Intergenerational economics

Transcription

1 Inergeneraional economics Rober Fenge

2 Srucure of he course 1. Public Deb 1.1 Inroducion 12OLG 1.2 model 1.3 Neoclassical Theory of Public Deb 1.4 Ricardian Neuraliy 1.5 Tax Smoohing Theory 1.6 Poliical Economy of Public Deb 2. Transfers wihinhe ihi h Family 2.1 Inroducion 2.2Modelswihone sided one sided alruism 2.3 Models wih wo sided alruism 2.4 Transacion cos approach

3 1. Governmen Deb Lieraure: Diamond, P.A. (1965) Naional db debin a neoclassical lgrowh model, dl American Economic Review 55, Seminal paper pp on public deb in he OLG model Myles, G.D. (1995) Public economics, Cambridge (Mass.), Chaper 13 Very good inroducion ino OLG models and overview of resuls Barro, R.J. (1974) Are governmen bonds ne wealh?, Journal of Poliical Economy 82, Seminal paper on Ricardian equivalence Buier, W.H. (1983) Governmen deb in an overlapping generaions model wih beques and gifs, American Economic Review 73,

4 Inroducion Measuring governmen db deb 1. Financing defici (ne borrowing), budgedefici raio (defici/gdp) 2. Deb (= sum ofpreviousdeficis) deficis), deb GDPraio 3. Primary defici: revenue expendiure (wihou ineres paymens) 4. Ineres paymens, ineres ax raio 5. Implici deb

5 Deb GDP raio in Germany Public deb in % of GDP 2005: 67,8 2009: 73,2 1999: 60,9 1988: 43,1 1970: 18,6 Source: Saisisches Bundesam, Fachserie 14, Reihe 5, Tab

6 Public expendiure, public revenues, and financial defici Germany (in % of GDP) 49% 48% 48,0% 48,1% 48,1% 47,6% 48,4% 47,6% 47% 46% 45% 44% 43% 42% 41% 40% 46,6% 46,9% 46,4% 46,7% 45,9% 45,1% 45,4% 44,7% 44,3% 44,4% 43,9% 44,3% 43,7% 43,7% 43,7% 43,4% 43,2% 5% 4,00% 3,71% 3,66% 3,32% 3,30% 4% 2,82% 3% 2,17% 1,46% 1,64% 2% 1% 1,31% 0,19% 0,04% 0% % Expendiure Revenues Finanzierungssaldo Defici 2% Source: Saisisches Jahrbuch 2010, Tab , S.651, own calculaions

7 Schuldensand 2006 in % des BIP Public deb 2009, inernaional (in % of GDP) 200,00 189,2 180,0 160,00 140,0 120,00 115,1 115,8 100,0 80,0 76,8 77,6 60,9 64,0 66,5 68,1 73,2 73,6 84,5 96,7 60,0 41,6 42,3 44,0 53,2 40,0 14,5 20,0 0,0 Source: BMF Monasberich Sepember 2010

8 Defici GDP raio, inernaional

9 Explici db( deb (Federal/sae/local) /l l) vs. implici deb (esp. pension claims of civil servans and PAG social securiy sysems) Ex. 2004: explici deb 63.2%, implici deb 172.3% of GDP Financial burden of fuure generaions: implici deb is relevan; effecs on capial marke: explici i deb isrelevan. Implici deb can be reduced by policy reforms (e.g. pension sysem), explici deb can be reduced only by repaymen. py

10 Expliciand implicideb GDP raio ingermany 2004

11 Deb limis and problems Deb limis: Maasrich crieria (defici raio 3%, db deb GDP raio 60%); German consiuion, Ar. 115: defici < gross invesmen Effecs of deb on wage raes, ineres rae, growh and welfare Poliical economy of public deb

12 OLG model Model dlof OverLapping Generaions Infinie many periods, = 1,2, Generaion : born in period ; in each period 2 generaions: he young (generaion ) andheold(generaion 1). Populaion grows wih consan rae n N N N : / 1 1 : Each individual lives 2 periods: period (working period) and +1 (reiremen period) N n 1 1 N

