Inflation, Debt, and Default

Transcription

1 Inflation, Debt, and Default Sewon Hur (University of Pittsburgh) Illenin Kondo (University of Notre Dame) Fabrizio Perri (Minneapolis Fed) March, 2018 The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. 0 / 36

2 Motivation: U.S. inflation cyclicality discount (a) Inflation and Consumption Growth Inflation Percent Percent Consumption growth (b) Real Interest Rates Real interest Rate (%) (c) Co-movement and Real Interest Rates Correlation of Inflation and Consumption Growth -4-6 Real rate Trend Year Note: Inflation is the log difference between CPI in quarter t and t-4. Consumption growth is the log difference in real personal consumption expenditures over the same interval. Real interest rates are nominal rates on government securities (from the IMF IFS database) minus expected inflation computed using a linear univariate forecasting model estimated on actual inflation. 1 / 36

3 Why inflation cyclicality matters The majority of sovereign debt in advanced economies is subject to inflation risk (nominal) held domestically data The co-movement between inflation and consumption growth varies over time and across countries Procyclical inflation makes nominal debt less risky to lender: less inflation in bad times (hedging) more risky to borrower: more payout bad times (default risk) in bad times, procyclical/countercyclical inflation complements/substitutes default 2 / 36

4 This paper We document an inflation-procyclicality discount higher covariance associated with lower real rates but not so much in bad states Build a sovereign default model with domestic nominal debt inflation-output co-movement taken as given e.g. changes in monetary policy regime or underlying shocks In the calibrated model, the pro-cyclical economy has lower real rates in normal times more debt crises and defaults in bad times Implications for secular fall in real rates and Euro debt crisis 3 / 36

5 Related literature Sovereign default: Eaton and Gersovitz (1981), Aguiar and Gopinath (2007), Arellano (2008), Chatterjee and Eyigungor (2012), Lizarazo (2013), Aguiar et al. (2016), and many others. Domestic/Selective default: Broner et al. (2010), Reinhart and Rogoff (2011), D Erasmo and Mendoza (2012), Pouzo and Presno (2014), Mallucci (2015), Arellano and Kocherlakota (2014). Default and inflation: Aguiar et al. (2012), Berriel and Bhattarai (2013), Faraglia et al. (2013), Nuno and Thomas (2015), Du and Schreger (2015), Kursat, Onder and Sunel (2016), Sunder-Plassman (2016), Perez and Ottonello (2016), Fried (2017). Cyclicality of inflation: Boudoukh (1993), Ang et al. (2008), Campbell et al. (2016), Song (2014), Du et al. (2016), Kang and Pflueger (2015), Albanesi et al. (2003) Monetary unions: Aguiar et al. (2013), Corsetti and Dedola (2013), Eijffinger et al. (2018) 4 / 36

6 Empirical evidence 4 / 36

7 Evidence on real yields and inflation cyclicality Compute country-specific time-varying co-movement between innovations to inflation and to consumption growth Follow Boudoukh (1993) s country-by-country VAR π it g c it = A i π i,t 1 gi,t 1 c + ε πit ε git sample: 19 OECD countries; quarterly data compute conditional co-movement between επit and ε git using overlapping ten-year windows Graph Real yields adjusted for expected future inflation 5 / 36

8 Real interest rates: the inflation cyclicality discount Real yield on government debt (1) (2) (3) Inflation consumption covariance (0.54) (0.38) (0.64) Lagged Debt Yes Yes Yes Mean of π and g c residuals No Yes Yes Variance of π and g c residuals No No Yes adj. R N Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, ITA,JPN,KOR,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country. p < 0.05, p < 0.01 All regressions include country and time fixed effects One standard deviation increase in cov(ε π it, ε gc it ) 0.17 is associated with 31 bp decrease in real sovereign yields 6 / 36

9 Procyclicality discount larger in good times Real yield on government debt (1) (2) (3) Inflation consumption covariance 1.80 (0.64) Covariance*1 good times (0.70) (0.91) Covariance*1 bad times (0.68) (0.79) 1 good times Yes Yes Yes other controls Yes Yes Yes adj. R N (2): 1 good times avg. residual cons. growth > 0. (3): 1 good times avg. credit rating = AAA (median). Standard errors clustered by country. p < 0.05, p < 0.01 All regressions include country and time fixed effects. Robustness: debt measures yield measures alternative windows 7 / 36

