Macro Uncertainty and Unemployment Risk

Macro Uncertainty and Unemployment Risk

Joonseok Oh Anna Rogantini Picco

Freie Universität Berlin Sveriges Riksbank

CBMMW October 2020

The views in these slides are solely those of the authors and should not be interpreted as reflecting the views of the Sveriges Riksbank

Motivation

Question: ‘How does uncertainty affect the macroeconomy?’

+ Empirical evidence: Identified macro uncertainty shock reduces

I Output, Consumption, Investment, Employment, Inflation

Bloom (2009), Fernandez-Villaverde et al. (2015), Leduc & Liu (2016), Basu & Bundick (2017), Oh (2020)

+ Existing models: Unable to match empirical evidence

I RANK: Response of macro variables muted

Born & Pfeifer (2014), de Groot et al. (2018)

I Inflation increases

Born & Pfeifer (2014), Fernandez-Villaverde et al. (2015), Mumtaz & Theodoridis (2015)

Literature

Our Paper

Households’ heterogeneity key for uncertainty propagation

+ VAR evidenceusing both aggregate and household-level data:

I Macro uncertainty shock acts like aggregate demand shock

I Households in bottom 60% of income distrib. most responsive to uncertainty

+ HANK model with SaM and Calvo:

I Unemployment risk reinforces precautionary savings of uninsured HHs

I Uncertainty generates drop in prices & amplifies responses to match data

Empirical Evidence

VAR Evidence

I Data: US quarterly, 1982Q1-2015Q3

I Macro uncertaintyJurado et al. (2015)

Common variation in macro indicators’ unforecastable factors

I Macro data: National Income and Product Account

I Household-level data: Consumer Expenditure Surveys ^More

I Identification: Cholesky ordering

I Macro uncertainty ordered first:

[Macro uncertainty, GDP, Job finding rate, Separation rate, Unemployment rate, Consumption, Inflation, Policy rate]