13 Period Generaion work reire Generaion +1 work reire Generaion +2 work reire Figure: OLG model

14 Consumer Consumers consider uiliy funcionwih consumpion in youh c and O old age c : O U u c, c (1 ) Workers supply inelasically one uni of labour. Households in period 1 can eiher save or consume and in period 2 consume heir savings: c c O s w (2) r s (3 ) 1 1 wih w : wage rae; r : ineres rae

15 The ineremporal budge consrain follows from (2) and (3): Maximise (1) w.r.. (4) : c O c 1 r 1 r 1 w (4) u u c c O 1 r 1 (5) or MRS = MRT (relaive price of consumpion when young o consumpion when old)

16 Producion Producion: many small firms under complee compeiion Linear homogeneous producion funcion (CRS) F K, N wih K capial, labor. : N : Diminishing marginal produc: F wih K, FN 0 FKK, FNN F F K, N K ec. K Definiion of linear homogeneiy: F K N FK, N (6),

17 f N 1 Define : N 1 ) (7,1, k f N N K N F N K F wih capial labor raio This yields : N k K K N K F k f, ' N Ressource consrain of he whole economy: producion= consumpion + savings (= invesmen) K f producion = consumpion + savings (= invesmen) ) (8, O K K c N N c N K F => ) ( O k k n n c c k f

18 Firms maximise profis: max K, N F K, N w N r K (10) (depreciaion rae =1) Or: max Firs order condiions: k N f k w r k (11) F K r ; FN w (12) or: f ' k r ; f k k f ' k w (13 ) ;

19 Ineremporal equilibrium Capial marke equilibrium: lb In each period, savings are equal o gross invesmen: N s K 1 (14) or: w c n k (15) 1 1 The condiions for he ineremporal equilibrium are: Capial marke equilibrium: (15) Consumers maximise uiliy: (5) Firms maximise profis: (13)

20 Seady sae In heseady sae, all endogenous per capia variables do no change: all consumers plan he same consumpion; capial labor raio is consan. This implies hebudge consrain: c O c 1 r f k kf ' k (16) From (15) and (13): c f k kf ' k 1 n k (17) Subsiuing in (16) and employing g( (13)yields c O 1 nk 1 f ' k (18)

21 In heseady sae, (17) and (18) mus hold. Differeniaion of (17) and (18) yields dc dc O dc dc O kf '' k 1 n dk (19) 1 n 1 f ' kf '' dk (20 ) 1 n1 f ' kf '' kf '' 1 n (21) Furhermore, in seady sae consumers maximise uiliy u u c c O 1 r

22 O c E Seigung (1+r) c Figure: Seady sae

23 Efficiency Efficien allocaion: Maximise uiliy (1) subjec o ressource consrain (9) or: max u max u O O c c, c s.. f k c nk (22 ) 1 n c, 1 n f k c nk (23 ) Firs order condiions: f ' * k n (24) u u c c O 1 n (25)

24 (24) is called he golden rule of capial accumulaion Inuiion: addiional uni of capial increases per capia oupu by Foregone consumpion in order o keep per capia p capial consan f is' n k (due o populaion growh) (25)means MRS = cos of foregone consumpion: one uni of consumpion of he young generaion coss 1+n unis of consumpion of he old generaion. Noe: Golden rule allocaion is no necessarily a seady sae (see nex figure): In F he GR allocaion is a seady sae bu no in G.

25 O c F G Seigung (1+n) c Figure: Seady sae and Golden rule

26 Pareo efficiency If If r f ' k n, allocaion is dynamically inefficien: oo much capial has been accumulaed. Lowering capial per capia implies ha he living generaions are able o consume more (inves less). Welfare of all subsequen generaions also increases because consumpion per capia is maximal in he Golden Rule. r f ' k n, allocaion is dynamically efficien: Invesmen has o be higher in order o reach he GR allocaion => living generaions suffer. A seady sae does no need o be dynamicallyefficien: here may be possible Pareo improving policy inervenions (bu only wih r n ).