What's the role of an independent central bank in a liquidity trap?

The following quote is from the introduction to a new paper by Paul Culley and Zoltan Poczsar with the title "Does Central Bank Independence Frustrate The Optimal Fiscal-Monetary Policy Mix in a Liquidity Trap?":

The United States and much of the developed world are in a liquidity trap. However, policymakers still have not embraced this diagnosis which is a problem as solutions to a liquidity trap require specific sets of policies. There are policies that will work, and there are policies that will not work. Correct diagnosis is necessary to prescribe the right policy medication.

A liquidity trap is a circumstance in which the private sector is deleveraging in the wake of enduring negative animal spirits caused by the bursting of joint asset price and credit bubbles that leave private sector balance sheets severely damaged. In a liquidity trap the animal spirits of the private sector cannot be revived by a reduction in short-term interest rates because there is no demand for credit. This effectively means that conventional monetary policy does not work in a liquidity trap. (...)

The importance of fiscal expansion and the impotence of conventional monetary policy measures in a liquidity trap have profound implications for the conduct of central banks. This is because in a liquidity trap, the fat tail risk of inflation is replaced by the fat tail risk of deflation. In turn, the fatness of the deflation tail is a function of the government’s willingness and ability to pump-prime, i.e. to borrow and spend.

For central banks, this is a game changer. (...)

In a liquidity trap the central bank’s role changes from one of policing the government to keep it from borrowing too much, to one of helping it to borrow and invest by targeting to keep long-term interest rates low by monetizing debt, with the aim of killing the fat tail risks of deflation and depression.

Go read the whole paper.