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Macroeconomics At The Zlb Notes

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Macroeconomics at the ZLB
- Great Recession
- ZLB, monetary policy responses
- Price path targeting
- Using unconventional monetary policy at the ZLB-

Expectations and speed of response:
o Consider a negative inflation shock
 With NKPC: A down to B then right to C then back to A
 With full price flexibility: A down to B then back to A (because PC is vertical)
ZLB:
o Consider a negative demand shock to the economy causing a large, sudden, leftward shift of the IS curve as in the traditional 3 equation model. Given this, CB's response would be to cut the nominal interest rate = fall in real interest rate = consumption and investment increase and economy returns to equilibrium. With flexible prices and rational expectations, this can occur quickly because if private sector predicts
CB's response, it adjusts expectations in period when shock occurs so inflation can return to equilibrium with no drop in output. With flexible prices, this also means slope of PC steeper and closer to vertical, so prices adjust quickly to small output changes and economy returns quickly (note, in normal times, adjustment is slowest with AE, quickest with RE, and somewhere in between with NKPC, due to sticky prices, with the more people can change prices the better.
o With a large shock: limit on how low CB can set nominal interest rate, depends on whether CB is setting monetary policy as a lending rate or spending rate. If it is a lending rate (rate at which it will lend money to commercial banks), then if CB sets negative rates it is imposing losses on itself. If CB is setting it at a deposit rate, rate at which commercial banks can deposit their cash in the CB, the rate cannot go negative becomes it becomes a tax on the cash deposits made by commercial banks,
so they get back less than what they put in. They will sometimes tolerate neg rates given there is a cost to the alternative (vaults, requiring security and fees), for simplicity assume lowest rate is 0.
o Real interest rates = nominal interest rates - inflation. If nominal rate can only go to zero, there is then also a lower bound on real interest rates, as lowest value is negative of the expected inflation rate.
o In this diagram, where inflation expectations are the target rate, minimum value for r is negative of target inflation (A). at A, output is below equilibrium output level so lowest possible r is below what is needed for full employment. To get to B, the economy would need a very negative inflation rate. Unlike in traditional 3-equation model where falling inflation =
low nominal interest rates via CB policy to achieve MR
line = changes in real interest rates; at ZLB, nominal interest rate part of this is missing so we are just left with adverse feedback from falling inflation and rising real rates which cannot be stabilised.
o At point A, economy at risk of deflationary spiral. Output < equilibrium, so inflation decreases, so expected inflation decreases, so minimum value of the real interest rate increases and output continues to decline, moving north-west along the IS
curve to a position with even lower output. So once economy is at ZLB, inflation

begins to fall triggering a sequence worsening the situation = further reductions away from equilibrium level

At ZLB, flexible prices and rational expectations make this spiral occur at a faster rate. If prices adjust very quickly, a in PC curve is larger so curve is steeper, so smaller changes in output cause larger changes in the minimum value of r that the
CB can achieve at the ZLB. Likewise, if expectations adjust quickly due to higher proportion of agents with RE, inflation expectations will adjust in the same period inflation falls (rather than in the next period as with AE) = deflationary spiral is quicker. Flexibility in prices and RE better away from ZLB because good for stability and allows quick adjustments, but worsens the shock at the ZLB
If everyone is fully rational, they know the CB can't do anything, so the more people adjust the worse the problem gets. Therefore, this is more severe with rational expectations.
Also affected by a large a parameter, which indicates more flexible prices.
o Why this doesn't happen: future fiscal expansion, wage and price setting aren't this rational, people don't want to change prices

Pigou argues that there will however be a positive demand effect from the deflation,
as the nominal value of cash and fixed assets remains the same so real value in terms of purchasing power increases. This would make consumers feel richer =
increases their demands.
However, this relies on economy being a net asset holder rather than a debtor economy, otherwise as price level falls, real value of debts increases, which is therefore a more restricting burden which detracts from consumption.
o Hysteresis effects: a deep recession, with a lower level of actual output, pulls down the equilibrium level of output in the model thus creating a permanent negative effect. Could happen if there is capital scrapping due to suspending investment and lack of capital returns, would permanently reduce productivity by shifting PS lower.
Alternative ways for CB to loosen monetary policy at the ZLB to prevent deflationary spiral:
o Forward guidance: CB signals it will keep nominal interest rates at the ZLB for a greater length of time than what would otherwise be expected. Eg. In 2012 US
Federal Reserve issued guidance to US private sector to indicate Fed Funds rate would remain at ZLB until end of 2014. Then both UK and US issue forward guidance that interest rates would stay at the ZLB until their economies' unemployment rates rose above a certain level, around 6.5%. if CB can convince markets it will leave interest rates low for quite a wall, then investors have an incentive to start investing more in the present to reap the benefits of this in the future.
 Signals regarding future interest rates can be fed into current long-term rate through this equation, which links up short and long term rates:

Where iit is the n-period interest rate eg. On a 10 year government bond, i is 1 period interest rate eg. Rate set by CB, and theta n is the risk premium required by an n-period lender
Long term interest rate cannot be below expected average of short term rates (otherwise investors simply leave long-term investment and invest in short-term investments). Also, can't be above because opposite occurs. So only difference is risk premium, as if expected average of short-term rates turns out to be wrong, there is a risk premium and long-term investor may lose out

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