The effects of stock market movements on consumption and investment: does the shock matter?

Transcription

1 The effecs of sock marke movemens on consumpion and invesmen: does he shock maer? Sephen Millard and John Power Working paper no. 236 Bank of England, Threadneedle Sree, London, EC2R 8AH. The views epressed are hose of he auhors and do no necessarily reflec hose of he Bank of England. The auhors would like o hank seminar paricipans a he Bank of England and London Meropolian Universiy as well as paricipans a he Sociey for Economic Dynamics Annual Conference 23 in Paris for helpful commens. Any remaining errors are, of course, he faul of he auhors. Copies of working papers may be obained from Publicaions Group, Bank of England, Threadneedle Sree, London, EC2R 8AH; elephone , fa , mapublicaions@bankofengland.co.uk. Working papers are also available a The Bank of England s working paper series is eernally refereed. Bank of England 24 ISSN

2 Conens Absrac 5 Summary 7 Inroducion and overview 9. Equiies and consumpion 9.2 Equiies and invesmen.3 Our approach 2 The model 2 2. Consumers Firms Eogenous variables 4 3 Equiies and consumpion 4 4 Equiies and invesmen 6 5 Some empirical evidence 9 6 Conclusions 24 References 25 3

3 Absrac This paper uses a simple model o eamine he links beween equiy price movemens and consumpion and invesmen. Generally, he effec of a given movemen in equiy prices on consumpion depends on he underlying source of he shock o equiy prices, and some empirical evidence is presened ha suppors his. Furhermore, in he model he effec of a given movemen in equiy prices on invesmen does no depend on he source of he shock. However, some heoreical argumens and empirical evidence are provided o sugges ha i migh in he real world. Key words: Consumpion, invesmen, equiy prices, VARs. JEL classificaion: E44. 5

4 Summary This paper eamines he impac of equiy prices on consumpion and invesmen. In paricular, i considers wheher he impac of any given movemen in equiy prices on consumpion and invesmen depends on he source of he shock ha caused he equiy price movemen. Clearly his is an imporan opical issue given he sharp falls winessed in he sock markes a few years ago. In he Unied Kingdom, for eample, he FTSE All-Share inde fell by abou 4% beween Sepember 2 and he end of 22. However, much of he lieraure on consumpion and invesmen equaions largely ignores he source of he underlying shock in deermining he consumpion and invesmen response; ypically, relaionships are esimaed using equiy prices as righ-hand side variables wihou any effor o disinguish he source of he shock o equiy prices. In he cone of he consumpion funcion, his leads researchers o presen esimaes of he marginal propensiy o consume ou of wealh. I would be beer o ask he quesion How large are he changes in consumpion and wealh following a shock of a paricular ype? If he shock does maer and i is no adequaely capured in macroeconomeric models, his could derac from heir forecas performance or give a misleading view abou he oulook for consumpion. To answer he above quesion, i is imporan firs o know wha sors of shocks move equiy prices. Theory suggess ha asse prices represen he presen value of fuure income o be derived from he underlying asse. So equiy prices migh move when eiher epeced fuure income or dividend growh changes, or when he discoun facor applied o hem changes. The discoun facor, in urn, will be he sum of he equiy risk premium and he risk-free ineres rae. Alernaively, of course, equiy prices migh no be accouned for by any of hose fundamenal reasons, bu raher reflec irraional responses o marke senimen, or noise. The paper hen approaches he problem from wo angles: heoreical and empirical. I develops a simple general equilibrium model ha links equiy prices o consumpion and invesmen for a small open economy. I hen analyses he link beween consumpion and equiy prices and eplains why he consumpion response is likely o be differen depending on he source of he shock. Imporanly, he response o a risk premium shock is likely o differ from ha o an ineres rae shock. Indeed, here are cases where risk premia movemens will have no effec on consumpion. Ne he focus is on he links beween invesmen and equiy prices. Unlike consumpion, he model suggess ha invesmen will always respond o movemens in equiy prices irrespecive of he source of he shock. Bu his migh no be rue in he real world. In paricular, movemens in equiy prices ha are unrelaed o fundamenals are likely o have a much smaller effec on invesmen (if any) han hose relaed o fundamenals. Finally, he paper presens some empirical evidence from a vecor auoregression model o idenify wheher he source of he shock maers in he daa. Tha analysis suggess ha i does maer for consumpion and, conrary o he simple predicions from he model, for invesmen oo. This paper has sill lef some quesions unresolved. In paricular, i would be good o model more eplicily he sors of shocks ha drive he economy and heir sochasic processes. Then i would be ineresing o invesigae wheher or no i makes sense, in a more complicaed model for shocks o equiy price volailiy o have no effec on consumpion volailiy. To do his, one would have o eamine he links beween he equiy risk premium and he volailiies of 7

5 fundamenal shocks. In urn, ha would mean considering models ha are able o eplain he magniude of observed equiy risk premia, somehing ha is no he case in he simple model presened here. I would also be ineresing o invesigae wheher here are any shocks (or specificaions of he model) under which invesmen would respond more or less o equiy price movemens han in he baseline case. 8

