Lecture 24: The Zero Lower Bound (ZLB)

Spring Semester ’13-’14 Akila Weerapana

Lecture 24: The Zero Lower Bound (ZLB)

I. OVERVIEW

• In the last section of this class, we hone in on the most pressing macroeconomic issue of the day, the sluggishness of the U.S. recovery from the Great Recession. Several explanations have been posited for the slow recovery speed including lingering housing sector problems, bad fiscal policy, outsourcing of jobs, the cautious lending behavior of banks, and the tendency of consumers whose balance sheets may have taken a hit to be cautious about spending

• But perhaps the most important factor, and one that differentiates this downturn and re- covery from past episodes is the fact that the Federal Reserve has moved interest rates to unprecedentedly low levels for unprecedented levels of time. The Fed funds rate is now in its FIFTH year at zero, and the Fed has implemented many unconventional programs in the last few years under the colorful names of QE, QEII, Operation Twist, etc. The Fed announced earlier this year that it would taper (or roll back) all of these unconventional programs over the next year but the Fed Funds rate looks like it will stay at zero through the end of 2014.

• In economics, we say that over the last few years, the Fed has been hampered by the zero lower bound (ZLB), which prevented it from lowering interest rates further to help the economy.

In today’s class, we explore this idea of a constraint on interest rates falling below zero and develop the implications of this zero lower bound some more in the context of the AD-IA/IS- MP framework.

II. THE ZERO LOWER BOUND

• In our MP curve we specified that the central bank chooses the real interest rate to satisfy a policy rule of the form

r _t = ¯ r ^∗ + γ _π (π _t − ¯ π) + γ _y Y ˆ

• Keep in mind that the Central bank chooses this nominal interest rate by manipulating the nominal interest rate. When the Fed can move the nominal interest rate freely to achieve any real interest rate it wants, fore modeling purposes it makes more sense to describe this behavior in terms of the real interest rate since that is what affects the IS curve in our model

• Notice that as inflation and the output gap falls, the nominal interest rate suggested by this policy rule also falls. At some point when inflation and the output gap are both low, the nominal interest rate will hit the lower bound of zero.

• We can illustrate this with the following two diagrams. The first figure shows how the output

gap and the inflation rate have evolved in the United States over the past two decades. As

you notice, both values fell sharply during the most recent recession.

• The second figure uses values from the Taylor Rule (γ _π = γ y = 0.5 and ¯ π = ¯ r ^∗ = 2%) to illustrate what that Rule would have required nominal interest rates in the United States to be during this period. When you compare to the actual Federal Funds rate you can clearly see that the zero lower bound was a significant problem during this downturn and recovery.

II. IMPLICATIONS OF THE ZLB FOR THE AD/IA MODEL

The ZLB and the MP Curve

• In our MP curve we specified that the central bank chooses the real interest rate to satisfy a policy rule of the form

r t = ¯ r ^∗ + γ π (π t − ¯ π) + γ y Y ˆ

• Since r = i − π, we can describe the central bank’s behavior using the following policy rule for the nominal interest rate of i _t − π _t = ¯ r ^∗ + γ _π (π _t − ¯ π) + γ _y Y , which simplifies to ˆ

i t = ¯ r ^∗ + (1 + γ π )π t − γ _π π + γ ¯ y Y ˆ

• But the Fed can’t lower nominal interest rates once the nominal interest rate reaches zero.

So in fact the setting of the nominal interest rate is given by i t = max(0, π t + ¯ r ^∗ + γ π (π t − ¯ π) + γ y Y ) ˆ

• When the nominal interest rate is constrained at zero, the real interest rate becomes equal to r _t = −π _t , so the MP curve is given by the equation

r _t = max(−π _t , ¯ r ^∗ + γ _π (π _t − ¯ π) + γ _y Y ) ˆ

• A graphical description of this relationship is given below.

r

Y ˆ

M P = M ax(r ^A , r ^B )

r _t ^A = −π _t

r ^B _t = ¯ r ^∗ + γ π (π t − ¯ π) + γ y Y ˆ

The ZLB and the AD Curve

• Next we look at how the concept of the ZLB affects the AD curve. If you go back and look at your notes, you will find that we traced out the AD curve by looking at how changes in inflation affected the real interest rate, which in turn affected the output gap.

• When we are not at the ZLB, the Fed can choose the nominal rate appropriate for the economic conditions prevailing in the economy. In other words, the policymaker can set the real interest rate the same way we have always been doing, r = ¯ r ^∗ + γ _π (π − ¯ π ^∗ ) + γ _y Y . So ˆ when inflation rises, the Fed will raise the real interest, which in turn lowers the output gap.

When inflation falls, the Fed will lower the real interest rate, which raises the output gap.

This gives us the traditional downward sloping AD curve.

π ↑ ⇒ r ↑ ⇒ ˆ Y ↓

π ↓ ⇒ r ↓ ⇒ ˆ Y ↑

• Things become very different when the ZLB binds, however. Once we hit the ZLB, the central bank must choose a nominal interest rate i = 0. That means the real interest rate will simply be r = −π, i.e. the real interest rate is no longer in the central bank’s control.

