AD-AS Analysis of Financial Crises, the ZLB, andUnconventional Policy

ECON 40364: Monetary Theory & Policy

Eric Sims

University of Notre Dame

Fall 2020

1 / 38

Readings

I Text:I Mishkin Ch. 15 pg. 355-361; Ch. 23 pg. 572-578

I Other:I Yu (2016), “Did Quantitative Easing Work?”I Bernanke (2016), “What Tools Does the Fed Have Left? Part

2: Targeting Longer-Term Interest Rates”

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Financial Crises

I Recall from earlier, that in a financial crisis credit marketsstop working well, which impedes the funneling of savings intoproductive investment

I The tell-tale sign of of a financial crisis is an increase ininterest rate spreads (decrease in bond prices) for risky andlong term debt

I There is a “flight to safety” – dumping risky and longmaturity bonds in favor of shorter maturity government debt

I Results in higher borrowing costs for consumers and firms

I Resulting in a collapse in spending

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Incorporating Financial Frictions into the AD-AS Model

I Recall earlier our investment demand function:

I = I − dr

I The (real) interest rate in our basic AD-AS model isshort-term and riskless

I In reality, the interest rates relevant for investment arelong-term and risky

I From earlier, we know that interest rates tend to be higherthe longer is the time to maturity (yield curves usually slopeup) and are higher the higher is the risk of the loan

I In normal times, moving short term riskless interest ratesmoves other interest rates in the same direction, so thinkingabout there being one interest rate in the economy isn’t a badabstraction

4 / 38

Financial Frictions

I A simple way to incorporate the risk and term structure ofinterest rates into our model is to assume that the interestrate relevant for investment differs from the short termriskless interest rate:

I = I − dri

ri = r + f

I Here f is an exogenous variable which we can think about asa credit spread (either a term premium or a risk premium)

I If f is more or less constant, abstracting from it isn’t a bigdeal

I But during financial crises, we see spreads rising

I A worsening of financial frictions can be thought of as anincrease in f

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myf.red/g/dU3z

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

fred.stlouisfed.orgSource:FederalReserveBankofSt.Louis

Moody'sSeasonedAaaCorporateBondYieldRelativetoYieldon10-YearTreasuryConstantMaturity©

Percent

6 / 38

myf.red/g/dTre

1

2

3

4

5

6

7

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

fred.stlouisfed.orgSource:FederalReserveBankofSt.Louis

Moody'sSeasonedBaaCorporateBondYieldRelativetoYieldon10-YearTreasuryConstantMaturity©

Percent

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-1.00

0.00

1.00

2.00

3.00

4.00

5.00

30 yr - 3 month spread

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Financial Crisis

I Easiest way to think about a financial crisis is as a bigincrease in f , which we clearly see either in term or riskpremia during the Great Recession

I IS curve is now:

Y =1

1 −mpcA− d + x

1 −mpcr

I Where:A = C −mpcT + I − df + G + NX

I Increase in f : IS curve shifts in, causing AD curve to shift in

9 / 38

𝜋𝜋 𝜋𝜋

𝜋𝜋

𝜋𝜋

𝑟𝑟 𝑟𝑟

𝑌𝑌

𝑌𝑌

𝜋𝜋 = 𝜋𝜋

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

��𝑟

𝐼𝐼𝐼𝐼

𝜋𝜋0

𝜋𝜋0

𝑟𝑟0

𝑌𝑌0

𝐴𝐴𝐴𝐴

𝐼𝐼𝐼𝐼′

𝑌𝑌1

𝐴𝐴𝐴𝐴′

↑ 𝑓𝑓

10 / 38

𝜋𝜋 𝜋𝜋

𝜋𝜋

𝜋𝜋

𝑟𝑟 𝑟𝑟

𝑌𝑌

𝑌𝑌

𝜋𝜋 = 𝜋𝜋

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

��𝑟

𝐼𝐼𝐼𝐼

𝜋𝜋0

𝜋𝜋0

𝑟𝑟0

𝑌𝑌0

𝐴𝐴𝐴𝐴

𝐼𝐼𝐼𝐼′

𝑌𝑌0′

𝐴𝐴𝐴𝐴′

↑ 𝑓𝑓

𝐴𝐴𝐼𝐼

𝜋𝜋1

𝑌𝑌1

𝑟𝑟1

𝜋𝜋1

(a) to (b): direct effect (b) to (c): indirect effect due to lower 𝜋𝜋

(a) (b)

(c)

(a)

(c)

(a)

(c)

(a) (b)

(c)

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Compared to the Data

I This is more or less what we see in the US data for 2007 intothe first half of 2008

I Output contracts, although not enormously, in part becausethe Fed aggressively lowered short term interest rates