10 Model 7 / 36

11 Model We develop a model of sovereign debt builds on standard model inflation, exogenous (e.g. changes in monetary independence, changes in nature of supply/demand shocks in the economy) risk-averse, domestic lenders hold nominal bonds Simple 2-period model to develop intuition Calibrated model to investigate how inflation cyclicality affects interest rates and debt crises dynamics 8 / 36

12 A two-period model Competitive lenders (patient) and borrowers (less patient) with endowments first period: yl = y b = 1 second period: yl = y b = x x F (x),e(x) = 1, Finite support, x [xmin, x max ] x aggregate risk, both agents exposed to it 9 / 36

13 A two-period model Competitive lenders (patient) and borrowers (less patient) with endowments first period: yl = y b = 1 second period: yl = y b = x x F (x),e(x) = 1, Finite support, x [xmin, x max ] x aggregate risk, both agents exposed to it Debt b is nominal with price q and nominal payoff of 1 Price level in period 1 normalized to 1 Cyclical prices (inflation) in period 2: π(x) = (1 + κ(x 1)) κ: cyclicality of inflation if κ > 0, high inflation in good times expected inflation is 0, hence 1/q is real interest rate 9 / 36

14 No default case Borrower solves (given q) ( max u(1 + qb b ) + β b u x b ) b df (x), b X π(x; κ) Lender solves (given q) ( max u(1 qb l ) + β l u x + b ) l df (x), b X π(x; κ) Equilibrium: {b l, b b, q} such that given q, {bl, b b } are optimal, and bl = b b 10 / 36

15 Real Interest rate, % Equilibrium interest rates and debt Saving Borrowing Borrowing/Saving 11 / 36

16 Real Interest rate, % Interest rates and cyclicality of inflation Countercyclical Procyclical Inflation Saving Borrowing Borrowing/Saving 12 / 36

17 Interest rates and cyclicality of inflation As inflation moves from countercyclical to procyclical: lenders want to save more (better hedging with bonds) borrowers want to borrow less (worse hedging with bonds) real interest rate unequivocally falls equilibrium debt levels can move in either direction 13 / 36

18 Interest rates and cyclicality of inflation As inflation moves from countercyclical to procyclical: lenders want to save more (better hedging with bonds) borrowers want to borrow less (worse hedging with bonds) real interest rate unequivocally falls equilibrium debt levels can move in either direction In the paper, we also show (in a 3-period model) that procylicality discount increases with debt maturity 13 / 36

19 Simple model with default Borrower can default by paying a cost C(x) = ψ(x x min ) 2 Equilibrium default when costs are below repayment Default set (typically is an interval) x : ψ(x x min ) 2 < b π(x; κ) Competitive default model (e.g. Dubey, et al. 2005): borrowers are atomistic, so do not internalize the effect of their own borrowing on spreads With default, cyclicality of inflation can change the default sets, thereby altering the hedging properties of bonds 14 / 36

20 Default sets Default Cost Repayment, Counter π, given b Repayment, Pro π, given b X (GDP) Default sets In the paper, we show that there exists a unique threshold x(κ, b b ) such that default occurs if and only if x x(κ, b b ) Further, we show that the threshold increases with κ 15 / 36

21 Simple model with default Borrower solves (given q) max b b u (1 + qb b )+β b xmax x(b b ) ( u x b ) b + π(x) } {{ } Repayment Lender solves (given q and x(b b )) max b l u (1 qb l ) + β l xmax ( u x + b l x(b b ) x min u (x C(x)) df (x) } {{ } Default and suffer cost ) x π(x) }{{} Repayment x + u (x) df (x) x } min {{} Defaulted on Equilibrium: {b l, b b, q} such that, given q, {b l, b b } are optimal, and b l = b b 16 / 36

22 Real Interest rate, % Equilibrium interest rates and debt with default Saving Borrowing Borrowing/Saving 17 / 36

23 Real Interest rate, % Inflation cyclicality and default Countercyclical Procyclical Inflation Saving Borrowing Borrowing/Saving 18 / 36

