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Engineering a Paradox of Thrift Recession

Zhen Huo, and Jose-Vıctor Rıos-Rull

University of Minnesota, Federal Reserve Bank of Minneapolis, CAERP, NBER

The Ohio State University, October 9 2012

Preliminary

Huo & Rıos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 1 / 32

Can a recession be the result of impovireshment?

• In most equilibrium models impoverishment, or in general the desire tosave more, induces agents to work harder: an expansion.

• This project:

1 We build a quantitative model where a contraction in demand (say,because of a shock to financial intermediation or sheerimpoverishment) generates a recession. We describe what does ittake for such recession to occur.

2 In addition, in our model a reduction in consumption decreasesmeasured TFP even though the technology is unchanged. Thischannel greatly contributes to the recession. Solow residual

Solow∗ residual: 1990-2011. Data source: OECD MEI

Return

What are major detonants for crisis in small countries?

1 Productivity/endowment shocks. (Many papers, Backus, Kehoe, and Kydland

(1992) RBC, Conesa and Kehoe (2011) with governments facing debt crisis.)

2 Interest rate risk. (Neumayer and Perri (2005)).

3 Financial Shocks that affect firms Some are based on missallocation of

investments (Bernanke and Gertler (1989) and others)). Others require insufficient assets

within a country (Mendoza (2010)).

4 Financial Shocks that affect households and reduce their consumptionI Midrigan and Philippon (2011) explore the role that less liquidity has in shaping

recessions. Wage and labor rigidity generate recessions. Guerrieri and Lorenzoni

(2009), Macera (2012)

I Mian and Sufi (2012) report that in the current US recession, employment in

nontradables drops more where household balance sheet suffers more. Not so for

tradables.

Our paper

• We complement the view that it is household consumption that triggersa recession, but it is not liquidity difficulties and wage rigidity, (Midrigan and

Philippon (2011)), or the zero bound of the interest rate and fixed prices(Guerrieri and Lorenzoni (2009), Eggertsson and Krugman (2011)), although fixed pricesand wages surely aggravate recessions.

• We build a model where the desire to save triggers a recession becauseit is difficult to reallocate resources from nontradables to tradables or ingeneral from consumption to investment.

• The recession is amplified by the fact that consumption affectsproductivity.

• The recession displays the paradox of thrift.

Ingredients

1 Exporting more is feasible but hard. It takes time to reallocate theeconomy to export more. (Tradables and Nontradables).

Closed Economy version

2 Labor markets are not competitive. We pose Mortensen-Pissaridesdetermination of labor market so the static Euler equation of thehousehold does not operate directly, although it does to some extent. We also

explore the role of fixed wages.

These are the only really necessary ingredients. Our contribution is topose another channel that makes the outcome easier (i.e. smallershocks for the same outcome):

3 Reductions in Demand (i.e. consumption expenditures)induceproductivity decreases. An extension of Bai, Rıos-Rull, andStoresletten (2011).

The environment: Consumers within a period

Households value varieties of nontradables:

[∫ IN0 c

Under equal consumption of each variety cN IρN =

[∫ IN0 c

]ρHouseholds also like tradables that combine through a standard(Armington) aggregator with nontradables and dislike work andsearch for goods yielding

u[c(cN IρN , cT ), d , n

Households have to search for varieties, its number is a choice.

IN = d Ψd(Qg )

Ψd(Qg ) Probability (per search unit) of finding a variety.

The environment: Production

Two sectors that we call tradables, & nontradables, small openeconomy: fixed r . We include in tradables two items normally deemed to be

nontradables: Housing Construction and Structures

The tradable sector has a measure one of firms. There are adjustmentcosts to both capital and labor, and its output is used for exports,investment, and (part of) consumption. FT (k, n, l) may havedecreasing returns.

The nontradable sector consists of a measure one of firms each oneproducing a different variety. Each firm/variety has a measure one oflocations, each location has its own production function FN(k , n).

Locations may or may not be filled (get a customer). They produceonly for consumption.

Firms post prices before the location is filled.Huo & Rıos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 8 / 32

Search Goods markets for nontradables.

• There is a large number of varieties. Agents need to search to findvarieties.

• Random search. There is a CRS matching function Ψ(1,D). Markettightness is Qg = 1

• The probability that a shopper finds a firm-variety: Ψd(Qg ) = ΨD

• The probability that a firm finds a shopper is the measure of filledlocations or of consumers buying the good: Ψf (Qg ) = Ψ

1 = IN .

