Presentation | An Economical Business-Cycle Model

AN ECONOMICAL BUSINESS-CYCLE MODEL

Pascal Michaillat, Emmanuel Saez

Oxford Economic Papers, 2022

Paper available at https://www.pascalmichaillat.org/7.html

LIMITATIONS OF THE NEW KEYNESIAN MODEL

1. lacks conceptual economy

– not taught to undergraduates– not used in related fields, outside of macroeconomics– not used by policymakers for day-to-day thinking (Krugman

2000, 2018)

2. does not not describe business cycles well

– does not feature unemployment– makes anomalous predictions about long-lasting ZLB

episodes (Michaillat, Saez 2021)

THIS PAPER’S BUSINESS-CYCLE MODEL

1. is more economical

– solved with an AD-AS diagram– effects of shocks derived by comparative statics– efficient unemployment & optimal policies described by

sufficient-statistic formulas– most complicated step: derivation of Euler equation

2. describes business cycles better

– features unemployment: fluctuating & generally inefficient– behaves well during long/permanent ZLB episodes

ASSUMPTIONS

SERVICE ECONOMY, WITHOUT FIRMS

SERVICE ECONOMY, WITHOUT FIRMS

MATCHING FUNCTION (MICHAILLAT, SAEZ 2015)

MATCHING FUNCTION (MICHAILLAT, SAEZ 2015)

MATCHING FUNCTION (MICHAILLAT, SAEZ 2015)

1990 2000 2010 0%

10%

20%

30%Idleness, non-manufacturingIdleness, manufacturingUnemployment

WEALTH IN UTILITY (MICHAILLAT, SAEZ 2021)

Peter CoyBloomberg Businessweek Writer

@petercoy

Peter Coy is the economics editor forBloomberg Businessweek and covers awide range of economic issues. Healso holds the position of senior writer.Coy joined the magazine in December1989 as telecommunications editor,then became technology editor inOctober 1992 and held that positionuntil joining the economics staff. Hecame to BusinessWeek from theAssociated Press in New York, wherehe had served as a business newswriter since 1985. Before that, Coyworked as a correspondent in the APRochester bureau. He began his careerat the AP in 1980 as an editor in theAlbany bureau. Prior to that, Coy was areporter for the Waterbury (Conn.)Republican. Coy holds a BA in historyfrom Cornell University.

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There’s a school of thought that you should spend down allyour assets in retirement and “bounce the check to theundertaker,” as Michael Bloomberg, founder and majorityowner of Bloomberg LP, our publisher, likes to say. But notmany Americans subscribe to that school of thought. Afascinating survey from the Employee Benefit Research Instituteexplores how people feel about spending in retirement. Itdoesn’t fit with finance theory. “There’s just something we’renot getting quite right in understanding how people navigate

retirement,” Lori Lucas, the president and chief executive officer of EBRI, saidMarch 24 in announcing the results.

As this first chart shows, only 14.1% of respondents think they’ll spenddown all their assets. If you add up the three left-most columns, 57% plan to

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Close to two-thirds say “saving as much as I can makes me feel happy and

fulfilled.”

By

Here’s Why So Many People Intend to

Die With Money in the Bank

Peter Coy

March 25, 2021, 8:36 AM PDT

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WEALTH IN UTILITY (MICHAILLAT, SAEZ 2021)

grow their assets in retirement, leave them untouched, or spend down only alittle. The survey by EBRI, a nonprofit research group, was conducted inSeptember and covered 2,000 Americans ages 62 to 75, 97% of whom wereretired. So U.S. undertakers don’t need to fear bounced checks.

The second chart zeroes in on the people who said they don’t plan tospend down their assets in retirement. They were asked why not, and multipleresponses were permitted. Three of the answers seem like different ways ofsaying the same thing: “saving for unforeseen costs,” “afraid of running out ofmoney,” and “once assets spent, cannot be recovered.”

