction term.

Another way to capture this kind of phenomenon, one that is not widely used but can sometimes be just the right thing, is to use the reciprocal of the sewage coverage as the outcome variable rather than the sewage coverage itself. This is because the same change in 1/y corresponds to a huge change in y itself when y starts out small, but continuously reduces as y increases and becomes negligible as y gets larger. Or, even more flexible, rather than taking 1/y as the outcome variable, you could keep y as the outcome but use the power(-1) link function in -glm-. It can be used with any of the supported distribution families.

[Fernando Martins]

Thanks, Clyde.

I included the average level of sewage coverage pre contract as a covariate and it managed to capture the decreasing return of the signature.

[George Ford]

might use the growth in coverage as the DV