A semiparametric IV estimation of the government debt/GDP-growth relationship for OECD countries.

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h?2 K2i?Q/QHQ;B+H TT`Q+? Q7 >2`M/QM- b?- M/ SQHHBM UkyRjV- i?i Bb iQ T@ THv MQMT`K2i`B+ 2biBKiQ` iQ i?2 2KTB`B+H MHvbBb Q7 i?2 /2#if:.S@;`Qri? `2HiBQMb?BT- Bb ;QQ/ biìBM; TQBMiX AM 7+i- i?Bb 2biBKiBQM biì2;v HHQrb iQ /2TB+i Mv MQM@HBM2`BiB2b BM i?2 `2HiBQMb?BT M/ bT`2b i?2 M22/ iQ BKTQb2 ?v@ TQi?2b2b QM i?2 KQ/2H bT2+B}+iBQMX JQ`2Qp2`- ;Bp2M i?i *X _2BM?ì M/ _Q;Qz

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jXR 1M/Q;2M2Biv

1M/Q;2M2Biv Bb T2`?Tb i?2 KQbi +?HH2M;BM; biiBbiB+H Bbbm2 i?i 2+QMQKBbib 7+2 r?2M i`vBM; iQ B/2MiB7v +mbHBiv 7`QK QM2 p`B#H2 iQ MQi?2`X h?2 bim/v Q7 i?2 /2#if:.S@;`Qri? `2HiBQMb?BT KF2b MQ 2t+2TiBQM M/ b2p2`H K2i?Q/QHQ;B+H TT`Q+?2b ?p2 #22M BKTH2K2Mi2/ iQ KBMBKBx2 i?2 `2Hi2/ 2biBKiBQM #BbX AM Q`/2` iQ +QMi`QH 7Q` QKBii2/ p`B#H2 #Bb M/ iQ T`iHv `2/m+2 i?2 `2p2`b2 +mbH@ Biv 2z2+i- *2++?2iiB- JQ?Miv- M/ wKTQHHB UkyRRV- qQQ M/ EmK` UkyRyV-*?2+?2`Bi@q2biT?H M/ _Qi?2` UkyRkV M/ SMBxx M/ S`2b#Bi2`Q UkyR9V 2biB@ Ki2 i?2 `2HiBQMb?BT i?`Qm;? i?2 7QHHQrBM; KQ/2H bT2+B}+iBQM,

¯

growthi,t+1,t+n = debt/GDPi,tφ + Xi,tβ + µi+ γt+ ϵi,t,t+n, 7Q` i = 1, . . . , n; t = 1, . . . , T.

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AM i?2 2tT`2bbBQM-_growth¯

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qQQ M/ EmK` UkyRyV- *?2+?2`Bi@q2biT?H M/ _Qi?2` UkyRkV M/ SMBxx M/ S`2b#Bi2`Q UkyR9V 7m`i?2` i+FH2 i?2 2M/Q;2M2Biv Bbbm2 #v BMbi`mK2MiBM; i?2 /2#i@iQ@:.S `iBQ- mbBM; p`B#H2b i?Qm;?i iQ #2 mM+Q``2Hi2/ iQ i?2 2``Q` i2`Kb M/ bi`QM;Hv HBMF2/ iQ ;Qp2`MK2Mi BM/2#i2/M2bbX qQQ M/ EmK` UkyRyV }M/ i?i

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i?2 bvbi2K :JJ 2biBKiQ`- r?B+? mb2b H;;2/ pHm2b M/ /Bz2`2M+2b Q7 i?2 2M@ /Q;2MQmb `2;`2bbQ` b BMbi`mK2Mib- #2bi ++QmMib 7Q` 2M/Q;2M2Biv BM i?2 2biBKiBQM Q7 i?2 Hbi KQ/2HX h?2 a:JJ 2biBKiBQM `2bmHib `2 bBKBH` iQ i?Qb2 Q7 *2++?2iiB-JQ?Miv- M/ wKTQHHB UkyRRV Udebt/GDP +Q2{+B2Mi, @yXykc bB;MB}+M+2 H2p2H, 8WV M/ `2 `Q#mbi iQ /Bz2`2Mi iBK2 T2`BQ/b- bKTH2b- bT2+B}+iBQMb M/ +QMi`QH p`B#H2bX SMBxx M/ S`2b#Bi2`Q UkyRjV i?BMF i?i i?2 `2bmHib bBKBH`BiB2b #2ir22M #Qi? TT2`b +M #2 2tTHBM2/ #v irQ TQbbB#H2 Qmi+QK2b, r?2i?2` i?2 /2#i@iQ@:.S Bb MQi 2M/Q;2MQmb BM i?2 +QM+2`M2/ KQ/2H bT2+B}+iBQM- Q` i?i a:JJ Bb MQi M TT`QT`Bi2 2biBKiBQM bi`i2;v iQ ++QmMi 7Q` BiX >Qr2p2`- SMBxx M/ S`2b@ #Bi2`Q UkyRjVǶb MHvbBb /Q MQi 2tTQb2 i?2 7+i i?i qQQ M/ EmK` UkyRyV HbQ Q#iBM [mBi2 /Bz2`2Mi `2bmHib #2ir22M i?2 61 M/ a:JJ 2biBKiBQMb Q7 i?2 +QK@ TH2i2 KQ/2H- r?B+? BM+Hm/2b T2`BQ/ bT2+B}+ 2z2+ib Udebt/GDP +Q2{+B2Mi, @yXyy9 pbX @yXyk VX

