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A Paradox of Thrift Recession

Zhen Huo and Jose-Vıctor Rıos-Rull

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

Banco of Portugal

October 29, 2013

Huo & Rıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 1 / 46

Can a recession be the result of impoverishment?

• 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: 1990-2011. Data source: OECD MEI

More data


What are major detonants of 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).

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 sticky 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:

[∫ I0 c

1ρ

Ni di

]ρ

Under equal consumption of each variety: cN Iρ =

[∫ I0 c

1ρ

Ni di

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

u [c(cN Iρ, cT ), d , n] .

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

I = d Ψd(Qg )

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


The environment: ProductionTwo 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) A Paradox of Thrift Recession Banco of Portugal 8 / 46

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

D .

• 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 = I.

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

p I cN = p Ψf (Qg ) FN(k , n).


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

Staggered wage contract

Constant labor share


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 ,I,d

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

subject to

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

I = 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 , p,S), cT (p, S).

2 Search Intensity I(p,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 I,

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′)

1 + r

subject to:

FN(k, n) ≥ C (pj ,S) =

(pj

p(S)

) ρ1−ρ

C (S)

k ′ = (1− δ)k + i − φN(i , k)

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

− φT ,n(n, n′) + E

ΩT (S ′, k ′, n′)

1 + r

subject to:

k ′ = (1− δ)k + i − φT ,k(i , k)

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

• Nash bargaining problem

w(S) = maxw

[Vn(S , b, n)]ϕ[NN

NΩNn (S ,KN ,NN) +

NT

NΩTn (S ,KT ,NT )

]1−ϕ

• First order condition:

ϕucT

[χΩN

n (S , kN , nN) + (1− χ)ΩTn (S , kT , nT )

]= (1− ϕ)Vn(S , b, n)

• In steady state, we have:

w = ϕ

[χ

(Ψf (Qg )pFN

n

1

ρ+ Qeκ

)+ (1− χ)(FT

n + Qeκ)

]+ (1− ϕ)

ς

ucT

Alternative Wage Determination


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 = βθbt 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).• Three wage protocols:

1 Standard Nash wage bargaining:

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

2 Staggered wage contract:

I Employment and vacancies drop more. Tradable firms increaseemployment and vacancies mainly because the vacancy filling rate ishigher.

3 Constant labor share:

I Wage drops less and employment drops more compared with flexibleNash bargaining.


Functional form

• Preference

u(c , d , n) =1

1− σ (c − ξ d)1−σ − ςn

c =

[ω(cNI

ρN)

η−1η + (1− ω)c

η−1η

T

] 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

2

(i

k− δ)2

k

• Capital adjustment cost in the tradable goods sector

φT ,k(i , k) =εT ,k

2

(i

k− δ)2

k

• Employment adjustment cost in the tradable goods sector

φT ,n(n′, n) =εT ,n

2

(n′

n− 1

)2

n


Calibration: Exogenously determined parameters

• A period is half a quarter.

Parameter Value

Risk aversion, σ 2.0

Annual rate of return, β 1β8 − 1 = 4%

Labor matching elasticity, µ 0.50

Elasticity of substitution bw tradables and nontradables, η 0.83

Price markup ρ 1.05


Calibration: Endogenously determined parameters

Target Value Parameter Value

Share of tradablesF∗T

Y∗ 0.3 ω 0.91

Unemployment rate, U∗ 7% λ 0.05

Monthly job finding rate 45% νe 0.67

Occupancy Rate,C∗N

F∗N

0.81 νg 0.81

Capital to output ratio K∗

Y∗ 2.75 δ 0.007

Labor Share in nontradables 0.6 θN 0.67

Labor Share in tradables 0.6 θNT 0.64

Equal Role of Capital and Land in Tradables, 2θKT + θNT = 1 θKT 0.18

Vacancy Posting to Output Ratio 0.037 ς 0.80

Value of home production, .5 ϕ 0.35

Units ParametersOutput, Y ∗ 1 zN 0.45

Relative price of nontradables, p∗ 1 zT 0.52

Market tightness in labor markets, U∗

V∗ 1 κ 0.53

Market tightness in goods markets, D∗ 1 ξ 0.02


Calibration: Dynamic parameters

Target Value Parameter Value

Response of nontradable investment ∆IN

∆YN = 4 εN 21.29

Response of tradable output ∆YT

∆Y= −5 εT ,n 9.84

Symmetry of tradable adjustment costs εT ,k = εT ,n εT ,k 9.84

Response of labor to output ∆N∆Y

= .5 α 0.19


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:

Baseline economy: wages determined via Nash bargaining andrelatively flexible tradable sector (tradable sector expands by 5%).

