Government Debt Maturity Structure, Fiscal Policy, and Default - PowerPoint PPT Presentation

Government Debt Maturity Structure, Fiscal Policy, and Default Sergii Kiiashko Kyiv School of Economics and National Bank of Ukraine August, 2019 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 1 / 21

Government Debt Maturity Structure Source: Bloomberg. Data collected on 17th of October, 2017. Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 2 / 21

Introduction Motivation : Empirical facts : decaying maturity profile No consensus on how debt maturity should be managed: more short-term debt or long-term debt? No theory that explains the decaying profile of maturity: ◮ Lucas and Stokey (1983): endogenous risk-free interest rates but no default ⇒ flat maturity structure ◮ Aguiar et al (2018): endogenous default but exogenous risk-free rates ⇒ issue only one-period debt Questions : 1 What is the optimal government debt maturity structure in an environment with lack of commitment and opportunity to default, if both risk-free interest rates and risk premiums are endogenous? 2 Are predictions of this model consistent with empirical observations? Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 3 / 21

This Project A la Lucas and Stokey (1983) model : closed economy: government borrows from households lack of commitment strictly concave utility over consumption ⇒ risk-free interest rates are endogenous With opportunity to default as in Aguiar, Amador, Hopenhayn, and Werning (2018): default risk is continuously increasing in outstanding debt ⇒ risk premiums are endogenous Results: Solution is time-consistent : government follows ex ante optimal fiscal policies conditional 1 on no default. 2 In the presence of sufficient default risk, the optimal maturity structure has a decaying profile. Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 4 / 21

Outline Introduction 1 A Three-Period Example 2 Markov Perfect Competitive Equilibrium 3 Optimal Maturity Structure 4 Numerical Exercises 5 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 5 / 21

A Three-Period Example Three periods A governemnt is endowed with τ every period and maximizes θ 0 ω ( g 0 ) + ω ( g 1 ) + ω ( g 2 ) No initial debt but θ 0 > 1 so there is incentive to borrow Government borrows from lenders ( b 1 0 , b 2 0 , b 2 1 ) Important features: ◮ lack of commitment ◮ risk-averse lenders with u ( c t ), c t + g t = 1 ◮ default risk in period 2 with π ′ ( b 2 1 ) ≥ 0 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 6 / 21

Modified Commitment Problem Consider a planner who can commit to policy in period 1. To simplify notation, let s t = τ − g t , c t = 1 − τ + s t , b 2 1 = s 2 Optimization problem is max θ 0 ω ( τ − s 0 ) + ω ( τ − s 1 ) + E V 2 ( τ − s 2 ) s 0 , s 1 , s 2 s.t. s 0 + u ′ (1 − τ + s 1 ) u ′ (1 − τ + s 0 ) s 1 + u ′ (1 − τ + s 2 ) u ′ (1 − τ + s 0 ) (1 − π ( s 2 )) s 2 = 0 The maturity structure is irrelevant . Let ( s ⋆ 0 , s ⋆ 1 , s ⋆ 2 ) denote the optimal policy. Can the government with lack of commitment achieve the planner’s allocation? Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 7 / 21

Optimal Maturity Structure Case of commitment : max ω ( τ − s 1 ) + E V 2 ( τ − s 2 ) s 1 , s 2 s.t. u ′ (1 − τ + s 1 ) s 1 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) s 2 = − u ′ (1 − τ + s 0 ) s 0 Case of no commitment (same utility function but different budget constraint): s.t. u ′ (1 − τ + s 1 ) s 1 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) s 2 = u ′ (1 − τ + s 1 ) b 1 0 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) b 2 0 Optimal maturity structure of debt should satisfy: ∂ u ′ (1 − τ + s ⋆ 0 + ∂ u ′ (1 − τ + s ⋆ 2 )(1 − π ( s ⋆ 1 ) 2 )) △ s 1 · b 1 △ s 2 · b 2 0 = 0 ∂ s 1 ∂ s 2 ∂ u ′ (1 − τ + s ⋆ 2 )(1 − π ( s ⋆ 2 )) ⇒ b 1 ∂ s 2 0 · MRS ⋆ = b 2 ∂ u ′ (1 − τ + s ⋆ 1 ) 0 ∂ s 1 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 8 / 21