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7+iQ` T`Q/m+iBpBivX SMBxx M/ S`2b#Bi2`Q UkyR9V mb2 i?2 bK2 KQ/2H bT2+B}@ +iBQM M/ /ib2i b *2++?2iiB- JQ?Miv- M/ wKTQHHB UkyRRV- M/ BMbi`mK2Mi i?2 /2#i@iQ@:.S `iBQ rBi? i?2 pHmiBQM 2z2+ib 7`QK i?2 BMi2`+iBQM #2ir22M i?2 ;Qp2`MK2Mi /2#i H#2HH2/ BM 7Q`2B;M +m``2M+v M/ KQp2K2Mib BM i?2 2t+?M;2 `i2,

V Ei,t = !N

j=1Dij,t(eij,t+1− eij,t) !N

j=1Dij,t

.

AM i?2 2tT`2bbBQM- Dij,t Bb i?2 biQ+F Q7 /2#i Q7 +QmMi`v i /2MQKBMi2/ BM +m``2M+v Q7 +QmMi`v j M/ eij,t Bb i?2 +m``2M+v 2t+?M;2 ì2 #2ir22M +QmMi`B2b i M/ j- i T2`BQ/ tX h?2 mi?Q`b i?2M b?Qr i?i i?Bb BMbi`mK2MiH p`B#H2 Bb `2H2pMi iQ i?2 /2#i@iQ@:.S p`B#H2- ;Bp2M i?i Bi T`QpB/2b bi`QM; 2tTHMiQ`v TQr2` BM i?2 }`bi bi2T `2;`2bbBQM M/ `2D2+ib b2p2`H r2F BMbi`mK2Mi i2bibX >Qr2p2`- i?2 KQ/2H Bb 2t+iHv B/2MiB}2/- bm+? i?i i2bi Q7 2t+HmbBQM `2bi`B+iBQM Bb MQi TQbbB#H2X h?2v /Bb+mbb i?2 +QM/BiBQMb mM/2` r?B+? i?2 BMbi`mK2Mi Bb HBF2Hv iQ #2 pHB/X h?2b2 +QMbBbi Q7 m;K2MiBM; i?2 KQ/2H rBi? i?2 p`B#H2b i?i `2T`2b2Mi i?2 +?MM2Hb i?`Qm;? r?B+? i?2 pHmiBQM 2z2+ib +M z2+i ;`Qri?X h?2v }M/ i?i i?2 b?`2 Q7 /2#i H#2HH2/ BM 7Q`2B;M +m``2M+v M/ i?2 i`/2@r2B;?i2/ 2z2+iBp2 2t+?M;2 ì2 `2 #Qi? +Q``2Hi2/ rBi? i?2 BMbi`mK2Mi M/ i?2 /2T2M/2Mi p`B#H2X AM Q`/2` 7Q` i?2 2t+HmbBQM `2bi`B+iBQM iQ #2 pHB/- i?2v m;K2Mi i?2B` KQ/2H rBi? #Qi? p`B@ #H2b- r?B+? +QMbBbib Q7 HKQbi i?2 bK2 2H2K2Mib mb2/ iQ ;2M2ì2 i?2 BMbi`mK2MiX 6mì?2`KQ`2- SMBxx M/ S`2b#Bi2`Q UkyR9V Ki?2KiB+HHv /2KQMbiì2 i?i i?2 #Bb `2Hi2/ iQ i?2 bBKmHiM2Biv M/ `2p2`b2 +mbHBiv 2z2+ib BM i?2 `2HiBQMb?BT Bb HBF2Hv iQ #2 M2;iBp2X h?2v +QM}`K i?Bb }M/BM; #v +QKT`BM; i?2 /2#i@iQ@:.S p`B#H2 +Q2{+B2Mib 7`QK i?2B` PGa M/ Ao 2biBKiBQMbX AM/22/- BMbi`mK2MiBM; i?2 2M/Q;2MQmb p`B#H2 +?M;2b i?2 /2#i@iQ@:.S 2biBKi2/ +Q2{+B2Mi 7`QK M2;iBp2 U@RXdNe V iQ TQbBiBp2 UyXjkkV M/ KF2b Bi HQb2 Bib bB;MB}+M+2- i?mb +QM}`KBM; i?2 i?2Q`2iB+H /2`BpiBQM i?i bm;;2bi2/ M2;iBp2 PGa #Bb2/ 2biBKi2X h?2 M2ti bm#b2+iBQM +Qp2`b ?Qr i?2 2KTB`B+H HBi2ìm`2 bT2+B}+HHv 2tTHQ`2/ i?2 T`2b2M+2 Q7 MQM@HBM2`BiB2b BM i?2 /2#if:.S@;`Qri? `2HiBQMb?BTX

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jXk LQM@HBM2`Biv

JBM2 M/ S`2Mi UkyRkV BMp2biB;i2 i?2 /2#if:.S@;`Qri? i?`2b?QH/ 2z2+i T`2@ pBQmbHv B/2MiB}2/ #v __ rBi? M mT@iQ@/i2 2+QMQK2i`B+ K2i?Q/X h?2v mb2 i?2 SM2H aKQQi? h?`2b?QH/ _2;`2bbBQM USah_V- K2i?Q/ /2p2HQT2/ #v :QMxH2b 2i HX Ukyy8V- r?B+? HHQrb iQ bT2+B7v 2M/Q;2MQmb i?`2b?QH/b rBi? ;`/mH i`MbBiBQMH 2z2+ib,

growthi,t = αi+ β1debt/GDPi,t + β2debt/GDPi,tΓ(debt/GDPi,t, T, γ) + ϵi,t,

Γ(debt/GDPi,t, T, γ) = [1 + exp(−γ H " h=1

(debt/GDPi,t− th))]−1.