I Constant and two lags

VAR Evidence: Macro Data

0 4 8 12 16 20

Quarter -1

0 1 2 3 4

Percent

Macro Uncertainty

0 4 8 12 16 20

Quarter -0.4

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

Percent

GDP

0 4 8 12 16 20

Quarter -1

-0.8 -0.6 -0.4 -0.2 0 0.2

Percentage Point

Job Finding Rate

0 4 8 12 16 20

Quarter -0.01

0 0.01 0.02 0.03 0.04

Percentage Point

Separation Rate

0 4 8 12 16 20

Quarter -0.05

0 0.05 0.1 0.15 0.2 0.25 0.3

Percentage Point

Unemployment Rate

0 4 8 12 16 20

Quarter -0.25

-0.2 -0.15 -0.1 -0.05 0

Percent

Consumption

0 4 8 12 16 20

Quarter -0.8

-0.6 -0.4 -0.2 0 0.2 0.4

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.2

-0.15 -0.1 -0.05 0 0.05

Percentage Point

Policy Rate

VAR Evidence: Micro Data

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percent

Bottom 60% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percent

Top 40% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percentage Point

Bottom 60%/Top 40%

Model

Feedback Loop

AD ⇓

Y⇓

Unemployment risk ⇑ Savings of imp. insured HHs⇑

Uncertainty ⇑

job finding rate⇓, separation rate⇑ IMRS⇑

C^Imp⇓

AD⇓& AS⇓

HANK: IRFs to 1SD Technology Uncertainty Shock

0 4 8 12 16 20 Quarter -0.15

-0.1 -0.05 0

Percent

Output

HANK RANK

0 4 8 12 16 20 Quarter -0.12

-0.1 -0.08 -0.06 -0.04 -0.02 0

Percent

Consumption

0 4 8 12 16 20 Quarter 0

0.02 0.04 0.06 0.08 0.1

Percentage Point

Unemployment Rate

0 4 8 12 16 20 Quarter -0.6

-0.5 -0.4 -0.3 -0.2 -0.1 0

Percent

Vacancy

0 4 8 12 16 20 Quarter -0.3

-0.25 -0.2 -0.15 -0.1 -0.05 0

Percentage Point

Job Finding Rate

0 4 8 12 16 20 Quarter -0.2

-0.15 -0.1 -0.05 0

Percent

Real Wage

0 4 8 12 16 20 Quarter -0.1

-0.05 0 0.05 0.1

Percentage Point

Inflation

0 4 8 12 16 20 Quarter -0.15

-0.1 -0.05 0 0.05 0.1

Percentage Point

Policy Rate

Consumption Heterogeneity

0 4 8 12 16 20

Quarter -0.25

-0.2 -0.15 -0.1 -0.05 0 0.05

Percent

Imp. Insured HHs Perf. Insured HHs Aggregation

Conclusion

Households’ heterogeneity important to uncertainty propagation

1. Macro uncertainty⇑ →consumption, inflation, policy rate⇓

2. Most responsive HHs: Bottom 60% of income distrib.

3. HA + Calvo + SaM

I Uncertainty reduces AD and AS

I Uninsured unemployment risk reinforces prec. savings (AD)

I Responses in line with data

Calvo vs Rotem

Appendix

Consumer Expenditure Surveys

CEX: Rotating panel data

I Consumption: Non-durable

Food and beverages, tobacco, apparel and services, personal care, gasoline, public transportation, household operation, medical care, entertainment, reading material, and education

I Income: before tax

Wages, salaries, business and farm income, financial income, and transfers

I Real per capita: divide by number of family members, deflate by CPI-U series, and seasonally adjust by X-12-ARIMA

Back

Literature

I HANK

McKay and Reis (2016), Kaplan et al. (2018)

I HANK and SaM

Gronemann et al. (2016), McKay and Reis (2017), Ravn & Sterk (2017, 2018), Cho (2018), Challe et al. (2017), Challe (2019)

I Uncertainty

Bloom (2009), Born & Pfeifer (2014), Jurado et al. (2015), Mumtaz & Theodoridis (2015), Leduc & Liu (2016), Basu & Bundick (2017), Fasani & Rossi (2018), Bayer et al. (2019), Ludvigson et al. (2019), Oh (2019)

Back

Robustness: Macro Data

0 10 20

Quarter -1

-0.5 0 0.5

Ordered Last Percentage Point

Find. Rate

0 10 20

Quarter -0.02

0 0.02 0.04

Percentage Point

Sep. Rate

0 10 20

Quarter -0.1

0 0.1 0.2

Percentage Point

Un. Rate

0 10 20

Quarter -0.2

-0.1 0 0.1

Percentage Point

Cons.

0 10 20

Quarter -1

-0.5 0 0.5

Percentage Point

Infl.

0 10 20

Quarter -1

-0.5 0 0.5

No ZLB Percentage Point

Find. Rate

0 10 20

Quarter -0.05

0 0.05

Percentage Point

Sep. Rate

0 10 20

Quarter -0.2

0 0.2 0.4

Percentage Point

Un. Rate

0 10 20

Quarter -0.3

-0.2 -0.1 0

Percentage Point

Cons.

0 10 20

Quarter -1

-0.5 0 0.5

Percentage Point

Infl.

0 10 20

Quarter -2

-1 0 1

GDP Def. Percentage Point

Find. Rate

0 10 20

Quarter -0.05

0 0.05

Percentage Point

Sep. Rate

0 10 20

Quarter -0.2

0 0.2 0.4

Percentage Point

Un. Rate

0 10 20

Quarter -0.3

-0.2 -0.1 0

Percentage Point

Cons.

0 10 20

Quarter -0.2

0 0.2

Percentage Point

Infl.

0 10 20

Quarter -2

-1 0 1

1 Lag Percentage Point

Find. Rate

0 10 20

Quarter -0.02

0 0.02 0.04

Percentage Point

Sep. Rate

0 10 20

Quarter -0.2

0 0.2 0.4

Percentage Point

Un. Rate

0 10 20

Quarter -0.3

-0.2 -0.1 0

Percentage Point

Cons.

0 10 20

Quarter -0.5

0 0.5

Percentage Point

Infl.

