time consistent fiscal policy in a debt crisis, by neele balke (university college london)

Time-consistent Fiscal Policy in a Debt Crisis

Neele Balke1,2,3 & Morten Ravn1,2,4 (2016)

University College London1, Centre for Macroeconomics2, IIES3, CEPR4

Barcelona, March 2017

Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 1 / 34

Motivation

• European sovereign debt crises

1 large recessions

2 rising debt and bond spreads

3 (concerns about) sovereign default and inequality

• This project investigates the design of optimal time-consistent fiscalpolicies in debt crises

I austerity? address debt crisis at the cost of possibly making therecession worse?

I stimulus? address the recession at the cost of higher debt?

I how is the choice affected by institutions (ability to commit)?


This paper: model building blocks

A small open economy of sovereign default in the Eaton and Gersovitz(1981) tradition

1 rich set of policy instruments(default, non-state contingent debt, distortionary income taxes,unemployment benefits and government consumption)

2 inequality through unemployment from a frictional labor market withtwo-sided search

3 policy maker lacks commitment to all instruments

4 exiting monetary union not an option, (costly) default is


This paper: focus on optimal policy

• Inter temporal trade-off (standard):stabilize debt to avoid falling sovereign debt prices and defaultor borrow to stabilize the economy?

• Intratemporal concerns about

1 incentives: taxes and transfers distort search for jobs

2 redistribution: only benefits insure unemployed workers

3 efficiency: public goods enter utility

... create additional trade-offs and possibly wedges to the standardinter temporal insurance channel


A small open economy modelof sovereign default


Model: agents

• Households: within period inequalityI employed households: work, pay taxes, consumeI unemployed households: receive transfers, consume

• FirmsI hire workers in frictional labor market to produce outputI stochastic aggregate productivity (affected by credit history)

• International lendersI purchase sovereign debtI exclude government from markets after default

• GovernmentI sets policy instruments to maximize social welfare


Model: households

Ex-ante identical but ex-post heterogeneous households i ∈ [0, 1]

• households exert search effort to find jobs, matches are resolved atend of each period

• idiosyncratic unemployment risk, common wage risk, no savings

E∞∑s=t

βs−t psei ,s︸︷︷︸job finding probability

[u(cwi ,s , ei ,s ,Gs)− κ]︸︷︷︸utility if employed

+

(1− psei ,s)︸︷︷︸unemployment risk

u(cui ,s , ei ,s ,G )︸︷︷︸utility if unemployed

cwi ,s = (1− τs)ws + πs

cui ,s = µs + πs

• c : consumption, G : public goods, e: effort, κ: disutility of work


Model: households

Optimal search effort of households

p[u(cwi , ei ,G )− κ− u(cui , ei ,G )]

= peiue(cwi , ei ,G ) + (1− pei )ue(cui , ei ,G )

⇒ ei = E(p, τ, µ,w ,G )

... is higher when

• search is more likely to produce a match

• income taxes are low

• transfers are low

• real wages are high


Model: firmsContinuum of competitive one-worker firms

• hire workers by posting vacancies at cost a, filled with prob. q

• technology

y =x(z , h′)

z follows AR(1) process

h =

0 if good credit history

1 if bad credit history

x(z , 0) ≥x(z , 1)∀z

• free entry drives value of vacancies to zero

x(z , h′)− w =a

q


Model: labor market

• Jobs are created by randomly matching workers searching foremployment and vacancies created by firms

I matching technology

n =ψeφv1−φ

v =

∫vjdj , e =

∫eidi

I aggregate employment n, vacancies v , effort e

• Nash bargaining over wages

w = argmax u(cwi , ei ,G )− κ− u(cui , ei ,G )λx(z , h′)− w1−λ

⇒ w = x(z , h′)− 1− λλ

u(cw , e,G )− κ− u(cu, e,G )

(1− τ)uc(cw , e,G )