AM i?2 2tT`2bbBQM- Γ(·) Bb i?2 HQ;BbiB+ 7mM+iBQM i?i r2B;?ib- ++Q`/BM; iQ i?2 bKQQi?BM; T`K2i2` γ- i?2 /BbiM+2 #2ir22M i?2 `2;BK2 brBi+?BM; p`B#H2 M/ i?2 i?`2b?QH/b T : t1, . . . , tHX AM i?Bb +b2- i?2 `2;BK2 brBi+?BM; p`B#H2 Bb HbQ i?2 /2#i@iQ@:.S p`B#H2X h?Bb K2i?Q/ bT`2b i?2 M22/ 7Q` ?vTQi?2bBb QM 2tQ;2@ MQmb i?`2b?QH/b- Bi T`QpB/2b i2biBM; T`Q+2/m`2 7Q` i?2 T`2b2M+2 Q7 MQM@HBM2`BiB2b M/ HHQrb 7Q` bKQQi? i`MbBiBQMb #2ir22M `2;BK2bX h?2 mi?Q`b /2i2`KBM2 i?i i?`22 i?`2b?QH/ bT2+B}+iBQM- bm+? i?i H = 3- T`QpB/2b i?2 #2bi KQ/2H }iX lbBM; i?2 bK2 +QmMi`v M/ iBK2 bKTH2 b __- #mi 7`QK /Bz2`2Mi /i#b2- i?2v }M/ /2#if:.S@;`Qri? `2HiBQMb?BT rBi? +QKTH2t MQM@HBM2`BiB2b- r?i +QMi`@ /B+ib i?2 mMBHi2`H /2+HBM2 Q7 ;`Qri? 7Q` +QmMi`B2b rBi? /2#i@iQ@:.S `iBQb #Qp2 NyWX h?2B` KQ/2H 2biBKiBQM B/2MiB}2b irQ bB;MB}+Mi i?`2b?QH/b- i i?2 Ny M/ RR8W /2#i@iQ@:.S H2p2HbX "2ir22M #Qi?- i?2 /2#if:.S@;`Qri? 2z2+i Bb M2;iBp2 M/ brBi+?2b iQ TQbBiBp2 Tbi i?2 RR8W TQBMiX h?Bb 7mM+iBQMH 7Q`K Bb `Q#mbi iQ HQM;2` iBK2 bTM- +Qp2`BM; R33y@kyyN- 7Q` r?B+? i?2 KQ/2H }M/b bHB;?iHv /Bz2`2Mi b2+QM/ i?`2b?QH/ i RjyW- BMbi2/ Q7 RR8WX h?2 mi?Q`b }M/ MQ bB;MB}+Mi /Bz2`@ 2M+2 #2ir22M i?2 /2#if:.S@;`Qri? 2z2+i BM i?2 y@NyW M/ i?2 RR8WY `2;BK2b-r?i T`QpB/2b 2pB/2M+2 ;BMbi /`biB+HHv /Bz2`2Mi 7mM+iBQMH 7Q`K 7Q` ?B;?Hv BM/2#i2/ +QmMi`B2bX

a2p2`H `iB+H2b bb2bb2/ i?2 MQM@HBM2` 7mM+iBQMH 7Q`K Q7 i?2 /2#if:.S@;`Qri? `2HiBQMb?BT mbBM; MQM@/vMKB+ M/ /vMKB+ ǳbiM/`/Ǵ i?`2b?QH/ `2;`2bbBQM KQ/@ 2HbX h?2 MQM@/vMKB+ K2i?Q/QHQ;B+H 7`K2rQ`F rb T`QTQb2/ #v >Mb2M URNNNV

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M/ HHQrb iQ 2biBKi2 i?`2b?QH/ KQ/2H 7Q` TM2H /i rBi? BM/BpB/mH@bT2+B}+ 2z2+ibX AM i?2 +QMi2ti Q7 KmHiBp`Bi2 /2#if:.S@;`Qri? KQ/2H- Bi +M #2 +?`@ +i2`Bx2/ #v i?2 7QHHQrBM; irQ@`2;BK2 2[miBQM,

gi,t = αi+ δ′Xi,t+ β1di,tI(qi,t ≤ T ) + β2di,t−1I(qi,t > T ) + ϵi,t.

