A Paradox of Thrift Recession Zhen Huo and Jos e-V ctor R os-Rull - - PowerPoint PPT Presentation

A Paradox of Thrift Recession

Zhen Huo and Jos´ e-V´ ıctor R´ ıos-Rull

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

Banco of Portugal October 29, 2013

Huo & R´ ıos-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 to

save 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 sheer impoverishment) generates a recession. We describe what does it take for such recession to occur.

2 In addition, in our model a reduction in consumption decreases

measured TFP even though the technology is unchanged. This channel greatly contributes to the recession.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 2 / 46

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

More data Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 3 / 46

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 consumption ◮ 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)

◮ 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.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 4 / 46

Our paper

• We complement the view that it is household consumption that triggers

a 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 prices

and wages surely aggravate recessions.

• We build a model where the desire to save triggers a recession because

it is difficult to reallocate resources from nontradables to tradables or in general from consumption to investment.

• The recession is amplified by the fact that consumption affects

productivity.

• The recession displays the paradox of thrift.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 5 / 46

Ingredients

1 Exporting more is feasible but hard. It takes time to reallocate the

economy to export more. (Tradables and Nontradables).

2 Labor markets are not competitive. We pose Mortensen-Pissarides

determination of labor market so the static Euler equation of the household 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 to pose another channel that makes the outcome easier (i.e. smaller shocks for the same outcome):

3 Reductions in Demand (i.e. consumption expenditures) induce

productivity decreases. An extension of Bai, R´ ıos-Rull, and Storesletten (2011).

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 6 / 46

The environment: Consumers within a period

Households value varieties of nontradables: I

0 c

1 ρ

Ni di

ρ Under equal consumption of each variety: cN Iρ = I

0 c

1 ρ

Ni di

ρ Households also like tradables that combine through a standard (Armington) aggregator with nontradables and dislike work and search 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.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 7 / 46

The environment: Production

Two sectors that we call tradables, & nontradables, small open economy: 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 adjustment costs to both capital and labor, and its output is used for exports, investment, and (part of) consumption. F T(k, n, l) may have decreasing returns. The nontradable sector consists of a measure one of firms each one producing a different variety. Each firm/variety has a measure one of locations, each location has its own production function F N(k, n). Locations may or may not be filled (get a customer). They produce

• nly for consumption.

Firms post prices before the location is filled.

Huo & R´ ıos-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 find

varieties.

• Random search. There is a CRS matching function

Ψ(1, D). Market tightness is Qg = 1

D .

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

D

• The probability that a firm finds a shopper is the measure of filled

locations or of consumers buying the good: Ψf (Qg) = Ψ

1 = I.

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

numeraire. p I cN = p Ψf (Qg) F N(k, n).

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 9 / 46

Frictional labor market

• Random search with market tightness: Qe =

V 1−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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 10 / 46

State Variables. Collapses to a simple Macro Model

• Aggregate. S = {θ, KN, NN, KT, NT, B}.

◮ Shocks ◮ Capital in the nontradable sector ◮ Labor in the nontradable sector ◮ Capital in the tradable sector. ◮ Labor in the tradable sector. ◮ Net foreign asset position.

Individual b, n.

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

• We use the (standard) trick that all local firms are in the hands of the

local agents and do not trade them.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 11 / 46

Consumers’ problem

V (S, b, n) = max

cN,cT ,I,d u(cN Iρ, cT, d, n) + β E{V (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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 12 / 46

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 net

foreign 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.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 13 / 46

Nontradable firms’ Choose prices pj and investments

ΩNj(S, k, n) = max

pj,i,v

Ψf [Qg(S)] C(pj, S) pj − w(S)n − i − vκ + E ΩNj(S′, k′, n′) 1 + r

• subject to:

F N(k, n) ≥ C(pj, S) = pj p(S)

• ρ

1−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.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 14 / 46

Tradable Goods Production: DRS & adjustment costs

ΩT(S, k, n) = max

i,v

F T(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.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 15 / 46

Representative Nash bargaining for wages

• Nash bargaining problem

w(S) = max

w

[Vn(S, b, n)]ϕ NN N ΩN

n (S, KN, NN) + NT

N ΩT

n (S, KT, NT)

1−ϕ

• First order condition:

ϕucT

• χΩN

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

• = (1 − ϕ)Vn(S, b, n)
• In steady state, we have:

w = ϕ

• χ
• Ψf (Qg)pF N

n

1 ρ + Qeκ

• + (1 − χ)(F T

n + Qeκ)

