2015-2016 { Econ590 Topics in Macroeconomics Liquidations ...€¦ · 1. Model setup Checklist IX...

2015-2016 – Econ590Topics in Macroeconomics

Liquidations and Deficient Demands :Reconciling Hayek’s and Keynes’ views of

recessions

Paul Beaudry & Franck [email protected]

Vancouver School of Economics

Version 1.031/03/2016

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[email protected]

0. IntroductionRecessions

I Recessions often come after periods of rapid accumulation ofassets (productive capital, houses, durable goods)

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0. IntroductionDepth of Recession and Length of Recovery vs. Cumulated Total Investment

-2 0 2 4 6 8 10 12

ci at peak (% deviation from trend)

-1

0

1

2

3

4

5

Dep

thoftherecession(%

)

1957Q3

1973Q4

1980Q1

1960Q21969Q4

1981Q3

1990Q3

2001Q1

2007Q4Corr: 0.85, P-value: 0

-2 0 2 4 6 8 10 12

ci at peak (% deviation from trend)

0

2

4

6

8

10

12

14

16

18

Len

gthofrecovery(quarters)

1957Q31960Q2

1969Q4

1973Q41981Q3

1990Q3

2001Q1

2007Q4

1980Q1

Corr: 0.77, P-value: 0.02

Note : Horizontal axis is capital over-accumulation, measured as cumulated percapita investment over previous 10 years, detrended using a cubic trend. Verticalaxis is either depth of recession, measured as percentage fall in real per capitaGDP from peak to subsequent trough, or length of recovery, measured as thenumber of quarters it takes for real per capita GDP to reach its previous peak.Dates correspond to peak quarters.

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0. IntroductionThe Relation Between Depth of Recession or Length of Recovery with CumulatedInvestment for US Postwar Recessions

xn = β0 + β1cin + εn, (1)

xn = β0 + β1cin + β2∆tfpn + εn, (2)

I n indexes recessions,

I x is either the depth of the recession or the length of therecovery,

I ∆tfpn is the percentage change in TFP from peak to trough

I ci represents deviations from trend of accumulated investmentfor either total, durable, non-residential or residential capital.

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Depth of recessionTot. Capital Resid. Capital N-Res. Capital Dur. Goods

Equation (1) (2) (1) (2) (1) (2) (1) (2)

constant 3.01 3.22 4.41 3.94 3.50 3.71 3.08 3.19(0.06) (0.09) (0.01) (0.04) (0.13) (0.14) (0.09) (0.13)

ci t 0.94 0.97 0.48 0.48 0.82 0.96 0.74 0.75(0.02) (0.03) (0.02) (0.03) (0.15) (0.17) (0.03) (0.05)

∆tfp - -0.19 - 0.30 - -0.42 - -0.10- (0.76) - (0.63) - (0.65) - (0.89)

Note : Numbers in parentheses are p-values.

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Length of RecoveryTot. Capital Resid. Capital N-Res. Capital Dur. Goods

Equation (1) (2) (1) (2) (1) (2) (1) (2)

constant 0.63 0.88 1.33 1.34 0.63 0.84 0.47 0.70(0.19) (0.10) (0.02) (0.08) (0.38) (0.21) (0.25) (0.11)

ci t 0.40 0.43 0.17 0.17 0.42 0.56 0.36 0.38(0.00) (0.00) (0.03) (0.05) (0.04) (0.02) (0.00) (0.00)

∆tfp - -0.22 - -0.01 - -0.42 - -0.20- (0.25) - (0.98) - (0.14) - (0.19)

Note : Numbers in parentheses are p-values.

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0. IntroductionRecessions

I Recessions often come after periods of rapid accumulation ofassets (productive capital, houses, durable goods)

I Two opposite views of economic policy in those recessions

× Hayek× Keynes

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0. IntroductionThe Liquidationist View (Friedrich Hayek)

I Recessions are needed to cleanse the economy.

