Assumptions: exogenous path of govenrment expenditure; financing by tax or public debt

Transcription

1 2.2 Neolassial heoryof of publi deb Analyse he effes of publi deb in he OLG model Assumpions: exogenous pah of govenrmen expendiure; finaning by ax or publi deb Exhange of finanial insrumens: In period governmen inreases he defii (ne borrowing) anereases heax. Posiive analysis: Impa on wage rae, ineres rae and apial formaion (shor run vs. long run) Normaive analysis: Impa on welfare of he generaions 1

2 Posiive analysis Expendiure exogenous and normalised o zero. Tax: eah member of he working populaion pays ax ; member of he old generaion do no pay pyaxes. Ineremporal budge onsrain of he young generaion: w O r 1 1 Governmen budge is saisfied in eah period: (2.1) N D D r D 1 (2.2) wih D : publi deb in period. Publi revenues (ax plus publi defii) = publi expenses (ineres on exising publi deb). 2

3 Dividing boh sides of (2)by yields: wih d N n d d r d (2.3) 1 1 : publi deb per apia. Capial marke equilibrium: savings of generaion = apial invesed plus publi deb: N s K D (2.4) 1 1 or: s 1 n k d (2.5 ) In he long run publi deb per apia is onsan. The governmen budge in a seady sae is: nd rd (2.6) 3

4 Seady sae Seady sae is df definedby: w f k kf ' k (2.7) r f ' k (2.8) u u w w O 1 r O 1 r (2.9) r n d (2.10 ) r nd 1 nk d (2.11) (10) is he budge onsrain of he household and (11) is he apial marke equilibrium in he seady sae. 4

5 The impa of publi deb on wages, ineres rae and apial sok Period : governmen raises df defii. Publi db debin henexperiod inreases by: dd n n N (2.12 ) Tax dereases by: d n (2.13) 1 1 In all subsequen periods he publi deb per apia remains on he higher level,

6 The shor runrun impa Wages: Gross wage rae does no hange in period beause of he w given apial sok from he pas. The ne wage w inreases by 1 n. Ineres rae and apial: Publi apial demand inreases by 1 n. Privae savings s ds hange by 1 d (12) 1 d (13) 1 1 n (14) 6

7 Assumpion: O, are normal goods: 0 => Par of he redued ax burden is used for higher onsumpion in youh => privae savings inrease by a lower amoun han he apial demand inreases 1 n. Exess demand for apial per apia = 1 n 1 n 1 1 n (2.14 ) Condiion (1.21)forsabiliy bl of he shor run equilibrium lb implies ha he ineres rae on he apial marke inreases (apial supply inreases by less han apial demand). 7

8 Formal derivaion Using w s for s in eq. (1.5) and aking aoun of s w w, r 1 apial marke equilibrium: yields he modified ondiion for a shor run nk d w ( w, r 1) Implii differeniaion and using dr dk dr kk 1 1 nc, r nf k C, r 1 kk 1 r 1 f k 0 yields (2.15) wih C follows. 0 (by assumpion) and he sabiliy ondiion (1.21 ) he sign Numeraor: size of he exess demand for apial Denominaor: Inrease of he ineres rae needed in order o redue apial demand and inrease savings o eliminae he gap. 8

9 r CD s 1 0 CD 0 s 1 r 1 r 0 k 1 k0 k 1 d k Figure: Publi deb and apial marke; parial rowding ou 9

10 Impainhe he mediumrun Wage rae is w f k r k and, hene : dw 1 k1 0 dr 1 (2.16) The inrease of he ineres rae redues he wage rae in period +1 beause he apial labour raio dereases. Furhermore, he ax in period d1i +1 rises due o he higherh ineres on publi deb by: Wih r n 1 d 1 r 1 n d he ax burden inreases. 1 dr 1 (2.17) 10

11 Wih (2.16) and (2.17) he ne wage in period +1 dereases: d dr 1 r n k d 0 (17) (2.18) if r 1 n. Ineres rae in period +1: Sine he ne wage dereases in period +1 he savings of generaion +1 derease as well (due o normaliy of, O ) This implies: ineres rae oninues o inrease. However: he inrease of he ineres rae mus fall from period o period so ha he eonomy onverges o a new seady sae. 11

