The Estates General of the Dutch Republic had a yearly budget in the 17th-18th and a formal process to approve it. But interestingly it had only four categories of expenses on the budget: Repayment of debts, War, Water management, and the Representative office of the Estates General (tasked mostly with negotiations), with Repayment of debts and War always taking most if it (even in peace time).

Still it was apparently light years ahead of enemies in budget keeping, since it always paid lower rates for debts and never defaulted on repayments, while regularly bankrupting kings like those of Spain and France during wars.

One of those Representatives of the Estates General (in practice a sort of PM), Johan de Witt, is credited with laying the scientific foundations of financial mathematics and contributing to the formalization of probability with his paper 'The worth of Life Annuities compared to Redemption bonds' which is discussed in letters between Bernouilli and Leibniz. The topic of the paper is of course a very practical matter for a guy tasked with negotiating the conditions of big loans.