• This has important implications for the AD curve’s shape. Think about how the same exercise as before. When inflation falls, since r = −π, the real interest rate INCREASES! When inflation rises, the real interest rate falls.

π ↑ ⇒ r ↓ ⇒ ˆ Y ↑ π ↓ ⇒ r ↑ ⇒ ˆ Y ↓

• This means that once the ZLB binds, the AD curve is upward sloping. Overall, the AD curve is said to have a backward bent to it.

π

Y ˆ AD

III. THE ZLB LINE

• So if lower inflation rates and lower output gaps are what drives the nomina interest rate lower, then at some point one or both of these variables will fall to a point such that the nominal interest rate is zero (and the real interest rate is 0 − π. We can then identify the set of points where the ZLB kicks in, we call this set of points the ZLB line, by solving for

r t = r ¯ ^∗ + γ π (π t − ¯ π ^∗ ) + γ y Y ˆ 0 − π t = r ¯ ^∗ + γ π π t − γ _π π ¯ ^∗ + γ y Y ˆ (1 + γ π )π t = −¯ r ^∗ + γ π ¯ π ^∗ − γ _y Y ˆ

π _t =  γ π π ¯ ^∗ − ¯ r ^∗ 1 + γ _π



−

 γ y

1 + γ _π

 Y ˆ

• If we take a AD-IA diagram, we can show the ZLB line on there. The ZLB line has the

following properties

1. It is downward sloping - you can see that the slope is negative in the equation above.

You can also see this intuitively, if the output gap is high then inflation has to be very low for the Fed to hit the ZLB; conversely, if the inflation rate is high then the output gap has to be very low for the Fed to be affected by the ZLB.

2. The intercept (where ˆ Y = 0) is equal to 

γ

π ¯

−¯ r

1+γ



. This value can be but need not be negative. However, it is lower than the ¯ π ^∗ that is the intercept for the AD curve in the long run equilibrium we strive for.

3. The slope of this ZLB line is flatter than the slope of the AD line. That is not obvious from just the equation above since we did not formally use the mathematical equation for the AD curve but I am happy to show anyone who is curious.

π

Y ˆ

ZLB (Slope=-  _γ

y

1+γ

 ) 0

 γ

¯ π

−¯ r

1+γ



• Keep in mind that we always have a ZLB line in an AD-IA diagram. But if IA and AD intersect well above the ZLB line then its existence does not change the analysis we have been doing thus far. But the ZLB remains hidden beneath the surface, almost like a hidden reef or a hidden iceberg that only threatens a ship when the ocean becomes shallow.

IV. WHEN DOES THE ZLB LINE MATTER?

• Let’s begin from our default position where inflation is at the target level and the output gap

is zero. We can show the AD curve looking normal until the ZLB line is reached at which

point it bends backwards.

π

Y ˆ

ZLB: Slope=-



+γ

γ

 0

 γ

¯ π

−¯ r

1+γ

 AD

¯

π ^∗ IA

Then consider an adverse shock that shifts the AD curve in. The short run output gap falls to Y ˆ 1 and over time inflation falls moving us back to potential output. In this case even though inflation has fallen to zero, the economy still is able to return to long run equilibrium

π

Y ˆ

ZLB 0

 γ

¯ π

−¯ r

1+γ

 AD AD ⁰

¯

π ^∗ IA

π LR IA ⁰

• The danger of the zero lower bound shows up when the economy gets hit by a more severe

shock that moves AD to AD ⁰⁰ in the diagram below. In that case the zero lower bound is

reached at the current rate of inflation and the economy gets trapped in a recession where

inflation keeps falling, potentially moving into deflation, while making the economy worse

off rather than better off. This can be seen in the diagram below where as IA falls, the output gap becomes more negative which leads to a further fall in inflation till in the end the economy is trapped in a deflationary recession where the monetary policymaker is powerless to intervene, this is called a liquidity trap.

π

Y ˆ

ZLB

 0

γ

π ¯

−¯ r

1+γ

 AD ⁰ AD

¯

π ^∗ IA

π LR IA ⁰

• Notice that you do not need the shock to be that severe. Any negative shock that forces us

to hit the ZLB before we get to zero will leave the economy in a liquidity trap. Any AD shift

greater than the one shown below will suffice to put the economy in a liquidity trap (I use

AD ^crit as short-hand for the critical value of AD.

π

Y ˆ

ZLB 0

 γ

π ¯

−¯ r

1+γ

 AD ^crit AD

¯

π ^∗ IA

π LR IA ⁰

• In such a situation, conventional monetary policy cannot work so the policymaker has to resort to other means such as quantitative easing, for example, to get the economy moving back towards potential.

• In such a setting, because of the relative impotence of monetary policy, fiscal policymakers need to play a big role in getting the economy to move back towards the long-run equilibrium.

Keep in mind that they have to push the AD curve out by enough to avoid the ZLB or else

the expansionary fiscal policy may have been in vain