• Total sales of nontradables in units of the tradable good that is thenumeraire

p IN cN = Ψf (Qg ) FN(k, n) p

Frictional labor market

• Random search with market tightness: Qe = V1−N .

• Total vacancies: V = VN + VT and employment: N = NN + NT .

• Job finding probability Φe(Qe)

• Vacancy filling probability Φf (Qe)

• Exogenous job destruction at rate λ

• Wages (we explore various mechanisms)

Nash bargaining

Complete rigidity.

State Variables. Collapses to a simple Macro Model

Aggregate. S = θ,KN ,NN ,KT ,NT ,B.I ShocksI Capital in the nontradable sectorI Labor in the nontradable sectorI Capital in the tradable sector.I Labor in the tradable sector.I Net foreign asset position.

Individual b, n.I Liquid wealth (bonds against the rest of the world, b)I Fraction of the household working n.

• We use the (standard) trick that all local firms are in the hands of thelocal agents and do not trade them.

Consumers’ problem

V (S , b, n) = maxcN ,cT ,IN,d

u(cN , IρN , cT , d , n) + β EV (S ′, b′, n′)

subject to

p(S)INcN + cT + b′ = (1 + r)b + w(S)n + πN(S) + πT (S) BC

IN = d Ψd [Qg (S)] SC

n′ = (1− λ) n + Φe [Qe(S)] (1− n) EC

S ′ = G (S) RE

Properties of the Solution (plus representative agent)

• It yields

1 Demand functions cNi (pi , S), cT (p, S).

2 Search Intensity IN(S).

• Shocks to patience, β (a stand in for impoverishment) or directly to netforeign asset position B, induce directly

1 A reduction in consumption per variety, cN ,

2 A reduction of varieties IN ,

3 No immediate possibility of working harder.

• A recession.

Nontradable firms’ Choose prices pj and investments

ΩNj(S , k , n) = maxpj ,i ,v

Ψf [Qg (S)] C (pj ,S) pj

− w(S)n − i − vκ+ E

ΩNj(S ′, k ′, n′)

subject to:

FN(k , n) ≥ C (pj ,S) =

) ρ1−ρ

k ′ = (1− δ)k + i − εN

k− δ)2

n′ = (1− λ)n + Φf [Qe(S)]v

•Capital and labor are predetermined, firms adapt demand by adjusting pj .

Tradable Goods Production: DRS & adjustment costs

ΩT (S , k , n) = maxi ,v

FT (k, n)− w(S)n − i − vκ

− εT ,n

n− 1

ΩT (S ′, k ′, n′)

subject to:

k ′ = (1− δ)k + i − εT ,k

k− δ)2

n′ = (1− λ) n + Φf [Qe(S)] v

These two properties will make it difficult to adjust both fast and a lot.

Representative Nash bargaining for wages (may not suffice)

w(S) = maxw

[Vn(S , b, n)]ϕ[NN

NΩNn (S ,KN ,NN) +

NΩTn (S ,KT ,NT )

]1−ϕ

In steady state, we have:

w = ϕ

(Ψf (Qg )pFN

ρ+ Qeκ

)+ (1− χ)(FT

n + Qeκ)

]+ (1− ϕ)

• Alternatively we also explore rigid wages.

Strategy

• We calibrate this economy to look like a modern economy.

• We study recessions made up of 1% reductions in output generated by

1 A (relatively) persistent increase to the discount rate β.

2 A destruction of wealth (net foreign asset position.)

Note that the effects are the opposite to those in the standard growthmodel.

These shocks are a stand–in for whatever deteriorates the financialsystem. Possibly a combination of the two.

• We then explore the properties of the recession generated.

First Experiment: Persistent shock to discount factor

• Assume βt = βeθbt the shock to the discount factor follows an AR(1)

process:log θbt = ρb log θbt−1 + εt , εt ∼ N(0, σb)

• We then pose an initial value for ε0 to reduce output 1%. The value ofρb is set equals to 0.95.

• Advantage: That induces a desire to increase saving temporarily andlater to increase consumption. It makes it similar to a financial shock thatincreases the wealth to income target of the households.