The most intriguing answer in this second chart is “makes me feel better.”In standard finance and economic theory, saving for its own sake makes nosense because the only purpose of money is to pay for things, which couldinclude bequests. You feel better when you spend, not when you refrain fromspending. Clearly, though, a lot of retirees find satisfaction in the very act ofsaving. This third chart gets at that:

Close to two-thirds of respondents agree somewhat or strongly that “savingas much as I can makes me feel happy and fulfilled.” In an EBRI conference

WEALTH IN UTILITY (MICHAILLAT, SAEZ 2021)

grow their assets in retirement, leave them untouched, or spend down only alittle. The survey by EBRI, a nonprofit research group, was conducted inSeptember and covered 2,000 Americans ages 62 to 75, 97% of whom wereretired. So U.S. undertakers don’t need to fear bounced checks.

The second chart zeroes in on the people who said they don’t plan tospend down their assets in retirement. They were asked why not, and multipleresponses were permitted. Three of the answers seem like different ways ofsaying the same thing: “saving for unforeseen costs,” “afraid of running out ofmoney,” and “once assets spent, cannot be recovered.”

The most intriguing answer in this second chart is “makes me feel better.”In standard finance and economic theory, saving for its own sake makes nosense because the only purpose of money is to pay for things, which couldinclude bequests. You feel better when you spend, not when you refrain fromspending. Clearly, though, a lot of retirees find satisfaction in the very act ofsaving. This third chart gets at that:

Close to two-thirds of respondents agree somewhat or strongly that “savingas much as I can makes me feel happy and fulfilled.” In an EBRI conference

SOLUTION

MATCHING FUNCTION BEVERIDGE CURVE

Unemployment rate

Vaca

ncy

rate Beveridge curve:

inflow into unemployment = outflow from unemployment

0

UNEMPLOYMENT: ALWAYS ON BEVERIDGE CURVE

1951 1970 1985 2000 2019 0%

3%

6%

9%

12%U

nem

ploy

men

t rat

e

Actual

Beveridgean

BEVERIDGE CURVE AGGREGATE SUPPLY

Output

Tightness = vacancy / unemployment

Capacity

BEVERIDGE CURVE AGGREGATE SUPPLY

Output

Tigh

tnes

sAS

Capacity

WEALTH IN UTILITY EULER EQUATIONEuler

EULER EQUATION AGGREGATE DEMAND

Output

ADTi

ghtn

ess

AS

Capacity

PRICE NORM: FIXED INFLATION• any model with a matching function needs a price mechanism

• we assume that prices grow at a fixed rate of inflation

– interpretation: fixed inflation is a social norm (Hall 2005)

• fixed inflation is realistic:

– inflation does not respond to unemployment (Stock,Watson 2010, 2019)

– inflation does not respond to monetary policy (Christiano,Eichenbaum, Evans 1999)

• fixed inflation does not create bilaterally inefficiencies:

– buyers & sellers are happy to transact at the given price

SOLUTION OF THE MODEL

Output

ADTi

ghtn

ess

AS

Capacity

SOLUTION OF THE MODEL

Output

ADTi

ghtn

ess

AS

Unemployment

Capacity

KEYNESIAN VS. FRICTIONAL UNEMPLOYMENT

Output

ADTi

ghtn

ess

AS

Capacity

Keynesian

KEYNESIAN VS. FRICTIONAL UNEMPLOYMENT

Output

ADTi

ghtn

ess

AS

Keynesian

Capacity

Frictional

INEFFICIENCY

EFFICIENT ALLOCATION (MICHAILLAT, SAEZ 2021)

Unemployment rate

Vaca

ncy

rate Beveridge curve

0

EFFICIENT ALLOCATION (MICHAILLAT, SAEZ 2021)

Unemployment rate

Vaca

ncy

rate Beveridge curve

0

Isowelfare curve: 1 – u – recruiting cost × v = const.

