The multiplier effect is well understood. It’s just that the compliment - the divisor effect of sucking money out of the productive economy for government purposes is ALWAYS ignored.
The way this analysis was done was to just look at the economies of the districts of powerful legislators like Murtha and compare to districts that had non-chairman Reps and Senators. They expected to see that the pork dollars increased the local economies compared to the less fortunately represented districts, but shock and surprise, this wasn't the case. In fact, the districts of power players like Murtha suffered. This means that the dollars the Federal Government was pumping in didn't seem to multiply or some other effect canceled out the benefit of those government dollars in that very district.
Your explanation of the divisor effect would not be specific to that district but more general. This would be one of those cynical adverse selection for the whole because of individual benefits sort of game, except.. the consequences actually did fall right where the Government money was targeted. So, something happens when government money comes in to a community that actually hurts it. This is the big question posed here.