Technological shocks mechanism on Macroeconomic Variables: A Dynamic Stochastic General Equilibrium (DSGE) approach.

Transcription

1 MPRA Munich Personal RePEc Archive Technological shocs mechanism on Macroeconomic Variables: A Dynamic Sochasic General Equilibrium (DSGE) approach Eric Amoo Bondzie and Gabriel Obed Fosu and Ernes Obu-Cann Universià Caolica del Sacro Cuore, Milan, Kwame Nrumah Universiy of Science and Technology, Ghana, Cenre for Inernaional Developmen, Universiy of Bradford, UK Ocober 2013 Online a hps://mpraubuni-muenchende/69286/ MPRA Paper No 69286, posed 7 February :42 UTC

2 TECHNOLOGICAL SHOCKS MECHANISM ON MACROECONOMIC VARIABLES: A DNAMIC STOCHASTIC GENERAL EQUILIBRIUM APPROACH Eric Amoo Bondzie, Gabriel Obed Fosu *, Ernes Obu-Cann, ABSTRACT: As Ghana assumes a posiion of oil producer and middle-income counry, i mus learn o effecively deal wih he relaed pressures from shocs We analyze he effecs of produciviy shocs on Ghana s oal oupu using he muli-secor dynamic sochasic general equilibrium (DSGE) model I was acualized ha a produciviy shoc resuls in a emporary shrinage in he final goods secors due o he reallocaion of labour from he final and inermediae goods secors We demonsraed ha echnological shoc induces an iniial fall in marginal cos of producion bu laer rises o reach equilibrium Keywords- DSGE models, Economic growh, Technological shocs I INTRODUCTION Technology is an essenial facor for developmen process A echnological shoc may eiher affec produciviy negaively or posiively Previous sudies [1-8] have shown ha an aggregae echnology improvemen is ofen consequenial on oal oupu of an economy, consumpion and hours wored Canova, López-Salido and Michelacci [9] analyzed he effecs of neural and invesmen-specific echnology shocs on hours wored and unemploymen They characerized he response of unemploymen in erms of job separaion and job finding raes and found ou ha job separaion raes mainly accoun for he impac response of unemploymen while job finding raes for movemens along is adjusmen pah In 2008, Canova, López-Salido and Michelacci [10] analyzed he effecs of neural and invesmen-specific echnology shocs on hours and oupu Their sudy revealed hours robusly fall in response o neural shocs and robusly increase in response o invesmen specific shocs For a newly oil producing counry lie Ghana, his shoc can cause considerable mixed feelings These issues call for his research o calibrae he influx of echnological shoc and is effecs on he economic growh of he Ghanaian economy The sudy applies a muli-secor dynamic sochasic general equilibrium (DSGE) model I feaures a learning-by-doing mechanism ha creaes an exernaliy associaed wih he producion of raded goods and capures he noion ha real exchange rae appreciaion may harm produciviy growh in he raded secor A role for public capial in producion, so ha governmen spending can raise oupu direcly and poenially crowd in privae invesmen and less-han-full conversion of public invesmen ino useful public capial *Corresponding Auhor: Gabriel O Fosu Kwame Nrumah Universiy of Science and Technology, Kumasi, Ghana 1 Page

3 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach II METHODOLOG This secion focuses on he DSGE model developed in Chrisiano e al [11, 12] I displays he problem solved by firms and households, as well as he behaviour of financial inermediaries and he moneary and fiscal auhoriies The model has srucural feaures ha are relevan in low-income counries, and as such i is ideally suied o loo a he case of Ghana The Consumer Problem There is a coninuum of households, indexed by j 0,1 The h j household maes a sequence of decisions during each period Firs, i maes is consumpion decision, is capial accumulaion decision, and i decides how many unis of capial services o supply Second, i purchases securiies whose payoffs are coningen upon wheher i can re-opimize is wage decision Third, i ses is wage rae afer finding ou wheher i can re-opimize or no Fourh, i receives a lump-sum ransfer from he moneary auhoriy Finally, i decides how much of is financial asses o hold in he form of deposis wih a financial inermediary and how much o hold in he form of cash Since he uncerainy faced by he household over wheher i can re-opimize is wage is idiosyncraic in naure, households wor differen amouns and earn differen wage raes So, in principle, hey are also heerogeneous wih respec o consumpion and asse holdings A sraighforward exension of argumens in Erceg, Henderson and Levin [13] esablish ha he exisence of sae coningen securiies ensures ha, in equilibrium, households are homogeneous wih respec o consumpion and asse holdings Reflecing his resul, he noaion assumes ha households are homogeneous wih respec o consumpion and asse holdings bu heerogeneous wih respec o he wage rae ha hey earn and hours wored The preferences of he h j household are given by: n j l 1 l l1 j, l l i1 E u c bc z h v q (1) where, j E 1 is he expecaion operaor, condiional on aggregae and household j idiosyncraic informaion up o, and including, ime 1 ; c denoes consumpion a ime ; q Q P denoes real cash balances; Q denoes nominal cash balances When b >0 h j denoes hours of wor a ime ;, equaion (1) allows for habi formaion in consumpion preferences The household s asse evoluion equaion (budge consrain) is given by: where, Addiionally, M R M Q M A Q W h R u a 1 1 j, j, j, D P i c a u M s he household s beginning of period soc of money and W i j, hj,, i s ime (2) labour income D and Aj, denoe, respecively, he physical soc of capial, firm profis and he ne cash inflow from paricipaing in sae-coningen securiies a ime The variable represens he gross growh rae of he economy-wide per capia soc of money, a M The quaniy 1 M made o households by he moneary auhoriy The quaniy 1 a a is a lump-sum paymen M Pq M is deposied by he *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 2 Page

