As you say, Particracy's in-game economic system was never fully developed. Actually, there are a few nations where the budget isn't even working properly.
The plan is that when it comes to petitioning for changes in ranking, a premium will be placed on forum role-play, especially when it comes to the Strong and Very Strong rankings. However, things like budgets and in-game bills can certainly be used to help support the case for a petition.
To quote what the document states,
The rankings system tries to take a long-term view and places a premium on active forum role-play, which at times will mean not so much weight is attached to game mechanic variables, such as legislative changes, taxation levels and spending allocations. It is not that these are unimportant or not valued, but good quality forum role-play will tend to be given priority. Do not be surprised, for example, if a nation is given a higher military ranking than another even though its military spending seems significantly less. It could be that that nation has been more active in terms of forum role-play, and in particular, has engaged in more military-related forum role-play which helps justify its military ranking.