Reinhart& Rogof(2010) , GDP 90%, ;, Cecchetietal(2011) 18 OECD , GDP 85%, Checherita-Westphal& Rother(2012) 12, GDP 90%~100% Kumar& Woo

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1 *,,,, 60%~ 76%,,,,, (,2017),,,,, GDP,, (,2014),,,,,, ;,,,,,,, *, , liulanbiao@nankai.edu.cn;, (17ZDA074) (14AZD032) (TJYY13-007), 30

2 Reinhart& Rogof(2010) , GDP 90%, ;, Cecchetietal(2011) 18 OECD , GDP 85%, Checherita-Westphal& Rother(2012) 12, GDP 90%~100% Kumar& Woo(2010), GDP 90%,, (2014), ( % ~ %) (90%~100%) (2017), GDP, 5, GDP,, ( 7 ),,,,,,, (Re- gime),,,,,, Woodford(1990),,,,, (Bernheim,1989), (Barro,1989),,, Woodford(1990),, 1, g e t=e(1+g) t, A,B Y t = (1+g) t-1 f(k t /(1+g) t-1 ) (1),Y t t,k t t,f( ), (CRS), 31

3 maxu = β t (1+g) t υ(c t/(1+g) i t ) (2) t=0, υ( ),, β C i t i t,, c=c t/(1+g) i t, c+τ/2+ (1+g)k =e+ [f(k)- (1+r)k]/2+d[(1+r)/(1+g)] (3), c=c t/(1+g) i t, c+τ/2+d =e+ [f(k)- (1+r)k]/2+ (1+r)k (4) (3)(4), τ=t t /(1+g) t, d=d t /(1+g) t, k=k t /(1+g) t, υ (c)/υ (c)=β ( 1+r) (5) υ (c)/υ (c)=βf (k) (6),, (5)(6) f (k)=β -2 (1+r) -1 (7),,, 1+r=f (k) (8) 1 Y t=(1+g) t k θ,0<θ<1,, 1 (3)(4) c-c k = (1+g)+ (1+r) + d 1+g (9), χ (r)=f (k)-(1+r)>0 (7) (9),, g>0, θ (0,1), β>0, k>0,(10) k d = 1 >0 (10) (c-c)(1-θ) (1+g)1+ [ β 2 θk θ (1+g+β -2 θ -1 k ] 1-θ ), χ (r)=f (k)-(1+r)=0 (8) (9),, k d =- 1 (1-θ)(c-c) (1+g)1- θkθ-2 (1+g+θk θ-1 2 ) [ ] <0 (11) (1-θ)(c-c) (11), θkθ-2 (1+g+θk θ-1 ) <1 2, c-c=αk θ, α (0,1) [αθ(1-θ)-θ 2 ]k 2θ-2-2(1+g)θk θ-1 -(1+g) 2 <0 x=k θ-1, (x)=[αθ(1-θ)-θ 2 ]x 2-2(1+g)θx-(1+g) 2, 32

4 Δ=4(1+g) 2 αθ(1-θ)>0 (x), (x)=0 1+g x 1=- 槡 αθ(1-θ )+θ <0,x 2 = 1+g (θ)= 槡 αθ(1-θ )-θ, (θ) 槡 αθ(1-θ )-θ = 槡 α(1-2θ) 2 槡 θ槡 1- θ -1 烄 θ1 = 烅 θ2 = 烆槡 1+ α-1 2 槡 1+α 槡 1+ α+1 2 槡 1+α (12) 0<θ1<1/ 2槡 2,1/ 2槡 2<θ2<1,, φ (θ) (0,θ1), (θ1,1) θ1 φ (θ), 槡 φ (θ1)= 1+ α-1 >0 2 φ (θ)=0 θ 0 1=0,θ 0 2=α/(1+α) θ (0,α/(1+α)),x 2>0;,x 2<0 α,,,θ 0 2 0,,x 2<0,x=k θ-1 >0,, (x) k,,, ;,,, 2 χ ( r)=f (k)-(1+r) χ ( r),,, χ (r)=0,,,,, (Lin,2010),,,,,,,,,,,,, ( ) 1. GDP (growth), X12 GDP, GDP, 2. (1) (debtrate), (,2014), GDP 33

5 GDP GDP, (2014) (2014), GDP,,, (2) (rate),,, Checherita-Westpha & Rother(2012) (2017) GDP,,, (3) (bad),,,,, 3., , 48 Wind Stata14, (2017), ( t+1 GDP t ), 1, (debtrate) 0.63, 55%~80%,,, (rate), (bad), 1 dlngdp debtrate rate(%) bad(%) ( ), (debtrate) (rate) (bad) ( 1) 1, X12,, ( ), , ,, ,,, 2009,, 34, 2006,