12 Impa in he long run In he seady sae, he effe on he ne wage is analogous o (2.18): d dr r n k d 0 (2.19) if r n and dr 0. The ne wage rae dereases by he dire effe ha a higher publi deb wih r n leads o a higher ax burden, and by he indire effe ha he inrease in he ineres rae redues apial formaionwhih h leads olower wages. From (2.11) an be dedued ha he long run ineres rae inreases: dr 0 (2.20) 12

13 Conlusion An inrease in publi deb and a ompensaing derease in he ax leads o lower gross wages, higher ineres raes and a lower apial sok in he medium and in he long run. If he eonomy is dynamially effiien ( r n ) he ne wages derease in he medium and in he long run. 13

14 Empirial evidene: Ne borrowing and ineres paymens Figure 1: Ne borrowing in seleed ounries (in % of GDP) 16% 14% 12% 10% 8% 6% 4% 2% 0% % 4% EU 15 Germany Greee Ialy Unied Saes Japan 14

15 14% 12% 10% 8% 6% 4% 2% 0% Figure2: Inerespaymens inseleed ounries (in % of GDP) EU 15 Germany Greee Ialy Unied Saes Japan 15

16 6,0% 5,0% 40% 4,0% 3,0% 2,0% 1,0% 0,0% Figure 3: Ne borrowing and ineres paymens in Germany (in % of GDP) ,0% 2,0% Ne borrowing Ineres paymens 16

17 12% 10% 8% 6% 4% 2% 0% Figure 4: Ne borrowing and ineres paymens in he Unied Saes (in % of GDP) % 4% Ne borrowing Ineres paymens 17

18 Normaive analysis Welfare effes of publi db deb: Change of represenaive indire uiliy By inroduing publi deb In he long run Indire uiliy funion of generaion Assumpions: V V w r u w, 1 r (2.21) O, w, r (2.22) O, 0,, 1 1 r 0 r O 18

19 Change in uiliy: dv V dw d V r dr 1 (2.23) wih r1 : ineres relevan for savings deision of generaion. Consider welfare of old generaion in period : No welfare effes by publi db debsine old generaion does neiher ih reeive wage inome nor pay axes; savings s1 and ineres rae r are deemined by he pas. 19

20 Generaion : subsiuion of d 1 n 2.12 and 2.13) in (2.23) yields: (finanial exhange from dv V V r dr 1 n 1 0 (2.24) 1 0 wih V r V s r from (1.21) (Roy s ideniy: Inrease in wage by s 1 r 1 unis is uiliy equivalen o an inrease in he ineres rae by one uni. Reason: Inrease in ineres rae by one uni raises he lifeime inome by s r unis.) 1 1 The working generaion in period gains a higher uiliy by expanding publi deb due o higher ne wages and a posiive effe of he inreasing ineres rae. 20

21 As o generaion +1, using (2.18) in (2.23) yields dv 1 V r n k d V 1 dr 2 r 2 dr (2.25) Welfare effes indeermined: ne wage dereases ( wih r n ) bu inreasing ineres rae has a posiive effe. Again: ne wage dereases beause higher ineres rae lowers apial inensiyi and hegrosswage. Furhermore, ax rae inreases beause higher deb burden (ineres paymens) makes higher ax revenue neessary and higher ineres rae on exising deb inreases deb burden furher. 1 21

22 Welfare in he long run: dv V dr V dr r r n k d (2.26) Wih V r V s 1 r and s 1 n k d (from (1.5)) dv V k d 1 r dr r n 1 0 (2.27) wih rn. Welfare dereases in he long run. Posiive ineres rae effe is overompensaed by he negaive effe of ne wages. 22

23 Conlusion In a dynamially effiien eonomy, he inrease in publi deb dereases welfare in he long run. The working generaion a he ime of he inrease in publi deb gains aiional welfare while he effe on ransiional generaions is indeermined. 23

24 If he alloaion is dynamially ineffiien ( rn ) publi deb may inrease welfare. Inuiion: r f ' k n implies oo muh apial has been aumulaed. Publi deb dereases he apial sok per apia in he long run whih has a posiive effe on welfare. All generaions may inrease onsumpion. However, in he pos war period we had in Germany r n dynamially effiien eonomy is a plausible assumpion. : The 24

25 10% 8% 6% 4% 2% 0% Empirial evidene: Populaion growh rae and real long erm ineres rae Figure 5: Unied Saes % 4% Pop growh US Real long erm ineres rae 25

26 Figure 6: Germany Pop growh Germany Real long erm ineres rae 26