I Model predicts inflation should fall

I We don’t really see this until the end of 2008 and into 2009

I Fairly easy to explain: big oil price increase from 2006-2008which would have shifted the AS in, keeping inflation fromfalling too much

I In addition, there was significant monetary easing (can thinkabout as a reduction in r), which would shift the AD curveback out to prevent inflation from falling much

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The ZLB

I The Great Recession wasn’t “great” through the middle of2008

I Confluence of events in fall of 2008 really made things worse:worsening financial conditions (e.g. failure of Lehman) plusthe zero lower bound on interest rates

I Nominal interest rates cannot go below zero – that wouldimply lending money and getting less back in return

I The Fed Funds Rate formally hit ZLB in December of 2008,and didn’t move away from zero until December of 2015

I What are implications of the ZLB for the AD-AS model?

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The Zero Lower Bound

I The zero lower bound (ZLB) requires that the nominalinterest rate be non-negative

I We ignored this in our earlier analysis. In terms of thenominal rate, the MP rule can be written:

i = r + (λ + 1)π

I i ≥ 0 requires that inflation satisfy:

π ≥ − r

λ + 1

I For π less than this, the Fed would like a negative nominalinterest rate. But the best it can do is i = 0, which meansr = −π. MP rule is:

r =

{r + λπ if π ≥ − r

λ+1

−π otherwise

14 / 38

MP Curve Taking the ZLB into Account

𝜋𝜋

𝑟𝑟

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

𝑟𝑟 = −𝜋𝜋

15 / 38

The AD Curve with the ZLB

I Away from the ZLB (i.e. π sufficiently high), the AD curve isthe same as above

I But in the ZLB region, the AD curve becomes upward-sloping

I Why? In the ZLB region, the real interest rate is decreasing(rather than increasing) in the inflation rate

I Higher inflation means a lower real interest rate, which meanshigher output, not lower

I In this way, being at the ZLB is similar to the Taylor principlenot being satisfied

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𝜋𝜋 𝜋𝜋

𝜋𝜋

𝜋𝜋

𝑟𝑟 𝑟𝑟

𝑌𝑌

𝑌𝑌

𝜋𝜋 = 𝜋𝜋

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

𝐼𝐼𝐼𝐼

𝑟𝑟 = −𝜋𝜋

−��𝑟

𝜆𝜆 + 1

𝜋𝜋0

𝜋𝜋1

𝜋𝜋2

𝑟𝑟0

𝑟𝑟1

𝑟𝑟2

𝑌𝑌0 𝑌𝑌1 𝑌𝑌2

𝐴𝐴𝐴𝐴

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Why is the ZLB Costly

I The ZLB is problematic chiefly for two reasons:

1. Economy much more susceptible to negative IS shocks. TheFed can’t lower interest rates, so negative IS shocks havebigger effect than in normal times

2. Self-correcting mechanism doesn’t workI Suppose economy finds itself at ZLB with negative output gapI Rightward shift of AS (assuming AD is steeper than AS)

results in inflation falling but output fallingI The output gap widensI Mechanism: falling inflation plus fixed nominal right means

rising real rate

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Failure of the Self-Correcting Mechanism

𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿

𝐿𝐿𝐿𝐿

𝐿𝐿𝐿𝐿′

𝜋𝜋

𝑌𝑌 𝑌𝑌𝑃𝑃 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡+1

𝜋𝜋𝑡𝑡

𝜋𝜋𝑡𝑡−1

𝜋𝜋𝑡𝑡+1

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Deflationary Spiral

I Suppose that the ZLB binds when Y < Y P (e.g. because of anegative IS shock that lowers inflation to the point wherenominal rate hits zero)

I Failure of self-correcting mechanism: not only will economynot transition back to potential, things will get worse

I Normal dynamics: AS curve will shift down, which causesinflation to fall

I But falling inflation causes the real interest rate to rise, whichcauses output to fall, which generates even more deflation(from the AS curve)

I Sometimes called a “deflationary spiral”

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Deflationary Spiral: Quantitative

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00 1 2 3 4 5 6 7

Inflation

0

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0 1 2 3 4 5 6 7

Output

0

2

4

6

8

10

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14

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0 1 2 3 4 5 6 7

r

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4 5 6 7

i

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Application: Japanese Experience

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3 Month T-Bill Rate

-2.0

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0.0

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Inflation

155.0

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Price Level

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-0.45

-0.4

-0.35

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-0.25

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-0.15

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-0.05

0

Detrended Real GDP

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The Height of the Financial Crisis

I From late summer of 2007 until early fall of 2008, the Fed hadlowered the Fed Funds Rate from 5 percent to nearly zero

I Then the worst of the financial crisis hit:

