what is the Relationship between Zero nominal interest rates and liquidity traps

Question

So I'm reading mankiw"s principles of economics and I'm in the chapter about the influence of monetary and fiscal policy on Aggregate demamd. The part about nominal Interest rates and liquidity traps left me confused and I didn't really understand what it meant. Can anyone elucidate the role of short run interest rates and their effect on the economy? More specifically, can anyone explain this particular paragraph:

"Some economists have suggested that the possibility of hitting the zero lower bound for interest rates justifies setting the target rate of inflation well above zero. Under zero inflation, the real interest rate, like the nominal interest, can never fall below zero. But if the normal rate of inflation is, say, 4 percent, then the central bank can easily push the real interest rate to negative 4 percent by lowering the nominal interest rate toward zero. Thus, moderate inflation gives monetary policymakers more room to stimulate the economy when needed, reducing the risk of hitting the zero lower bound and having the economy fall into a liquidity trap."

Answer 1

The paragraph that you included likely assumes that nominal rates won't go below zero, and therefore that $r_n$>=0 at the zero lower bound. This has been challenged by unconventional monetary and exchange rate policies (i.e. the EU, Switzerland). This likely leads to a few assumptions under classical economic frameworks:

-The Money Demand curve is not horizontally asymptotic at $r_n$=0

-If it is assumed that there is rate mobility below a zero nominal rate (it can go lower and lower with market manipulation), $\frac{d\left(r_n\right)}{d\left(Q_{md}\right)}$≠0 where $r_n$<0. Logically, a -0.41% rate affects consumers differently than does a -0.68% rate (remember that this is effectively the risk free rate; risk premiums will yield positive rates that can be interpreted using classical liquidity preference theory)

This tool has been used for different reasons. Switzerland isn't using negative nominal rates to escape a liquidity trap, but to keep the Franc from appreciating and sending their trade deficit through the roof. The EU on the other hand has resorted to this unconventional monetary policy to try to stimulate growth and avoid a deflationary spiral. They hope to incentivize banks to lend money at the negative rate plus a risk premium rather than be charged to hold money as reserves by the ECB. Consequences exist for these policies, however. Because consumers would rather hold money as cash than lose it in a negative yielding savings account, the money supply of the banking system weakens, and rates can rise back up. Due to its only recent implementation, negative interest rates are likely still considered experimental at best.

Anyways, the paragraph argues that an above zero inflation target allows more policy flexibility, as $r_r$=$r_n$ when inflation equals zero. This effectively gives borrowers cheaper "real" lending while lenders still gain a rate on their assets above holding money as cash (and therefore no bank runs or contracted money supply). Again, this paragraph is either assuming that the ZLB equals zero, or that negative nominal rates are not sustainable. Mankiw would probably argue that a higher inflation target (which leads to generally higher nominal rates in equilibrium), would've given the EU a better ability to manipulate aggregate demand with a "target" lower bound of 0% nominal interest.