Road to Inflation #1: Repeating the Political Cycle
When the central bank is not independent, politicians have historically pumped up the money supply (for temporary economic boost) shortly before an election to buy votes with a lower unemployment rate. After the election, the effects wear off, returning the economy to its natural rate of unemployment but at a higher inflation rate than before. Because it is hard to fight off inflation quickly, by the time the next election rolls around the economy has not been squeezed back to its original inflation rate. Politicians pump up the money supply again, this time from a higher base inflation. As this cycle repeats itself, the central bank loses control of the money supply.
Road to Inflation #2: Financing Government Spending
A central bank that lacks independence from politicians makes it tempting for the government to finance an inappropriately large portion of its spending through printing money. A central bank that promises to finance too much government spending also loses control of the money supply.