Model: lenders

Large number of identical risk-neutral international lenders

• maximize expected revenue

Λ = q(B ′, z)b′ − E(

1− d ′

1 + r

)b′

• B: assets, d : default, r : risk-free rate

• free entry implies the bond price schedule

q(B ′, z) = E(

1− d ′

1 + r

)

• default punishment: productivity loss and temporary marketexclusion, bad credit history (h′ = 1) reverts with prob. (1− α)


Model: government

• Set of policy instrumentsI spending on public goods, GI taxation of employed workers, τI transfers to unemployed workers, µI borrowing and lending in international markets, B ′

I default, d

• Maximizes utilitarian social welfare

Et

∞∑s=t

βs−tuG (cwt , cut , et , nt ,Gt)

uG (cw , cu, e, n,G ) = n[u(cw , e,G )− κ]︸︷︷︸employed agents’ utility

+ (1− n)u(cu, e,G )︸︷︷︸unemployed agents’ utility


Model: government

• Constraints

budget: G + (1− n)µ =τwn + (1− h′)[B − q(B ′, z)B ′]

resource: G + ncw + (1− n)cu =xn − av + (1− h′)[B − q(B ′, z)B ′]

implementability: e =E(p, τ, µ,w ,G )

w =x(z , h)− a

q

w =x(z , h′)− 1− λλ

u(cw , e,G )− κ− u(cu, e,G )

(1− τ)uc(cw , e,G )

• Lack of commitment, here focus on Markov policies


Model: equilibrium

Definition (Markov-perfect equilibrium)

Given the aggregate state S, a Markov-perfect equilibrium is a set ofpolicies Ω(S), an allocation Y (S ,Ω) and a set of future policies Ω′(S)such that(i) the policies and allocation solve the government’s problem(ii) the bond price solves the lenders’ problem(iii) Ω(S) = Ω′(S).


Policy trade-offs


Policy trade-offs

• Recursive formulationI value of integration with good credit history (h = 0)

Qi (B, z) = maxd∈0,1

(1− d)Qnd(B, z) + dQd(z)

I values of not defaulting Qnd and defaulting Qd

Qnd(B, z) = maxY ,Ω0

uG (Y ,Ω0,S) + βEQi (B ′, z ′)

Qd(z) = maxY ,Ω1

uG (Y ,Ω1,S) + βE[αQi (0, z ′) + (1− α)Qd(z ′)]

subject to constraints

– Ω0 indicates h′ = 0– Ω1 indicates h′ = 1

Timing


Policy trade-offs

1 Implement Samuelson condition (efficient spending)?

uGG = nucw (cw , e,G ) + (1− n)ucu(cu, e,G )

I static wedge: distortionary tax financeI crisis wedge: elastic debt price impedes debt finance

2 Redistribution (perfect unemployment insurance)?

ucw = ucu

I static wedge: need to incentivize search, distortionary taxI crisis wedge: elastic debt price impedes debt finance

3 Intertemporal smoothing?

ucw = β(1 + r)Eu′cw

I static wedge: need to incentivize search, distortionary taxI crisis wedge: elastic debt price in bad times

4 Commit to never defaulting?


Policy trade-offs: austerity vs. default

Without commitment government chooses between

1 austerity: cutting spending+transfers and hiking taxes

2 default: eliminate outstanding debt but suffer from temporaryexclusion from financial markets and fall in productivity

• Default may be optimalI austerity is costly (insurance, incentives, efficiency)I default is costly (less scope for smoothing, productivity loss)

• Austerity may be optimal prior to default


Quantitative analysis


Quantitative analysis: functional forms

• Quarterly basis

• Functional forms

utility function: u(c , e,G ) =c1−σc − 1

1− σc− ϑ e1+σe

1 + σe+ ζ log(G )

productivity: log(zt) = ρ log(zt−1) + εt , ε ∼ N (0, σ2ε )

production technology: x (z , h′) =

z if h′ = 0z if h′ = 1 ∧ z < zz if h′ = 1 ∧ z ≥ z


Quantitative analysis: calibration

Table 1. Calibrated Parameters

Parameter Description Value

r risk-free rate 1%σc Risk aversion 21/σe Search elasticity 1/3λ Workers’ bargaining weight 0.4φ Matching elasticity 0.4ρz Productivity persistence 0.88σ2z Variance of productivity shocks 0.032