4 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach household wih a financial inermediary where i earns he gross nominal rae of ineres, R The remaining pars of equaion (2), aside from Pc perain o he soc of insalled capial, which is assumed o be owned by he household The household s soc of physical capial evolves according o: 1, F i i 1 1 (3) where, denoes he physical rae of depreciaion and i denoes purchases of invesmen goods a ime The funcion, F, summarizes he echnology ha ransforms curren and pas invesmen ino insalled capial for use in he following period The properies of F is discussed as follows: Capial services, are relaed o he physical soc of capial by u (4) where, u denoes he uilizaion rae of capial, which is assumed o be se by he household This assumpion ha households mae he capial accumulaion and uilizaion decisions is a maer of convenience A he cos of a more complicaed noaion, an alernaive decenralizaion scheme in which firms mae hese decisions could be wor wih From equaion (2) R u services The increasing, convex funcion au he uilizaion rae o The Wage Decision u represens he household s earnings from supplying capial denoes he cos, in unis of consumpion goods, of seing As in Erceg, Henderson and Levin [13], i is assumed ha he household is a monopoly supplier of a differeniaed labour service, h j, I sells his service o a represenaive, compeiive firm ha ransforms i ino an aggregae labour inpu, L, using he following echnology: w j L h dj w (5) The demand curve for h j is given by: h j w w 1 W L,1 w< W j (6) where, o W is he aggregae wage rae, ha is, he price of W j hrough he relaionship: L I is sraighforward o show ha W is relaed *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 3 Page

5 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach W W 0 j w dj 1w (7) The household aes L and W as given They also se heir wage rae according o a varian of he mechanism used o model price seing by firms In each period, a household faces a consan probabiliy, 1w of being, able o re-opimize is nominal wage The abiliy o re-opimize is independen across households and ime If a household canno re-opimize is wage a ime, i ses W according o: j W W j 1 j, 1 (8) Final Good Firms A ime, a final consumpion good,, is produced by a perfecly compeiive, represenaive firm The firm produces he final good by combining a coninuum of inermediae goods, indexed by j 0,1, using he echnology: 1 1 f 0 j dj f (9) where 1 f < and j P and is inpu prices, denoes he ime inpu of inermediae good j The firm aes is oupu price, P as given and beyond is conrol Profi maximizaion implies he Euler equaion j, f f 1 P P j j (10) By inegraing equaion (10) and imposing equaion (9), he following relaionship beween he price of he final good and he price of he inermediae good is obained: f 0 j P P dj 1 f (11) Inermediae Good Firms Inermediae good j 0,1 is produced by a monopolis who uses he following echnology: j 1 1 jlj if jlj 0 oherwise *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana (12) 4 Page