1. Failure of Lehman Brothers on Sept. 152. Failure and ensuing engineered rescue of AIG on Sept. 16

I AIG had written over $400 billion in credit default swaps onmortgage-related securities, which are essentially insurancecontracts (hedges) on declining valuue of those securities.With mortgage markets collapsing and Lehman failing, AIG’sshort term financing dried up

3. Run on the Reserve Primary Fund “breaking the buck”I Money market mutual fund offers checking-like services to

depositors and invests in short term commercial paper andgovernment securities. It seeks to always maintain a net assetvalue of $1 (total equity divided by shares) by payingdividends daily. Value below $1 is “breaking the buck”

4. Political uncertainty from Troubled Asset Relief Program(TARP)

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The Height of the Financial Crisis and the AD-AS Model

I Can think about the height of the financial crisis in terms ofthe AD-AS model as a further increase in f

I This widening of credit spreads in the last quarter of 2008 andinto 2009 is exactly what we observe in the data

I Think about the economy as being effectively at the ZLBduring the period in which this increase in f hits

I This results in output declining much more than it would havehad the ZLB not been binding and the Fed had been able tolower interest rates

24 / 38

The ZLB and the US Financial Crisis

𝜋𝜋 𝜋𝜋

𝜋𝜋

𝜋𝜋

𝑟𝑟 𝑟𝑟

𝑌𝑌

𝑌𝑌

𝜋𝜋 = 𝜋𝜋

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

𝐼𝐼𝐼𝐼

𝑟𝑟 = −𝜋𝜋

−��𝑟

𝜆𝜆 + 1

𝜋𝜋08

𝑟𝑟08

𝑌𝑌08

𝐴𝐴𝐴𝐴 𝐴𝐴𝐼𝐼

𝐴𝐴𝐴𝐴′

𝐼𝐼𝐼𝐼′

𝜋𝜋09

𝑟𝑟09

↑ 𝑓𝑓

(a) to (b): direct effect (b) to (c): indirect effect due to lower 𝜋𝜋

(a) (b)

(a) (b)

(c)

(c)

(a)

(c)

(a)

(c)

𝑌𝑌08′ 𝑌𝑌09

25 / 38

US Economy in the Financial Crisis

-30

-20

-10

0

10

20

30

84

88

92

96

100

104

108

III IV I II III IV I II III IV I II III IV I

2007 2008 2009 2010 2011

Fed FundsCPI InflationReal RateIndustrial Production

IP

Ra

tes

26 / 38

Unconventional Monetary Policy

I We’ve already mentioned several of the Fed’s unconventionalpolicies

I The ones we’ve mentioned have dealt with the Fed’s role aslender of last resort: TAF, TSLF, AIG, Bear Stearns, TALF,etc

I We can think about all of these as the Fed trying to reduce fin the model – i.e. to arrest the increase in credit spreads

27 / 38

Unconventional Policy and Desired Effects in AD-AS Model

𝜋𝜋 𝜋𝜋

𝜋𝜋

𝜋𝜋

𝑟𝑟 𝑟𝑟

𝑌𝑌

𝑌𝑌

𝜋𝜋 = 𝜋𝜋

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

𝐼𝐼𝐼𝐼′

𝑟𝑟 = −𝜋𝜋

−��𝑟

𝜆𝜆 + 1

𝜋𝜋09

𝑟𝑟09

𝑌𝑌09

𝐴𝐴𝐴𝐴′ 𝐴𝐴𝐼𝐼

𝐴𝐴𝐴𝐴

𝐼𝐼𝐼𝐼

𝜋𝜋08−09

𝑟𝑟08−09

Unconventional policy aimed at ↓ 𝑓𝑓

(a) to (b): direct effect (b) to (c): indirect effect due to higher 𝜋𝜋

(c)

(b)

(c)

(b) (a)

(a)

(c)

(a)

(c)

(a)

𝑌𝑌08−09′ 𝑌𝑌08−09

28 / 38

Other Forms of Unconventional PolicyI In addition to the lender of last resort type of actions, the Fed

engaged in two other forms of unconventional policy:1. Quantitative Easing2. Forward Guidance

I Both types of policies are unconventional in the sense of trying toimpact longer term and/or riskier interest rates

I Easy way to think about this in terms of term structure:I Conventional policy aims to indirectly affect the “long end” of

the yield curve (longer maturity rates) by adjusting the “shortend” (adjusting short term interest rates)

I Unconventional policy rather aims to directly impact “longend” of the yield curve

I Quantitative easing by buying longer maturity bonds hoping tolower yields (relies on some failure of expectations hypothesis)

I Forward guidance by promising to keep short term rates lowfor a long time (relies on expectations hypothesis)

I QE and forward guidance were generally tried after the immediate

lender of last resort activities and should be thought of as

conceptually distinct. These were trying to provide stimulus in spite

of the ZLB, not trying to provide liquidity to stem a run29 / 38

Forward Guidance

I Forward guidance involves either the explicit (Odyssean) orimplicit (Delphic) signaling from a central bank about itsintentions about the path of future short term interest rates

I August 9, 2011 FOMC statement: “Economic conditions . . .are likely to warrant exceptionally low levels of the federalfunds rate at least through mid-2013.”