• Disadvantage. If taken literally, it is silly, but we will not take itliterally. Financial Friction version

More details about the experiments

• Output in terms of the tradable goods is:

Y = p Ψf (Qg )FN(KN ,NN) + FT (KT ,NT )

• Real output, Y is in base year prices (Use steady state, p∗ instead ofcurrent p).

• Two wage protocols: Nash bargaining and complete rigidity

1 Standard Nash wage bargaining:

I A larger shock is needed.I Nontradable firms decrease employment and vacancies but tradable

firms increase employment and vacancies.

2 Completely rigid wage:

I Employment and vacancies drop more.I Tradable firms increase employment and vacancies only because the

vacancy filling rate is higher.

Functional form

• Preference

u(c , d , n) =1

1− σ(c − ξ d)1−σ − ςn

[ω(cNI

η−1η + (1− ω)c

η−1η

] ηη−1

• Production function

FN(k , n) = zNkθNn1−θN , FT (k, n) = zTk

θTk nθTn

• Matching technology

Me(U,V ) = νeUµV 1−µ, Mg (D,T ) = νgDαT 1−α

Functional form

• Capital adjustment cost in the nontradable goods sector

φN(i , k) =εN

k− δ)2

• Capital adjustment cost in the tradable goods sector

φT ,k(i , k) =εT ,k

k− δ)2

• Employment adjustment cost in the tradable goods sector

φT ,n(n′, n) =εT ,n

n− 1

Calibration: Exogenously determined parameters

• A period is half a quarter.Remark Parameter Value Target Value

Risk aversion σ 2.0 Risk aversion 2

Discount factor β 0.995 Real interest rate 4%

Price mark-up ρ 1.05 Literature on price mark-up 1.05

Goods matching prob νg 0.80 Matching prob 81%

Labor matching prob νe 0.675 Monthly job finding rate 45%

Labor matching elast µ 0.7 Matching elasticity 0.7

Job separation prob λ 0.05 Average duration of job 2.5 year

Elasticity of substitution η 0.83 Elasticity of substitution T/N 0.83

Bargaining power of worker ϕ 0.35 Middle of Shimer & HM 0.35

Calibration: Endogenously determined parameters

Remark Parameter Value Target Target value

Search disutility ξ 0.03 Goods market tightness 1

Working disutility ς 0.89 Consumption / output 80%

Production function zN 0.48 Output 1

Production function zT 0.53 Price of nontradable goods 1

Production function θN 0.33 Labor share in nontradable 60%

Production function θTn 0.64 Labor share in tradable 60%

Production function θTk 0.18 2θTk + θTn 1

Depreciation δ 0.008 Capital / output 2.5

Vacancy cost κ 0.55 Employment level 93%

Home bias ω 0.92 Tradable goods / output 30%

Calibration: Dynamic parameters

Remark Parameter Value Target

Capital adjustment εN 43.59 Decrease of iN =4YN

Capital adjustment εT ,k 14.68 Tradable goods sector expands 5%

Labor adjustment εT ,n 14.68 εT ,n = εT ,k

Goods matching elast α, η 0.42 Employment decreases 0.5%

Results: I. Shock to patience, households increase savings

• We look for shocks to β, that follows an AR(1) with .95 persistencethat induces an increased desire to save and that generates a 1% outputdrop in various economies:

1 Baseline economy:I wages determined via Nash bargaining and relatively flexible tradable

sector (tradable sector expands by 5%).

2 Baseline economy with high adjustment cost in tradable sector:Figures

I Wages determined via Nash bargaining and very rigid tradable sector.(tradable sector expands by 1%).

3 Baseline economy with fixed wage rate: Figures

I same dynamic parameters as the baseline economy but with fixed wagerate.

4 Baseline economy without goods market frictions: Figures

I same dynamic parameters as the baseline economy but withoutshopping.

Other features: Size of the Shocks

Percentage increase

Model economy β N Solow C Recover time Output in RBC

Baseline 2.06 -0.50 -0.65 -4.32 2 year 11.83

Baseline+Fixed wage 0.56 -1.11 -0.33 -2.11 3.5 year 3.23

Baseline+high adj 2.03 -0.55 -0.62 -4.65 5 year 11.55

Baseline, no shopping 5.45 -1.31 -0.09 -10.14 2 year 29.14

Compare with financial shock

• Does Shopping Matter? Yes Figures

• Without the contribution of shopping to productivity, the required sizeof the shock to generate a 1% drop in output is much larger. This is themain contribution of the paper.