α Persistence of exclusion 0.917


Quantitative analysis: indirect inference

Table 2. Parameters estimated with indirect inference

Parameter Value Target Model

β (discount factor) 0.90 Default prob. 3% 3%a (vacancy costs) 0.04 Hiring costs 4.5% 4.4%ϑ (pref. weight) 0.02 Employment rate 89% 89%κ (pref. cost) 1.03 cu/cw = 58% 58%ξ (pref. weight) 0.54 G/c = 33% 32.8%z (prod. ceiling) 0.97 Output loss in default 5% 5.0%

Computation


Normal times, crises, and default

• Normal timesI ability to borrow at risk-free rate produces incentive to issue debt

(β < 1/(1 + r))I strong incentive to roll over debt and smooth deficitsI cheap to finance transfers and spending

• Crisis timesI price of debt responds elastically to debt issuanceI default premia rise as debt goes up and/or productivity fallsI strong incentive to stabilize debt

• DefaultI servicing of debt not worth itI countries with lower debt are more resistant to recessions


Policy functions and productivity

B-0.6 -0.4 -0.2 0

-0.2

-0.15

-0.1

-0.05

0

Debt Policy Bt+1

B-0.6 -0.4 -0.2 0

0.25

0.3

0.35

0.4

Tax Policy τ

B-0.6 -0.4 -0.2 0

0.32

0.34

0.36

0.38

0.4

Transfer Policy T

B-0.6 -0.4 -0.2 0

0.15

0.2

0.25

Spending Policy G

B-0.6 -0.4 -0.2 0

0

0.05

0.1

0.15

0.2

Interest Rate Spread

low z (−2σϵ)mean z

high z (+2σϵ)

B-0.6 -0.4 -0.2 0

0.2

0.25

0.3

Total Expenditure

B-0.6 -0.4 -0.2 0

0.2

0.25

0.3

0.35

Tax Revenue

B-0.6 -0.4 -0.2 0

-0.15

-0.1

-0.05

0

0.05

Primary Deficit to GDP

B-0.6 -0.4 -0.2 0

0.85

0.9

0.95

GDP Y

B-0.6 -0.4 -0.2 0

0.87

0.88

0.89

0.9

0.91

0.92

Search Effort E

B-0.6 -0.4 -0.2 0

0.55

0.6

0.65

Consumption C

B-0.6 -0.4 -0.2 0

0.55

0.6

0.65

0.7

Consumption Cw

B-0.6 -0.4 -0.2 0

1.55

1.6

1.65

Search Effort E

B-0.6 -0.4 -0.2 0

2.5

2.6

2.7

2.8

Vacancies V


high z (+2σϵ)


Policy functions and debt

z0.9 1 1.1 1.2

-0.4

-0.3

-0.2

-0.1

0

Debt Policy Bt+1

z0.9 1 1.1 1.2

0.3

0.35

0.4

0.45

Tax Policy τ

z0.9 1 1.1 1.2

0.3

0.35

0.4

Transfer Policy T

z0.9 1 1.1 1.2

0.15

0.2

0.25

0.3

Spending Policy G

z0.9 1 1.1 1.2

0

0.05

0.1

0.15

0.2


z0.9 1 1.1 1.2

0.2

0.25

0.3

0.35

Total Expenditure

z0.9 1 1.1 1.2

0.2

0.25

0.3

0.35

0.4

Tax Revenue

z0.9 1 1.1 1.2

-0.2

-0.15

-0.1

-0.05

0

0.05


z0.9 1 1.1 1.2

0.7

0.8

0.9

1

1.1

GDP Y

z0.9 1 1.1 1.2

0.87

0.88

0.89

0.9

0.91

0.92

Employment N

z0.9 1 1.1 1.2

0.5

0.55

0.6

0.65

0.7

0.75

Consumption C

z0.9 1 1.1 1.2

0.5

0.6

0.7

0.8

Consumption Cw

z0.9 1 1.1 1.2

1.5

1.55

1.6

1.65

1.7

Search effort E

z0.9 1 1.1 1.2

V

2.4

2.6

2.8

Vacancies V

high debt (B=-0.45)med. debt (B=-0.37)low debt (B=-0.22)