We also look at many other economies:

1 Baseline with staggered wage contract: same dynamic parameters asthe baseline economy, average wage contract duration is 1 year.

2 Baseline e with high adjustment cost in tradable sector: (tradablesector expands by 1%).

3 Baseline economy with constant labor share:4 No frictions either in labor markets.5 No shopping (no frictions in goods markets)


The shock in action in the Baseline economy

Real output Solow residual Employment

Total consumption Cons of each variety Number of varieties


Statistics for a 1% Drop in Output from Shocks to βModel economy Pref Shock Employment TFP Cons

Baseline economy 1.12 -0.50 -0.72 -4.50

+ high adjustment cost 1.01 -0.74 -0.52 -3.14

+ staggered wage 0.55 -0.85 -0.47 -2.72

+ staggered wage + high cost 0.45 -1.02 -0.36 -2.03

Constant labor share 0.69 -0.76 -0.51 -3.06

Baseline with very low adjustment costs 1.44 0.35 -1.51 -8.42

Frictionless markets -0.50 -1.76 0.01 4.37

Frictionless labor & goods market friction -0.62 -2.25 0.25 5.22

without goods market friction 2.59 -1.25 -0.20 -9.00

w/o goods market friction and high adj cost 1.79 -1.39 -0.10 -4.69

w/o goods market friction; staggered wages 0.83 -1.38 -0.14 -3.59

w/o goods market friction, constant lab sh 1.14 -1.34 -0.14 -4.41

• Does Shopping Matter? Yes: Baseline economy without shopping.

• Without shopping, the required size of the shock is much larger. This isthe main contribution of the paper.


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

• This is our theory of the recession in Southern Europe. A permanentimpovireshment.

• A wealth destruction shock that induces a 1% output drop.

1 Baseline economy

2 Baseline economy without goods market frictions

Model economy Wealth Shock Employment TFP Consumption

Baseline 11.25 -0.21 -0.37 -3.44

Baseline, no shopping 21.30 -0.39 -0.07 -5.01


Baseline, Wealth Shock


Investment Output of nontradable Output of tradable

Baseline economy


Baseline, Wealth Shock

Number of varieties Price for nontradable Wage

Wealth Consumption Net export/output ratio

Baseline economy


β shock vs Wealth shock Return


Consumption Output of nontradable Output of tradable

Staggered wage + high adj costs, β shock Staggered wage + high adj costs, wealth shock




Investment Wealth Net export/output ratio

Staggered wage + high adj costs, β shock Staggered wage + high adj costs, wealth shock


Prolonged Recession and Slow Recovery

• Current recession in U.S. and southern Europe has been stagnated for arelatively long period, featuring a prolonged low level of employment.

• With shock to wealth, the recovery speed is lower than with shock to β.

β shock and wealth shock with staggered wage. Figures

β shock and wealth shock with staggered wage and high adj cost.Figures

Model economy Employment TFP Consumption Recover

β shock -0.50 -0.72 -4.50 4

β shock + staggered wage -0.85 -0.47 -2.72 7

β shock + staggered wage + high cost -1.02 -0.36 -2.03 9

Wealth shock -0.21 -0.37 -3.44 2

Wealth shock + staggered wage -0.46 -0.43 -3.44 9

Wealth hock + staggered wage + high cost -0.82 -0.46 -3.25 14


Properties of Shocks to wealth B

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

Mild permanent increase 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.


Another possible interpretation to the shocks

• Throughout shocks to patience or wealth, but there is anotherpossibility:

• A shock to the financial system that induces people to want to savemore.

