Can monetary policy help attain stabilisation objectives? Incomplete Nominal Adjustment & Co-ordination Failure in the Fischer Model

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1 he sraegy ank Economic Discussion Paper Can moneary policy help aain sabilisaion objecives? Incomplee Nominal Adjusmen & Co-ordinaion Failure in he Fischer Model George Mendes Copyrigh Auhors and The Sraegy Tank Every endeavour has been made o recognise works cied wihin his documen. For furher copies or publicaion permission, or ciaion please us a hesraegyank@gmail.com

2 Absrac Overview This economic discussion paper discusses he role of moneary policy wihin he Fischer model and examines is implicaions wih paricular aenion o wheher changes o he money supply can help in aaining sabilisaion objecives. I is found ha unlike he Lucas Imperfec-Informaion model, moneary policy has he abiliy o affec he shor-run behaviour of oupu in he model, alhough he persisence of his impac is variable dependen on he lengh of ime-periods in which periodic price-seing decisions are made. Furhermore, he role of real rigidiy and is abiliy o amplify or dampen he affecs of changes in moneary supply by he policymaker is also discussed.

3 Wha is he Fisher Model & Wha is he Role of Moneary Policy? Sanley Fischer s saggered price adjusmen model developed in he lae 970s was one of a wave of new economic hinking ha used microeconomic foundaions of macroeconomics pioneered by he New-Keynesian economiss ha included himself as well as John Taylor and Edmund Phelps. The approach offered by Fischer differs o early Keynesian views and ha of he Lucas Imperfec-Informaion model by demonsraing ha business cycles occur no because of agens holding imperfec informaion and no specifically because of imperfecly compeiive markes, bu because nominal wages and prices are slow o adjus o changes in aggregae demand as a resul of saggered prices and wages. Fischer s model consrucs a saggered, wo-period overlapping labour conrac imeline allowing agens given he opporuniy o se prices a given imes, - and -, such ha wage raes are pre-deermined and differen prices can be se every oher period, bu no fixed as in he Lucas and Taylor Models. Under each discree ime period in his model, imperfecly compeiive firms produce oupu by using labour as heir only inpu n periods p p E P 3 E P Curren prices depend on pas prices and expecaions of fuure prices For a given period, i is assumed ha half of he prices are se in he previous period and half are ones se wo periods ago as alhough agens are given he opion of adjusing prices a each sage, only half are expeced o do so. p = ( p + p ) A erm coined by Michael Parkin in 98 Caplin-Spulber, developed Fischer s work furher and allowed price changes o be deermined endogenously so ha he fracion of prices ha changes each period can vary. 3 Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill 3

4 As no everyone in he economy 4 ses new wages and prices every period, saggering makes he overall level of wages and prices adjus slowly and provides an explanaion for incomplee nominal adjusmen. As Fischer shows, he use of longer-erm nominal conracs which are aribued o he coss of frequen price seing and wage negoiaion, 5 places an elemen of wage-sickiness ino he nominal wage which creaes a nominal price rigidiy, which iself is responsible for he effeciveness of moneary policy. 6 The equaion assumes ha agens can only forecas one period ahead, bu no wo periods, and hus Fischer suggess ha he role of a moneary auhoriy could be o inervene and reac o new informaion abou recen economic disurbances. This is furher demonsraed by solving he model, which generaes he following equaions for price p and oupu y: p = E φ m + ( E + φ m E m ) y = ( E + φ m E m ) + ( m E m ) Anicipaed porion Unanicipaed porion Unlike he Lucas model where moneary policy can only affec oupu by creaing a difference beween acual and expeced prices, 7 his model demonsraes ha boh he unanicipaed and anicipaed porions of he model affec oupu. As expeced, unanicipaed aggregae demand shifs have real effecs as explained by he erm ) as i is assumed ha m E m ( agens do no know he erm m when hey se heir prices, and hus hese shocks are passed one-for-one uno oupu. 8 The firs porion of he equaion demonsraes ha aggregae demand shifs ha become anicipaed afer he firs prices in he model are se do in fac affec oupu. Informaion ha becomes available beween he periods - and - is passed ino oupu and he remainder goes ino prices, as no all prices are flexible in he shor run. 9 The proporion of he change ha affecs oupu is no half-and-half, bu insead is 4 This saggered effec is ofen observed in he US, where ~0% of workers in he economy are unionised, and will have wagechanges made a discree poins during he year. 5 Ineresingly, he welfare effecs of he implied oupu movemens are likely o be much larger han he coss of changing prices. 6 Fischer, S. 977, Long-Term Conracs, Raional Expecaions, and he Opimal Money Supply Rule, Journal of Poliical Economy 85, pp Ibid 8 Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill 9 Ibid 4

