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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