6 Inroducion and overview In his paper, we eamine he impac of equiy prices on consumpion and invesmen. In paricular, we consider wheher he impac of any given movemen in equiy prices on consumpion and invesmen depends on he source of he shock ha caused he equiy price movemen. Clearly his is an imporan opical issue given he sharp falls winessed in he sock markes recenly. In he Unied Kingdom, for eample, he FTSE All-Share inde fell by abou 4% beween Sepember 2 and he end of 22. However, on he whole he lieraure in which consumpion and invesmen funcions are esimaed largely ignores he source of he underlying shock in deermining he consumpion and invesmen response; ypically relaionships are esimaed using equiy prices as righ-hand side variables wihou any effor o disinguish he source of he shock. In he cone of he consumpion funcion, his leads o researchers o presen esimaes of he marginal propensiy o consume ou of wealh. In our view, i would be beer o ask he quesion How large are he changes in consumpion and wealh following a shock of a paricular ype? This is imporan as if he shock does maer and his is no adequaely capured in macroeconomeric models, hen his could derac from heir forecas performance or give a misleading view abou he oulook for consumpion.. Equiies and consumpion When analysing he effec of sock marke wealh on consumpion, we normally look a empirical esimaes of he marginal propensiy o consume ou of wealh. The marginal propensiy o consume ou of wealh measures by how much he value of consumpion is epeced o rise given a uni increase in wealh. The permanen income hypohesis (Friedman (957)) implies ha any shocks o income, ransiory or permanen, (which will lead o a measured rise in wealh) will be consumed over he lifeime of he consumer, since consumers prefer a smooher consumpion profile han an erraic one. This resul implies a low marginal propensiy o consume ou of ransiory income, roughly relaed o he annuiy value of he change in wealh (shock o ransiory income). As such, in he long run, you would epec he marginal propensiy o consume o be very similar o he real ineres rae. () Therefore, a value of around 3% o 5% would be a reasonable prior for he marginal propensiy o consume ou of wealh. There is an eensive lieraure on empirically deriving he marginal propensiy o consume ou of sock marke wealh on household consumpion. While his has been largely concenraed in he Unied Saes (in par driven by he desire o eplain consumpion behaviour over he mid o lae 99s), recen esimaes for he Unied Kingdom and oher counries have been compiled by, among ohers, he OECD and IMF. In he Unied Kingdom, Berau (22) found ha he long-run marginal propensiies o consume for oal, financial and housing wealh are all around.4, or a four pence increase in consumpion for an increase of one pound in wealh. Ludwig and Sløk (2) esimae he long-run marginal propensiy o consume ou of equiy wealh for he Unied Kingdom o be around.55, or a 5.5 pence increase in consumpion for an increase of one pound in wealh. Boone, Girouard and Wanner (2) find ha he long-run marginal () Wih he possibiliy ha i may be a lile higher if you rela he assumpion of infiniely lived agens and a lile lower o he een ha credi marke imperfecions limi he een o which agens can smooh consumpion. 9

7 propensiy o consume for equiy and housing wealh in he Unied Kingdom o be he same as Berau, a around.4. All hese esimaes are close o esimaes of he real ineres rae..2 Equiies and invesmen Esimaes of he effecs of equiy prices movemens on invesmen have been based on he neoclassical model, which can be used o specify invesmen as a funcion of eiher he user cos or q. Firms desired capial socks are deermined no only by heir planned producion levels, bu also by he real user cos of capial, ha is, he cos faced by he firm in acquiring and holding an addiional uni of capial. One imporan componen of he user cos is he cos of finance, a weighed average of he cos of equiy finance and oher forms of finance. Rises in equiy valuaions unrelaed o curren or fuure dividend payous are associaed wih falls in he cos of equiy finance and should be a posiive influence on firms invesmen decisions. The lieraure on invesmen and he cos of capial is vas and has already been reviewed eensively (eg Chirinko (993) and Caballero (999)). Alhough he heoreical foundaions of he cos of capial and he ineracion wih invesmen are well esablished, empirical resuls have been less encouraging. Blanchard (986) summarises ha i is well known ha o ge he user cos of capial o appear a all in he invesmen equaion, one has o display more han he usual amoun of economeric ingenuiy, alhough Ellis and Price (23) find a well defined and sensible effec on he mos recen vinage of aggregae UK business daa. Caballero (999) agrees ha he shor-run response of invesmen o changes in he cos of capial is comple and depends on he shock o he cos of capial. Bu he concludes ha he cos of capial is neverheless an imporan variable, deermining he long-run relaionship beween capial, oupu and he cos of capial. (2) Q is derived from he same heory. A is simples, when he marke value of an addiional uni of capial eceeds i replacemen cos, a firm can increase profis by invesing. Given ha his raio, marginal q, is difficul o measure, economiss have focused on Tobin s (969) average q: he raio of he sock marke value of a firm o he replacemen cos of is asses. Under sric assumpions, average q is a sufficien saisic for invesmen raes. Bu q has also generally fared poorly in empirical sudies of is predicive power for invesmen. Firs, q models usually imply ha i would ake a very long ime ofen decades for firms capial sock o fully adjus o a change in q. Second, even hough q should heoreically be a sufficien saisic for invesmen, a large lieraure has found cash-flow variables o be significan in q regressions. (3) This has been widely inerpreed as suggesive of he eisence of financing consrains. The poor performance of q may also parly reflec measuremen issues. Sudies have ypically focused on he role of average q, which is only equal o marginal q under resricive (2) Caballero (999) argues ha because of adjusmen coss he long-run coefficien in neoclassical invesmen equaions is biased downward in finie samples. The basic idea is ha adjusmen coss resul in he observed capialoupu raio o be less volaile han he desired capial-oupu raio and he cos of capial. (3) See Fazzari, Hubbard and Peersen (988) for early evidence in his area.

