AGGREGATE DEMAND, INSTABILITY, AND GROWTH*

Transcription

1 AGGREGATE DEMAND, INSTABILITY, AND GROWTH* Seven M. Fazzari (Washingon Universiy, S. Louis, USA) Piero E. Ferri (Universiy of Bergamo, Ialy) Edward G. Greenberg (Washingon Universiy, S. Louis, USA) Anna Maria Variao (Universiy of Bergamo, Ialy) (This version: Sepember, 2012) JEL Codes: E32, E12, O40 Keywords: economic growh, insabiliy, aggregae demand, floors and ceilings Absrac: This paper considers a puzzle in growh heory from a Keynesian perspecive. If neiher wage and price adjusmen nor moneary policy are effecive a simulaing demand, no endogenous dynamic process exiss o assure ha demand grows fas enough o employ a growing labor force. Ye oupu grows persisenly over long periods, occasionally reaching approximae full employmen. We resolve his puzzle by invoking Harrods s insabiliy resuls. Demand grows because i follows an explosive upward pah ha is ulimaely limied by resource consrains. Downward demand insabiliy is conained by inroducing an auonomous componen o aggregae demand. *This paper has benefied from commens and discussion wih Jan Kregel, Mark Seerfield, and Peer Sko in addiion o an anonymous referee and paricipans a conferences including he Macroeconomic Policy Insiue (IMK) annual conference (Berlin, Ocober 2011), a workshop a he SKEMA business school (Sophia Anipolis, France, June 2011) and seminars a he Universiy of Missouri Kansas Ciy and he Universiy of Kansas. The auhors hank he Insiue for New Economic Thinking, he Universiy of Bergamo, and he Weidenbaum Cener a Washingon Universiy for generous financial suppor. 1

2 Why do modern economies grow? Since he pioneering work of Solow (1956), almos all mainsream economiss would answer his quesion by invoking he supply side: growh arises from expansion in he supply of inpus and improvemens of echnology. Bu how do we know ha aggregae expendiure will grow o employ supply-side resources? Mainsream growh heory provides a simple, alhough usually implici, answer: because growh heory is he domain of he long run, demand consideraions fade ino he background. Shor-run sicky wages or prices may cause Say s Law o fail over some horizons, bu nominal variables evenually adjus o clear markes and supply creaes is own demand over he long periods relevan for he concerns of growh heory. In his sense, demand growh is assumed o be auomaic over he long run and is herefore ignored, a characerisic of he famous neoclassical synhesis. While nominal rigidiy is considered he sine qua non of Keynesian macroeconomics in mainsream inerpreaions, Keynes himself did no believe ha nominal adjusmen would cure he problem of inadequae demand. He argued ha falling nominal wages and prices would likely magnify he problem of under-uilized resources (see chaper 19 of he General Theory). This perspecive is manifes in modern effors o avoid deflaion. In his case, we argue ha i is inappropriae o assume ha demand growh endogenously accommodaes o supply in macroeconomic growh models. While supply growh is undoubedly necessary for long-erm expansion, i may no be sufficien. The observaion ha demand growh is no auomaic, however, suggess a puzzle. Aggregae oupu saisics for developed counries over long sweeps of ime show 2

3 persisen growh. Alhough here are periods when economies operae below poenial, someimes for an exended ime, measures of resource use such as he unemploymen rae approach levels consisen wih full uilizaion, a leas momenarily. If aggregae demand does no auomaically adjus o poenial oupu, as assumed in he neoclassical synhesis, wha is here abou he dynamics of demand growh ha generaes persisen expansion over long horizons ha occasionally employs mos resources? To explore his quesion, we consruc a dynamic model of demand growh in he Keynesian radiion. We begin wih a simple model ha reproduces he basic resuls discovered by Harrod (1939). Thus our approach mus address wo well-known and imporan issues ha quesion he empirical relevance of Harrod s growh model. Firs, he seady sae of his model is dynamically unsable. The model predics explosion or collapse should acual growh deviae slighly from wha Harrod calls he warraned pah. Second, he seady-sae pah of he model does no generae full employmen over any horizon, excep by coincidence, if he demand-deermined seady-sae warraned rae of growh happens o equal he naural growh rae of he labor force and produciviy. These issues have been aken up in an exensive lieraure over he years, which we selecively survey in he nex secion of he paper. We offer a new, and remarkably simple, approach. Insead of rejecing insabiliy as empirically unrealisic, we show how insabiliy, conained by modificaions of he basic Harrod model, can resolve he puzzle described above. The downward direcion of shor-run insabiliy endogenously swiches from conracion o expansion if par of aggregae demand does no depend on he sae of he business cycle. In oher words, he presence of some auonomous demand acyclical 3