• + (1 − ϕ) ς

ucT

Alternative Wage Determination Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 16 / 46

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 growth model. These shocks are a stand–in for whatever deteriorates the financial

• system. Possibly a combination of the two.
• We then explore the properties of the recession generated.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 17 / 46

First Experiment: Persistent shock to discount factor

• Assume βt = βθb

t the shock to the discount factor follows an AR(1)

process: log θb

t = ρb log θb t−1 + εt,

εt ∼ N(0, σb)

• We then pose an initial value for ε0 to reduce output 1%. The value of

ρb is set equals to 0.95.

• Advantage: That induces a desire to increase saving temporarily and

later to increase consumption. It makes it similar to a financial shock that increases the wealth to income target of the households.

• Disadvantage. If taken literally, it is silly, but we will not take it

literally.

Financial Friction version Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 18 / 46

More details about the experiments

• Output in terms of the tradable goods is:

Y = p Ψf (Qg)F N(KN, NN) + F T(KT, NT)

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

current p).

• Three wage protocols:

1 Standard Nash wage bargaining: ◮ A larger shock is needed. Nontradable firms decrease employment and

vacancies but tradable firms increase employment and vacancies.

2 Staggered wage contract: ◮ Employment and vacancies drop more. Tradable firms increase

employment and vacancies mainly because the vacancy filling rate is higher.

3 Constant labor share: ◮ Wage drops less and employment drops more compared with flexible

Nash bargaining.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 19 / 46

Functional form

• Preference

u(c, d, n) = 1 1 − σ (c − ξ d)1−σ − ςn c =

• ω(cNIρ

N)

η−1 η

+ (1 − ω)c

η−1 η

T

• η

η−1

• Production function

F N(k, n) = zNkθNn1−θN, F T(k, n) = zTkθT

k nθT n

• Matching technology

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 20 / 46

Functional form

• Capital adjustment cost in the nontradable goods sector

φN(i, k) = ǫN 2 i k − δ 2 k

• Capital adjustment cost in the tradable goods sector

φT,k(i, k) = ǫT,k 2 i k − δ 2 k

• Employment adjustment cost in the tradable goods sector

φT,n(n′, n) = ǫT,n 2 n′ n − 1 2 n

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 21 / 46

Calibration: Exogenously determined parameters

• A period is half a quarter.

Parameter Value Risk aversion, σ 2.0 Annual rate of return, β

1 β8 − 1 = 4%

Labor matching elasticity, µ 0.50 Elasticity of substitution bw tradables and nontradables, η 0.83 Price markup ρ 1.05

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 22 / 46

Calibration: Endogenously determined parameters

Target Value Parameter Value Share of tradables F ∗

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 θN

T

0.64 Equal Role of Capital and Land in Tradables, 2θK

T + θN T = 1

θK

T

0.18 Vacancy Posting to Output Ratio 0.037 ς 0.80 Value of home production, .5 ϕ 0.35 Units Parameters Output, 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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 23 / 46

Calibration: Dynamic parameters

Target Value Parameter Value Response of nontradable investment

∆I N ∆Y N = 4

ǫN 21.29 Response of tradable output

∆Y T ∆Y

= −5 ǫT,n 9.84 Symmetry of tradable adjustment costs ǫT,k = ǫT,n ǫT,k 9.84 Response of labor to output

∆N ∆Y = .5

α 0.19

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 24 / 46

Results: I. Shock to patience, households increase savings

• We look for shocks to β, that follows an AR(1) with .95 persistence

that induces an increased desire to save and that generates a 1% output drop in various economies: Baseline economy: wages determined via Nash bargaining and relatively flexible tradable sector (tradable sector expands by 5%). We also look at many other economies:

1

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

2

Baseline e with high adjustment cost in tradable sector: (tradable sector 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)

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 25 / 46

The shock in action in the Baseline economy

Real output Solow residual Employment Total consumption Cons of each variety Number of varieties

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 26 / 46

Statistics for a 1% Drop in Output from Shocks to β

Model 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 is

the main contribution of the paper.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 27 / 46

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

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

Technology is unchanged, but measured Solow residual decreases.

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

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 28 / 46

Results II: Impoverishment, Permanent Consumption Drop

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

impovireshment.