I Gvt spendings only delays necessary adjustment

I “Any revival which is merely due to artificial stimulus leavespart of the work of depressions undone”, J. Schumpeter,The Economics of the Recovery Program, 1934

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0. IntroductionThe Aggregate Demand View (John Maynard Keynes)

I Recessions are periods of insufficient demand

I Activist fiscal policy is needed

I “”If the Treasury were to fill old bottles with bank-notes, burythem at suitable depths in disused coal-mines which are thenfilled up to the surface with town rubbish, and leave it toprivate enterprise on well-tried principles of laissez-faire to digthe notes up again (the right to do so being obtained, ofcourse, by tendering for leases of the note-bearing territory),there need be no more unemployment and, with the help ofrepercussions, the real income of the community, and itscapital wealth, would probably become a good deal greaterthan it actually is”, J.M. Keynes, The General Theory ofEmployment, Interest and Money, 1936

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0. IntroductionTwo opposite views

The Liquidationist View(Friedrich Hayek)

I Recessions are needed to cleansethe economy.

I Gvt spendings, aggregatedemand management onlydelays necessary adjustment

The Aggregate Demand View(John Maynard Keynes)

I Recessions are periods ofinsufficient demand

I Activist fiscal policy is neededmanagement only delaysnecessary adjustment

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0. IntroductionThis Lecture

I We show that the two views are not mutually exclusive

I “Over-” (“mal-”) accumulation of physical assets creates theneed for liquidation recession

I This liquidation will cause the economy to functionparticularly inefficiently.

I Some stimulative policies may remain desirable even if theypostpone a recovery.

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0. IntroductionMain Ingredients

I Environment with decentralized markets & flexible prices .I Two imperfections :

× Labor market matching friction in the spirit ofDiamond-Mortensen-Pissarides unemployment risk

× Adverse selection in the insurance market : unemployment riskis not (fully) insurable.

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0. IntroductionWhat we do not do

I We do not propose a specific theory of why the economymight find itself with a (too) large stock of houses, durablesand/or capital goods.

× Noisy news× Lax monetary policy× Exuberance× Perfect foresights limit cycle

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0. IntroductionWhat I will present

I Static version of model (except for a few slides).

I Version where “capital” is indeed “durable goods” or”houses” (simpler)

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0. IntroductionRoadmap

1. Model setup

2. Equilibrium

3. Interesting Properties of the Static Equilibrium

4. Extensions / Dynamics / Policy Trade-offs

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1. Model setup

2. Equilibrium



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1. Model setup

Figure 1 – Overview : timeline

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1. Model setup

Figure 2 – Overview : Initial goods

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1. Model setup

Figure 3 – Overview : markets

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1. Model setup


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1. Model setup


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1. Model setup

Figure 6 – Overview : firms

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1. Model setup

Figure 7 – Overview : firms

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1. Model setup

Figure 8 – Overview : households

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1. Model setup


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1. Model setup


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1. Model setup


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1. Model setup


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1. Model setupChecklist

I Xj : exogenous amount of good that is already in household jhands

I Mass L of households always looking for jobs

I Afternoon is centralized, all the action is in the morning

I Frictions on the morning labor market

I Unemployment risk that is not insured

I No coordination between firms, shoppers and workers

I Shoppers and workers credit/debit a bank account that theywill clear in the afternoon.

I Morning good is referred to as “durable” as it will be in thedynamic extension

I Afternoon good is non durable and serves as the numeraire.

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1. Model setupPreferences

I

U(Xj + ej︸︷︷︸cj

)− ν(`j) + V (−pej + Ijw`j︸︷︷︸aj

).

I Initial endowment of Xj units of durable good.

I Continuation value V (aj) given (in this talk)

I Ij =

{1 if employed0 if unemployed

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1. Model setupFirms

I Vacancy posting cost Φ.

I Decreasing-returns-to-scale production function F (`).

I Net production of a firm hiring ` hours of labor from oneworker is F (`)− Φ.

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1. Model setupMatching

I N = number firms who decide to search for workers.

I M(N, L) = number of matches (CRS).

I “Competitive” match surplus split within-a-match hoursdemand :

F ′(`) =w

p

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1. Model setupNormalization and Assumption

I Normalization : L = 1

I Symmetry : Xj = X

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1. Model setupHousehold morning decisions

I Worker problem :

max`j−ν(`j) + V (−pej + Ijw`j︸︷︷︸

aj

)

I Shopper problem :

maxej

U (X + ej) + µV (w`j − pej) + (1− µ)V (−pej)

µ ≡ M(N, L)/L job finding probability.