Crisis management and austerity

Once a country enters crisis zone

• hike in taxes to generate tax revenues

• dramatic cuts in transfers and in public goods provision

• consumption below default level

B-0.6 -0.4 -0.2 0

-0.2

-0.15

-0.1

-0.05

0

Debt Policy Bt+1

B-0.6 -0.4 -0.2 0

0.25

0.3

0.35

0.4

Tax Policy τ

B-0.6 -0.4 -0.2 0

0.32

0.34

0.36

0.38

0.4

Transfer Policy T

B-0.6 -0.4 -0.2 0

0.15

0.2

0.25

Spending Policy G

B-0.6 -0.4 -0.2 0

0

0.05

0.1

0.15

0.2



high z (+2σϵ)

B-0.6 -0.4 -0.2 0

0.2

0.25

0.3

Total Expenditure

B-0.6 -0.4 -0.2 0

0.2

0.25

0.3

0.35

Tax Revenue

B-0.6 -0.4 -0.2 0

-0.15

-0.1

-0.05

0

0.05


B-0.6 -0.4 -0.2 0

0.85

0.9

0.95

GDP Y

B-0.6 -0.4 -0.2 0

0.87

0.88

0.89

0.9

0.91

0.92

Search Effort E

B-0.6 -0.4 -0.2 0

0.55

0.6

0.65

Consumption C

B-0.6 -0.4 -0.2 0

0.55

0.6

0.65

0.7

Consumption Cw

B-0.6 -0.4 -0.2 0

1.55

1.6

1.65

Search Effort E

B-0.6 -0.4 -0.2 0

2.5

2.6

2.7

2.8

Vacancies V


high z (+2σϵ)

z0.9 1 1.1 1.2

-0.4

-0.3

-0.2

-0.1

0

Debt Policy Bt+1

z0.9 1 1.1 1.2

0.3

0.35

0.4

0.45

Tax Policy τ

z0.9 1 1.1 1.2

0.3

0.35

0.4

Transfer Policy T

z0.9 1 1.1 1.2

0.15

0.2

0.25

0.3

Spending Policy G

z0.9 1 1.1 1.2

0

0.05

0.1

0.15

0.2


z0.9 1 1.1 1.2

0.2

0.25

0.3

0.35

Total Expenditure

z0.9 1 1.1 1.2

0.2

0.25

0.3

0.35

0.4

Tax Revenue

z0.9 1 1.1 1.2

-0.2

-0.15

-0.1

-0.05

0

0.05


z0.9 1 1.1 1.2

0.7

0.8

0.9

1

1.1

GDP Y

z0.9 1 1.1 1.2

0.87

0.88

0.89

0.9

0.91

0.92

Employment N

z0.9 1 1.1 1.2

0.5

0.55

0.6

0.65

0.7

0.75

Consumption C

z0.9 1 1.1 1.2

0.5

0.6

0.7

0.8

Consumption Cw

z0.9 1 1.1 1.2

1.5

1.55

1.6

1.65

1.7

Search effort E

z0.9 1 1.1 1.2

V

2.4

2.6

2.8

Vacancies V

high debt (B=-0.45)med. debt (B=-0.37)low debt (B=-0.22)

⇒ Austerity!

Do we see this before a country defaults?