• 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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 29 / 46

Baseline, Wealth Shock

Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 30 / 46

Baseline, Wealth Shock

Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 31 / 46

β shock vs Wealth shock

Return Real output Solow residual Employment Consumption Output of nontradable Output of tradable

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 32 / 46

β shock vs Wealth shock

Return Number of varieties Price for nontradable Wage Investment Wealth Net export/output ratio

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 33 / 46

Prolonged Recession and Slow Recovery

• Current recession in U.S. and southern Europe has been stagnated for a

relatively 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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 34 / 46

Properties of Shocks to wealth B

A permanent output and consumption drop can be triggered by a loss

• f wealth.

Mild permanent increase in employment There is a permanent deterioration of relative prices. Technology is unchanged, but measured Solow residual decreases.

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

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 35 / 46

Another possible interpretation to the shocks

• Throughout shocks to patience or wealth, but there is another

possibility:

• A shock to the financial system that induces people to want to save

more.

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 36 / 46

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

• Imagine that the household has to use financial services to provide

insurance to its non working members.

• The total net transfer of resources to non-working members is sublect

to a financial cost ψ per unit transferred. There are shocks to ψ. These shocks act like a shock to β.

• In this world there will be specialization: there is enough of a

competitive search structure to differentiate goods by markets.

• Consequently, the unemployed get fewer, cheaper, and harder-to-find

nontradable goods. The actual quantity of each variety is the same (But in

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 37 / 46

The implied household problem in a two class world,

V (S, b, n) = max

c0

N,c0 T ,I0,d0

c1

N,c1 T ,I1 N,d1

n u

• c1

NI1 N ρ, c1 T, d1, 1

• + (1 − n)u
• c0

NI0ρ, c0 T, d0, 0

• + β E {V (S′, b′, n′)}

subject to (1 − n)[p0(S)I0

Nc0 N + c1 T] + b′ + FC(1 − n)+

n[p1(S)I1

Nc1 N + c1 T] = (1 + r)b + w(S)n + πN(S) + πT(S)

BC Ij

N = d Ψd[Qgj(S)],

j ∈ {0, 1} SC n′ = (1 − λ) n + Φe[Qe(S)] (1 − n), EC S′ = G(S), SV FC = ψ

• c0

T + p0(S)c0 NI0 N − [π(S) + (1 + r)b]

• .

FC

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 38 / 46

Nontradable firms’ problem in a two class world

ΩNj(S, k, n) = max

{pjℓ,kℓ,nℓ,xℓ}1

ℓ=0

v,i 1

• ℓ=0

xℓ Ψf [Qgℓ(S)] C(pjℓ, S) pjℓ − w(S)n − i − vκ + E ΩN(S′, k′, n′) 1 + r

• subject to:

F N(kℓ, nℓ) ≥ C(pjℓ, S) = pjℓ p(S)

• ρ

1−ρ

C ℓ(S), ℓ = 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.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 39 / 46

Search frictions in a two class world

• Market tightness in both types of non-tradable goods is different

because 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 that

caters to the unemployed because. Ψf (Qg1)p1 = Ψf (Qg0)p0

• The prices for nontradable goods pi imply:

c1

N = c0 N

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

N > C 0 N). A suitable

implementation of noise has both C 1

N > C 0 N and p1 > p0

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 40 / 46

Mapping from the shock to ψ to the shock to β

• Euler conditions of the household

uc1

T = (1 + r)E

• β[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′

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 41 / 46

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 42 / 46

Financial shock: two class world

Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Financial friction: II

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 43 / 46

Financial shock: two class world

Discount factor Financial cost/output ratio Ratio of Ce to Cu Wealth Consumption Net export/output ratio

Baseline economy Financial friction: II

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 44 / 46

Summarizing

1 We have developed a theory of how a desire to save generates a

recession 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 increase

savings due to some financial mishap. The crucial ingredients are:

◮ Rigidities in the economy (sector reallocation, wages). ◮ The shopping structure amplifies the recession.

• All these are important departures from the standard model with

productivity shocks (either new keynesian or neoclassical).