*Recover time is measured by the duration of employment below the trend.

Output in RBC is the initial increase of output a one-good small open economy business cycle model.Huo & Rıos-Rull (UMN, Mpls Fed, CAERP) Engineering a Paradox of Thrift Recession October 9, OSU, Econ 26 / 32

Properties of Shocks to β

A recession can be triggered by a desired to save which generates(temporarily) the paradox of thrift.

After consumers cut their consumption:

I Output, consumption, investment and employment decrease.I Prices for nontradables and wage rate (if set by bargarning) decrease.

Technology is unchanged, but measured Solow residual decreases.

I It becomes more difficult for the nontradable firms to find a shopper.I Tradable sector with decreasing returns to scale expands.

The extent of the recessions depend on the rigidity of prices and theflexibility of factor reallocation.

Results II: Impoverishment, Permanent Consumption Drop

We look for wealth destruction shocks that induce 1% output drops ineconomies with shopping (demand increases productivity) and a labormatching model a la Mortensen-Pissarides. The economies are

1 Baseline economy

2 Baseline economy with high adjustment cost in tradable sector Figures

3 Baseline economy with fixed wage rate Figures

4 Baseline economy without goods market frictions Figures

Model economy Wealth N Solow C

Baseline 10.12 -0.11 -0.23 -3.03

Baseline+Fixed wage 8.13 -0.69 -0.18 -1.77

Baseline+high adj 5.82 -0.09 -0.10 -1.79

Baseline, no shopping 16.25 -0.16 0.22 -4.30

Properties of Shocks to wealth B

A permanent output and consumption drop can be triggered by a lossof wealth.

Mild permanent reduction in employment

There is a permanent deterioration of relative prices.

I It becomes more difficult for the nontradable firms to find a shopper.

The extent of the recessions depend on the rigidity of prices and theflexibility of factor reallocation.

Version of the Model with Financial Frictions

Financial Friction version

Conclusions and Summary

1 We have developed a theory of how a desire to save generates arecession and via the paradox of thrift, a temporal reduction of wealth.

2 We have found that recessions can be the result of a desire to increasesavings due to some financial mishap. The crucial ingredients are:

I Limited drop in interest rates.

I The more rigid the economy (prices, wages, sector reallocation), theworse the recessions.

I The shopping structure allow the shocks to be smaller than morestandard models with similar ingredients (small open economy, rigidwages, Mortensen-Pissarides).

• All these are important departures from the standard model withproductivity shocks (either new keynesian or neoclassical).

References

Backus, D. K., P. J. Kehoe, and F. Kydland. 1992. “International Business Cycles.” Journal of Political Economy100 (4):745–75.

Bai, Yan, Jose-Vıctor Rıos-Rull, and Kjetil Storesletten. 2011. “Demand Shocks as Productivity Shocks.” Working Paper,Federal Reserve Bank of Minneapolis.

Bernanke, B. and M. Gertler. 1989. “Agency Costs, Net Worth and Business Fluctuations.” American Economic Review79 (1):14–31.

Conesa, J.C. and T.J. Kehoe. 2011. “Gambling for Redemption and Self-Fulfilling Debt Crises.” Manuscript, University ofMinnesota.

Eggertsson, G. and P. Krugman. 2011. “Debt, deleveraging, and the liquidity trap: a Fisher-Minsky-Koo approach.” FederalReserve Bank of New York, unpublished manuscript, February.

Guerrieri, Veronica and Guido Lorenzoni. 2009. “Liquidity and Trading Dynamics.” Econometrica 77 (6):1751–1790.

Mendoza, E.G. 2010. “Sudden stops, financial crises, and leverage.” The American Economic Review 100 (5):1941–1966.

Mian, A. and A. Sufi. 2012. “What Explains High Unemployment? The Aggregate Demand Channel.” Unpublished Manuscript,Booth School of Business.

Midrigan, V. and T. Philippon. 2011. “Household Leverage and the Recession.” NYU Working Paper No. FIN-11-038.

Neumayer, P.A. and Fabrizio Perri. 2005. “Business Cycles in Emerging Economies: The Role of Interest Rates.” Journal ofMonetary Economics 52 (2):345.

A Theory of Household Financial Distress and Savings I

• Imagine that the household has to use financial services to provideinsurance to its non-working members.