I This is essentially an expectations hypothesis channel: if thecurrent long term interest rate is an average of expectedfuture short term rates, promising low future short term ratesought to lower current long term interest rates

I Some evidence suggests that forward guidance works to affectyields on longer maturity and riskier debt

30 / 38

Source: Campbell, Jeffrey, Charles Evans, Jonas Fisher, and Alejandro Justiniano. 2016. “Macroeconomic Effectsof Federal Reserve Forward Guidance” Brookings Papers on Economic Activity, 1-63.

31 / 38

Quantitative Easing

I QE (or LSAPs) involves purchasing longer maturity debt topush down yields on the longer end of the yield curve

I Under the expectations hypothesis, this shouldn’t work: youcannot impact longer term yields without affecting path ofshort term yields

I Ben Bernanke: “The problem with QE is it works in practice,but it doesn’t work in theory.”

I What about the liquidity premium theory? Can QE affect theterm premium? Not obvious – term premium depends oncovariances

I Why might QE work?

1. Markets may be segmented2. It may make forward guidance more credible3. Portfolio effect: by removing riskier long term debt, reduced

liquidity premium

32 / 38

Source: Yu, Edison. 2016. “Did Quantitative Easing Work?” Federal Reserve Bank of Philadelphia EconomicInsights, 5-13.

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Source: Krishnamurthy, Arvind and Annette Vissing-Jorgensen. 2013. “The Ins and Outs of LSAPs.” EconomicPolicy Symposium - Jackson Hole, 57-111. 34 / 38

Mechanics of Unconventional Monetary Policy

I Unconventional monetary policy aims to lower the creditspread, f , through different means

I If it can do this, it can also lower short term real interest rates,even though it can’t lower short term nominal interest rates

I What is the mechanism? Lowering the credit spreadstimulates demand, which creates inflation

I In normal times, Fed would respond to more inflation byraising short term real rates

I But at ZLB, more inflation lowers real rate, which providesfurther stimulus

I At the ZLB, the Fed wants to create inflation. Makes sense –create inflation to avoid the deflationary spiral

I Alternative channel of unconventional policy: raise expectedinflation, which could shift AS up. Normal times this wouldbe bad, but at ZLB could be expansionary

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Expected Inflation Channel of Unconventional Policy

𝜋𝜋 𝜋𝜋

𝜋𝜋

𝜋𝜋

𝑟𝑟 𝑟𝑟

𝑌𝑌

𝑌𝑌

𝜋𝜋 = 𝜋𝜋

𝑟𝑟 = ��𝑟 + 𝜆𝜆𝜋𝜋

𝑟𝑟 = −𝜋𝜋

−��𝑟

𝜆𝜆 + 1

𝜋𝜋09

𝑟𝑟09

𝑌𝑌09

𝐴𝐴𝐴𝐴

𝐴𝐴𝐴𝐴

𝐼𝐼𝐴𝐴

𝜋𝜋08−09

𝑟𝑟08−09

(a) to (b): direct effect (b) to (c): indirect effect due to higher 𝜋𝜋

(b)

(a)

(a)

(c)

(a)

(c)

(a)

𝑌𝑌08−09

𝐴𝐴𝐴𝐴′

(c)

(c)

Unconventional policy aimed at stimulating expected inflation

36 / 38

Is Monetary Policy and the Macro Economy So Differentat the ZLB?

I Conventional wisdom is that the economy behaves verydifferently when monetary policy is constrained by the ZLB:

I Self-correcting mechanism fails: deflationary spiralI Positive supply shocks can lower outputI Non-monetary demand shocks (e.g. fiscal shocks) can have

much larger effects than in normal times

I In a series of papers, Cynthia Wu and co-authors (Wu andXia, JMCB 2016, Wu and Zhang working paper 2016) haveargued that monetary policy and the economy are not sodifferent at the ZLB

I Fed just uses unconventional tools to move relevant rates in(more or less) the same way it did pre-ZLB

I Construct “shadow rate”: the FFR the Fed’s unconventionalpolicies would imply absent a ZLB constraint. Looks similarto pre-ZLB behavior

37 / 38

The Shadow Rate and the FFR

Source: Wu and Zhang, (2016): “A Shadow Rate New Keynesian Model” (working paper)

38 / 38