Robustness: Micro Data

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Ordered Last Percent

Bottom 60% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percent

Top 40% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percentage Point

Bottom 60%/Top 40%

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

No ZLB Percent

Bottom 60% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percent

Top 40% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percentage Point

Bottom 60%/Top 40%

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

1 Lag Percent

Bottom 60% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percent

Top 40% Income

0 4 8 12 16 20

Quarter -0.5

-0.25 0 0.25 0.5

Percentage Point

Bottom 60%/Top 40%

HANK with SaM and Uncertainty

+ Unit mass of Households

I Share 1−Ωperfectly insured against unemployment risk

⇒Assets and C donotdepend on employment status

I ShareΩimperfectly insured against unemployment risk

⇒Subject to borrowing limit tighter than natural

⇒Assets and Cdodepend on employment status

Details

Imperfectly Insured Households

ASSUMPTION:Borrowing limit binding after 1 period unemp. (Challe et al. (2017))

I Three corresponding types of imperfectly insured households:

1. Employed

2. Unemployed for 1 period 3. Unemployed for > 1 period

I Three consumption levels

I Two asset levels

1. Assets for the employed impatient 2. Borrowing limit

With 3 types of imperfectly insured, no need to keep track of whole distribution

HANK with SaM and Uncertainty

+ Firms ^More

I Search and matching frictions

I Calvo pricing

+ Monetary authority

I Taylor rule

+ Uncertaintyin technology process

logz =ρ_zlogz₋₁+σ^zε^z

logσ^z= (1−ρ_σz) log ¯σ^z+ρ_σzlogσ₋₁^z +σ^σzε^σz

+ Third-order perturbation method

(Fernandez-Villaverde et al., 2011)

RANK: IRFs to 1SD Technology Uncertainty Shock

0 4 8 12 16 20 Quarter -0.04

-0.03 -0.02 -0.01 0

Percent

Output

RANK

0 4 8 12 16 20 Quarter -0.04

-0.03 -0.02 -0.01 0

Percent

Consumption

0 4 8 12 16 20 Quarter 0

0.005 0.01 0.015 0.02 0.025 0.03

Percentage Point

Unemployment Rate

0 4 8 12 16 20 Quarter -0.2

-0.15 -0.1 -0.05 0

Percent

Vacancy

0 4 8 12 16 20 Quarter -0.1

-0.08 -0.06 -0.04 -0.02 0

Percentage Point

Job Finding Rate

0 4 8 12 16 20 Quarter -0.05

-0.04 -0.03 -0.02 -0.01 0

Percent

Real Wage

0 4 8 12 16 20 Quarter 0

0.01 0.02 0.03 0.04 0.05 0.06

Percentage Point

Inflation

0 4 8 12 16 20 Quarter 0

0.01 0.02 0.03 0.04 0.05 0.06

Percentage Point

Policy Rate

Direct Effect of Increased Uncertainty (RANK)

I Households: Precautionary savings ^Example U⇑ → C⇓∵ Risk aversion

→ Nominal marginal cost⇓ →Price ↓ →Markup⇑∵ Sticky prices

⇒ Y⇓, P⇓ ∵AD⇓

I Firms: Precautionary pricing ^Example U⇑ → P⇑ →Markup⇑∵Risk aversion

⇒ Y⇓, P⇑ ∵AS⇓

I P⇑since AS⇓ > AD⇓

AS-AD

Indirect Effect: Uninsured Unemployment Risk (HANK)

I Uncertainty ⇑

1. Precautionary savings: AD⇓

2. Precautionary pricing: AS⇓

I Y⇓ →Vacancy⇓ → Job finding rate⇓ →Separation rate⇑

I Unemployment risk⇑ → Imperfectly insured HHs’ savings⇑

I C^I⇓ →AD⇓

IMRS AS-AD Back

Perfectly Insured Households

V^p(a^p,n^p,X) = max

a^p0,c^p

u(c^p) +β^pE

V^p a^p0,n^p0,X⁰ subject to:

c^p+a^p0 =w^pn^p+ (1+r)a^p+ Π

Perfect insurance⇒ a^p0 & c^p do not depend on employment status

Imperfectly Insured Households

ASSUMPTIONS:

1. Partial risk sharing

2. Borrowing limit tighter than natural

I Cross-sectional distribution µ(a,N)over:

I Assetsa∈R

I Length of unemployment spellN∈Z+

I Becomes with countable and finite support

I Can be summarized by:

I Assets: aⁱ(N)

I Associated number of HHs: nⁱ(N) ^aiandni

Imperfectly Insured Households

Vⁱ

aⁱ(N),nⁱ(N),X

=

max {^ai0(N),ci(N)}_N∈Z

+





 X

N≥0

nⁱ(N)u cⁱ(N)

+βⁱEµ,X

h Vⁱ

aⁱ⁰(N),nⁱ⁰(N),X⁰i







subject to:

I Borrowing constraint

aⁱ⁰(N)≥a

I Budget constraint if employed, N=0

aⁱ⁰(0) +cⁱ(0) = (1−τ)w + (1+r)A

I Budget constraint if unemployed for N≥1 periods aⁱ(N) +cⁱ(N) =b^u+ (1+r)a

State Vector

Tilde variables corresepond to beginning of labor transition stage.