• We now develop such a model within the representative agent structure.


A Version of the Model with (shocks to) Financial Frictions

• 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. Theseshocks act like a shock to β.

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

• Consequently, the unemployed get fewer, cheaper, and harder-to-findnontradable goods. The actual quantity of each variety is the same (But in

an extension they can also get smaller quantities of each variety.)


The implied household problem in a two class world,

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

0T ,I

0,d0

c1N ,c

1T ,I

1N,d

1

n u(c1NI

1Nρ, c1

T , d1, 1)

+ (1− n)u(c0NI

0ρ, c0T , d

0, 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

IjN = d Ψd [Qgj(S)], j ∈ 0, 1 SC

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]

). FC


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′)

1 + r

subject to:

FN(k`, n`) ≥ C (pj`,S) =

(pj`

p(S)

) ρ1−ρ

C `(S), ` = 1, 2

k ′ = (1− δ)k + i − φN(i , k)

n′ = (1− λ)n + Φf [Qe(S)]v ,

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


Search frictions in a two class world• Market tightness in both types of non-tradable goods is differentbecause firms allocate different fractions of its plants-locations differently:

Qg0 =X 0

N D0,

Qg1 =X 1

(1− N)D1.

• Clearly, the price is lower and the tightness higher in the market thatcaters to the unemployed because.

Ψf (Qg1)p1 = Ψf (Qg0)p0

• The prices for nontradable goods pi imply:

c1N = c0

N

• We have posed a version with undirected search (C 1N > C 0

N). A suitableimplementation of noise has both C 1

N > C 0N and p1 > p0


Mapping from the shock to ψ to the shock to β

• Euler conditions of the household

uc1T

= (1 + r)Eβ[1 + ψ′(1− n′)]u′c1

T

uc0

T= (1 + r)E

β[1 + ψ′(1− n′)]

1 + ψ

1 + ψ′u′c0

T

• 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 Financial friction model: constant labor share.

2 Financial friction model: fixed wage rate.

Model economy β Empl. TFP Cons Cost/Output

Baseline+constant labor share 0.69 -0.76 -0.51 -3.06 —

Non-segmented goods mrkts FFI 0.81 -0.82 -0.49 -2.75 1.23

Segmented goods mrkts FFII 0.83 -0.83 -0.47 -2.80 1.23


Financial shock: two class world



Baseline economy Financial friction: II


Financial shock: two class world

Discount factor Financial cost/output ratio Ratio of Ce to Cu


Baseline economy Financial friction: II


Summarizing

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 Rigidities in the economy (sector reallocation, wages).

I The shopping structure amplifies the recession.

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

• We are working on extending to uninsurable income risk economies andto price discrimination so the poor shop longer.


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.” Manuscript, FederalReserve 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.” Working Paper FIN-11-038, New YorkUniversity.

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


The household problem

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

0T ,c

1N

c1T ,I,d

n u(c1NIρ, c1

T , d , 1)

+ (1− n)u(c0NIρ, c0

T , d , 0)

+ β E V (S ′, b′, n′) subject to

(1− n)[p(S)Ic0N + c1

T ] + b′ + FC (1− n)+

n[p(S)Ic1N + c1

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

I = d Ψd [Qg (S)] SC

n′ = (1− λ) n + Φe [Qe(S)] (1− n) EC

S ′ = G (S) RE

FC = ψ(c0T + p(S)c0

NI− [π(S) + (1 + r)b])

FC

Back to Experiments


Results

1 Financial friction, one class: constant labor share.

2 Financial friction, one class: fixed wage rate.

Model economy β N Solow C Financial cost

Financial+constant labor share 0.76 -0.87 -0.45 -2.49 1.21

Financial+Fixed wage 0.64 -1.05 -0.35 -1.87 1.19


Financial shock: one class world



Baseline economy Financial friction: I


Financial shock: one class world

Discount factor Financial cost/output ratio Ratio of Ce to Cu


Baseline economy Financial friction: I


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

β

Θ′

ΘΩCj(S ′, k ′, n′)

subject to:

FC (k , n) ≥ C (pj ,S) =

(pj

p(S)

) ρ1−ρ

C (S)

k ′ = (1− δ)k + i − εC

2

(i

k− δ)2

k

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

2

(n′

n− 1

)2

n + E

β

Θ′

ΘΩI (S ′, k ′, n′)

subject to:

k ′ = (1− δ)k + i − εI ,k

2

(i

k− δ)2

k

n′ = (1− λ) n + Φf [Qe(S)] v


Properties of shock to β

A recession is triggered by a desired to save.