8 assumpions. And average q iself may be poorly measured if esimaes of he capial sock are unreliable. To ge around his, Bond and Cummins (2) followed an alernaive firm-level approach. They calculaed a fundamenal q based on analyss earnings forecass from he Insiuional Brokers Esimae Sysem (IBES), and found ha when his measure was included, a simple sock marke-based q does no have any eplanaory power for invesmen. (4) In a similar vein, Bond e al (24) found ha when hey conrolled for epeced profiabiliy using IBES forecass, convenional q measures provided lile addiional informaion. (5).3 Our approach Bu mos of his empirical work ignores he key quesion: can we be confiden in using such equaions o predic consumpion and invesmen when we know ha equiy prices will be driven by differen shocks in differen ime periods? The dividend discoun model (DDM) offers a framework which can isolae he facors or shocks ha affec equiy prices. Theory suggess ha asse prices represen he presen value of fuure income o be derived from he underlying asse. So we migh epec equiy prices o move when eiher epeced fuure income or dividend growh changes (which we migh epec o be closely relaed o firms produciviy), or when he discoun facor applied o hem changes. The discoun facor, in urn, will be he sum of he equiy risk premium and he risk-free ineres rae. Alernaively, in his framework, equiy prices migh no be accouned for by any of hose fundamenal reasons, raher reflecing irraional responses o marke senimen, or noise. We noe however ha his is jus one way of characerising he shocks ha can affec equiy prices. In he real world, i is likely ha here is a wider range of shocks driving equiy prices. And he impac of hose underlying shocks on he variables in he DDM could be comple. For eample an oil price shock could affec boh he equiy risk premium (as a resul of he uncerainy i generaes), and fuure dividend growh (by affecing firms fuure coss of producion). There has been lile research along hese lines. Lanz and Sare (2) have a relaed paper which addresses he quesion of how varying he shock o wealh resuls in varying responses in consumpion, bu wih he emphasis on wheher shocks are anicipaed, a raher differen emphasis from ha aken in our paper. The auhors use a closed-economy model in which here is only one shock: produciviy. They show ha consumpion and wealh can acually move in differen direcions depending on wheher he shock is anicipaed or no. An unanicipaed fall in he level of produciviy causes consumpion and wealh o fall when he shock is realised. However, wih an anicipaed rise in fuure produciviy, consumpion increases immediaely while wealh falls. This happens since, for consumpion o rise immediaely, consumers in a closed economy mus dispose of some of heir capial. And in response, he value of equiy falls, a leas iniially. An imporan insigh from Lanz and Sare s paper is ha i is inappropriae o (4) I is likely ha IBES forecass are biased upwards, as suggesed by Chan, Karceski and Lakonishok (2), alhough i is no obvious ha he size of his bias will vary markedly over ime. (5) Cash flow is insignifican under his specificaion, suggesing ha cash-flow variables widely used in invesmen equaions capure informaion abou firms fuure profiabiliy raher han financing consrains.

9 consider a general consumpion response o changes in wealh (or indeed for changes in wealh o cause changes in consumpion). Raher wealh and consumpion are joinly deermined: boh reac o various disurbances in he economy. On he invesmen side, Leau and Ludvigson (22) have noed ha changes in curren sock reurns (and equiy prices) which also affec fuure discoun raes, would have implicaions for boh curren and fuure invesmen. Under ha condiion (which hey believe is valid for US daa), a fall in he equiy risk premium could simulae invesmen growh in he near erm bu reduce i over he longer run. In his paper, we approach he problem from wo angles heoreical and empirical. In Secion 2 we develop a simple general equilibrium model of equiy prices of consumpion and invesmen for a small open economy (in conras o he closed-economy model used by Lanz and Sare (2)). In Secion 3 we analyse he link beween consumpion and equiy prices and conclude ha he consumpion response is likely o be differen depending on he source of he shock. Imporanly, he model implies ha he response from a risk premium shock is likely o differ han ha from an ineres rae shock. Indeed, in he model here are cases where risk premia movemens will have no effec on consumpion. Secion 4 oulines he links beween invesmen and equiy prices. Unlike consumpion, he model suggess ha invesmen will always respond o movemen in equiy prices irrespecive of he source of he shock. In Secion 5 we presen some empirical evidence from a VAR which ries o idenify wheher he source of he shock maers in he daa. Tha analysis implies ha i does maer for consumpion and, conrary o he simple predicions from he model, for invesmen oo. 2 The model We use a fairly sandard, small open-economy model such as can be found in, say, Obsfeld and Rogoff (996). The model is simple and highly sylised: we do no sugges ha our model is a all represenaive of all he channels linking equiy prices o consumpion and invesmen in he Unied Kingdom. However i is rich enough o disinguish beween shocks o ineres raes, produciviy and risk premia and how hey migh affec consumpion/invesmen. 2. Consumers The represenaive consumer eiher consumes or invess in financial asses in order o maimise his uiliy subjec o an asse accumulaion consrain. The consumer can inves in eiher a risky asse or an inernaionally raded, risk-free asse. We assume ha he can borrow or lend as much as he wans on he world capial markes a he prevailing world real ineres rae (subjec o a No Ponzi Game condiion). This assumpion amouns o assuming ha he consumer lives in a small open economy. I is access o he world capial markes ha allows consumers o insure hemselves agains movemens in domesically generaed income and, in urn, his drives he key resul ha shocks o domesic produciviy will have differen effecs on consumpion han shocks o he world real ineres rae. Mahemaically, we can wrie his problem as: 2

