Central Banks and Price Stability
Your question has been addresses in different ways. Kydland and Prescott (1977) argue that a central bank should follow defined policy rules instead of active stabilization methods because the latter contributes to economic instability. Barro and Gordon (1983) prove that under a discretionary regime, the central bank has an incentive to print money to improve the economic performance in the short run, but this doesn't happen in the long run. Walsh (1995) discuss the way central bankers incentives should be design in order for the central bank to follow a socially optimal policy.

On Central Bank Independence (CBI), Grilli, Masciandaro and Tabellini (1991) and Cukierman, Webb and Neyapti (1992) developed a methodology to assess CBI  from different countries, and how the degree of independence impacts on the economic performance of this countries. Alesina and Summers (1993) studied 16 OECD countries and they compared the countries CBI score against economic performance measures (GDP growth, unemployment rate, and inflation). Then, there are several papers that cite these researches and build upon them.

The CBI scores are based on multiple criteria, Grilli et al., have a different approach than Cukierman et al. Alesina and Summers used a combination of both, so for the case of Zimbabwe you'll have to analyze if the laws of its central bank have the characteristics that the researches take into account when they build their indices.