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.


Closed economy


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


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


Representative Nash bargaining with staggered contract

• Each employed worker renegotiate their wage with probability θw .

• w(S) is the newly negotiated wage.

• Average wage index w(S) in the economy evolves according to:

w(S) = (1− θw )w(S−) + θw w(S)

• A worker who just becomes employed receive w(S−) if they do nothave the chance to negotiate the wage.


• The value of a worker and for a firm if they renegotiate the wage at w .

V (w , S) = wucT (S)−ς+(1−λ)E

β(1− θw )V (w ,S ′) + βθw V (w(S ′), S ′)

−Ψe [Qe(S)]EβVn(S ′, b′(S , b, n), n′(S , b, n))

JN(w ,S) = Ψf [Qg (S)]p(S)FNn (S)

1

ρ− w

+(1− λ)

1 + rE(1− θw )JN(w ,S ′) + θw J

N(w(S ′),S ′) | θ

• Nash bargaining problem:

w(S) = maxw

[V (w , S)

]ϕ [χ(S)JN(w ,S) + (1− χ(S))JTn (w , S)

]1−ϕ

Return


β shock: Baseline vs high adjustment cost Return



Baseline economy Baseline economy with high adj cost


β shock: Baseline vs high adjustment cost Return





β shock: Baseline vs constant labor share Return



Baseline economy Baseline economy with constant labor share


Wealth shock: Baseline vs high adjustment cost Return





Wealth shock: Baseline vs staggered wage Return



Baseline economy Baseline economy with staggered wage


Wealth shock: Baseline vs staggered wage Return





Wealth shock: Baseline vs constant labor share Return



Baseline economy Baseline with constant labor share


Wealth shock: Baseline vs no shopping Return



Baseline economy Baseline economy without shopping


Wealth shock: Baseline vs no shopping Return







Consumption Output of nontradable Output of tradable

Staggered wage, β shock Staggered wage, wealth shock




Investment Wealth Net export/output ratio

Staggered wage, β shock Staggered wage, wealth shock


Southern Europe Return

Figure 1: Aggregate Economic Variables in Southern European Countries

1992:q1 1996:q1 2000:q1 2004:q1 2008:q1 2012:q1−0.15

−0.1

−0.05

0

0.05

0.1

1992:q1 1996:q1 2000:q1 2004:q1 2008:q1 2012:q1−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

TFP Employment

1992:q1 1996:q1 2000:q1 2004:q1 2008:q1 2012:q1−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

1992:q1 1996:q1 2000:q1 2004:q1 2008:q1 2012:q1−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

Consumption Net Export/output ratio

Greece Ireland Italy -•-•-•- Portugal Spain


Spanish Labor Share

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

0.500

0.550

0.600

0.650

0.700

0.750

Labor Share

Labor share (including residential investment)

Labor share (excluding residential investment)


Spain: Output Growth

1980 1985 1990 1995 2000 2005 2010−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1PIB, Salarios y Empleo, 1978:Q3−2011:Q3

PIB


Spain: Output Growth, Employment Growth

1980 1985 1990 1995 2000 2005 2010−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1Salarios y Trabajo, 1978:Q3−2011:Q3

PIBEmpleo


Spain: Output Growth, Employment Growth, Real WageGrowth

1980 1985 1990 1995 2000 2005 2010−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1Salarios y Trabajo, 1978:Q3−2011:Q3

PIBEmpleoSalarios reales


Labor share in Spain: 2010-2011


Baseline vs Staggered wage





Baseline vs no Shopping





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