10 Maimise τ c E β () = τ Subjec o: V + B = ( V + D ) + ( + r ) B + w c (2) where c is consumpion, is he consumer s end-of-period holdings of equiy shares, V is he real value of a share in he domesic firm, D are he real dividends paid on each share, B is he consumer s holdings of real bonds, r is he world real ineres rae and w is real labour income. We assume ha he akes dividends, real labour income, share prices and he world real ineres rae as given. Furher, we have assumed ha domesic consumers are unable o hold foreign equiy and vice versa. 2.2 Firms We assume ha he represenaive firm operaes in a perfecly compeiive world marke and ha he domesic economy forms a negligible fracion of he world (ie i is small ). Tha implies ha he domesic firm can always sell is enire oupu a he world marke price. As he represenaive consumer owns he represenaive firm, he firm s problem will be o maimise he presen discouned uiliy value of is curren and epeced fuure dividends. I does his by choosing he opimal pahs for is inpus of capial and labour. If we le λ denoe he marginal uiliy of a uni of consumpion, hen is problem will be: Maimise E β λ D (3) = Subjec o D 2 χ I = y I + w h (4) k 2 y = A k h α α (5) k I δ k (6) = + ( ) where A is a produciviy shock, h is labour inpu, which will equal uniy in equilibrium since we have assumed ha labour is inelasically supplied, I is invesmen and k is he end-of-period capial sock. Noe ha he quadraic erm in (4) implies ha he firm faces coss of adjusing is capial sock. 3

11 2.3 Eogenous variables Finally, we assume ha he eogenous variables in he model world real ineres raes and produciviy follow known sochasic processes ha are independen of each oher. (6) 3 Equiies and consumpion In his secion, we eamine he links beween he deerminans of equiy prices and consumpion and he effecs of a emporary ineres rae shock, emporary and permanen produciviy shocks and shocks o he deerminans of he equiy risk premium. We firs consider he consumer s decision o inves in he risk-free bond. This simply implies ha: c τ ( + r ) E c τ = β + (7) and assuming ha consumpion growh is log-normally disribued, we can rearrange equaion (7) o obain: E ln c c+ r ) = + ln( β + τ τ σ c (8) Here 2 σ c is he variance of consumpion growh. Despie heir relaive simpliciy, in his model hese equaions yield imporan resuls. Mos noably hey deermine consumpion growh. In he absence of uncerainy, consumpion growh will be deermined by real ineres raes (7). Under uncerainy, consumpion growh will also be affeced by he volailiy of consumpion ouurns; as consumpion growh becomes more volaile, individuals migh wish o save more for any given real ineres raes. Equaion (8) shows ha an increase in he risk-free rae (which would be epeced o lead o a fall in equiy prices) would cause consumpion o fall oday relaive o omorrow. Tha reflecs he subsiuion effec: consumpion oday becomes more cosly relaive o omorrow. A negaive produciviy shock, if i persiss ino he ne period, lowers equiy prices in his model. If he shock is permanen, he level of oupu will be permanenly lower; his will be passed on o consumers as permanenly lower income and, hence, hey will have o permanenly consume less. If he shock is emporary, hen iniially, consumpion will fall by less han oupu resuling in a rade defici; his defici can only be financed by borrowing from abroad (selling real bonds o foreigners). As consumers mus pay fuure ineres paymens on he bonds, ha (6) We migh epec shocks o he world real ineres rae o be relaed o shocks o world produciviy and, hence, domesic produciviy. Bu we assume ha he diffusion of produciviy shocks beween counries akes a subsanial amoun of ime so ha movemens in domesic produciviy follow ha of world produciviy (and world ineres raes) a a long lag and vice versa. 4

12 implies ha consumpion has o be permanenly lower han income (and he iniial level of consumpion) in he fuure. (7) This sory is idenical o ha pu forward by Friedman (957) in his original eposiion of he permanen income hypohesis, via a permanen negaive produciviy shock lowers he consumer s permanen income and, hence, permanen consumpion; whereas a emporary negaive produciviy shock will lower he consumer s ransiory income, and only lower permanen consumpion by is amorised value. In he case of a permanen shock o produciviy, equiy prices will be permanenly lower; in he case of a emporary shock o produciviy equiy prices will recover o heir iniial rend as oupu recovers. So, clearly, he relaionship beween he iniial falls in consumpion and equiy prices will depend on wheher he shock is emporary or permanen. In addiion, he fall in consumpion will no necessarily be he same as he fall brough abou by higher ineres raes and we can recall ha for an ineres rae shock he fall is emporary wih consumpion higher han is iniial rend in he fuure. We ne consider equiies more specifically. The firs-order condiion for he consumer s desired equiy holdings will be: V c τ ( c ( V + D )) τ = E β (9) If we assume ha consumpion growh and equiy reurns are joinly log-normally disribued, we can combine equaions (9) and (7) o ge: V+ + D+ V+ + D + c+ E = + + r τ Cov, () V V c In words, he reurn on equiies depends on he risk-free rae and an equiy risk premium. In equilibrium, equiies are priced (he required reurn is se) as a funcion of he covariance of he yield wih marginal uiliy. When equiy reurns are covarying posiively wih consumpion growh (negaively wih marginal uiliy) hen consumers are requiring a reurn higher han he risk-free rae. Tha reflecs risk-averse consumers desire o mainain a smooh consumpion sream: equiies which give invesors a high payoff when consumpion is high (and marginal uiliy low) are less desirable han hose which are epeced o be a good hedge agains poor consumpion ouurns. Hence hey require a higher rae of reurn. We can furher break down he equiy risk premium as follows: (7) We can noe, again, ha he small open-economy assumpion implies ha he fall in consumpion will be less han he fall in oupu. If he consumer did no have access o he world capial markes or could only access hem a a premium, hen for a given impac on equiy prices he effec of a emporary produciviy shock on consumpion would be much larger. 5