24 Takeaways Without default more procyclical inflation reduces real rates 19 / 36

25 Takeaways Without default more procyclical inflation reduces real rates With default more procyclical inflation might increase rates Countercyclical/Procyclical inflation = low/high repayments substitutes/complements default in bad times A country following procyclical inflation will face lower real rates if not at default risk, but might face a sudden spike in rates in bad times 19 / 36

26 Quantitative Model Closed economy, discrete time t = 0, 1, 2,..., one good Endowments y and inflation π follow a joint Markov process Default cost regime, indexed by k {0, 1} Let s (y, π, k) Debt market structure long-term nominal bond matures with probability δ pays coupon payment r each period subject to inflation risk 20 / 36

27 Lenders As in Arellano (2008) and Hatchondo et al. (2016), lenders value flows using a stochastic discount factor m(y t, y t+1 ) We assume that ( ) 1 yt+1 m(y t, y t+1 ) = β l y t W 1 γ l t+1 E t [ W 1 γ l t+1 ] (1) where β l and γ l denote the lender s discount factor and risk aversion, respectively, and W t is defined recursively (Epstein-Zin-Weil) as log W t = (1 β l ) log y t + β l log ( [ ]) E t W 1 γ l t+1 1 γ l (2) 21 / 36

28 Government Government preferences are given by E 0 βgu t g (g t ) t=0 where 0 < β g < β l < 1, g is government consumption, and Government revenue: τ y u g (g) = g 1 γg 1 γ g 22 / 36

29 Government Government preferences are given by E 0 βgu t g (g t ) t=0 where 0 < β g < β l < 1, g is government consumption, and Government revenue: τ y u g (g) = g 1 γg 1 γ g Given the option to default, the government chooses { V o (B, s) = max V c (B, s), V d (B, s) } c,d 22 / 36

30 Value of repayment The value, conditional on not defaulting, is given by V c (B, s) = max B u g (τy q(s, B )(B (1 δ)b) + B(r + δ)) + β g E s s where q(s, B ) is the bond price [ ( )] B V o 1 + π, s Real yield is stochastic (even w/o default) In bad times, countercyclical inflation substitute to default 23 / 36

31 Value of default The value of default is given by V d (B, s) = ( )) u g (τ y φ d (y) [ ( ) λb +β g E s s θv o 1 + π, s ( )] λb + (1 θ)v d 1 + π, s 0 θ 1 : probability of regaining access to credit, 23 / 36

32 Value of default The value of default is given by V d (B, s) = ( )) u g (τ y φ d (y) [ ( ) λb +β g E s s θv o 1 + π, s ( )] λb + (1 θ)v d 1 + π, s 0 θ 1 : probability of regaining access to credit, 0 λ 1 : recovery rate, and 24 / 36

33 Value of default The value of default is given by V d (B, s) = ( )) u g (τ y φ d (y) [ ( ) λb +β g E s s θv o 1 + π, s ( )] λb + (1 θ)v d 1 + π, s 0 θ 1 : probability of regaining access to credit, 0 λ 1 : recovery rate, and quadratic cost of default φ d (y) = d 1 (k) max { 0, 1 y + (1 1 ) } y 2 d 0 d0 default cost at mean is φ d (1) = d 1 (k), where d 1 (1) > d 1 (0) default costs matter when φ d (y) > 0, when y < 1 + d 0 24 / 36

34 Bond price In this environment, the bond price schedule satisfies [ ] 1 d q(s, B ) = β l E s s 1 + π (r + δ + (1 δ)q(s, B ))m(y, y ) [ ( ) ] d B + β l E s s 1 + π qd 1 + π, s m(y, y ) where q d is the price of a bond in default. default price 25 / 36

35 Cyclicality of inflation and borrowing costs With full default (λ = 0) and short term debt (δ = 1), the spread definition can be written as spr t Pr t [d t+1 = 1] }{{} default premium [ ] [ ] mt,t+1 + cov t E t [m t,t+1 ], d Et [1 + π t+1 ] t+1 + cov t, d t π t+1 [ mt,t+1 Pr t [d t+1 = 0] cov t E t [m t,t+1 ], E ] t [1 + π t+1 ]. 1 + π t+1 }{{} procylicality discount Spreads are increasing in default probability and decreasing in inflation cyclicality 26 / 36

