time consistent fiscal policy in a debt crisis, by neele balke (university college london)
TRANSCRIPT
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)?
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 2 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 3 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 4 / 34
A small open economy modelof sovereign default
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 5 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 6 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 7 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 8 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 9 / 34
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 )
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 10 / 34
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)
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 11 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 12 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 13 / 34
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).
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 14 / 34
Policy trade-offs
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 15 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 16 / 34
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?
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 17 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 18 / 34
Quantitative analysis
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 19 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 20 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 21 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 22 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 23 / 34
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
low z (−2σϵ)mean z
high z (+2σϵ)
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 24 / 34
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
Interest Rate Spread
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
Primary Deficit to GDP
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)
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 25 / 34
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
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
low z (−2σϵ)mean z
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
Interest Rate Spread
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
Primary Deficit to GDP
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?
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 26 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 27 / 34
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
• defaults preceded by short-lived austerity
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 28 / 34
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
0.02Primary deficit to GDP
-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
0.041Total transfers
-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
0.66Consumption, employed
• long sequence of low productivity, but recovers before default• spread rising• lasting austerity, govt builds up primary surplus
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 29 / 34
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
0.02Primary deficit to GDP
-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
0.041Total transfers
-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
0.66Consumption, employed
• lasting austerity• recession in output and consumption
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 30 / 34
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
Interest Rate Spread
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
Primary Deficit to GDP
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 31 / 34
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
Interest Rate Spread
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
Primary Deficit to GDP
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 32 / 34
Conclusion
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 33 / 34
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
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 34 / 34
Model: Timing
Figure – Timing of the Model
back
Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 35 / 34
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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Balke, Ravn (2016) Time-consistent Fiscal Policy in a Debt Crisis Barcelona, March 2017 36 / 34