EFFICIENT ALLOCATION (MICHAILLAT, SAEZ 2021)

Unemployment rate

Vaca

ncy

rate Beveridge curve

0

Efficiency

Isowelfare curve

EFFICIENT ALLOCATION (MICHAILLAT, SAEZ 2021)Beveridge curve

0

Efficiency

Efficient tightness

Unemployment rate

Vaca

ncy

rate

Isowelfare curve

INEFFICIENT ALLOCATIONSBeveridge curve

0

Inefficiently low tightness

Unemployment rate

Vaca

ncy

rate

Isowelfare curve

INEFFICIENT ALLOCATIONS

0

Beveridge curve

Inefficiently high tightness

Unemployment rate

Vaca

ncy

rate

Isowelfare curve

EFFICIENT TIGHTNESS

Output

Tigh

tnes

sAS

Capacity

BUSINESS CYCLES

NEGATIVE DEMAND SHOCK

AS

AD

Output

Tigh

tnes

s

Capacity

NEGATIVE DEMAND SHOCK

AS

AD

Output

Tigh

tnes

s

Capacity

NEGATIVE SUPPLY SHOCK

AS

Output

Tigh

tnes

s AD

Capacity

NEGATIVE SUPPLY SHOCK

ASAD

Tigh

tnes

s

OutputCapacity

OKUN’S LAW⇒ DEMAND SHOCKS ARE PREVALENT1420 : MONEY, CREDIT AND BANKING

(a)

(b)

(c)

FIG. 1. United States: Okun’s Law, 1948–2013. (Annual data) (a) Levels: Natural Rates Based on HPF with λ = 100. (b)Levels: Natural Rates Based on HPF with λ = 1,000. (c) First Differences.

NOTE: HPF denotes Hodrick–Prescott filter. This figure reports change in unemployment rate and in log of real GDP inpercentage points, and output gap and unemployment gap in percent.

1420 : MONEY, CREDIT AND BANKING

(a)

(b)

(c)

FIG. 1. United States: Okun’s Law, 1948–2013. (Annual data) (a) Levels: Natural Rates Based on HPF with λ = 100. (b)Levels: Natural Rates Based on HPF with λ = 1,000. (c) First Differences.

NOTE: HPF denotes Hodrick–Prescott filter. This figure reports change in unemployment rate and in log of real GDP inpercentage points, and output gap and unemployment gap in percent.

Okun’s law in the United States, 1948–2013 [Ball, Leigh, Loungani 2017]

1420 : MONEY, CREDIT AND BANKING

(a)

(b)

(c)

FIG. 1. United States: Okun’s Law, 1948–2013. (Annual data) (a) Levels: Natural Rates Based on HPF with λ = 100. (b)Levels: Natural Rates Based on HPF with λ = 1,000. (c) First Differences.

NOTE: HPF denotes Hodrick–Prescott filter. This figure reports change in unemployment rate and in log of real GDP inpercentage points, and output gap and unemployment gap in percent.

OKUN’S LAW⇒ DEMAND SHOCKS ARE PREVALENT

1420 : MONEY, CREDIT AND BANKING

(a)

(b)

(c)

FIG. 1. United States: Okun’s Law, 1948–2013. (Annual data) (a) Levels: Natural Rates Based on HPF with λ = 100. (b)Levels: Natural Rates Based on HPF with λ = 1,000. (c) First Differences.

NOTE: HPF denotes Hodrick–Prescott filter. This figure reports change in unemployment rate and in log of real GDP inpercentage points, and output gap and unemployment gap in percent.

1420 : MONEY, CREDIT AND BANKING

(a)

(b)

(c)

FIG. 1. United States: Okun’s Law, 1948–2013. (Annual data) (a) Levels: Natural Rates Based on HPF with λ = 100. (b)Levels: Natural Rates Based on HPF with λ = 1,000. (c) First Differences.

NOTE: HPF denotes Hodrick–Prescott filter. This figure reports change in unemployment rate and in log of real GDP inpercentage points, and output gap and unemployment gap in percent.

Okun’s law in the United States, 1948–2013 [Ball, Leigh, Loungani 2017]

1420 : MONEY, CREDIT AND BANKING

(a)

(b)

(c)

FIG. 1. United States: Okun’s Law, 1948–2013. (Annual data) (a) Levels: Natural Rates Based on HPF with λ = 100. (b)Levels: Natural Rates Based on HPF with λ = 1,000. (c) First Differences.