36 Quantitative experiment Impact of inflation cyclicality on interest rates and debt crises Calibrate model with zero covariance benchmark model Contrast the effects of inflation cyclicality over the cycle 27 / 36

37 Stochastic Process Output and inflation follow log y = ρ y π ρ y,π ρ π,y ρ π log y π + ε y ε π where ε y = N 0, σ2 y ε π 0 σ π,y σ π,y σπ 2 Estimates on OECD sample ( ) Parameters Values Source Persistence ρ y, ρ π 0.80 author estimates Spillovers ρ π,y, ρ y,π 0.00 author estimates Volatility σ y, σ π 0.01 author estimates Covariance σ π,y 0.00 acyclical baseline 28 / 36

38 Regime switching The default cost regimes follow a Markov switching process with transition matrix P = p h 1 p h 1 p l p l Estimates on subsample (Eurozone ex. Germany, ) Parameters Values Source High cost persistence p h persistence of low spreads (< 2%) Low cost persistence p l persistence of high spreads (> 2%) : Nominal rates minus German rates 29 / 36

39 Calibration of other parameters Parameters Values Targets / Source Gov t discount factor β g default prob.: 0.2 percent sensitivity Default cost at mean d 1 (0) bad times def. prob. (k = 0): 0.8% Default cost at mean d 1 (1) bad times def. prob. (k = 1): 0.3% Default cost cutoff d st. dev. below mean output Lender discount factor β l risk-free rate: 4 percent Lender risk aversion γ l 59 Hatchondo et al. (2016) Gov t risk aversion γ g 2 Hatchondo et al. (2016) Probability of re-entry θ average exclusion: 10 quarters Recovery parameter λ recovery rate: 50 percent Tax rate τ OECD gov t consumption share Maturity δ OECD average maturity: 4.6 years : Richmond and Dias (2008), : Benjamin and Wright (2009) 30 / 36

40 Results The procyclical inflation regime has lower borrowing costs despite more default crises lower debt levels Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Default prob. (percent) Spreads (percent) definition Debt (pct. of tax receipts) b.p. discount accounts for 42 percent of the empirical discount 31 / 36

41 Procyclicality discount stronger in good times During goods times + high default cost regime default risk is immaterial larger procyclicality discount Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (high default cost regime) in good times (pct) in bad times (pct) Default prob. (high default cost regime) in good times (pct) in bad times (pct) / 36

42 Procyclicality premium with material default risk During bad times + low default cost regime default risk is material procyclicality premium Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (low default cost regime) in good times (pct) in bad times (pct) Default prob. (low default cost regime) in good times (pct) in bad times (pct) / 36

43 Discussion of robustness The main result of a stronger procylicality discount in good times is qualitatively robust to preferences, debt maturity, and regime switching assumptions These assumptions matter quantitatively: procylicality discount is decreasing in risk aversion details CRRA preferences with high risk aversion features high spreads and volatile risk-free rates details procylicality discount is increasing in debt maturity details procylicality discount is smaller in single default cost regimes details 34 / 36

44 y y Preferences for inflation cyclicality regime Government (Borrowers, Italy/Spain?) typically prefers countercylicality Lenders (Germany?) prefer procyclicality Preferences strongly diverge in bad states (a) Borrower Borrower (b) Lender Lender prefer procyclical 1.02 prefer procyclical indifferent prefer countercyclical B B indifferent Figure: Welfare comparison of cyclicality regimes across states 35 / 36

45 Conclusion In good times, the procyclical economy enjoys lower real rates In bad times, the risk of default increases more for the procylical economy which leads to higher real rates Recessions increase the contrast over monetary policy Potential explanation for the secular decline in real rates 36 / 36

46 Appendix 36 / 36

47 Domestic share of government debt is high back Year Country Mean Australia Belgium Canada Denmark Finland France Germany Italy Japan Netherlands Norway Portugal Spain Sweden United Kingdom United States Mean Sources: BIS, Haver 37 / 36

48 Conditional correlation between inflation and consumption growth back AUS AUT BEL CAN CHE DEU DNK ESP FIN FRA GBR ITA JPN KOR correlation 1990q1 2000q1 2010q1 1990q1 2000q1 2010q1 NLD NOR PRT SWE USA 1990q1 2000q1 2010q1 1990q1 2000q1 2010q1 1990q1 2000q1 2010q1 1990q1 2000q1 2010q1 1990q1 2000q1 2010q1 Graphs by Country code (numeric) 38 / 36