13 ERP = τcov V+ + D V + V + + D = τsdev V c, c + + c SDev c + V + + D Corr V + c, c + () This equaion enables us o make a simple poin: an increase in he degree of risk aversion, he variance of consumpion growh, he variance of equiy reurns and/or he correlaion beween equiy reurns and consumpion growh would lead o an increase in he equiy risk premium. Bu equaion (8) shows ha in a wo-period model, curren consumpion will only fall as a resul of precauionary saving if he degree of risk aversion or he variance of consumpion rises. A rise in equiy reurn volailiy ha was no accompanied by a rise in consumpion volailiy would have no effec on consumpion. Wha sor of shock could produce his? In he model, as laid ou in Secion 2, he variances of equiy prices and consumpion will depend on he variances of he underlying shocks o world ineres raes and produciviy. An increase in he variance of eiher shock will increase he variance of boh equiy prices and consumpion. Bu, hinking ouside he model, suppose equiy reurns are parly driven by noise and his is common knowledge. Eamples of his could be hin markes a cerain imes of he day or cerain days of he year or paricular rades ha were large enough o drive prices for a shor period of ime. Suppose ha he variance of his noise increases. In his case, we migh again epec he equiy risk premium o increase bu wihou any effec on he volailiy of consumpion growh and, hence, on he level of consumpion, alhough in he absence of a formal model his is speculaion. To conclude his secion, we have shown ha he effecs of a given movemen in equiy prices on consumpion depend criically upon he source of he underlying shock. In our simple model, a emporary posiive produciviy shock will raise equiy prices bu have no effec on consumpion. A negaive shock o he real ineres rae would raise equiy prices and lead o a rise in he level of consumpion from he wealh effec and a fall in he growh rae of consumpion from he subsiuion effec. A fall in he equiy risk premium ha was no purely due o less volaile share prices would raise consumpion oday by decreasing precauionary savings. And, finally, any remaining movemen in equiy prices unrelaed o fundamenals migh no have any effec on consumpion. (8) 4 Equiies and invesmen In his secion, we analyse he links beween equiy price movemens and invesmen, again paying paricular aenion o he een o which a given movemen in equiy prices may have differen implicaions for invesmen depending on he source of he shock. We sar by noing ha he firm s firs-order condiions imply: (8) Alhough, arguably, if equiy prices are driven purely by senimen (which subsequenly proved o be unfounded), consumpion migh be affeced hrough is effecs on consumer confidence. Tha channel is no modelled in his paper. 6

14 I q = k χ (2) 2 χ I αy λq = βe λ q+ δ (3) 2 k k and + + ( ) where q is he Lagrange muliplier on he capial accumulaion equaion and, in our model, will be equivalen o Tobin s q. If we muliply boh sides of equaion (3) by k and combine he resul wih equaion (4), we ge: ( q k D ) λ q k (4) = βeλ and comparing his o he consumer s firs-order condiion shows ha: V = q k (5) In oher words he value of he sock marke, V, is equal o he value of he capial sock muliplied by Tobin s q. Now, combining equaions (6), (2) and (5) gives us: χ V I + + ( δ ) χ I + ( δ ) 2 2 I V χ + 2 χi + V 2 V V = V (6) So, we can see ha unlike he resul we obained for consumpion, a given movemen in equiy prices will be associaed wih a given movemen in invesmen irrespecive of he source of he shock: di dv = 2χI V + + ( δ ) χi χ + V 2 (7) Q is he shadow price of capial, embodying he relevan marginal condiions in a single number, and consequenly is a sufficien saisic o ell us wheher marginal invesmen is profiable. A change in q caused by a change in equiy prices causes ha marginal profiabiliy o change: clearly, he source is irrelevan. So once we know wha has happened o sock prices, and hence q, we will know wha has happened o invesmen. (9) Bu, here are, of course, oher shocks ha could affec equiy prices ha are no capured by his simple model. A shif in firms mi of (9) Typically, he neoclassical model is also eended o consider he role of oupu in deermining invesmen. In acceleraor models, higher oupu leads o higher invesmen (and ofen here is a role for oupu in empirical esimaes of he invesmen equaion). Alhough here is no oupu erm in equaion (6), he simple q heory is consisen wih he acceleraor model: an increase in oupu should raise he marke value of he firm s equiy (capial canno adjus insananeously o higher demand for he firm s produc) hereby increasing q and simulaing invesmen. 7