AM i?2 2tT`2bbBQM- gi,t Bb i?2 `2H :.S MMmH ;`Qri? Q7 +QmMi`v i i iBK2 t- Xi,t Bb b2i Q7 ;`Qri? `2Hi2/ 2tTHMiQ`v p`B#H2b- r?B+? +M BM+Hm/2 i?2 /2#i@iQ@ :.S Q` `2H :.S p`B#H2b- M/ qi,t Bb i?2 `2;BK2 brBi+?BM; p`B#H2- mbmHHv i?2 ;Qp2`MK2Mi /2#i p`B#H2X h?2 i2biBM; T`Q+2/m`2 2biBKi2b i?2 KQ/2H 7Q` T`2@/2i2`KBM2/ b2i Q7 i?`2b?QH/b M/ }M/b T∗ i?i KBMBKBx2b i?2 bmK Q7 b[m`2/ `2bB/mHbX lbBM; i?Bb 7`K2rQ`F- ú;2ì UkyRkV 2biBKi2b #Bp`Bi2 /2#if:.S@ ;`Qri? KQ/2H M/ b2H2+ib i?2 /2#i@iQ@:.S ìBQ b i?2 `2;BK2 brBi+?BM; p`B#H2 BM i?`22@`2;BK2 bT2+B}+iBQMX 6Q` /pM+2/ +QmMi`B2b- Qp2` i?2 RdNy@kyyN T2`BQ/-?2 }M/b irQ QTiBKH i?`2b?QH/b i iT2`BQ/-?2 /2#i@iQ@:.S H2p2Hb Q7 kyXj3W M/ 88Xj8W-r?B+? /2}M2 TQbBiBp2 M/ bB;MB}+Mi +Q2{+B2Mib 7Q` i?2 }`bi irQ `2;BK2b- M/ TQbBiBp2- #mi MQM@bB;MB}+Mi- i?B`/ `2;BK2 +Q2{+B2MiX 6Q` b?Qì2` iBK2 bTM-?2 }M/b i?i irQ@`2;BK2 KQ/2H Bb KQ`2 TT`QT`Bi2- rBi? bBM;H2 2biBKi2/ i?`2b?QH/ i i?2 bK2 kyXj3W H2p2H M/ irQ bB;MB}+Mi +Q2{+B2Mib i?i +?M;2 bB;Mb 7`QK TQbBiBp2 iQ M2;iBp2 ++Q`/BM;HvX h?2 `2bmHib bQK2?Qr BM/B+i2 /2#if:.S@ ;`Qri? 2z2+i i?i +?M;2b 7`QK TQbBiBp2 iQ MmHH Q` M2;iBp2 b i?2 ìBQ Q7 /2#i@ iQ@:.S BM+`2b2b M/ bm;;2bi i?`2b?QH/b i Km+? HQr2` H2p2Hb i?M T`2pBQmbHv bm;;2bi2/X PM2 BKTQìMi /`r#+F Q7 i?Bb bim/v Bb i?2 H+F Q7 bT2+B}+ i?`2b?QH/ bB;MB}+M+2 i2biBM;- r?B+? Bb BM/B`2+iHv `2TH+2/ #v i2bib ;BMbi i?2 MmHH ?vTQi?2bBb Q7 2[mHBiv #2ir22M i?2 T`K2i2`b Q7 i?2 /Bz2`2Mi `2;BK2bX

PM i?Bb ++QmMi- >Mb2M UkyyyV T`QTQb2b +Q``2+i T`Q+2/m`2 7Q` i2biBM; i?2 bB;MB}+M+2 Q7 i?`2b?QH/ BM i?2 T`2pBQmb `2;`2bbBQM 7`K2rQ`F- r?B+? M2+2bbBii2b iQ TT`QtBKi2 i?2 +`BiB+H pHm2 Q7 i?2 i2bi biiBbiB+ mbBM; #QQibi`T K2i?Q/-FMQrM b i?2 amT`2KmK 6@- GJ@ Q` qH/@i2biX h?2 amT`2KmK 6@i2bi +QKT`2b i?2 F∗@biiBbiB+ Q7 i?2 QTiBKH i?`2b?QH/ UT∗V KQ/2H iQ i?2 TT`QtBKi2/ /Bbi`B@ #miBQM Q7 T`2/2i2`KBM2/ MmK#2` Q7 F∗

MmHH@biiBbiB+b- 2+? Q#iBM2/ 7`QK bT2+B}+ #QQibi`T bKTH2b Q7 i?2 KQ/2H mM/2` i?2 MmHH ?vTQi?2bBb Q7 HBM2`BivX h?2 i?`2b?@ QH/ UT∗V Bb bB;MB}+Mi B7 i?2 F∗@biiBbiB+ Bb ?B;?2` i?M i?2 8W +`BiB+H@pHm2 Q7