• We are working on extending to uninsurable income risk economies and

to price discrimination so the poor shop longer.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 45 / 46

References

Backus, D. K., P. J. Kehoe, and F. Kydland. 1992. “International Business Cycles.” Journal of Political Economy 100 (4):745–75. Bai, Yan, Jos´ e-V´ ıctor R´ ıos-Rull, and Kjetil Storesletten. 2011. “Demand Shocks as Productivity Shocks.” Manuscript, Federal Reserve Bank of Minneapolis. Bernanke, B. and M. Gertler. 1989. “Agency Costs, Net Worth, and Business Fluctuations.” American Economic Review 79 (1):14–31. Conesa, J.C. and T.J. Kehoe. 2011. “Gambling for Redemption and Self-Fulfilling Debt Crises.” Manuscript, University of Minnesota. Eggertsson, G. and P. Krugman. 2011. “Debt, deleveraging, and the liquidity trap: a Fisher-Minsky-Koo approach.” Federal Reserve 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 York University. Neumayer, P.A. and Fabrizio Perri. 2005. “Business Cycles in Emerging Economies: The Role of Interest Rates.” Journal of Monetary Economics 52 (2):345. Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 46 / 46

The household problem

V (S, b, n) = max

c0

N,c0 T ,c1 N

c1

T ,I,d

n u

• c1

NIρ, c1 T, d, 1

• + (1 − n)u
• c0

NIρ, c0 T, d, 0

• + β E {V (S′, b′, n′)}

subject to (1 − n)[p(S)Ic0

N + c1 T] + b′ + FC(1 − n)+

n[p(S)Ic1

N + 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

• c0

T + p(S)c0 NI − [π(S) + (1 + r)b]

• FC

Back to Experiments Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 47 / 46

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

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 48 / 46

Financial shock: one class world

Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Financial friction: I

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 49 / 46

Financial shock: one class world

Discount factor Financial cost/output ratio Ratio of Ce to Cu Wealth Consumption Net export/output ratio

Baseline economy Financial friction: I

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 50 / 46

A Theory of Household Financial Distress and Savings III

• Consider a version of this economy with heterogenous agents and

idyosyncratic risks.

• Let the agents borrow up to the natural borrowing limit b.
• Let the interest rate for borrowing have a premium over the world

interest rate rb = r∗ + ε with ε being an AR(1).

• We are now exploring the relation between the size of a shock β and a

shock to rb. How big do they have to be to generate the same expenditure drop?

Return Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 51 / 46

Two-sector closed economy

• Consider a version with a consumption goods sector and an investment

goods 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 Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 52 / 46

Household problem

V (S, b, n) = max

c,I,d u(cIρ, d, n) + β E

• V (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 =

uc p(S)I

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 53 / 46

Consumption firm’s problem

ΩCj(S, k, n) = max

pj,i,v Ψf [Qg(S)] C(pj, S) pj

− w(S)n − i − vκ + E

• β Θ′

Θ ΩCj(S′, k′, n′)

• subject to:

F C(k, n) ≥ C(pj, S) = pj p(S)

• ρ

1−ρ

C(S) k′ = (1 − δ)k + i − ǫC 2 i k − δ 2 k n′ = (1 − λ)n + Φf [Qe(S)]v

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 54 / 46

Investment firm’s problem

ΩI(S, k, n) = max

i,v

F I(k, n) − w(S)n − i − vκ − ǫI,n 2 n′ n − 1 2 n + E

• β Θ′

Θ ΩI(S′, k′, n′)

• subject to:

k′ = (1 − δ)k + i − ǫI,k 2 i k − δ 2 k n′ = (1 − λ) n + Φf [Qe(S)] v

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 55 / 46

Properties of shock to β

A recession is triggered by a desired to save. After consumers cut their consumption:

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

decrease.

Technology is unchanged, but measured Solow residual decreases. Investment increases due to a lower real interest rate.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 56 / 46

Closed economy

Real output Solow residual Employment Investment Consumption Output of investment firm Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 57 / 46

Closed economy

Return Number of varieties Price for consumption Wage Labor market tightness Vacancy of consumption firms Vacancy of investment firms Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 58 / 46

Ideas are useful to study International Business Cycles

Data: for US and EU15 Quantities Data Standard IRBC Shopping model cor z shocks cor θ shocks

• A. Variance relative to output (US)

Consumption 0.65 0.10 0.92 Investment 14.35 11.29 39.66 Employment 1.05 0.23 0.56 Net exports 2.28 0.02 0.01

• B. International comovement

Output 0.40 0.36 0.37 Consumption 0.25 0.32 0.28 Investment 0.23 0.16 0.41 Employment 0.21 0.48 0.36

• C. Co-movement within a country

NX/output, Output

• 0.31
• 0.34
• 0.49

Real Exchange Rate, cH/cF

• 0.20

1.00

• 0.25

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 59 / 46

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 not

have the chance to negotiate the wage.