5 deermined by he erm /( + φ), which has he abiliy o eiher amplify or dampen he degree of effec ono oupu. 5

6 Can moneary policy help in aaining sabilisaion objecives? Moneary policy can help aain sabilisaion objecives m + * * = m v m If we le, where is conrolled by he policy maker, and assume hey are under he same informaion consrains as price-seers, he policymaker mus choose * m v before he exac value of is known. However, as he policymaker can choose in response o informaion learn beween - and - hen here is a role for sabilisaion policy. Clearly his model demonsraes ha oupu can be influenced by responses of he moneary auhoriy, and Fischer furher demonsraes ha indeed he policymaker should do so. If nominal wage conracs are se for more han one period in advance, and are no indexed o inflaion hen even under raional expecaions, moneary policy can and should be used o sabilise he economy. Alhough he policymaker is unable o conrol he unanicipaed * m porion, hey do have conrol over he anicipaed componen, 0 and hus he role of he moneary auhoriy should be o reduce he asympoic variance of oupu and hus reduce loss of economic welfare. y = m p + v Where a variable eiher or for anher ime period are non-policy shocks o aggregae demand; u v u = p u v = p v + ε + η p p <, < The money sock a ime will be dependen on all demand shocks up o - m a ε + aε anε n +... = and solving oupu for ou pu is herefore; y = ε ( )( ) + + b + a ε 3 0 Furher research, by Chadha, 989 on his opic relaed he asympoic variance in oupu o he conrac lengh, and deermined his o be 3.73 quarers for he US economy. As hese conracs ac as shock absorbers for he economy, one could argue ha par of he role of he policy maker would be o enforce a conrac period duraion of his opimal lengh. Heijdra, B. J., and F. van der Ploeg, 000, The Foundaions of Modern Macroeconomics, Oxford Universiy Press. Fischer, S. 977, Long-Term Conracs, Raional Expecaions, and he Opimal Money Supply Rule, Journal of Poliical Economy 85, pp Blanchard, O. and Fischer, S. 989, Lecures in Macroeconomics, The MIT Press, Cambridge MA and London 6

7 Ulimaely, he aim of moneary policy will be o minimise he variance of oupu by opimally seing he moneary rule o a = as his offses he anicipaed non-policy shock in he nex period. 4 However, movemens in aggregae demand (wheher hey are non-policy shocks or in money) ha are more han wo periods in advance have no effec on oupu. Harris and Holsrom noe ha he role of moneary policy is simply o ac as a subsiue for conrac indexaion, and ha one role of aggregae policy is o convey informaion ha would oherwise be more cosly o obain. If he moneary auhoriy could se he money sock each period afer he velociy shock becomes known, i could preven all divergences of oupu from a given consan level. 5 Persisence in he Model Alhough persisence is observed in he Fischer model, i is limied. In he absence of oher sources of persisence he effec of aggregae demand on oupu lass only for a period equal o he period for which prices are predeermined. 6 This arises as a resul of he fac ha he value of an aggregae demand shif ha becomes known afer he firs prices are se; E m does no have any effec on oupu, as price seers have had a chance o respond o oupu, and his change and will no lead o changes in oupu. 7 We can compare his resul o oher models; he Lucas model, ha uilises only one ime period does no consider persisence, alhough he Taylor model wih more han one ime period observes lenghy persisence in changes in oupu. In he Taylor model which more realisically reflecs he economy, boh wages and price levels adjus slowly o a permanen increase in money, ε, and as a resul, he effecs of a nominal disurbance on oupu are long lived, dying exponenially a a rae λ 8 and persisence in his produciviy disurbance generaes coninued oupu persisence. 9 4 Blanchard, O. and Fischer, S. 989, Lecures in Macroeconomics, The MIT Press, Cambridge MA and London 5 Ibid 6 Ibid 7 Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill 8 Where lambda = [-sqr(-b)]/b ; and 0< lambda < furher deails are given in he appendix of his paper. 9 Walsh, C., 003, Moneary Theory and Policy, (nd Ed), The MIT Press, Cambridge MA and London Press. 7