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i?2 TT`QtBKi2/ F∗

MmHH@biiBbiB+ /Bbi`B#miBQMX 7QMbQ M/ CHH2b UkyRjV TTHv i?Bb i?`2b?QH/ bB;MB}+M+2 T`Q+2/m`2 iQ irQ@`2;BK2 i?`2b?QH/ `2;`2bbBQM KQ/2H Q7 i?2 /2#if:.S@;`Qri? `2HiBQMb?BT- mbBM; /i 7Q` R88 /2p2HQTBM; M/ /pM+2/ +QmM@ i`B2b Qp2` i?2 RN3y@kyy3 T2`BQ/X AM i?2B` KQ/2H bT2+B}+iBQM- Xi,t BM+Hm/2b i?2 BMBiBH `2H :.S- TQTmHiBQM ;`Qri?- i`/2 QT2MM2bb- 2/m+iBQM M/ BMp2biK2Mi p`B#H2b- bm+? i?i i?2 /2#i@iQ@:.S `iBQ Bb QMHv i?2 `2;BK2 brBi+?BM; p`B#H2X aBKBH`Hv iQ JBM2 M/ S`2Mi UkyRkV- i?2v }M/ i?i :.S ;`Qri? `i2b 7Q` HQr UIjyWV M/ ?B;? U=NyWV BM/2#i2/ P1*. +QmMi`B2b `2 biiBbiB+HHv MQi /Bz2`2MiX h?2v HbQ }M/ bB;MB}+Mi QTiBKH i?`2b?QH/ i i?2 8NW /2#i@iQ@:.S H2p2H- rBi? M TT`QtBKi2/ T@pHm2 Q7 yXydN ++Q`/BM; iQ amT`2KmK qH/@i2bi T`Q+2/m`2X h?2 Hbi +Qp2`2/ TT2`b MHvx2 i?2 MQM@HBM2` 7mM+iBQMH 7Q`K Q7 i?2 +QM@ i2KTQ`M2Qmb 2z2+i Q7 ;Qp2`MK2Mi BM/2#i2/M2bb QM ;`Qri?- r?B+? `2bmHib Kv MQi ?QH/ B7 i`MbTQb2/ iQ /vMKB+ bT2+B}+iBQMX 6QHHQrBM; i?Bb B/2- "mK-*?2+?2`Bi@q2biT?H- M/ _Qi?2` UkyRjV 2biBKi2 irQ@`2;BK2 /vMKB+ BMbi`m@ K2MiH p`B#H2 i?`2b?QH/ KQ/2H- K2i?Q/QHQ;B+H TT`Q+? T`2pBQmbHv T`QTQb2/ #v *M2` M/ >Mb2M Ukyy9V M/ Hi2` /Ti2/ iQ TM2H /i #v E`2K2`- "B+F-M/ Lmix UkyRjVX h?2 2[miBQM Q7 i?Bb KQ/2H Bb i?2 7QHHQrBM;,

gi,t = αi+ δ1gi,t−1+ δ2′Xi,t+ β1di,t−1I(di,t−1 ≤ T ) + β2di,t−1I(di,t−1 > T ) + ϵi,t, gi,t−1 = ξ′Zi+ ui,t,

r?2`2 gi,t−1 M/ di,t−1 `2 H;;2/ pHm2b Q7 i?2 ;`Qri? M/ /2#i@iQ@:.S p`B#H2b-r?BH2 Zi b2i Q7 BMbi`mK2Mib 7Q` gi,t−1X "mK- *?2+?2`Bi@q2biT?H- M/ _Qi?2` UkyRjV +?QQb2 iQ bT2+B7v i?2 ;`Qri? p`B#H2 b 2M/Q;2MQmb- BMbi2/ Q7 i?2 /2#i@iQ@ :.S ìBQ- mbBM; Bib H;;2/ pHm2b b BMbi`mK2Mib BM ZiX h?2 mi?Q`b +?`+i2`Bx2 i?2 b?Qì@i2`K /vMKB+ 2z2+i Q7 i?2B` bT2+B}+iBQM b M2` +QMi2KTQ`M2QmbX h?2v 2biBKi2 i?2B` KQ/2H mbBM; i?2 :JJ 2biBKiQ` 7Q` Rk 2m`Q +QmMi`B2b- +Qp2`BM; i?2 RNNy@kyydfkyRy T2`BQ/- M/ bT2+B7v j +QMi`QH p`B#H2b BM Xi,t , K2bm`2 Q7 i`/2 QT2MM2bb- i?2 ìBQ Q7 ;`Qbb +TBiH 7Q`KiBQM iQ :.S M/ /mKKv p`B#H2 BM/B+iBM; i?2 1m`QT2M JQM2i`v lMBQM K2K#2`b?BTX PKBiiBM; i?2 ;`2i `2+2bbBQM BM i?2 iBK2 bKTH2- i?2v }M/ M QTiBKH i?`2b?QH/ i i?2 edW /2#i@iQ@:.S H2p2H- rBi? amT`2KmK@6 i2bi T@pHm2 Q7 yXyd3- bm+? i?i Bi /2}M2b bB;MB}+Mi M/ TQbBiBp2 /2#if:.S@;`Qri? 2z2+i BM i?2 }`bi `2;BK2 M/ MQM@

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bB;MB}+Mi M2` MmHH 2z2+i BM i?2 b2+QM/ `2;BK2X h?Bb bm;;2bib i?i HQr BM/2#i2/ 2m`Q +QmMi`B2b TQi2MiBHHv 7+2 TQbBiBp2- #mi `TB/Hv /2+`2bBM;- ;`Qri? 2z2+i 7Q` //BiBQMH /2#i@iQ@:.S BM+`2K2MibX 6Q` i?2 RNNy@kyRy bKTH2- i?2 QTiBKH i?`2b?QH/ Bb +HQb2` iQ __Ƕb }M/BM;b- i i?2 N8W /2#i H2p2H UT@pHm2 , yXyN3V- r?B+? MQr /2}M2b bB;MB}+Mi M/ M2;iBp2 b?Q`i i2`K BKT+i Q7 ;Qp2`MK2Mi /2#i@iQ@ :.S QM ;`Qri? 7Q` ?B;?Hv UN8WYV BM/2#i2/ 2m`Q +QmMi`B2bX