6 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach where 0 < < 1 and Lj and j denoe ime inermediae good Also > 0 producion of inermediae good j are ruled ou labour and capial services used o produce he h denoes he fixed cos of producion The assumpion of enry and exi ino he Inermediae firms ren capial and labour in perfecly compeiive facor mares Profis are disribued o households a he end of each ime period Le R and j W denoe he nominal renal rae on capial services and he wage rae, respecively Worers mus be paid in advance of producion As a resul, he h j firm mus borrow is wage bill, W L j, from he financial inermediary a he beginning of he period Repaymen occurs a he end of ime period a he gross ineres rae, The firm s real marginal cos is: R S s, where S min, r w Rl, given by equaion 12 l (13) where r R P and w W P Given he funcional forms, marginal cos is given as: s r w R 1 1 (14) Apar from fixed coss, he firm s ime profis are: P P j s P j, (15) where P j is firm j ' s price Assuming firms se prices according o a varian of he mechanism spelled ou in Calvo [14] This model has been widely used o characerize price-seing fricions A useful feaure of he model is ha i can be solved wihou explicily racing he disribuion of prices across firms In each period, a firm faces a consan probabiliy, 1 p of being able o re-opimize is nominal price The abiliy o re-opimize is price is, independen across firms and ime If a firm can re-opimize is price, i does so before he realizaion of he ime growh rae of money Firms ha canno re-opimize heir price simply index o lagged inflaion: P P j 1 j, 1 (16) P P where, 1 This price-seing rule is referred o as lagged inflaion indexaion Leing P denoe he value of P j se by a firm ha can re-opimize a ime This noaion does no allow o depend on j This is done in anicipaion of he well-nown resul ha, in models lie his, all firms who can re-opimize heir price a ime choose he same price The firm chooses P o maximize: *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 5 Page P

7 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach l E v P X s P 1 p l l l l j, l l0, (17) subjec o equaions (10) and (14) and X l x l x x l 1 for l 1 1 l 0 (18) In equaion (17), v is he marginal value of a dollar o he household, which is reaed as exogenous by he firm Laer, i will be shown ha he value of a dollar, in uiliy erms, is consan across households Also E 1 denoes he expecaions operaor condiioned on lagged growh raes of money,, l 1 This specificaion of he informaion se capures he assumpion ha he firm chooses l P before he realizaion of he ime growh rae of money To undersand equaion (17), one should noe ha P influences firm long as i canno re-opimize is price The probabiliy ha his happens for l periods is l P P l X The presence of j, l l idiosyncraic uncerainy in which Moneary and Fiscal Policy The moneary policy is assumed o be given by: p j ' s profis only as p in which case, in equaion (17) has he effec of isolaing fuure realizaions of P coninues o affec he firm s profis (19) where denoes he mean growh rae of money and j is he response of E j o a ime moneary policy shoc We assume ha he governmen has access o lump sum axes and pursues a Ricardian fiscal policy Under his ype of policy, he deails of ax policy have no impac on inflaion and oher aggregae economic variables As a resul, here is no need o specify he deails of he fiscal policy Loan Mare Clearing, Final Goods Clearing And Equilibrium M Financial inermediaries receive Q from households and a ransfer, 1 M from he moneary a auhoriy The noaion here reflecs he equilibrium condiion, M M Financial inermediaries lend all of heir money o inermediae good firms, which use he funds o pay for L Loan mare clearing requires: W L M Q The aggregae resource consrain is given as: c i a u (20) (21) In his seing he research adops a sandard sequence-of-mares equilibrium concep This sraegy involves aing a linear approximaion abou he non-sochasic seady sae of he economy [11,12] In principle, he *Corresponding Auhor: Gabriel Obed Fosu 6 Page Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana

8 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach non-negaiviy consrain on inermediae good oupu in equaion (12) is a problem for his approximaion I urns ou ha he consrain is no binding for he experimens ha he research considers and so i is ignored Finally, i is worh noing ha since profis are sochasic, he fac ha hey are zero, on average, implies ha hey are ofen negaive As a consequence, he assumpion ha firms canno exi is binding Allowing for firm enry and exi dynamics would considerably complicae he analysis Funcional Form Assumpions Given he funcions characerizing uiliy as: u log z v q q 1 In addiion, invesmen adjusmen coss are given by: q (22) i F i, i 1 1 S i i 1 (23) The funcion S ' '' is resriced o saisfy he following properies: S 1 S 1 0, and S 1 0 I is easy o verify ha he seady sae of he model does no depend on he adjusmen cos parameer, Of course, he dynamics of he model are influenced by Given he soluion procedure, no oher feaures of he S funcion need o be specified for he analysis Two resricions are imposed on capial uilisaion funcion a u Firsly, in he seady sae u is required o be u 1 Secondly, a is also required o be Under his assumpions, he seady sae of he model is independen of on '' a a ' a 1 1 a1 0 The dynamics do depend Given he soluion procedure, here is no need o specify any oher feaures of he funcion a a Technological Mechanism For proper undersanding of he echnological shoc mechanism, our model does well in accouning for his by employing final good and inermediae good secors in he economy Exploraion of oil has always come along wih he movemen of resources from one secor of he economy o he oil secor Ghana s economy is dominaed by he agriculural secor; which conribues larger amoun o i GDP; herefore wih he discovery of oil ha secor is definiely going o be affeced Firsly here is going o be an invesmen in he agriculural secor o he newly founded oil secor Secondly, labour is going o be moved from he oher par of he economy o he oil secor Since oil producion forms par of he inermediae goods secor, he final goods secor is going o experience a shrinage hrough labour movemens which is normally referred as he Duch Disease Our model accoun for his by shocing he producion funcions wih a echnological shoc and calibraing o now how his affecs he economy hrough equaions 9-12 The muli-secor naure of he model allows his shoc o impac on he oher agens of he model *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 7 Page