• The total net transfer of resources to non-working members is subjectto a financial cost ψ per unit transferred. There are shocks to ψ.

• Assuming the working and non-working members must exert the sameshopping effort, but the level of consumption could be different for the twogroups.

• Nontradable firms catter some of its locations for the employed andsome for the unemploeyed.

The household problem

V (S , b, n) = maxc0N ,c

c1T ,IN,d

n u(c1NIN

ρ, c1T , d , 1

)+ (1− n)u

(c0NIN

ρ, c0T , d , 0

)+ β E V (S ′, b′, n′) subject to

(1− n)[p(S)INc0N + c1

T ] + b′ + FC (1− n)+

n[p(S)INc1N + c1

T ] = (1 + r)b + w(S)n + πN(S) + πT (S) BC

n′ = (1− λ) n + Φe [Qe(S)] (1− n) EC

S ′ = G (S) RE

FC = ψ(c0T + p(S)c0

NIN − [π(S) + (1 + r)b])

Back to Experiments

Mapping from the shock to ψ to the shock to β

• Euler conditions of the household

= (1 + r)Eβ[1 + ψ′(1− n′)]u′c1

T= (1 + r)E

β[1 + ψ′(1− n′)]

1 + ψ

1 + ψ′u′c0

• The effect of a shock to the financial cost is similar to a shock to β:

β = nβ[1 + ψ′(1− n′)] + (1− n)β[1 + ψ′(1− n′)]1 + ψ

1 + ψ′

Results

1 Baseline economy

Model economy β N Solow C (1− n)FC/Y

Baseline 2.00 -0.50 -0.67 -2.88 0.72

Baseline+Fixed wage 0.95 -0.80 -0.50 -2.11 0.00

Baseline+high adj 2.00 -0.53 -0.63 -2.67 0.69

Compare with β shock

A Theory of Household Financial Distress and Savings II

• Imagine that the household has to use financial services to provideinsurance to its non working members.

• The total net transfer of resources to non-working members is sublectto a financial cost ψ per unit transferred. There are shocks to ψ.

• In this world there will be specialization: there is enough of acompetitive search structure to differentiate goods by markets.

• Consequently, the unemployed household members will buy cheaperand harder-to-find non-tradable goods.

The implied household problem in a two classworldcolumbusus,

V (S , b, n) = maxc0N ,c

c1N ,c

n u(c1NI

1Nρ, c1

T , d1, 1)

+ (1− n)u(c0NI

0Nρ, c0

T , d0, 0)

+ β E V (S ′, b′, n′) subject to

(1− n)[p0(S)I0Nc0N + c1

T ] + b′ + FC (1− n)+

n[p1(S)I1Nc1N + c1

T ] = (1 + r)b + w(S)n + πN(S) + πT (S) BC

n′ = (1− λ) n + Φe [Qe(S)] (1− n) EC

S ′ = G (S) SV

FC = ψ(c0T + p0(S)c0

NI0N − [π(S) + (1 + r)b]

Nontradable firms’ problem in a two class world

ΩNj(S , k , n) = maxpj`,k`,n`,x`1

`=0v ,i

1∑`=0

x` Ψf [Qg`(S)] C (pj`,S) pj`

− w(S)n − i − vκ+ E

ΩN(S ′, k ′, n′)

subject to:

FN(k`, n`) ≥ C (pj`,S) =

) ρ1−ρ

C `(S), ` = 1, 2

k ′ = (1− δ)k + i − εN

k− δ)2

n′ = (1− λ)n + Φf [Qe(S)]v ,

x0k0 + x1k1 = k , x0n0 + x1n1 = n, x0 + x1 = 1.

Search frictions in a two class world

• Now market tightness in both types of non-tradable goods will bedifferent because firms allocate different fractions of its plants or locationsdifferently:

Qg0 =X 0

Qg1 =X 1

(1− N)D1.

• Clearly, the price will be lower and the tightness higher in the marketthat caters to the unemployed.

Ψf (Qg1)p1 = Ψf (Qg0)p0

• The prices for nontradable goods pi make sure:

c1N = c0

Results

1 Baseline economy

Model economy β N Solow C (1− n)FC/Y

Baseline 1.99 -0.58 -0.62 -2.77 0.55

Baseline+Fixed wage 0.62 -0.78 -0.51 -2.08 0.42

Baseline+high adj 1.99 -0.65 -0.57 -2.52 0.54

A Theory of Household Financial Distress and Savings III

• Consider a version of this economy with heterogenous agents andidyosyncratic risks.