8 Wha is he role of real rigidiy? Real rigidiy refers o he models ha explain why real wages or prices are unresponsive o changes in economic aciviy. Alhough for symmery, he Fischer model assume ha a ime, only half of he prices seers have updaed heir prices so ha p = ( + ), he rue proporion is in fac deermined by he fracion; +φ p p The parameer φ measures he degree of real rigidiy, such ha a smaller value of φ corresponds o a greaer real rigidiy. As Romer noes, when real rigidiy is large ( φ < ), price seers are relucan o allow variaions in heir relaive prices and hus do no allow heir prices o differ grealy from he level ha hey are iniially se, leading o a large real affec from a moneary shock. Conversely, if he value of φ is large, hen he real effecs of changes in m are small, 0 and furhermore an undesired inflaionary effec may be observed if φ is oo large. If we consider how a firm migh change is real price in response o a change in aggregae real oupu, is opimal price seer i is demonsraed by; p * i p = c + φy A lower value of φ corresponds o greaer real rigidiy since firms are unwilling o adjus heir real prices when aggregae oupu changes. Real rigidiy alone does no cause moneary disurbances o have real effecs: if prices can adjus freely, money is neural regardless of he value of φ. Bu real rigidiy magnifies he effec of nominal rigidiy: a low value of φ implies ha price-seers are unwilling o allow variaions in heir relaive prices. As a resul, 0 Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill If φ = 0 hen here is complee real rigidiy. 8

9 he price-seers ha are free o adjus heir prices do no allow heir prices o differ grealy from hose already se. Ulimaely, real rigidiy alone does no cause moneary non-neuraliy if prices are compleely flexible bu in conjuncion wih nominal rigidiy i increases he real effec of moneary shocks, and a greaer degree of real rigidiy increases persisence of he effecs of changes in he money supply. The Imporance of Real Rigidiy & Poenial Sources Alhough in a given economic sysem figures are ofen denominaed in nominal erms, hey are no of grea imporance o agens in ha economy. Individuals clearly care more abou he real level of wages, prices and consumpion levels and will use hese figures in heir economic aciviies. According o New Keynesian Economics, if nominal imperfecions are imporan o flucuaions in aggregae aciviy, i mus be ha small nominal fricions a he microeconomic level have a large effec of he macroeconomy. Price A Firm s Incenive o Change is Price in Response o a Fall in Aggregae Oupu MC D D Shaded area MR MR Quaniy Source: Romer, D., 006, (Fig. 6., pg 9), Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill Cameron, G., Macroeconomic Theory IV: New Keynesian Economics, Lady Margare Hall, Nuffield College, Universiy of Oxford 9