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1. Model setupDeriving the value function V (a)

I Not here...

I V (a) is strictly concave, with the key property thatV ′(a1) > V ′(a2) if a1 < 0 < a2

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Figure 13 – The Value Function V (a)

a

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a

V (a)

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a

V (a)

a1 < 0

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a

V (a)

a1 < 0 a2 > 0

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a

V (a)

a1 < 0

V′ (a

1)

a2 > 0

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a

V (a)

a1 < 0

V′ (a

1)

a2 > 0

V ′(a2)

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1. Model setup

2. Equilibrium



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2. Equilibrium

I Afternoon : V (aj)

I Morning : markets clear and agents optimize

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2. EquilibriumFirst sub-period

I The equilibrium is given by the following equationsI

1

pU ′(c) =

M(N, L)

LV ′ (w`− p (c − X ))

+

[1− M(N, L)

L

]V ′ (−p (c − X ))

I

ν ′(`) = V ′ (w`− p (c − X ))w

I

pF ′(`) = w

IM(N, L)

N[pF (`)− w`] = pΦ

I

M(N, L)F (`) = L(c − X ) + NΦ

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2. EquilibriumA labor market wedge

ν ′(`)

U ′(c)

{1 + (1− µ)

[V ′ (−p (c − X ))

V ′ (w`− p (c − X ))− 1

]}︸︷︷︸

1+ labor wedge

= F ′(`)

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1. Model setup

2. Equilibrium



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3. Interesting Properties of the Static EquilibriumGoal and parametric restrictions

I Our main goal now is to explore the effects of changes in Xon equilibrium outcomes.

I Why and when an increase in X can actually lead to areduction in consumption and/or welfare ?

I Can liquidation periods be socially painful ?I In this talk I restrict the analysis to

× M(N, L) = min{N, L}

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Figure 14 – The Matching Function M(N, L)

N

L

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Figure 14 – The Matching Function M(N, L)

N

L

M(N, L)

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3. Interesting Properties of the Static EquilibriumGoal and parametric restrictions

I Our main goal now is to explore the effects of changes in Xon equilibrium outcomes.

I Why and when an increase in X can actually lead to areduction in consumption and/or welfare ?

I Can liquidation periods be socially painful ?I In this talk I restrict the analysis to

× M(N, L) = min{N, L}

× V (a) =

{(1 + τ) · v · a if a < 0v · a if a ≥ 0

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a

V (a)

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a

V (a)

a1 < 0

slope(1 + τ)v

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a

V (a)

a1 < 0

slope(1 + τ)v

a2 > 0

slope v

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3. Interesting Properties of the Static EquilibriumWith piecewise linear V

ν ′(`)

U ′(c)

1 + (1− µ)

[V ′ (−p (c − X ))

V ′ (w`− p (c − X ))− 1

]︸︷︷︸

τ

= F ′(`)

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3. Interesting Properties of the Static EquilibriumWith piecewise linear V

ν ′(`)

U ′(c)

1 + (1− µ︸︷︷︸µ(X )

)

[V ′ (−p (c − X ))

V ′ (w`− p (c − X ))− 1

]︸︷︷︸

τ

= F ′(`)

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3. Interesting Properties of the Static EquilibriumTwo key parameters (1)

X47 / 64

3. Interesting Properties of the Static EquilibriumTwo key parameters (2)

τ48 / 64

Figure 16 – Proposition 1 : Existence and Uniqueness

ττ0

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ττ0

Uniqueequilibrium

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ττ0

Uniqueequilibrium

Multipleequilibria

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Figure 17 – Proposition 2 : The three regimes

X0

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X0 X ?

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X0 X ? X ??

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X0 X ? X ??

Full em-ployment

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X0 X ? X ??

Full em-ployment

No employment

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X0 X ? X ??

Full em-ployment

Unemployment No employment

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3. Interesting Properties of the Static EquilibriumConsumption as a function of X

I How does vary equilibrium consumption when X increases ?

I In the full employment regime :

× Marginal utility of spendings decrease with X lessproduction

× But less than proportional to the increase in X× Overall, c increases with X

I In the no employment regime :

× c = X× c increases one to one with X

I In the unemployment regime

× “Multiplier > 1”× Spendings decrease more than one to one with X× Therefore c decreases with X

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3. Interesting Properties of the Static EquilibriumFigure 18 – Proposition 3, Consumption as function of X .