15 deb and equiy finance migh change he cos of equiy wihou any change in he cos of capial or invesmen, for eample, under he Modigliani-Miller condiions when variaions in he mi of deb o equiy leave he value of he firm and all real decisions, including invesmen, unaffeced. The model ignores financial acceleraor ype effecs resuling from he change in corporae balance shees ha movemens in equiy prices bring abou. For eample, by reducing firm s collaeral, or ne worh, a large fall in equiy prices migh lead o a reducion in lending by financial insiuions o firms. Tha migh ac o resrain invesmen for credi-consrained firms. Finally, he source of he shock o equiy prices may maer if company managers respond differenly o changes hey perceive as permanen raher han ransiory, or if hey believe equiy price changes reflec fundamenals or noise. MacGorain and Thompson (22) eamined his las poin. Consisen wih simple invesmen heory, hey hypohesised ha movemens in epeced fuure profis (produciviy in our model) would be likely o affec boh share prices and invesmen. Bu hey argued ha, a imes, he epecaions of a firm s fuure earnings implied by he firm s share price may differ from managers own opinions abou heir firm s fuure profiabiliy. They calculaed a measure of q based on analyss forecass of earnings per share growh (as provided by IBES) arguing ha his was a good indicaor of managers opinions. They hen esimaed a simple aggregae economeric equaion for invesmen including boh Tobin s q and his analyss q. They found ha o he een ha he equaion could eplain variaions in he rae of invesmen, i did so almos enirely by he q measure based on analyss earnings forecass raher han he sock marke. This suggess ha movemens in equiy prices unrelaed o fundamenals have lile effec on invesmen. Their resuls corroborae he firm-level resuls of Bond e al (24) repored in he inroducion. To conclude his secion, we have shown ha he effecs of a given movemen in equiy prices on invesmen do no, in a sandard model, depend upon he source of he underlying shock. However, ha ignores some heoreical argumens and empirical evidence o he conrary. 8

16 5 Some empirical evidence Given he heoreical predicions of he effec of he source of he equiy price shock on consumpion and invesmen, i is useful o eamine hose conclusions wihin an idenified vecor auoregression (VAR) model for he Unied Kingdom. This also allows us o work hrough he dynamics of he change in consumpion and invesmen. To do his we used a VAR in which we idenified a ransiory shock o world ineres raes, a permanen shock o domesic produciviy and a ransiory shock o he equiy risk premium. More specifically, we esimaed a VAR conaining he following variables: world hree-monh nominal ineres raes (consruced as a GDP-weighed average of non-uk G7 raes), i f, consumpion or invesmen (depending on which variable we are considering), C or I, reail prices (as measured by RPIX), P, he UK bank base rae, i, FTSE All-Share dividends, D, and he FTSE All-Share inde, V. We used quarerly daa from 978 Q o 22 Q. () In our VAR, we assumed ha world ineres raes were eogenous; we used he VAR o calculae he response of consumpion (invesmen) and equiy prices o a shock o world ineres raes. () By dividing he response of consumpion (invesmen) by he iniial response of equiy prices, we obained he consumpion (invesmen) response o a uni shock o equiy prices where he acual source of he shock was world ineres raes. In doing his we were asking ourselves he quesion, Wha would happen o consumpion/invesmen over he ne few quarers if we see equiy prices move by % oday as a resul of a world ineres rae shock? Over ime, he response of equiy prices hemselves will differ depending on he source of he shock meaning ha he raio of he consumpion/invesmen response o he equiy price response will no be equal o ha shown in our chars bu his does no derac from he poin we wish o make in his paper ha a given observed movemen in equiy prices will be associaed wih differen responses of consumpion and invesmen depending on he source of he shock. To idenify he domesic produciviy shock we used he approach of Chrisiano e al (23). We firs noe ha, if we are prepared o assume ha shocks o he world real ineres rae and he equiy risk premium are emporary, our model implies ha he only shock ha can permanenly affec he level of oupu, invesmen and he capial sock is a permanen produciviy shock. So, consider he relaionship: () There has been much debae among researchers working on esimaing consumpion funcions as o wha are he bes variables o use in he empirical work in paricular, wheher or no o use oal labour income or disposable labour income, oal consumpion or consumpion of non-durables and how o define wealh. (See Blake, Fernandez-Corugedo and Price (23) for a much fuller descripion of hese issues.) However, his is no an issue in his paper since we are no concerned abou eplaining consumpion behaviour per se, we are simply rying o idenify differen shocks. () Ideally we would like o eamine he effecs of shocks o world real ineres raes so as o ie he empirical work in more closely wih he heoreical model. However, here are several problems associaed wih obaining he daa required o do his calculaion. One way of doing his is o consruc a world price inde, use his series o derive world inflaion epecaions and subrac his series from he world nominal ineres rae used in our work. Problems wih his approach include he fac ha individual counry s price indices are ofen no direcly comparable, convering hem ino a common currency is no sraighforward do you use marke echange raes or some esimae of PPP and hen he esimaes of inflaion epecaions will rely on he assumed process driving he world price level. Calculaing a real ineres rae counry-by-counry and hen averaging ges around some of hese problems bu no all. In paricular, he quesion of how inflaion epecaions are formed sill remains. For a much fuller discussion of hese issues see Jenkinson (996). 9