• Let the agents borrow up to the natural borrowing limit b.

• Let the interest rate for borrowing have a premium over the worldinterest rate rb = r∗ + ε with ε being an AR(1).

• We are now exploring the relation between the size of a shock β and ashock to rb. How big do they have to be to generate the sameexpenditure drop?

Return

Two-sector closed economy

• Consider a version with a consumption goods sector and an investmentgoods sector in a closed economy.

• The consumption goods sector faces search frictions as before.

• The investment goods sector has DRS and is difficult to expand quickly.

• The households trade stocks instead of bonds.

• The experiment is a shock to β.Return

Household problem

V (S , b, n) = maxc,I,d

u(cIρ, d , n) + β EV (S ′, b′, n′) | θ

subject to:

p(S)cI + pb(S)b′ = b[pb(S) + πC (S) + πI (S)] + w(S)n BC

I = Ψd [Qg (S)] d SC

n′ = (1− λ)n + Φe [Qe(S)](1− n) EC

S ′ = G (S) SV.

The stochastic discount factor is Θ = ucp(S)I

Consumption firm’s problem

ΩCj(S , k , n) = maxpj ,i ,v

Ψf [Qg (S)] C (pj , S) pj

− w(S)n − i − vκ+ E

ΘΩCj(S ′, k ′, n′)

subject to:

FC (k , n) ≥ C (pj ,S) =

) ρ1−ρ

k ′ = (1− δ)k + i − εC

k− δ)2

n′ = (1− λ)n + Φf [Qe(S)]v

Investment firm’s problem

ΩI (S , k, n) = maxi ,v

F I (k , n)− w(S)n − i − vκ

− εI ,n

n− 1

ΘΩI (S ′, k ′, n′)

subject to:

k ′ = (1− δ)k + i − εI ,k

k− δ)2

n′ = (1− λ) n + Φf [Qe(S)] v

Properties of shock to β

A recession is triggered by a desired to save. Figures

After consumers cut their consumption:

I Output, consumption and employment decrease.I Prices for consumption goods and wage rate (if set by bargarning)

decrease.

Investment increases due to a lower real interest rate.

Ideas are useful to study International Business Cycles

Data: for US and EU15

Quantities Data Standard IRBC Shopping modelcor z shocks cor θ shocks

A. Variance relative to output (US)Consumption 0.65 0.10 0.92Investment 14.35 11.29 39.66Employment 1.05 0.23 0.56Net exports 2.28 0.02 0.01

B. International comovementOutput 0.40 0.36 0.37Consumption 0.25 0.32 0.28Investment 0.23 0.16 0.41Employment 0.21 0.48 0.36

C. Co-movement within a countryNX/output, Output -0.31 -0.34 -0.49Real Exchange Rate, cH/cF -0.20 1.00 -0.25

β shock Return

Real output Solow residual Employment

Investment Output of nontradable Output of tradable

Baseline economy Baseline economy with high adj cost

β shock Return

Number of varieties Price for nontradable Real wage

Wealth Consumption Net export/output ratio

β shock Return

Baseline economy Baseline economy with fixed wage

β shock Return

Baseline economy Baseline economy without shopping

β shock Return

Wealth shock Return

Financial shock I Return

Number of varieties Price for nontradable Real Wage

Consumption of employed Consumption of unemployed Financial cost-Output ratio

Vacancy of nontradable Vacancy of tradable Wage

Number of varieties Price for nontradable Real Wage

Consumption of employed Consumption of unemployed Financial cost-Output ratio

Vacancy of nontradable Vacancy of tradable Wage

Financial shock II Return

Capacity of firms for employed Capacity of firms for unemployed Wage

Consumption of employed Consumption of unemployed Vacancy of nontradable

Vacancy of tradable Price for employed Price for unemployed

Capacity of firms for employed Capacity of firms for unemployed Wage

Consumption of employed Consumption of unemployed Vacancy of nontradable

Vacancy of tradable Price for employed Price for unemployed

Closed economy Return

Investment Consumption Output of investment firm

Closed economy Return

Number of varieties Price for consumption Wage

Labor market tightness Vacancy of consumption firms Vacancy of investment firms

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