X =

nµ(.),˜ a^p,aⁱ(0),R−1,∆−1,~n,z, σ^z o

Back

FOCs Impatient Households

I If N =0

A⁰= 1 nⁱ⁰(0)



 1−s⁰

aⁱ⁰(0) +f⁰X

N≥1

aⁱ⁰(N)nⁱ(N)





nⁱ⁰(0) = 1−s⁰

nⁱ(0) +f⁰ 1−nⁱ(0)

I If N ≥1

aⁱ(N) =aⁱ⁰(N−1) nⁱ⁰(1) =s⁰nⁱ(0) andnⁱ⁰(N) = 1−f⁰

nⁱ(N−1) ifN≥2

Back

Monetary Policy and Unemployment Insurance Scheme

I Taylor rule

1+R 1+ ¯R =

1+R−1

1+ ¯R

ρR 1+π 1+ ¯π

φπ y y−1

φy!1−ρR

I Balanced unemployment insurance scheme τwnⁱ=b^u

1−nⁱ τw^pn^p=b^{u p}(1−n^p)

Back

Firms

1. Final goods firms: Perfectly competitive ^Final

2. Intermediate goods firms: Face Calvo pricing Intermediate

3. Wholesale goods firms: Perfectly competitive ^Wholesale

I Use technologyy_m=znˇ

4. Labor intermediaries: Hire both types of households Labor inter I Job finding rate

f =m

u = µu^χv^1−χ u

I Period-to-period job loss rate

s=ρ(1−f)

I Wages set according to rule

Back

Final Goods Firms

I Solve

maxy y− Z 1

0

p_iy_idi

subject to

y = Z 1

0

y

ε−1 ε

i di _ε−1^ε

I Solution: final goods firms’ demand of intermediate good yi(pi) =p_i^−εy

Back

Intermediate Goods Firms I

I Linear technology with fixed cost: y_i =x_i−Φ

I Produce intermediate goods sold at pricep_m

I Earn profit: Ξ = (pi −pm)yi −pmΦ

I Value if reset prices:

V^R(X) = max

p_i

n Ξ +θE^X

h

M^P0V^N pi,X⁰i

+ (1−θ)E^X h

M^P0V^R X⁰io

I Set optimal price:

p^?= ε ε−1

p^A p^B

p^A=pmy+θEX

M^P0

1+π⁰ 1+ ¯π

ε

p^A0

p^B=y+θEX

"

M^P0 1+π⁰

1+ ¯π ε−1

p^B0

#

I

Back

Intermediate Goods Firms II

I Inflation law of motion:

π= θ(1+ ¯π) (1−(1−θ)p^?1−ε)^1−ε1

−1

I Price dispersion:

∆ = (1−θ)p^?−ε+θ

1+π 1+ ¯π

^ε

∆₋₁

I Value if do not reset prices:

V^N(p_i,−1,X) = Ξ +θEX

M^P0V^N(p_i,X⁰)

+ (1−θ)EX

M^P0V^R(X⁰)

I Index price

p_i = 1+ ¯π 1+πpi,−1

Back

Wholesale Firms

I Perfectly competitive, use linear technology: y_m =znˇ

I Solve:

max

n^d

{p_mznˇ−Qn}ˇ

I Q is real unit price of labor servicesn, given by FOC:

Q =p_mz

Back

Labor Intermediaries

I Beginning of period exogenous separation rate ρ

I Skill premium ψ for patient households

I Value of match with impatient and patient Jⁱ =Q−w+EX

(1−ρ⁰)Mⁱ⁰Jⁱ⁰ J^p=ψQ−ψw+EX[(1−ρ⁰)M^p0J^p0]

I Free entry condition where λis job filling rate λ ΩJⁱ+ (1−Ω)J^p

| {z }

value

= κ

|{z}

cost

I Wage rule

w =w₋₁^γw

¯ wn

¯ n

φw1−γw

Back

Uncertainty

logz =ρ_zlogz−1+σ^zε^z

logσ^z= (1−ρ_σ^z) log ¯σ^z+ρ_σ^z logσ₋₁^z +σ^σzε^σz

I Third-order perturbation method

(Fernandez-Villaverde et al., 2011)