10 The shaded area of he graph above shows he addiional profis o be gained from reducing price and increasing quaniy produced, 3 hough he firm has an incenive no o adjus is price if he size of his area is smaller han he menu coss i has o pay in order o adjus. 4 The imporance of real rigidiy in he Fischer model is herefore clear; he incenive for firms o reduce price may be small, even hough here may be a large change in demand, and if many firms behave his way, hen a recessionary siuaion - wih no firm adjusing- becomes an equilibrium. 5 Rober Gordon reaffirms his finding suggesing ha in a response o a nominal demand change, no single privae agen has an incenive o move is price unless i believes ha all oher agens will do likewise, and will do so wihou delay. 6 However, if firms have a srong incenive o cu prices, hen a recession can be avoided. 7 The wo facors ha will influence a firm s incenive o cu prices are marginal cos and marginal revenue, and how hey respond o a fall in demand. The more marginal cos falls as oupu drops, hen he greaer he incenive of he firm will be o lower is price. Conversely, he more he marginal revenue curve shifs o he lef due o a decrease in demand, he smaller he firm s incenive o change price. 8 Boh a small cyclical sensiiviy of marginal coss and a larger cyclical sensiiviy of marginal revenues increase real rigidiy. There is an imporan link beween muliple equilibria and real rigidiy, as co-ordinaion failure requires ha real rigidiy be very srong over some range and as a resul since here are many poenial sources of real rigidiy, here are many poenial sources of co-ordinaion failure. 9 Generally, sources of real rigidiy in he marke can be classified under hree or four opics, namely; cusomer markes, he independence of coss and demand and he role of he inpuoupu able. Alhough he insensiiviy of he profi funcion is recognised as an imporan facor of real rigidiy, he labour marke is ofen viewed as an equally imporan, if no even 3 Romer, D., The New Keynesian Synhesis, The Journal of Economic Perspecives, Vol. 7, No.. (Winer, 993) pp.5-4 Professor Mira, K. Lecures in Advanced Macroeconomics, Handou 3, 006, Universiy of S Andrews 5 Professor Mira, K. Lecures in Advanced Macroeconomics, Handou 3, 006, Universiy of S Andrews 6 Gordon, R. J., Journal of Economic Lieraure, Vol. 8, No..3. (Sep., 990), pp Professor Mira, K. Lecures in Advanced Macroeconomics, Handou 3, 006, Universiy of S Andrews 8 Ibid 9 Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill 0

11 more influenial source, 30 paricularly if labour markes clear and labour supply is inelasic, hen real wages are highly procyclical. 3 Oher reasons include he exen of labour mobiliy or differences in he goods and credi markes. 3 However, real wages may no be highly procyclical as a resul of eiher elasic shor-run labour supply under ineremporalsubsiuion, or some oher labour marke imperfecion such as an efficiency wage designed o increase he produciviy of workers and reduce shirking, as well as reducing hiring and firing coss, bu which resuls in seing real wages above marke clearing levels. 33 Generally, he incenive o change prices in response o a change in aggregae oupu depends on wo facors: he impac of he change on he firms profi maximising real price and on he cos o he firm of a given deparure from he profi maximising level. For he incenive of price adjusmen o be small, eiher profi maximising real prices mus respond lile o changes in aggregae demand he degree of real rigidiy mus be large, or large deparures from profi maximising prices mus have small coss. 30 Ibid 3 Professor Mira, K. Lecures in Advanced Macroeconomics, Handou 3, 006, Universiy of S Andrews 3 Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill 33 Rober Gordon discusses cusomer markes, invenory models and heories of mark-ups under imperfec compeiion, and labour marke rigidiies as implici conracs, efficiency wages and insider ousider models as some explanaions.

12 Conclusion The Fischer model demonsraes how he early Keynesian view ha he moneary policy can have no significan role in deermining he behaviour is no necessarily rue, and ha in fac here is a very real abiliy for policymakers o impac he economy. As he money sock is changed by moneary auhoriies more frequenly han labour conracs are renegoiaed, moneary policy has he abiliy o affec he shor-run behaviour of oupu, hough i has no effecs on long-run oupu behaviour. The model builds on he work of Lucas o creae a model ha more accuraely describes he economy and he opporuniies for policymakers o inervene, alhough he Taylor model provides a furher developmen ha more accuraely describes he economy. In conclusion, Fischer draws our aenion o he fac ha boh anicipaed and unanicipaed changes in he money supply have an effec on oupu, and i is clear ha saggered price decisions can generae long-lasing effecs of money on oupu, hough limied o he ime periods se by he model. Furhermore, in he presence of non-policy shocks, policy can decrease he ampliude of oupu flucuaions, alhough he abiliy o do so is regulaed by he real rigidiy of he economy. Taylor s model provides a furher developmen of his widely debaed opic in macroeconomics.