9 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach III ANALSIS AND DISCUSSION The parameers of he model are calibraed o sui he Ghanaian economy The analyses of he model rely on calibraed numerical simulaions wih he use of dynare The micro-founded naure of he model maes some parameers being chosen based on microeconomic evidence, such as he efficiency of invesmen; oherwise, heir values are chosen in line wih he lieraure and he naional income accouns of he Ghanaian economy wih he year 2008 as he base year Table 1: Baseline Calibraion and Parameers Parameer Value Source/Mehod b 05 Degree of habi persisence Maches real ineres raes equal 8 percen 12 Sandard value in Lieraure R Ensures nominal ineres rae is zero a seady sae 001 Habi parameer 2 for experimen 1 Marginal disuiliy of hours q Relaes cash holding and he ineres rae 15 Price elasiciy of demand for differeniaed goods 07 Labor share of producion (Sandard value in lieraure) 0015 Capial depreciaion rae [16] 30 Implies prices are sicy for 6 monhs on average p 09 Calvo s parameer on wage w f 12 Firms mare power R 15 Taylor rule inflaion response (Sandard in Lieraure) 05 Moneary rule parameer on oupu Moneary rule parameer on lagged ineres rae The simulaions showed a emporary shrinage in he final goods secors, which resuled from he reallocaion of labour beween he final and inermediae goods secors As such, his conracion is an equilibrium oucome However, if he final goods secor is a special source of produciviy growh, as i is someimes argued in he lieraure on Duch disease for reasons relaed o produciviy advances being more liely in he manufacuring secor, hen he shrinage of he final goods secor could lead o a permanen or persisen loss in produciviy The las oucome is indeed undesirable The laer effec is referred o as he effec as represening Duch disease effecs To give a special produciviy enhancing role o he producion secor, he model assumes ha increases in he size of he radable secor have an impac on overall produciviy The larger his secor is, he larger is mulifacor produciviy in he secor When he producion secor shrins however, he overall produciviy decreases oo, hus leading o a poenially long-erm negaive impac on he growh rae of he economy This is illusraed in figure 1 In he presence of such exernal shocs, he impac on oupu from higher public invesmen is smaller, and he conracion in he producion secor more pronounced While he effec on GDP migh be smaller, i would be larger if less of he oil boom were used for public invesmen Alernaively, he simulaion above assumes a large subsiuabiliy of labour beween secors yielded a large and susained decline in he radable secor Combining hese wo assumpions now leads o a more subsanial Duch disease effec, wih oupu considerably below is rend These oupu losses do no ouweigh he benefis of he oil windfall, since overall GDP is sill be above is levels *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 8 Page

10 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach Figure 1 Variable Responses To Produciviy Shoc Consumpion (c), Invesmen (i), Oupu (y), Money Supply (m), Money Growh Rae (mu), Inflaion (pi), Real Wage (w), Real Ineres Rae (r), Capial Service () These echnological shocs come up wih he following scenarios: Firsly, Duch disease effecs do no necessarily need o be large They depend on he exen o which he final goods secor shrins, which in urn is a funcion of a number of parameers For example, a limied subsiuabiliy of producion facors beween he final and inermediae goods secors curbs he exen o which he firs declines when an oil windfall occurs and herefore also conains he Duch disease effecs; he downside is ha limied subsiuabiliy also implies large wage pressures, higher inflaion, and a more pronounced real appreciaion Secondly, policy measures ha boos he final goods secor limi he overall Duch disease effecs as well In he simulaion, invesmen spending will evenually lead o an increase in he size of he producion secor, a ha poin Duch disease effecs migh have disappeared In fac, he same mechanism ha yields Duch disease effecs when he secor shrins generaes posiive produciviy effecs when he secor expands due o invesmen Even if large Duch disease effecs occur, hese do no necessarily ouweigh he benefis from he oil windfall Of course, he analysis here applies only one specific mechanism for simulaing Duch disease effecs Alernaive mechanisms, for example, lining he size of he producion secor o he produciviy growh rae insead of he level, could yield much larger effecs, in which case i would be more liely ha Duch disease effecs ouweigh oil windfall benefis These Duch Disease effecs are already prevalence in he Ghanaian economy An economy which was moved by he agriculural secor has now seen a drasic increase in he service secor, moving agriculural secor o be he second larges conribuor of he economy s gross domesic produc *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 9 Page