MP andb^u Clearing

Market Clearing

I Labor market

Beginning of period n˜^p= ˜nⁱ =~n^p=~nⁱ=~n End of period n^p=nⁱ =n^p=nⁱ=n Ωnⁱ+ (1−Ω)ψn^p = (Ω + (1−Ω)ψ)n= ˇn

I Asset market

Ω (A+ (1−n)a) + (1−Ω)a^p=0

I Goods market

I Final

c+κv=y

I Intermediate

∆y =y_m−Φ

I Wholesale

Z 1 0

xidi =ym=znˇ

Back

Quarterly Calibration 1

Parameter Description Value Target/Source

Households

Ω Share of imperf. households 0.60 Challe et al. (2017)

a Borrowing limit 0 Challe et al. (2017)

σ Risk aversion 2.00 Standard

β^I Discount factor of imperf. households 0.917 21%consumption loss β^P Discount factor of pat. households 0.993 3%annual real interest rate

b^u Unemployment benefits 0.27 33%replacement rate

Firms

ε Elasticity of substitution btw goods 6.00 20%markup

Φ Production fixed cost 0.22 Zero steady-state profit

θ Price stickiness 0.75 4-quarter stickiness

Quarterly Calibration 2

Parameter Description Value Target/Source

Labor Market

µ Matching efficiency 0.72 71%job filling rate χ Matching function elasticity 0.50 Standard

ρ Job separation rate 0.23 73%job find. & 6.1%job loss rates

κ Vacancy posting cost 0.037 1%of output

ψ Skill premium 2.04 Bottom 60%cons. share (42%)

γw Wage stickiness 0.75 Challe et al. (2017)

φw Wage elasticity wrt employment 1.50 Challe et al. (2017) Monetary Authority

¯

π Steady-state inflation 1.005 2%annual inflation rate

ρR Interest rate inertia 0 Standard

φπ Taylor rule coefficient for inflation 1.50 Standard φy Taylor rule coefficient for output 0.20 Standard

Quarterly Calibration 3

Parameter Description Value Target/Source

Exogenous Processes

ρz Persistence of technology shock 0.95 Standard

¯

σ^z Volatility of technology shock 0.007 Standard

ρσ^z Persistence of uncertainty shock 0.85 Katayama & Kim (2018) σ^σz Volatility of uncertainty shock 0.37 Katayama & Kim (2018)