13 Bibliography and Appendix Ball, L. and Romer D., 990, Real Rigidiies and he Non-Neuraliy of Money, Review of Economic Sudies, 57, pp Blanchard, O. and Fischer, S. 989, Lecures in Macroeconomics, The MIT Press, Cambridge MA and London Brasiois, G. J. and Marin C., Moneary Policy Rules, Real Rigidiy and Endogenous Persisence, Universiy of Mancheser and Elsevier Science Calvo, G., 983, Saggered Conracs in a Uiliy-Maximizing Framework, Journal of Moneary Economics,, pp Cameron, G., Macroeconomic Theory IV: New Keynesian Economics, Lady Margare Hall, Nuffield College, Universiy of Oxford Clarida, R., Gali, J. and Gerler M., 999, The Science of Moneary Policy: A New Keynesian Perspecive, Journal of Economic Lieraure 37 (December) pp.,66-,707. Fischer, S., 977, Long-Term Conracs, Raional Expecaions, and he Opimal Money Supply Rule, Journal of Poliical Economy 85, pp Gordon, R. J., Wha is New-Keynesian Economics, Journal of Economic Lieraure, Vol. 8, No..3. (Sep., 990), pp. 5-7 Heijdra, B. J., and F. van der Ploeg, 000, The Foundaions of Modern Macroeconomics, Oxford Universiy Press Professor Mira, K. Lecures in Advanced Macroeconomics, Handou 3, 006, Universiy of S Andrews Romer, D., 006, Advanced Macroeconomics, (3rd Ed), New York: McGraw-Hill Romer, D., The New Keynesian Synhesis, The Journal of Economic Perspecives, Vol. 7, No.. (Winer, 993) pp.5- Sargen, T. J., and Wallace, N., Raional Expecaions, he Opimal Moneary Insrumen, and he Opimal Money Supply Rule, Journal of Poliical Economy, 83, no. (April 975): 4-54 EC303 Advanced Economics 3

14 Taylor, J., 979, Saggered Wage-Seing in a Macro Model, American Economic Review, Papers and Proceedings, 69, pp 08-3 Walsh, C., 003, Moneary Theory and Policy, (nd Ed), The MIT Press, Cambridge MA and London Press EC303 Advanced Economics 4

15 Appendix Co-ordinaion Failure Co-ordinaion failure demonsraes how more han one normal level of oupu may exis: Source: Romer, D., The New Keynesian Synhesis, The Journal of Economic Perspecives, Vol. 7, No.. (Winer, 993) pp.5- Persisence in he Taylor Model Solving he model generaes he following equaions for price p and oupu y gives; 34 p λ p + ( λ)( m + m = ) y + [ m ( + λ) m ( λ) m ] = λ y If λ is close o one, hen he effecs of money on oupu are large for periods of ime much longer han he lengh of ime during which each price is pre-deermined on he imeline. Fischer demonsraes herefore ha under ime-dependen rules, for fixed and saggered price decisions, nominal money can have long-lasing effecs on oupu as a resul of he inerdependence beween price decisions. 35 Similarly, if lambda, or he degree of ineria is close o one hen here will be lile incenive for price-seers whose urn i is o change 34 Blanchard, O. and Fischer, S. 989, Lecures in Macroeconomics, The MIT Press, Cambridge MA and London 35 Ibid EC303 Advanced Economics 5

16 prices o do so, as hey will no wan o increase heir relaive price much vis-à-vis oher price-seers. The Fischer and Taylor model was developed furher in 987 by Caplin & Spulber The Fischer and Taylor models assume ha he iming of price changes is deermined by he passage of ime. However, since all conracs are, in principle, renegoiable, perhaps i is beer o hink of he iming as being endogenous. In he Caplin-Spulber model a siuaion wih an Ss rule: whenever a price-seer adjuss her price, she ses i so ha he difference beween he acual and he opimal price is some arge level S. The nominal price is hen fixed unil he opimal level has changed such ha he rigger level s is reached. This is opimal when inflaion is seady. In conras o he Fischer model, money is neural in he Caplin-Spulber model since he number of price-seers changing heir prices a any one ime is an increasing funcion of he money supply growh rae. Caplin-Spulber shows ha saedependen price changes are imporan and ha even when prices are fixed for mos priceseers, he acions of oher price-seers can be offseing. EC303 Advanced Economics 6