0 0.2 0.4 0.6 0.8 10.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

X⋆

X⋆⋆

X

c

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3. Interesting Properties of the Static EquilibriumIs there deficient demand in the unemployment regime ?

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Definition : Deficient demand is a situation where

I increased demand by one agent would favor increased demandby other agents,

I a feasible coordinated increased in demand by all agentswould leave everyone better off.

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Definition : Deficient demand is a situation where

I increased demand by one agent would favor increased demandby other agents,

I a feasible coordinated increased in demand by all agentswould leave everyone better off.

Proposition 1

When the economy is in the unemployment regime(X ? < X < X ??), there is deficient demand.

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3. Interesting Properties of the Static EquilibriumEffects of changes in X on welfare

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3. Interesting Properties of the Static EquilibriumEffects of changes in X on welfare

Proposition 2 (Welfare)

I If the economy is the unemployment regime and if τ is largeenough (close enough to τ),

I then an increase in X leads to a fall in welfare.

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3. Interesting Properties of the Static EquilibriumFigure 19 – Welfare as function of X

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

X⋆

X⋆⋆

X

Welfare

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3. Interesting Properties of the Static EquilibriumIntroducing government spending

I Add a government in the morning

I u(X + e + Gn) + γu(Gu)I Government :

× purchase Gn that is perfectly substitutable with privateconsumption

× purchase Gw that is useless (γ = 0), or enters additively inutility

× Lump-sum taxes× Balance budget

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3. Interesting Properties of the Static EquilibriumIntroducing government spending (continued)

u(X + e + Gn) + γu(Gu)

Proposition 3 (Fiscal Mulitpliers)

I An increase in Gn has no effect

I An increase in Gw increases activity.I The multiplier de/dGw is

× greater than one in the unemployment regime× smaller than one in the full-employment regime

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3. Interesting Properties of the Static EquilibriumIntroducing government spending (continued)

Proposition 4 (Fiscal policy and welfare)

I In the unemployment regime

I in the zone where a fall in X would increase welfare,

I an increase in Gw will increase welfare.

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1. Model setup

2. Equilibrium



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4. Extensions / Dynamics / Policy Trade-offsRelaxing functional-form assumptions

I Results are robust to :

× Relaxing functional assumptions (matching function)× Other ways of splitting the surplus (Nash Bargaining, directed

search)× Introduction of productive capital× Addition of another good in the morning (cf Krugman)

I Simple characterization is not always possible

I but main results hold.

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4. Extensions / Dynamics / Policy Trade-offsEndogenous imperfect insurance

I We endogenize the absence of unemployment insurance.

I Information friction : adverse selection.

I We can then compute the constrained efficient plannerallocations

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4. Extensions / Dynamics / Policy Trade-offsDynamic Setup

I An infinite number of periods t,

I Each period consists of a morning and an afternoon

I The only financial trade is between morning and afternoon byassumption

I

Xt+1 = (1− δ)Xt + γet

I

U =∞∑t=0

βt(U(ct)− ν(`t) + V (at)

)

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4. Extensions / Dynamics / Policy Trade-offsPolicy Trade-off

I When X is high, the economy will converge with the SS withinefficiently low demand on the way.

I Welfare today would be increased by stimulating demandtoday.

I But this would imply higher X tomorrow,

I And therefore lower consumption in all subsequent periodsuntil the liquidation is complete.

I This tradeoff is aimed at capturing the tension between theKeynesian and Hayekian prescriptions in recession.

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Proposition 5 (Aggregate demand management is desirable )

I Suppose the economy is in steady state in the unemploymentregime.

I Then, to a first-order approximation, a (feasible) change in thepath of expenditures from this steady state equilibrium willincrease the present discounted value of expected welfare ...

I ... if and only if it increases the presented discounted sum ofthe resulting expenditure path,

∑∞i=0 β

iet+i .

I Aggregate demand management is therefore desirable.

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2015-2016 { Econ590 Topics in Macroeconomics Liquidations ...€¦ · 1. Model setup Checklist IX...

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Transcript of 2015-2016 { Econ590 Topics in Macroeconomics Liquidations ...€¦ · 1. Model setup Checklist IX...