49 Predicted default probability back Regress CDS-implied default prob. on credit ratings, cons. growth, and debt (with time and country fixed effects) AUS AUT BEL CAN CHE DEU DNK predicted default probability ESP FIN FRA GBR ITA JPN KOR NLD NOR PRT SWE USA 1985q1 1995q1 2005q1 2015q1 1985q1 1995q1 2005q1 2015q1 1985q1 1995q1 2005q1 2015q1 1985q1 1995q1 2005q1 2015q1 1985q1 1995q1 2005q1 2015q1 1985q1 1995q1 2005q1 2015q1 1985q1 1995q1 2005q1 2015q1 Fitted values CDS implied default probability Graphs by Country code (numeric) 39 / 36

50 Bond price in default back The price of a bond in default satisfies [ ] 1 d q d (B, s) = λθe s s 1 + π (r + δ + (1 δ)q(s, B ))m(y, y ) [ ( ) ] 1 θ + θd λb + λe s s q d 1 + π 1 + π, s m(y, y ) where d and B are default and assets given respectively ( ) λb 1 + π, s, 40 / 36

51 Measuring spreads in the model decomposition results We measure spread as the real rate minus the risk-free rate: where spr t = 1 q t+1 1 q RF t+1 1 q t+1 = 1 q t+1 q RF t+1 [ q(s, B ) = E s s (1 d ) 1 + π(s) ] 1 + π (r + δ + (1 δ) q(s, B ))m(y, y ) [ + E s s d 1 + π(s) ( B 1 + π q d ) ] 1 + π, s m(y, y ) [ ] q RF (s) = E s s (r + δ + (1 δ)q RF (s ))m(y, y ) 41 / 36

52 Robust to alternative yield measures back Real yield on government debt (1) (2) (3) Yield source IFS Fame 5-year Fame 10-year Inflation consumption covariance (.64) (.92) (1.12) other controls Yes Yes Yes adj. R N Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, ITA,JPN,KOR,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country. p < 0.05, p < 0.01 All regressions include country and time fixed effects 42 / 36

53 Robust to alternative debt measures back Real yield on government debt (1) (2) (3) (4) Debt source Oxford & OECD Oxford OECD & OECD Oxford Inflation consumption covariance (.64) (1.60) (0.56) (0.64) other controls Yes Yes Yes Yes adj. R N Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, ITA,JPN,KOR,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country. p < 0.05, p < 0.01 All regressions include country and time fixed effects 43 / 36

54 Robust to alternative windows back Real yield on government debt (1) (2) (3) Window length 10 years 7 years 5 years Inflation consumption covariance (0.64) (0.57) (0.49) other controls Yes Yes Yes adj. R N Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, ITA,JPN,KOR,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country. p < 0.05, p < 0.01 All regressions include country and time fixed effects 44 / 36

55 Robustness to government discount factor back Stronger procylicality discount in good times Lower patience (β g = 0.985) Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) Higher patience (β g = 0.989) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) / 36

56 Robustness to default cost threshold d 0 back Stronger procylicality discount in good times Lower output threshold (d 0 = 0.035) Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) Higher output threshold (d 0 = 0.020) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) / 36

57 Robustness to utility function back Stronger procylicality discount in good times Epstein-Zin (γ l = 8) Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) CRRA (γ l = 8) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) / 36

58 Robustness to risk aversion back Stronger procylicality discount in good times Procylicality discount increasing in risk aversion Lower risk aversion (γ l = 8) Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) Higher risk aversion (γ l = 120) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) / 36

59 Robustness to debt maturity back Stronger procylicality discount in good times Good times discount increasing in debt maturity Shorter debt maturity (4 years) Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) Longer debt maturity (6 years) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) / 36

60 Robustness to single default cost regime back Stronger procylicality discount in good times Pprocylicality discount increasing in default cost High default cost regime (p h = 1) Positive Negative co-movement co-movement Difference (+1.5 s.d.) ( 1.5 s.d.) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) Low default cost regime (p l = 1) Spreads (pct) Spreads in good times (pct) Spreads in bad times (pct) Def. prob. in good times (pct) Def. prob. in bad times (pct) / 36