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 60 / 46

• 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)]E{βVn(S′, b′(S, b, n), n′(S, b, n))}
• JN(w, S) = Ψf [Qg(S)]p(S)F N

n (S)1

ρ − w + (1 − λ) 1 + r E{(1 − θw) JN(w, S′) + θw JN( w(S′), S′) | θ}

• Nash bargaining problem:
• w(S) = max

w

• V (w, S)

ϕ χ(S) JN(w, S) + (1 − χ(S)) JT

n (w, S)

1−ϕ

Return Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 61 / 46

β shock: Baseline vs high adjustment cost

Return Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy with high adj cost

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 62 / 46

β shock: Baseline vs high adjustment cost

Return Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy with high adj cost

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 63 / 46

β shock: Baseline vs constant labor share

Return Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy with constant labor share

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 64 / 46

β shock: Baseline vs constant labor share

Return Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy with constant labor share

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 65 / 46

Wealth shock: Baseline vs high adjustment cost

Return Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy with high adj cost

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 66 / 46

Wealth shock: Baseline vs high adjustment cost

Return Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy with high adj cost

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 67 / 46

Wealth shock: Baseline vs staggered wage

Return Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy with staggered wage

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 68 / 46

Wealth shock: Baseline vs staggered wage

Return Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy with staggered wage

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 69 / 46

Wealth shock: Baseline vs constant labor share

Return Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline with constant labor share

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 70 / 46

Wealth shock: Baseline vs constant labor share

Return Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline with constant labor share

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 71 / 46

Wealth shock: Baseline vs no shopping

Return Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy without shopping

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 72 / 46

Wealth shock: Baseline vs no shopping

Return Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy without shopping

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 73 / 46

β shock vs Wealth shock

Return Real output Solow residual Employment Consumption Output of nontradable Output of tradable

Staggered wage, β shock Staggered wage, wealth shock

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 74 / 46

β shock vs Wealth shock

Return Number of varieties Price for nontradable Wage Investment Wealth Net export/output ratio

Staggered wage, β shock Staggered wage, wealth shock

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 75 / 46

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 0.05 0.1 1992:q1 1996:q1 2000:q1 2004:q1 2008:q1 2012:q1 −0.25 −0.2 −0.15 −0.1 −0.05 0.05 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 0.05 0.1 0.15 1992:q1 1996:q1 2000:q1 2004:q1 2008:q1 2012:q1 −0.08 −0.06 −0.04 −0.02 0.02 0.04 0.06

Consumption Net Export/output ratio Greece Ireland Italy

• •-•-•- Portugal

Spain

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 76 / 46

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) Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 77 / 46

Spain: Output Growth

1980 1985 1990 1995 2000 2005 2010 −0.1 −0.08 −0.06 −0.04 −0.02 0.02 0.04 0.06 0.08 0.1 PIB, Salarios y Empleo, 1978:Q3−2011:Q3 PIB

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 78 / 46

Spain: Output Growth, Employment Growth

1980 1985 1990 1995 2000 2005 2010 −0.1 −0.08 −0.06 −0.04 −0.02 0.02 0.04 0.06 0.08 0.1 Salarios y Trabajo, 1978:Q3−2011:Q3 PIB Empleo

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 79 / 46

Spain: Output Growth, Employment Growth, Real Wage Growth

1980 1985 1990 1995 2000 2005 2010 −0.1 −0.08 −0.06 −0.04 −0.02 0.02 0.04 0.06 0.08 0.1 Salarios y Trabajo, 1978:Q3−2011:Q3 PIB Empleo Salarios reales

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 80 / 46

Labor share in Spain: 2010-2011

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 81 / 46

Baseline vs Staggered wage

Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy with staggered wage

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 82 / 46

Baseline vs Staggered wage

Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy with staggered wage

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 83 / 46

Baseline vs no Shopping

Real output Solow residual Employment Investment Output of nontradable Output of tradable

Baseline economy Baseline economy without shopping

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 84 / 46

Baseline vs no Shopping

Number of varieties Price for nontradable Wage Wealth Consumption Net export/output ratio

Baseline economy Baseline economy without shopping

Huo & R´ ıos-Rull (UMN, Mpls Fed, CAERP) A Paradox of Thrift Recession Banco of Portugal 85 / 46