17 ( L) A X (8) I = g + β I + α + ε, where α(l) is a second-order lag-polynomial and X conains he world ineres rae, consumpion, he price level, he domesic ineres rae, dividends and equiy prices. Assuming ha non-echnology shocks have no effec on he level of invesmen in he long run implies α =. ( ) This resricion can be used o esimae a ime series for he produciviy shock, ε A,. We calculaed he response of consumpion (invesmen) and equiy prices o his shock and, using he same mehod as before, wen on o calculae he consumpion (invesmen) response o a uni shock o equiy prices where he acual source of he shock was produciviy. Finally, o idenify he equiy reurn shock, we draw on he Campbell and Shiller (988) dynamic version of he DDM described earlier. By log-linearising a simple epression for equiy reurns, we can wrie he curren equiy price, V, as he presen value of epeced fuure dividends, D, and reurns, r: Vˆ = E + j= ( r r) κ j β [( β ) Dˆ + j+ + j ] + (9) where ha variables represen log-deviaions from rend and r is he seady-sae level of reurns. I is frequenly argued ha dividends follow a random walk and so are no condiionally forecasable. Using his assumpion, we can ake he dividend erm in equaion (9) ou of he epecaion. Tha implies ha equiy price movemens reflec shocks o fuure dividends and epeced fuure reurns. We assume ha he FTSE All-Share inde responds o shocks o all he oher variables wihin period. And assuming ha shocks o epeced reurns accoun for almos all movemen in he equiy price, we can inerpre he errors in he equaion for he FTSE All-Share as a shock o epeced equiy reurns, ha is, he equiy risk premium. Bu, even if we believe ha dividends are condiionally forecasable, i seems likely ha he oher informaion in he sysem consumpion/invesmen, he price level, world and domesic ineres raes, and dividends should capure mos of he predicable componen. Given hese assumpions, we calculaed he response of consumpion (invesmen) and equiy prices o our idenified equiy risk premium shock and, using he same mehod as before, wen on o calculae he consumpion (invesmen) response o a uni equiy price shock. (2) We summarise hese resricions as follows. The srucural moving average represenaion for our VAR is: where ( i i Cˆ or Iˆ Pˆ i i Dˆ V ) = C(L)ε (2) = F, F, ε is our vecor of shocks, i F is he average level of foreign ineres raes, i is he average level of domesic ineres raes and ha variables refer o log-deviaions from rend. C(L) is a mari lag polynomial: (2) As oulined earlier equiy prices can move for reasons unrelaed o fundamenals. In our framework ha noise would also be capured wihin he equiy risk premium. 2

18 C 2 ( L) = C + CL + C2L + K (2) If we le our world ineres rae shock be he firs elemen of ε, he produciviy shock be he second elemen of ε and he equiy risk premium shock be he hird elemen of ε, hen our resricions imply he following: C = (22) C C2 = C3 = K (23),2 6 =,2 6,2 6 = C ) = C() = C() = C() = C() (24) (,2 3,2 4,2 5,2 6, 2 = Chars o 3 plo he responses of consumpion o a % rise in equiy prices where his rise is caused by a world ineres rae shock, a permanen produciviy shock and an equiy risk premium shock, respecively. Char : Response of consumpion o a world ine re s rae shock Quarers afer shock Percenage deviaion from rend Noe: The shock is such ha i would resul in an immediae % rise in equiy prices. 2

19 Char 2: Response of consumpion o a produciviy shock Quarers afer shock Percenage deviaion from rend.9 Noe: The shock is such ha i would resul in an immediae % rise in equiy prices Char 3: Response of consumpion o an equiy risk premium shock Quarers afer shock Percenage deviaion from rend Noe: The shock is such ha i would resul in an immediae % rise in equiy prices. Shocks o world ineres raes or he equiy risk premium have a qualiaively similar effec on consumpion. Consumpion rises for abou nine quarers before falling back owards rend. Bu he ineres rae shock has a much bigger impac on consumpion being approimaely eigh imes larger han ha from he equiy risk premium. This is in line wih he discussion of Secion 3, which suggesed ha movemens in he equiy risk premium could, a imes, be associaed wih no movemen in consumpion. The immediae response of consumpion o a produciviy shock is similar in magniude o he response o a world ineres rae shock bu afer abou a year consumpion flaens ou saying abou.6% higher han is previous rend. The fac ha his shock resuls in permanenly higher oupu means ha domesic consumers can afford o permanenly raise heir consumpion. Chars 4 o 6 show he effecs on invesmen of a % rise in equiy prices brough abou by shocks o world ineres raes, produciviy and he equiy risk premium, respecively. 22

20 Char 4: Response of invesmen o a world ineres rae shock Percenage deviaion from rend Quarers afer shock -.5 Noe: The shock is such ha i would resul in an immediae % rise in equiy prices. Char 5: Response of invesmen o a produciviy shock Percenage deviaion from rend Quarers afer shock Noe: The shock is such ha i would resul in an immediae % rise in equiy prices. Char 6: Response of invesmen o an equiy risk premium shock Quarers afer shock Percenage deviaion from rend Noe: The shock is such ha i would resul in an immediae % rise in equiy prices. The response of invesmen o each of hese shocks is qualiaively similar o ha of consumpion. In he case of a shock o world ineres raes or he equiy risk premium, invesmen rises iniially 23