EQmì2HHQb- ai2M;Qb- M/ hM UkyRjV 2tTHQ`2 i?2 `2HiBQMb?BT mbBM; i?2 bi`m+@ im`H i?`2b?QH/ `2;`2bbBQM Uah_V KQ/2H- K2i?Q/QHQ;B+H TT`Q+? i?2v T`QTQb2 BM EQmì2HHQb- ai2M;Qb- M/ hM UkyR8V- r?B+? Bb #mBHi QM i?2 7`K2rQ`F Q7 >Mb2M URNNNV M/ *M2` M/ >Mb2M Ukyy9VX h?2B` +QMi`B#miBQM iQ i?2 biM/`/ KmHiB@ `2;BK2 TM2H KQ/2H +QMbBbib Q7 bT2+B7vBM; i?2 i?`2b?QH/ M/ i?2 `2;BK2 brBi+?BM; p`B#H2 b 2M/Q;2MQmbX h?2 KQ/2H 2[miBQM bT2+B}2/ BM EQmì2HHQb- ai2M;Qb- M/ hM UkyRjV Bb i?2 7QHHQrBM;,

growthi,t = β′Xi,t+ δ′Xi,tI(qi,t ≤ T ) + κλi,t(γ) + ϵi,t, I(qi,t ≤ T ) = ⎧ ⎨ ⎩ 1, B7 qi,t ≤ T 0, B7 qi,t > T , qi,t = π′Zi,t+ vi,t,

r?2`2 Xi,t Bb b2i Q7 p`B#H2b i?Qm;?i iQ 2tTHBM ;`Qri? i?i BM+Hm/2b i?2 /2#i@iQ@ :.S ìBQ- qi,t Bb i?2 `2;BK2 brBi+?BM; p`B#H2- T Bb i?2 i?`2b?QH/ iQ #2 QTiBKBx2/-Zi,t Bb b2i Q7 BMbi`mK2Mib 7Q` qi,t- r?BH2 λi,t(γ) Bb b+H` p`B#H2 i?i `2biQ`2b i?2 +QM/BiBQMH K2M Q7 2``Q`bX h?2v 2biBKi2 i?2B` KQ/2H mbBM; R8 /Bz2`2Mi p`B@ #H2b 7Q` qi,t- QM Ry@v2` p2`;2 MQM@Qp2`HTTBM; TM2H /ib2i i?i +Qp2`b 38 +QmMi`B2b Qp2` i?2 RN3y@kyyN T2`BQ/X "v +QKT`BM; i?2 C@biiBbiB+b- K2bm`2 Q7 KQ/2H pHB/Biv- 7`QK i?2 :JJ 2biBKiBQMb Q7 HH R8 KQ/2Hb- i?2v }M/ i?2 /2KQ+@ `+v p`B#H2 iQ #2 i?2 KQbi `2H2pMi `2;BK2 brBi+?BM; p`B#H2X ++Q`/BM; iQ i?2B` i2biBM; T`Q+2/m`2- i?2 /2#i@iQ@:.S p`B#H2 Bb MQi bB;MB}+Mi `2;BK2 brBi+?BM; p`B#H2- BM QTTQbBiBQM iQ JBM2 M/ S`2Mi UkyRkV- 7QMbQ M/ CHH2b UkyRjV M/ ú;2ì UkyRkVǶb KQ/2HHBM; TT`Q+?X h?2 2biBKiBQM Q7 i?2B` ǳQTiBKHǴ KQ/2H-BM+Hm/BM; i?2 /2KQ+`+v K2bm`2 b i?2 `2;BK2 brBi+?BM; p`B#H2- `2bmHib BM bB;MB}Mi M/ M2;iBp2 2z2+i Q7 i?2 /2#i@iQ@:.S ìBQ QM 2+QMQKB+ ;`Qri? 7Q` HQr

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¯ growthi,t+1,t+6= 1 5 t+6 & j=t+1 growthi,j.

HH BM/2T2M/2Mi p`B#H2b UBM+Hm/BM; i?2 +QmMi`v M/ T2`BQ/ bT2+B}+ 2z2+ibV `2 ;`Qri? T`2/2i2`KBM2/- bm+? i?i i?2B` iBK2 bT2+B}+iBQM Bb QM2 T2`BQ/ H;;2/ `2HiBp2 iQ i?2 ;`Qri? KQpBM; p2`;2X q2 2biBKi2 i?2 7QHHQrBM; HBM2`- Ao-b2KBT`K2i`B+ M/ Ao-b2KBT`K2i`B+ Ao KQ/2Hb,

UV GBM2` KQ/2H, ¯

growth_i,t+1,t+6 = debt/GDPi,tφ + Xi,tβ + µi+ γt+ ϵi,t,t+6. 7Q` i = 1, . . . , n; t = 1, . . . , T.

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U"V Ao KQ/2H, ¯

growth_i,t+1,t+6 = debt/GDPi,tφ + Xi,tβ + µi+ γt+ ϵi,t,t+6, debt/GDPi,t = Zi,tψ + vi,t,

7Q` i = 1, . . . , n; t = 1, . . . , T. U*V a2KBT`K2i`B+ KQ/2H,

¯

growthi,t+1,t+6 = g(debt/GDPi,t) + Xi,tβ + µi+ γt+ ϵi,t,t+6. 7Q` i = 1, . . . , n; t = 1, . . . , T. U.V a2KBT`K2i`B+ Ao KQ/2H,

¯

growth_i,t+1,t+6 = g(debt/GDPi,t) + Xi,tβ + µi+ γt+ ϵi,t,t+6, debt/GDPi,t = G(Z1i,t) + Z2i,tψ + vi,t,

7Q` i = 1, . . . , n; t = 1, . . . , T.