Default episodes

-10 0 100.92

0.94

0.96

0.98

1

1.02

1.04

1.06Productivity

-10 0 10-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0Assets to GDP

-10 0 10-0.03

-0.02

-0.01

0

0.01

0.02Primary deficit to GDP

-10 0 100

0.01

0.02

0.03

0.04

0.05

0.06

0.07Spread

-10 0 100.21

0.22

0.23

0.24

0.25

0.26Tax revenue

-10 0 100.0385

0.039

0.0395

0.04

0.0405Total transfers

-10 0 100.17

0.18

0.19

0.2

0.21

0.22Spending

-10 0 100.82

0.84

0.86

0.88

0.9

0.92

0.94Output

-10 0 100.886

0.887

0.888

0.889

0.89

0.891

0.892Employment

-10 0 100.55

0.56

0.57

0.58

0.59

0.6

0.61

0.62Consumption

-10 0 100.58

0.59

0.6

0.61

0.62

0.63

0.64

0.65Consumption, employed

• moderate growth followed by abrupt unusually low productivity• defaults preceded by short-lived austerity• post-default fiscal stimulus


Default episodes

-10 0 100.92

0.94

0.96

0.98

1

1.02

1.04

1.06Productivity

-10 0 10-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0Assets to GDP

-10 0 10-0.03

-0.02

-0.01

0

0.01


-10 0 100

0.01

0.02

0.03

0.04

0.05

0.06

0.07Spread

-10 0 100.21

0.22

0.23

0.24

0.25

0.26Tax revenue

-10 0 100.0385

0.039

0.0395

0.04


-10 0 100.17

0.18

0.19

0.2

0.21

0.22Spending

-10 0 100.82

0.84

0.86

0.88

0.9

0.92

0.94Output

-10 0 100.886

0.887

0.888

0.889

0.89

0.891

0.892Employment

-10 0 100.55

0.56

0.57

0.58

0.59

0.6

0.61

0.62Consumption

-10 0 100.58

0.59

0.6

0.61

0.62

0.63

0.64


• defaults preceded by short-lived austerity


Debt crises

-10 0 100.96

0.98

1

1.02

1.04

1.06Productivity

-10 0 10-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04Assets to GDP

-10 0 10-0.04

-0.03

-0.02

-0.01

0

0.01


-10 0 100

0.02

0.04

0.06

0.08

0.1Spread

-10 0 100.22

0.23

0.24

0.25

0.26Tax revenue

-10 0 100.038

0.0385

0.039

0.0395

0.04

0.0405


-10 0 100.17

0.18

0.19

0.2

0.21

0.22Spending

-10 0 100.86

0.88

0.9

0.92

0.94

0.96Output

-10 0 100.888

0.889

0.89

0.891

0.892

0.893Employment

-10 0 100.56

0.57

0.58

0.59

0.6

0.61

0.62

0.63Consumption

-10 0 100.58

0.6

0.62

0.64


• long sequence of low productivity, but recovers before default• spread rising• lasting austerity, govt builds up primary surplus