NOTE: HPF denotes Hodrick–Prescott filter. This figure reports change in unemployment rate and in log of real GDP inpercentage points, and output gap and unemployment gap in percent.

MONETARY POLICY

REDUCTION IN INTEREST RATE

Output

Tigh

tnes

sAS

AD

Capacity

REDUCTION IN INTEREST RATE

Output

Tigh

tnes

sAS

AD

Capacity

ZERO LOWER BOUND

AD

AD @ ZLB

Output

Tigh

tnes

sAS

Capacity

ZERO LOWER BOUND

AD @ ZLB

Output

Tigh

tnes

sAS

Capacity

INCREASE IN WEALTH TAX

Output

Tigh

tnes

sAS

AD

Capacity

INCREASE IN WEALTH TAX

Output

Tigh

tnes

sAS

AD

Capacity

OPTIMAL MONETARY POLICY: BOOM

AD

Output

Tigh

tnes

sAS

Capacity

OPTIMAL MONETARY POLICY: BOOM

AD

Output

Tigh

tnes

sAS

Capacity

OPTIMAL MONETARY POLICY: SMALL SLUMP

AD

Output

Tigh

tnes

sAS

Capacity

OPTIMAL MONETARY POLICY: SMALL SLUMP

AD

Output

Tigh

tnes

sAS

AD @ ZLB

Capacity

OPTIMAL MONETARY POLICY: SMALL SLUMP

AD

Output

Tigh

tnes

sAS

AD @ ZLB

Capacity

OPTIMAL MONETARY POLICY: LARGE SLUMP

ADTigh

tnes

sAS

Output

AD @ ZLB

Capacity

OPTIMAL MONETARY POLICY: LARGE SLUMP

Tigh

tnes

sAS

Output

AD @ ZLB

Capacity

LARGE SLUMP: ROLE FOR WEALTH TAX

Tigh

tnes

sAS

Output

AD with wealth tax

Capacity

MONETARY MULTIPLIER: du/di = 0.5

study du/di method

Bernanke, Blinder (1992) 0.6 VARLeeper, Sims, Zha (1996) 0.1 VARChristiano, Eichenbaum, Evans (1996) 0.1 VARRomer, Romer (2003) 0.9 narrativeBernanke, Boivin, Eliasz (2005) 0.2 FAVARCoibion (2012) 0.5 narrative & VAR

UNEMPLOYMENT GAP: MICHAILLAT, SAEZ (2021)

1951 1970 1985 2000 2019 0%

3%

6%

9%

12%U

nem

ploy

men

t rat

e

Efficient

Actual

OPTIMAL MONETARY POLICY FORMULA

• linear expansion around suboptimal [i, u] assessed at optimal[i∗, u∗

]: u∗ ≈ u + (du/di) · (i∗ – i)

• sufficient-statistic formula:

i – i∗ ≈ u – u∗du/di

Fed should reduce interest rate by 2 percentage points for eachpercentage point of unemployment gap

in line with observed Fed behavior (Bernanke, Blinder 1992)

CONCLUSION

SUMMARY OF MODEL PROPERTIES

property NK model this model

AD relation Euler equation discounted Euler equationAS relation Phillips curve Beveridge curveinflation fluctuating fixedunemployment zero fluctuatingZLB world topsy-turvy normalZLB duration must be short can be permanent

SUMMARY OF MONETARY POLICY PROPERTIES

property NK model this model

response to inflation must be strong not required(Taylor principle) (interest-rate peg works)

policy target inflation rate unemployment rateoptimal rule not implementable implementable

w/ sufficient statisticsmultiplier du/di useless key statisticforward guidance very powerful less & less potent

at ZLB as ZLB lasts longerisomorphic policy – wealth tax

OTHER POLICIES

• public hiring or spending (Michaillat 2014; Michaillat, Saez 2019)

– multiplier is higher when unemployment is higher– optimal policy deviates from the Samuelson rule to reduce

the unemployment gap

• unemployment insurance (Landais, Michaillat, Saez 2018)

– optimal policy deviates from the Baily-Chetty rule to reducethe tightness gap