6 1, 2008,, 2010,,, 1, (debtrate) (bad),, ; (rate),,, growth t =β 0 + β 1debtratet + β 2debtrate2 t +β 3ratet + β 4badt +εt (13), β i(i=0,1,2,3,4),εt (13) 2 2 Constant debtrate 2 debtrate rate bad R ,*** ** * 1% 5% 10%, 2, 33.55%,,,,,, 72%,,,, GDP 35

7 2018 5,, ( ),,, (Shu & Zhang,2012;,2013;,2013), ( ),, ( ) (thresholdlevel),,,hansen (2000) ( ), {yi,x i,qi} i=1, n qi (thresholdvariable), x i yi =β 1x i +εi, qi 烄 γ 烅 yi =β 2x i +εi, qi 烆 >γ (14),γ,x i, εi yi =β 1x i I(qi γ)+β 2x i I(qi >γ)+εi (15),I( ),Hansen(2000), ^γ 1. (debtrate) (rate) (bad) (debtrate), Hansen(2000), Stata,,LM , p 0.017, 5%, Hansen (2000) γ, (NLS) (15),, γ SSR(γ) Stata14 γ

8 2 (15), 3 1, R %,,, 60.20, (0.1593), ( ),,, ( ), ( ), 3,, 60.20%, ; 60.20%, ; 60.20%, 77.25% ;, 16.97% 60.20%,,, 3 debtrate rate bad Constant ( ) ** (3.6471) ( ) debtrate ( ) ** (8.3842) ( ) Regime1 debtrate ( ) ** ( ) ( ) rate *** (0.0195) (0.0383) *** (0.0195) bad (0.0047) (0.0276) (0.0047) Constant (2.0384) *** (1.4311) (2.0384) debtrate (4.2380) *** (3.3935) (4.2380) Regime2 debtrate (5.9014) *** (4.5776) (5.9014) rate (0.0171) *** (0.0359) (0.0171) bad (0.0155) ** (0.0087) (0.0155) R Regime1,Regime2,, 1% (0.1593);,, ( ), 37

9 2018 5,,,,, 1 2.,, (rate),,lm , p 0.048, 5%, Hansen (2000) γ 3 3 3, (3), 3 2, R %,,, 5.81%, ( ) ( ),,, 5.81%, 70% ; 70%, ; 70%, 5.81%, 72%, (2014),,,, 38

10 ,,,,,, 3., (bad),,lm , p , 1%,, Hansen(2000) γ 4 4 4, (15), 3 3, R %,,,,, 3.50%,, 3.50%, (0.0784), ( ),, 68.80% 68.80%, ; 68.80%,, ( ), (0.0491),, 76.49%,,,,,,, 39

11 2018 5,,, ,,,,, 1,, 68% ,,,, (debtrate) (rate) (bad), 1,,,,,,,,,,,,,,,,, ;,,, ( ) Hansen(2000),,,, LM, 3, 10%,, 1,,,, (debtrate) (rate) (bad), 60%~76%, (2014) (2017),,, (2014), , 40

12 ,,,,,, ;, ;,,,,,,,,, GDP,,,,, R&D ;,,,,,,, ;, 1,2014, ( ) 1,2015, 6,2013 CPI PPI, 3,2013, 5,2017, Barro,R.J.(1989), TheRicardianapproachtobudgetdeficits,Journalof Economic Perspectives3(2) Bernheim,B.D.(1989), Aneoclassicalperspectiveonbudgetdeficits,Journalof Economic Perspectives3(2) Ceccheti,S.etal(2011), Therealefectsofdebt,BIS WorkingPapers,No.352. Checherita-Westphal,C.& P.Rother(2012), Theimpactofhighgovernmentdebtoneconomicgrowthanditschan- nelsanempiricalinvestigationfortheeuroarea,european Economic Review 56(7) Kumar,M.& J.Woo(2010), Publicdebtandgrowth,IMF WorkingPaper,No.10/174. Hansen,B.E.(2000), Samplesplitingandthresholdestimation,Econometrica68(3) Lin,J.Y.(2010), NewstructuraleconomicsAframeworkforrethinkingdevelopment,WorldBankPolicyRe- searchpaper,no Reinhart,C.M.& K.S.Rogof(2010), Growthinatimeofdebt,American Economic Review 100(2) Shu,J.& J.E.Zhang(2012), CausalityintheVIXfuturesmarket,Journalof Futures Markets32(1) Woodford,M.(1990), Publicdebtasprivateliquidity,American Economic Review 80(2) ( ) ( ) 41

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