Back

Different Degrees of Heterogeneity

0 4 8 12 16 20 Quarter -0.15

-0.1 -0.05 0

Percent

Output

+ = 0.6 + = 0.5 + = 0.4 + = 0.3 + = 0.2 + = 0.1 + = 0.0

0 4 8 12 16 20 Quarter -0.12

-0.1 -0.08 -0.06 -0.04 -0.02 0

Percent

Consumption

0 4 8 12 16 20 Quarter 0

0.02 0.04 0.06 0.08 0.1

Percentage Point

Unemployment Rate

0 4 8 12 16 20 Quarter -0.6

-0.5 -0.4 -0.3 -0.2 -0.1 0

Percent

Vacancy

0 4 8 12 16 20 Quarter -0.3

-0.25 -0.2 -0.15 -0.1 -0.05 0

Percentage Point

Job Finding Rate

0 4 8 12 16 20 Quarter -0.2

-0.15 -0.1 -0.05 0

Percent

Real Wage

0 4 8 12 16 20 Quarter -0.1

-0.05 0 0.05 0.1

Percentage Point

Inflation

0 4 8 12 16 20 Quarter -0.15

-0.1 -0.05 0 0.05 0.1

Percentage Point

Policy Rate

Robustness Check 1

0 4 8 12 16 20

Quarter -0.5

-0.4 -0.3 -0.2 -0.1 0

Percent

Consumption

<=1.00

<=1.50

<=2.00

0 4 8 12 16 20

Quarter -0.4

-0.3 -0.2 -0.1 0 0.1 0.2

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.2

-0.15 -0.1 -0.05 0

Percent

Consumption

C Loss=11%

C Loss=21%

C Loss=31%

0 4 8 12 16 20

Quarter -0.15

-0.1 -0.05 0 0.05 0.1

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.2

-0.15 -0.1 -0.05 0

Percent

Consumption

C60/C=32%

C60/C=42%

C60/C=52%

0 4 8 12 16 20

Quarter -0.2

-0.15 -0.1 -0.05 0 0.05 0.1

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.25

-0.2 -0.15 -0.1 -0.05 0

Percent

Consumption

0 4 8 12 16 20

Quarter -0.2

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Percentage Point

Inflation

Robustness Check 2

0 4 8 12 16 20

Quarter -0.12

-0.1 -0.08 -0.06 -0.04 -0.02 0

Percent

Consumption

.w=0 ._w=0.35 .w=0.70

0 4 8 12 16 20

Quarter -0.1

-0.05 0 0.05 0.1 0.15

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.12

-0.1 -0.08 -0.06 -0.04 -0.02 0

Percent

Consumption

;R=0

;_R=0.35

;R=0.70

0 4 8 12 16 20

Quarter -0.1

-0.05 0 0.05 0.1

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.25

-0.2 -0.15 -0.1 -0.05 0

Percent

Consumption

?_:=1.3

?:=1.5

?:=2.0

0 4 8 12 16 20

Quarter -0.15

-0.1 -0.05 0 0.05 0.1 0.15

Percentage Point

Inflation

0 4 8 12 16 20

Quarter -0.14

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0

Percent

Consumption

?y=0

?_y=0.25

?y=0.50

0 4 8 12 16 20

Quarter -0.15

-0.1 -0.05 0 0.05 0.1

Percentage Point

Inflation

Calvo vs. Rotemberg

0 4 8 12 16 20 Quarter -0.15

-0.1 -0.05 0

Percent

Output

Calvo HANK Rotem HANK Calvo RANK Rotem RANK

0 4 8 12 16 20 Quarter -0.12

-0.1 -0.08 -0.06 -0.04 -0.02 0

Percent

Consumption

0 4 8 12 16 20 Quarter 0

0.02 0.04 0.06 0.08 0.1

Percentage Point

Unemployment Rate

0 4 8 12 16 20 Quarter -0.6

-0.5 -0.4 -0.3 -0.2 -0.1 0

Percent

Vacancy

0 4 8 12 16 20 Quarter -0.3

-0.25 -0.2 -0.15 -0.1 -0.05 0

Percentage Point

Job Finding Rate

0 4 8 12 16 20 Quarter -0.2

-0.15 -0.1 -0.05 0

Percent

Real Wage

0 4 8 12 16 20 Quarter -0.1

-0.05 0 0.05 0.1

Percentage Point

Inflation

0 4 8 12 16 20 Quarter -0.15

-0.1 -0.05 0 0.05 0.1

Percentage Point

Policy Rate

Precautionary Savings

I Risk averse households

β c⁰

c −γ

=IMRS⁰

I Jensen’s inequality(0<q<1) IMRScertainty =β(cc)^−γ

≤qβ cc^l−γ

+ (1−q)β cc^h−γ

=IMRSuncertainty

IMRS of Impatient Households

I N =0

I IMRS increasing in separation rate

Mⁱ(0) =βⁱ(1−s⁰)uⁱ_c⁰(0) +s⁰u_cⁱ⁰(1) uⁱ_c(0)

Back

Precautionary Savings

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Relative Consumption 0

0.5 1 1.5 2 2.5 3 3.5 4

Stochastic Discount Factor

Precautionary Pricing

I Certainty

MP = (1−ε)

P_certainty^? P

^1−ε +εmc

P_certainty^? P

^−ε! Y

I Uncertainty: EMP>MP ⇒ Risk averse

EMP=q (1−ε)

Puncertainty^?

P^l

^1−ε +εmc

Puncertainty^?

P^l

^−ε! Y

+ (1−q) (1−ε)

Puncertainty^?

P^h

^1−ε +εmc

Puncertainty^?

P^h

^−ε! Y

Precautionary Pricing

0.95 1 1.05

Reset Price -0.4

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

Marginal Profit

Certainty Uncertainty

AS-AD: Households

2 AD0

AD1 AS1

AS0

1 P

Y P0

P1

Y1 Y0

AS-AD: Firms

2 AD0

AD1 AS1

AS0

1 P

Y P0

P1

Y1 Y0 AS2

3

P2

Y2

AS-AD: HHs’ Heterogeneity

2 AD0

AD1 AS1

AS0

1 P

Y P0

P1

Y1 Y0 AS2

3

P2

Y2 P3 4

Y3 AD2