AM i?2 2tT`2bbBQMb- g(·) M/ G(·) `2 mMFMQrM MQMT`K2i`B+ 7mM+iBQMb- r?BH2 Z = _{Z1, Z2} Bb b2i Q7 BMbi`mK2MiH p`B#H2b 7Q` debt/GDPi,tX h?2 Ki`Bt Q7 T`2/2i2`KBM2/ `2;`2bbQ`b Xi,t +QMiBMb i?2 7QHHQrBM; p`B#H2b, i?2 HQ; Q7 `2H :.S U−RGDPi,tV ++QmMib 7Q` i?2 +i+?@mT 2z2+i Q7 i?2 2+QMQKv iQ Bib bi2/v bii2- i?2 ;`Qbb /QK2biB+ bpBM;b b W Q7 :.S Ungsi,tV M/ i?2 MMmH TQTmHiBQM ;`Qri? `i2 Upopi,tV ++QmMi `2bT2+iBp2Hv 7Q` i?2 TQbBiBp2 M/ M2;iBp2 2z2+ib QM i?2 bi2/v bii2 BM i?2 +HbbB+H ;`Qri? KQ/2H Q7 aQHQr- r?BH2 i?2 p2`;2 v2` Q7 iQiH b+?QQHBM; Uschooli,tV- i`/2 b W Q7 :.S Uopenci,tV- i?2 ;2 /2T2M/2M+v `iBQ Udepi,tV M/ #MFBM; +`BbBb /mKKv p`B#H2 Ucrisisi,tV `2T`2b2Mi /2b+`BTiBQM Q7 i?2 i2+?MQHQ;v M/ T`272`2M+2b Q7 i?2 +QmMi`B2bX µi M/ γt `2 +QmMi`v M/ T2`BQ/ bT2+B}+ b2ib Q7 /mKKv p`B#H2bX

h?2 p`B#H2 b2H2+iBQM `2THB+i2b *2++?2iiB- JQ?Miv- M/ wKTQHHB UkyRRV M/ SMBxx M/ S`2b#Bi2`Q UkyR9V- irQ BKTQìMi ìB+H2b Q7 i?2 2KTB`B+H HBi2ìm`2-BM Q`/2` 7Q` Qm` KQ/2H 2biBKiBQMb iQ ?p2 +QKT`#H2 #b2bX q2 `2 +QM}/2Mi i?i i?2 TQi2MiBH 7Q` QKBii2/ p`B#H2 #Bb Bb H`;2Hv `2/m+2/ #v i?2 ++QmMi Q7

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8Xk 1biBKiQ`b

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8XkXR LQMT`K2i`B+

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.2MbBiv 2biBKiBQM

h?2 2bB2bi rv iQ BHHmbi`i2 i?2 mM/2`HvBM; K2+?MBbK Q7 i?2 MQMT`K2i`B+ F2`M2H 7`K2rQ`F Bb rBi? i?2 2KTB`B+H 2biBKiBQM Q7 +mKmHiBp2 /Bbi`B#miBQM 7mM+iBQM U*.6V, ˆ F (x) = 1 n n & i=1 G(x− xi h ) UjV

r?2`2- G(·) Bb r2B;?i 7mM+iBQM- +QKKQMHv i?2 *.6 Q7 i?2 MQ`KH /Bbi`B#miBQM-M/ h Bb TQbBiBp2 bKQQi?BM; T`K2i2` FMQrM b i?2 #/Bbi`B#miBQM-M/rB/i?X h?2 b2H2+iBQM Q7 i?2 bKQQi?BM; T`K2i2` Bb +`BiB+HX AM 7+i- /Bz2`2Mi pHm2b Q7 h H2/ iQ [mBi2 /Bp2`;2Mi 2biBKiBQM `2bmHib 7Q` }t2/ /ib2iX h?Bb TQBMi Bb #2bi BHHmbi`i2/ #v

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2pHmiBM; i?2 bKQQi?BM; T`K2i2` i Bib HBKBib, lim h→0: G(±∞) = ⎧ ⎨ ⎩ 0, B7 x < xt 1, B7 x > xt lim h→∞ : G(0) = 0.5.

>2`2- r2 bmTTQb2 i?i G(·) = Φ- i?2 +mKmHiBp2 MQ`KH /Bbi`B#miBQMX q2 b22 i?i-b h TT`Q+?2b ∞- i?2 2biBKi2 Bb }t2/ 7Q` HH Q#b2`piBQM TQBMib- r?BH2 i?i-b h ;Q2b iQ y- i?2 2biBKi2 Bb /Bz2`2Mi 7Q` 2+? xX h?2`27Q`2- i?2 p`BM+2 Q7 i?2 2biBKi2/ 7mM+iBQM Bb M2;iBp2 7mM+iBQM Q7 i?2 bKQQi?BM; T`K2i2` hX

LQMT`K2i`B+ 2biBKiBQM Q7 T`Q##BHBiv /2MbBiv 7mM+iBQM US.6V Bb M2bi2/ BM i?2 `2;`2bbBQM 7`K2rQ`F- `2[mB`2/ iQ 2biBKi2 +QM/BiBQMH 2tT2+iiBQMX h?2 2KTB`B+H MQMT`K2i`B+ 2biBKiQ` Q7 S.6 7QHHQrb 7`QK UjV,

ˆ f (x) = 1 nh n & i=1 k(x− xi h ) U9V r?2`2 k(·) = ∂G(z)

∂z - +QKKQMHv i?2 S.6 Q7 i?2 MQ`KH /Bbi`B#miBQMX 6BM/BM; M QTiBKH bKQQi?BM; T`K2i2` 7Q` i?Bb bT2+B}+ MQMT`K2i`B+ 2biBKiQ` +M #2 +?B2p2/ #v KBMBKBxBM; Bib BMi2;`i2/ K2M b[m`2/ 2``Q` UAJa1V,

