I am writing a dissertation on the factors behind firm relocation. I have a dataset of firms’ origins, destinations, and the year of their relocation. I also have data on some characteristics of the origin and destinations (e.g. union density, % of college graduates, distance between the two locations).

I intend to estimate a gravity model with count-data, using Poisson regression. The explanatory variable is the number of firms that relocated from one location to another in a given year, e.g. 12 firms moved from New Jersey to New York in 1994.

My question is: Which would make more sense - 1) using origin and destination characteristics as regressors or 2) using ratios of origin and destination characteristics as regressors?

I found a paper that does the former: https://www.redalyc.org/pdf/289/28943151005.pdf (Table 6). However, my understanding is that the origin coefficients capture the firm’s decision to set up there initially, as well as its decision to leave. For instance, if firms set up at the origin destination because education levels were high, the coefficient on % of college graduates would be positive - but this is what firms liked about the destination in the first place, not why they wanted to leave!

I only care about the relocation decision, not the initial location decision. Hence, I feel like using ratios of origin and destination characteristics might make more sense. If there is a positive coefficient on the ratio of % college grads in destination to origin, that tells me that firms prefer to relocate somewhere with relatively higher education levels.

Is my interpretation correct? Would this be a better way to specify the model?

Thank you so much!