Debt crises

-10 0 100.96

0.98

1

1.02

1.04

1.06Productivity

-10 0 10-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04Assets to GDP

-10 0 10-0.04

-0.03

-0.02

-0.01

0

0.01


-10 0 100

0.02

0.04

0.06

0.08

0.1Spread

-10 0 100.22

0.23

0.24

0.25

0.26Tax revenue

-10 0 100.038

0.0385

0.039

0.0395

0.04

0.0405


-10 0 100.17

0.18

0.19

0.2

0.21

0.22Spending

-10 0 100.86

0.88

0.9

0.92

0.94

0.96Output

-10 0 100.888

0.889

0.89

0.891

0.892

0.893Employment

-10 0 100.56

0.57

0.58

0.59

0.6

0.61

0.62

0.63Consumption

-10 0 100.58

0.6

0.62

0.64


• lasting austerity• recession in output and consumption


The role of commitment

z0.9 1 1.1 1.2

-0.4

-0.3

-0.2

-0.1

0

Debt Policy Bt+1

z0.9 1 1.1 1.2

0.2

0.3

0.4

Tax Policy τ

z0.9 1 1.1 1.2

0.3

0.35

0.4

Transfer Policy T

z0.9 1 1.1 1.2

0.1

0.2

0.3

0.4

Spending Policy G

z0.9 1 1.1 1.2

0

0.1

0.2

0.3

0.4


z0.9 1 1.1 1.2

0.1

0.2

0.3

0.4

Total Expenditure

z0.9 1 1.1 1.2

0.1

0.2

0.3

0.4

Tax Revenue

z0.9 1 1.1 1.2

-0.15

-0.1

-0.05

0


z0.9 1 1.1 1.2

0.7

0.8

0.9

1

1.1

GDP Y

z0.9 1 1.1 1.2

0.84

0.86

0.88

0.9

0.92

0.94

Employment N

z0.9 1 1.1 1.2

0.5

0.55

0.6

0.65

0.7

0.75

Consumption C

z0.9 1 1.1 1.2

0.5

0.6

0.7

0.8

Consumption Cw

z0.9 1 1.1 1.2

1.5

1.55

1.6

1.65

1.7

Search Effort E

z0.9 1 1.1 1.2

2

2.5

3

3.5

Vacancies V

Baseline

Fixed τ

Fixed T


The role of commitment

Partial commitment

• lack of commitment matters only in a debt crisis

• allows sovereign to delay default

• still fiscal reasons for austerity

• but austerity can now be implemented without sacrificingconsumption beyond default level

z0.9 1 1.1 1.2

-0.4

-0.3

-0.2

-0.1

0

Debt Policy Bt+1

z0.9 1 1.1 1.2

0.2

0.3

0.4

Tax Policy τ

z0.9 1 1.1 1.2

0.3

0.35

0.4

Transfer Policy T

z0.9 1 1.1 1.2

0.1

0.2

0.3

0.4

Spending Policy G

z0.9 1 1.1 1.2

0

0.1

0.2

0.3

0.4


z0.9 1 1.1 1.2

0.1

0.2

0.3

0.4

Total Expenditure

z0.9 1 1.1 1.2

0.1

0.2

0.3

0.4

Tax Revenue

z0.9 1 1.1 1.2

-0.15

-0.1

-0.05

0


z0.9 1 1.1 1.2

0.7

0.8

0.9

1

1.1

GDP Y

z0.9 1 1.1 1.2

0.84

0.86

0.88

0.9

0.92

0.94

Employment N

z0.9 1 1.1 1.2

0.5

0.55

0.6

0.65

0.7

0.75

Consumption C

z0.9 1 1.1 1.2

0.5

0.6

0.7

0.8

Consumption Cw

z0.9 1 1.1 1.2

1.5

1.55

1.6

1.65

1.7

Search Effort E

z0.9 1 1.1 1.2

2

2.5

3

3.5

Vacancies V

Baseline

Fixed τ

Fixed T

⇒ Commitment matters for the reasons and implementation of austerity


Conclusion


Conclusion

Key insights

1 optimal policy problem differs across normal and crisis times

2 trade-off between austerity and default in a sovereign debt crisisI intertemporal smoothingI intratemporal concerns about incentives and insurance

3 austerity implemented in crisis times riggered byI fiscal reasonsI lack of commitment


Model: Timing

Figure – Timing of the Model

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ComputationDifficult to solve nurmerially due to discrete default decision, computationof optimal policy and precision required

1 Precomputation: Approximate static problem’s solution as a functionof state and capital inflow (knitromatlab, spline)

2 Collocation methodI Approximate (expected) value functions and pricing function for full

problem (CompEcon, spline)I Initialize at last period of finite horizon model, get shape with a few

Bellman iterations, Newton method

3 Expectation: Approximate error distribution with a Gaussianquadrature scheme

4 Stationary distributionI Approximate ergodic distribution with a fine histogram (eigenvector)I Endogenous transitions off the grid are weighted towards neighboring

points according to relative distance

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time consistent fiscal policy in a debt crisis, by neele balke (university college london)

Economy & Finance