KBM h

'

[ ˆf (x)− f(x)]2_dx,

r?2`2 f(x) Bb i?2 i`m2 /Bbi`B#miBQM Q7 i?2 mM/2`HvBM; /i ;2M2`iBM; T`Q+2bb M/ ˆ

f (x) +QMbBbib Q7 Bib MQMT`K2i`B+ 2biBKi2X :Bp2M i?i f(x) Bb mMFMQrM BM T`+@ iB+2- r2 +M mb2 +`Qbb@pHB/iBQM i2+?MB[m2- r?B+? }M/b i?2 QTiBKH bKQQi?BM; T`K2i2` #v MmK2`B+HHv KBMBKBxBM; i?2 AJa1X lbBM; bQK2 KMBTmHiBQMb- i?2 *o i2+?MB[m2 /Bb+`/b i?2 mMFMQrM f(x) M/ KBMBKBx2b i?2 7QHHQrBM; 2tT`2bbBQM mbBM; MmK2`B+H b2`+? H;Q`Bi?Kb, KBM h CVf(h) = 1 n2_h n & i=1 n & j=1 ¯ k(xi− xj h )− 2 n(n− 1)h n & i=1 n & j̸=i,j=1 k(xi − xj h ) j9

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r?2`2 ¯k(v) Bb i?2 irQ7QH/ +QMpQHmiBQM F2`M2H #b2/ QM k(v)X A7 k(v) = e− v2 √

2π- MQ`KH S.6- i?2M i?2 irQ7QH/ +QMpQHmiBQM F2`M2H Bb ¯k(v) = e− v4

√

4πX h?2 *o i2+?MB[m2 ?b i?2 /pMi;2 iQ #2 2MiB`2Hv /i@/`Bp2MX

JmHiBp`Bi2 /2MbBiv 2biBKiBQM Bb bi`B;?i7Q`r`/X h?2 2biBKiQ` Q7 i?2 KmH@ iBp`Bi2 S.6 f(x) = f(x1, . . . , xq) Bb, ˆ f (x) = 1 nh1. . . hq n & i=1 K(x− xi h ), r?2`2 K(x− xi h ) = k( x1− xi,1 h1 )_{× · · · × k(}xq− xi,q hq ) GQ+H +QMbiMi F2`M2H 2biBKiQ`

q2 MQr T`2b2Mi i?2 MQMT`K2i`B+ `2;`2bbBQM HQ+H +QMbiMi 2biBKiQ`- r?B+? mb2b i?2 MQiBQMb Q7 MQMT`K2i`B+ /2MbBiv 2biBKiBQM Dmbi +Qp2`2/X q2 bi`i rBi? i?2 7QHHQrBM; KQ/2H,

y = g(x) + u, r?2`2 g(x) Bb M mMFMQrM 7mM+iBQM i?i `2T`2b2Mib,

E[y|x]. U8V

AM M B/2HBx2/ bBimiBQM- r2 rQmH/ TQbb2bb bKTH2 Q7 Q#b2`piBQMb {yj, x}mj=1- bm+? i?i i?2 bKTH2 +QM/BiBQMH 2tT2+iiBQM +QK2b /QrM iQ i?2 7QHHQrBM; 2[mBpH2M+2,

E[y|x] ≡ 1 m m & j=1 yj,

r?B+? rQmH/ H2/ iQ +QMbBbi2Mi 2biBKiBQM b m → ∞X >Qr2p2` BM T`+iB+2-+?M+2b `2 i?i xi ̸= x, ∀iX h?2 Hi2`MiBp2 +QMbBbib Q7 T`QpB/BM; ?B;?2` r2B;?ib iQ Q#b2`piBQMb i?i `2 +HQb2` iQ i?2 2pHmiBQM TQBMi BM i?2 p2`;BM; T`Q+2bbX

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h?2 HQ+H +QMbiMi MQMT`K2i`B+ 2biBKiQ` Q7 U8V Bb, E[y|x] = ' yfy,x(x, y) f (x) dy, UeV ˆ fy,x(x, y) = 1 nh0h1. . . hq n & i=1 K(x− xi h )k( y− yi h0 ), r?2`2 K(x− xi h ) = k( x1− x1i h1 )_{× · · · × k(}xq− xqi hq ), ' y ˆfy,x(x, y)dy = 1 nh0h1. . . hq n & i=1 K(x− xi h )yi.

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ˆ g(x) = ' y ˆfy,x(x, y)dy ˆ f (x) = !n i=1yiK( x−xi h ) !n i=1K(x−xh i) . UdV

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Bb i?2 H2p2 QM2 Qmi 2biBKiQ` Q7 g(xi)- M/ 0 ≤ M (_{·) ≤ 1 Bb r2B;?i 7mM+iBQM i?i +Q``2+ib 7Q` bHQr +QMp2`;2M+2 Bbbm2bX a22 GB M/} _+BM2 UkyRRV 7Q` KQ`2 2ti2MbBp2 /Bb+mbbBQM QM i?2 +`Qbb@pHB/iBQM i2+?MB[m2X ;BM- i?Bb KBMBKBxiBQM Bb bQHp2/ mbBM; MmK2`B+H b2`+? H;Q`Bi?KbX

GQ+H HBM2` F2`M2H 2biBKiQ`

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A semiparametric IV estimation of the government debt/GDP-growth relationship for OECD countries.

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