21 before subsequenly falling back o rend. However, here are some differences beween he responses of invesmen o hese wo shocks. A shock o world ineres raes leads invesmen o fall iniially, hen o rise for abou wo years before falling back o rend. A shock o he equiy risk premium has, by assumpion, no immediae effec on invesmen; invesmen hen rises for only five quarers before falling back o rend. Again, he magniude of he response o an equiy risk premium shock is much smaller abou a fifh han ha o a world ineres rae shock. This goes agains he resuls of our heoreical model. However, he empirical resuls migh also reflec he fac ha he equiy risk premium shock also picks up movemens in equiy prices unrelaed o fundamenals. As we argued earlier, i is possible ha invesmen does no respond a all o movemens in equiy prices ha are seen as noise. And he resuls of MacGorain and Thompson (22) lend furher evidence o his suggesion. In he case of he produciviy shock, invesmen jumps immediaely o a level.3% above is iniial rend and seles around.5% higher han is iniial rend. This is a much sronger response han o eiher of he oher wo shocks, and ha is shown by consumpion o he same shock. Again, he produciviy shock has led o a permanen rise in invesmen as oupu and he capial sock will be permanenly higher. 6 Conclusions In his paper we used a simple model o eamine he links beween equiy price movemens, on he one hand, and consumpion and invesmen, on he oher. We showed ha he effec of a given movemen in equiy prices on consumpion would be differen depending on wha fundamenal shock had caused equiy prices o move in he firs place. In paricular, a shock o he risk premium could have a differen effec on consumpion han a shock o he risk-free rae, even if he wo have idenical impacs on wealh. We showed some empirical evidence o suppor his conenion, which also enabled us o eplore dynamics. We found ha, in our simple model, he effec of a given movemen in equiy prices on invesmen did no depend on he source of he shock. Bu we provided some argumens as o why his migh no be rue in he real world. In paricular, we suggesed ha movemens in equiy prices unrelaed o fundamenals may have a smaller effec on invesmen (if any) han hose relaed o fundamenals. Our empirical work, ogeher wih he earlier work of MacGorain and Thompson (22) and Bond e al (24), suggess ha his argumen seems o hold rue in UK daa. This paper has sill lef some quesions unresolved. In paricular, i would be good o model more eplicily he sors of shocks ha drive he economy and heir sochasic processes. Then i would be ineresing o invesigae wheher or no i makes sense in a more complicaed model for shocks o equiy price volailiy o have no effec on consumpion volailiy. To do his, one would have o eamine he links beween he equiy risk premium and he volailiies of fundamenal shocks. In urn, ha would mean considering models ha are able o eplain he magniude of observed equiy risk premia, somehing ha is no he case in he simple model we presened. I would also be ineresing o invesigae wheher here are any shocks (or specificaions of he model) under which invesmen would respond more or less o equiy price movemens han in he baseline case. 24

22 References Berau, C (22), Equiy prices, household wealh, and consumpion growh in foreign indusrial counries: wealh effecs in he 99s, Federal Reserve Board Inernaional Finance Discussion Paper no Blake, A, Fernandez-Corugedo, E and Price, S (23), The dynamics of consumers ependiure: he UK consumpion ECM redu, Bank of England Working Paper no. 24. Blanchard, O J (986), Commens and discussion, Brooking Papers on Economic Aciviy, Vol.. Bond, S and Cummins, J (2), The sock marke and invesmen in he New Economy: some angible facs and inangible ficions, Brookings Papers on Economic Aciviy, Vol., pages 6-8. Bond, S, Klemm, A, Newon-Smih, R, Syed, M and Vlieghe, G (24), The role of epeced profiabiliy, Tobin s Q and cash flow in economeric models of company invesmen, Bank of England Working Paper no Boone, L, Girouard, N and Wanner, I (2), Financial marke liberalisaion, wealh and consumpion, OECD Working Paper no. 38. Caballero, R J (999), Aggregae invesmen, in Taylor, J B and Woodford, M (eds), Handbook of macroeconomics, Vol., pages Campbell, J Y and Shiller, R J (988), The dividend-price raio and epecaions of fuure dividends and discoun facors, Review of Financial Sudies, Vol., pages Chan, L, Karceski, J and Lakonishok, J (2), The level and persisence of growh raes, NBER Working Paper no Chirinko, R S (993), Business fied invesmen spending: modeling sraegies, empirical resuls and policy implicaions, Journal of Economic Lieraure, Vol. 3, Issue 4, pages, Chrisiano, L J, Eichenbaum, M and Vigfusson, R (23), Wha happens afer a produciviy shock?, Norhwesern Universiy, mimeo. Davis, M A and Palumbo, M G (2), A primer on he economics of ime series economerics of wealh effecs, Federal Reserve Board Finance and Discussion Series Working Paper no Ellis, C and Price, S (23), UK business invesmen: long-run elasiciies and shor-run dynamics, Bank of England Working Paper no. 96. Fazzari, S M, Hubbard, R G and Peersen, B C (988), Financing consrains and corporae invesmen, Brookings Papers on Economic Aciviy, Vol., pages Friedman, M (957), A heory of he consumpion funcion, Princeon: Princeon Universiy Press. Hall, S (2), Financial effecs on corporae invesmen in UK business cycles, Bank of England Quarerly Bullein, Winer, pages

23 Jenkinson, N (996), Saving, invesmen and real ineres raes, Bank of England Quarerly Bullein, February, pages Lanz, C D and Sare, P G (2), Consumpion, savings and he meaning of he wealh effec in general equilibrium, Federal Reserve Bank of Richmond Economic Quarerly, Vol. 87/3, Summer, pages Leau, M and Ludvigson, S C (22), Time-varying risk premia and he cos of capial: an alernaive implicaion of he Q heory of invesmen, Journal of Moneary Economics, Vol. 49, pages Leau, M and Ludvigson, S C (23), Undersanding rend and cycle in asse values: reevaluaing he wealh effec on consumpion, American Economic Review, forhcoming. Ludwig, A and Sløk, T (2), Impac of sock prices and house prices on consumpion in OECD counries, IMF, mimeo. MacGorain, S and Thompson, J (22), Profi epecaions and invesmen, Bank of England Quarerly Bullein, Winer, pages Obsfeld, M and Rogoff, K (996), Foundaions of inernaional macroeconomics, Cambridge, Massachuses: MIT Press. Roberson, D and Wrigh, S (22), Wha does q predic?, Universiy of London, mimeo. Tobin, J (969), A general equilibrium approach o moneary heory, Journal of Money, Credi and Banking, Vol., pages