I figure that either someone already uses this statistic, and is collecting it somewhere, or there is some other statistic that is considered more useful when trying to determine how "self serving" is a country's rulling class. Where can I find such a statistic?
That's tough, since a "self-serving" expense would be one that takes money without returning value to the country. It's usually easy to figure out the total COST of running a government (from salaries of legislators, bureaucrats, judges, etc.) because those costs are usually pretty well documented unless your government is repressive and totalitarian.
What's hard is determining the value added by government and expressing it as a monetary value. I'm not quite sure how to do that, but that may be another question worth asking on this stack exchange. Once you have a good way to calculate the value added, then just subtract the value added from the total cost, and you have your "self-serving" cost.