Optimal Maturity Structure Case of commitment : max ω ( τ − s 1 ) + E V 2 ( τ − s 2 ) s 1 , s 2 s.t. u ′ (1 − τ + s 1 ) s 1 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) s 2 = − u ′ (1 − τ + s 0 ) s 0 Case of no commitment (same utility function but different budget constraint): s.t. u ′ (1 − τ + s 1 ) s 1 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) s 2 = u ′ (1 − τ + s 1 ) b 1 0 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) b 2 0 Optimal maturity structure of debt should satisfy: ∂ u ′ (1 − τ + s ⋆ 0 + ∂ u ′ (1 − τ + s ⋆ 2 )(1 − π ( s ⋆ 1 ) 2 )) △ s 1 · b 1 △ s 2 · b 2 0 = 0 ∂ s 1 ∂ s 2 ∂ u ′ (1 − τ + s ⋆ 2 )(1 − π ( s ⋆ 2 )) ⇒ b 1 ∂ s 2 0 · MRS ⋆ = b 2 ∂ u ′ (1 − τ + s ⋆ 1 ) 0 ∂ s 1 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 8 / 21

Optimal Maturity Structure Case of commitment : max ω ( τ − s 1 ) + E V 2 ( τ − s 2 ) s 1 , s 2 s.t. u ′ (1 − τ + s 1 ) s 1 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) s 2 = − u ′ (1 − τ + s 0 ) s 0 Case of no commitment (same utility function but different budget constraint): s.t. u ′ (1 − τ + s 1 ) s 1 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) s 2 = u ′ (1 − τ + s 1 ) b 1 0 + u ′ (1 − τ + s 2 )(1 − π ( s 2 )) b 2 0 Optimal maturity structure of debt should satisfy: ∂ u ′ (1 − τ + s ⋆ 0 + ∂ u ′ (1 − τ + s ⋆ 2 )(1 − π ( s ⋆ 1 ) 2 )) △ s 1 · b 1 △ s 2 · b 2 0 = 0 ∂ s 1 ∂ s 2 ∂ u ′ (1 − τ + s ⋆ 2 )(1 − π ( s ⋆ 2 )) ⇒ b 1 ∂ s 2 0 · MRS ⋆ = b 2 ∂ u ′ (1 − τ + s ⋆ 1 ) 0 ∂ s 1 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 8 / 21

Discussion Lucas and Stokey, 1983: suppose π = π ′ = 0 ⇒ s ⋆ 1 = s ⋆ 2 ⇒ b 1 0 = b 2 0 if maturity is not flat, say b 1 0 > b 2 0 , government has incentive to increase s 1 and decrease s 2 . Aguiar et al., 2018: suppose u ′ = const ⇒ b 2 0 = 0 if b 2 > 0, government has incentive to increase s 2 and decrease s 1 This model: ST debt is manipulated by changes in risk-free interest rate LT debt is manipulated by changes in rf interest rate AND default premium ⇒ generally, once government changes surplus, LT interest rates respond stronger than ST ⇒ b 1 0 > b 2 0 > 0 Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 9 / 21

Overview of the Model Representative household: values private consumption c t and government spending g t : ∞ � β t ( u ( c t ) + θ t ω ( g t )) E t =0 endowed with 1 unit of consumption optimally chooses consumption and savings (government bonds) Government: benevolent (same preference) collects τ in taxes optimally chooses government spending and issues bonds b t + k , q t + k is price t t lacks commitment (makes decisions every period) and can default if defaults receives V def which is stochastic and continuously distributed t Resource constraint: c t + g t ≤ 1 ∀ t . Assumptions: θ 0 > θ 1 = θ 2 = ... = θ T = 1, ω ′ ( τ ) ≥ u ′ (1 − τ ). Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 10 / 21

Overview of the Model Representative household: values private consumption c t and government spending g t : ∞ � β t ( u ( c t ) + θ t ω ( g t )) E t =0 endowed with 1 unit of consumption optimally chooses consumption and savings (government bonds) Government: benevolent (same preference) collects τ in taxes optimally chooses government spending and issues bonds b t + k , q t + k is price t t lacks commitment (makes decisions every period) and can default if defaults receives V def which is stochastic and continuously distributed t Resource constraint: c t + g t ≤ 1 ∀ t . Assumptions: θ 0 > θ 1 = θ 2 = ... = θ T = 1, ω ′ ( τ ) ≥ u ′ (1 − τ ). Sergii Kiiashko (Kyiv School of Economics and National Bank of Ukraine ) Optimal Maturity Structure August, 2019 10 / 21