11 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach Addiionally, his shoc also induces a sharp (bu shor-lived) fall in he producion secors marginal cos and hen afer cerain wo years marginal cos begins o rise o aain equilibrium This is accompanied by a conemporaneous rise in labour force for shor period hen afer boh labour and wage falls drasically before reaching equilibrium as shown in Figures 2 Figure 2: Oher Variable Responses o Technological Shoc Real Marginal Cos (s), Real Transacion Money (qbar), MU of Consumpion (q), marginal uiliy of consumpion (psi), MP of Capial (p_i), Labour (l), Habi (h), Capial Soc (bar), Capial Uilisaion (u) IV CONCLUSION The sudy examined he impac of echnological shocs of oil prices on he economic aciviies of Ghana The model was calibraed based on he micro-founded evidence and seady sae raios deermined from naional income accouns of Ghana I was acualized ha a produciviy shoc which indicaes a emporary shrinage in he final goods secors is as a resul of he reallocaion of labour from he final and inermediae goods secors This Duch disease effec is accouned for as he model assumes ha increases in he size of he radable secor have an impac on overall produciviy When his secor shrins, he overall produciviy decreases oo, hus leading o a poenially long-erm negaive impac on he growh rae of he economy The research alernaively assumed a large subsiuabiliy of labour beween secors which yielded a large and susained decline in he radable secor Combining hese wo assumpions led o a more subsanial Duch disease effec, wih oupu considerably below is rend These oupu losses do no ouweigh he benefis of he oil windfall, since overall GDP will is sill be above is levels *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 10 Page

12 Technological Shocs Mechanism On Macroeconomic Variables: A DSGE Approach REFERENCES [1] Galí, J (1999) Technology, Employmen, and he Business Cycle: Do Technology Shocs Explain Aggregae Flucuaions? American Economic Review, 89, pp [2] Francis, N, and V Ramey (2001) Is he Technology-Driven Real Business Cycle Hypohesis Dead? Shocs and Aggregae Flucuaions Revisied, mimeo [3] Dedola, L and S Neri (2004) Wha does a echnology shoc do? A VAR Analysis wih model-based sign resricions, EABCN Discussion Paper [4] Alig, D, J Chrisiano, M Eichenbaum and J Linde (2005) Firm- Specific Capial, Nominal Rigidiies and he Business Cycle, NBERWoring Paper [5] Fernlad, J (2004) Trend Breas, Long Run Resricions, and he Conracionary Effecs of Technology Shocs, mimeo, Federal Reserve Ban of Chicago [6] Fisher, J (2006) The Dynamic Effecs of Neural and Invesmen-Specific Technology Shoc Journal of Poliical Economy, 114, pp [7] Uhlig, H (2004) Do echnology shocs lead o a fall in oal hours wored? Journal of he European Economic Associaion, 2, pp [8] Basu, S, J G Fernald, and M S Kimball (2006) Are Technology Improvemens Conracionary? American Economic Review, 96(5), [9] Canova, F, D López-Salido and C Michelacci (2007) The Labor Mare Effecs of Technology Shocs Documenos de Trabajo No 0719 [10] Canova F, D Lopez-Salido and C Michelacci (2009) The effecs of echnology shocs on hours and oupu: A robusness analysis Journal of Applied Economerics [11] Chrisiano, L, M Eichenbaum, and C Evans, (2001) Nominal Rigidiies and he Dynamic Effecs of a Shoc o Moneary Policy Woring Paper no 8403 (July), NBER, Cambridge, MA [12] Chrisiano, L, M Eichenbaum, and C Evans, (2005) Nominal Rigidiies and he Dynamic Effecs of a Shoc o Moneary Policy, Journal of Poliical Economy Vol 113(1), pp 1-45 [13] Erceg, C J, D W Henderson, and A T Levin, (2000) Opimal Moneary Policy wih Saggered Wage and Price Conracs Journal of Moneary Economics, 46(2), Ocober, pages [14] Calvo, G (1983) Saggered Prices in a Uiliy-Maximizing Framewor Journal of Moneary Economics, 12(3): [15] Bu,, (2004) Fixed Capial Soc Depreciaion in Developing Counries: Some Evidence from Firm Level Daa Libery Muual Group, Manuscrip *Corresponding Auhor: Gabriel Obed Fosu Deparmen of Mahemaics, Kwame Nrumah Universiy of Science and Technology, Ghana 11 Page