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

Transcription

1 .3 Neolassial heory 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

2 .3.. 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 Y O r Governmen budge is saisfied in eah period: () N D D r D (2) wih D : publi deb in period. Publi revenues (ax plus publi defii) = publi expenses (ineres on exising publi deb).

3 Dividing boh sides of (2)by yields: N n d d r d (3) wih d : publi deb per apia. Capial marke equilibrium: savings of generaion = apial invesed plus publi deb: N s K D (4) or: s n k d (5 ) In he long run publi deb per apia is onsan. The governmen budge in a seady sae is: nd rd (6)

4 Seady sae Seady sae is df definedby: w f k kf ' k (7) r u u f ' k (8) Y O r (9) w w O r Y r n d (0 ) Y r nd nk d () (0) is he budge onsrain of he household and () is he apial marke equilibrium in he seady sae.

5 The impa of publi deb on wages, ineres rae and apial sok Period : governmen raises df defii. Publi db debin henexperiod inreases by: Tax dereases by: n N dd n n d In all subsequen periods he publi deb per apia remains on he higher level,. 2

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 n. Ineres rae and apial: Publi apial demand inreases by n. Privae savings s ds Y hange by Y d (2) Y d (3) Y n (4)

7 Assumpion: Y Y, 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 n. This implies ha he ineres rae on he apial marke inreases (apial supply inreases by less han apial demand).

8 r CD s 0 CD 0 s r r 0 k k0 k d k Figure: Publi deb and apial marke

9 Impainhe he mediumrun Wage rae is w f k r k and, hene : dw k 0 dr (5) The inrease of he ineres rae redues he wage rae in period + beause he apial labour raio dereases. Furhermore, he ax in period di + rises due o he higherh ineres on publi deb by: d r n d Wih r n he ax burden inreases. dr (6)

10 Wih (5) and (6) he ne wage in period + dereases: d dr r n k d 0 (7) if r n. Ineres rae in period +: Sine he ne wage dereases in period + he savings of generaion + derease as well (due o normaliy of Y, 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 Impa in he long run In heseady sae, heeffe on henewage is analogous o (7): d dr r n k d 0 (8 ) 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 formaion whih leads o lower wages. From () an be dedued ha he long run ineres rae inreases: dr 0 (9)

12 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 Empirial evidene: Ne borrowing and ineres paymens Figure : Ne borrowing in seleed ounries (in % of GDP) 6% 4% 2% 0% 8% 6% 4% 2% 0% % 4% EU 5 Germany Greee Ialy Unied Saes Japan

14 4% 2% 0% 8% 6% 4% 2% 0% Figure2: Inerespaymens inseleed ounries (in % of GDP) EU 5 Germany Greee Ialy Unied Saes Japan

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

16 2% 0% 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 32 Normaive analysis.3.2. Normaive analysis lf ff f bl db h f d l Welfare effes of publi deb: Change of represenaive indire uiliy By inroduing publi deb In he long run g Indire uiliy funion of generaion (20), r w V V 3 2 Assumpions: ) (2,,, r w r w u O Y p r r O Y O Y 0 0,,

18 Change in uiliy: dv V dw d V r dr wih ihr : ineres relevan for savings deision i of generaion. (22) Consider welfare of old generaion in period : No welfare effes by publi dbi deb sine old generaion does neiher reeive wage inome nor pay axes; savings s and ineres rae r are deemined by he pas. Generaion : subsiuion of d n in (22) yields: dv V V r dr n 0 (23 ) 0 wih V r V s r from (2).

19 The working generaion in period gains a higher uiliy by expanding publi deb due o higherh ne wages and a posiive effe of he inreasingi ineres rae. As o generaion +, using (7) in (22) yields dv V dr r n k d V dr r (24) Welfare effes indeermined: ne wage dereases ( wih r n ) bu inreasing ineres rae has a posiive effe.

20 Welfare in he long run: dv V dr V dr r r n k d (25) Wih V r V s r and s n k d (from (5)) dv V k d r dr r n 0 (26) wih rn. Welfare dereases in he long run. Posiive ineres rae effe is overompensaed by he negaive effe of ne wages.

21 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.

22 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

23 0% 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

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