4 governmen spending, for example conains shor-run insabiliy. Posiive insabiliy is consrained hrough a differen mechanism. When unsable demand rises enough o fully employ he economy s resources, he supply side becomes he binding consrain on growh. Once his happens, he sysem will push up agains he neoclassical growh pah emphasized in mainsream heory. Bu his pah can be fundamenally unsable, a resul never considered in mainsream heory. When full employmen is reached, he sysem s dynamics can sar a new cumulaive process ha pushes he economy below he neoclassical growh pah, unil he auonomous demand floor (or a posiive demand shock) once again urns he pah upward. In our approach, Harrod s insabiliy, raher han being inerpreed as empirically unrealisic, becomes he engine of demand dynamics ha exhibi secular bu unsable growh. This perspecive has imporan implicaions for how we undersand growh in modern economies. The model generaes several differen qualiaive paerns for growh over long periods of ime. I is possible ha demand is so robus ha i coninually pushes up agains supply consrains. I is also possible ha auonomous demand limis posiive growh prior o he economy reaching full employmen and he acual growh pah never reaches full employmen. In he paern mos consisen wih he behavior of modern developed economies in recen decades, however, economic growh and employmen are almos always consrained by he demand side. Noneheless, he sysem occasionally approaches full employmen. Alhough he occasional poins of full employmen are ransiory and unsable, hey consiue a sequence of cyclical peaks of he long-erm pah. The ouer envelope of hese peaks will demonsrae persisen growh if resources grow and echnology improves over ime. I is he peaks of he growh 4

5 process only ha are consrained by supply. This resul provides a kind of synhesis beween mainsream growh heory and realisic Keynesian macroeconomics, one ha does no rely on he weak price adjusmen-demand link o relegae demand o he shadows in he long run relevan for growh models. Following he lieraure review in he subsequen secion, we revisi Harrod s resuls and explore he inerpreaion of his key insabiliy resul in secion 2. We conclude ha he basic Harrod model is a naural way o model demand dynamics and ha he model predics generic insabiliy ha does no depend on paricular parameer values. We discuss how resource consrains and he presence of auonomous demand conain growh insabiliy in secion 3. The resuls show ha he model generaes a corridor ha conains demand growh beween a resource-deermined ceiling and a floor ha evolves hrough ime in a way ha is similar o he equilibrium oupu arising from a simple saic Keynesian muliplier model. Secion 4 describes he basic qualiaive growh paerns ha emerge from he model. The concluding secion presens a variey of links beween he approach pursued here and issues in economic dynamics ha meri furher research. 5

6 1. Moivaion: Lieraure on Demand and Growh In radiional growh heory, here is no role for demand. In he foundaional Solow (1956) model, for example, long-run growh occurs a full employmen. The possibiliy ha nominal adjusmen may no resore demand o full-employmen levels, and herefore ha demand consrains migh bind beyond he shor run, is no considered by Solow or in he massive mainsream growh lieraure ha his paper spawned, including endogenous growh heory (see Aghion and Howi, 1998). In his sense, mainsream growh heory does no prove he irrelevance of Keynesian demand problems in he long run. As Sko (1989, page 21) wries, [b]y imposing full employmen, he neoclassical economiss had effecively assumed away mos of he problems which worried Harrod. The possibiliy ha nominal flexibiliy does no endogenously resore demand o a supply-driven pah was discussed in deail in he General Theory, chaper 19, and his issue has been developed in a small, bu persisen, srand of lieraure. The key insigh is ha wage and price adjusmen canno solve problems of insufficien aggregae demand. Wages and prices will likely decline for paricular firms or in paricular secors wih under-uilized resources. Bu any rise in spending direced oward some par of he economy due o a change in relaive wages or prices comes a he expense of demand in oher secors. Generalized deflaion (or disinflaion relaive o he previous rend of prices) could have favorable real balance effecs ha push aggregae demand back oward full employmen. Bu hese sabilizing effecs can be offse by (1) desabilizing effecs of expecaions on real ineres raes, (2) redisribuion from high-spending borrowers o low-spending debors, or (3) deerioraing condiions in credi markes ha curail 6

7 spending. 1 Thus, in heory, nominal adjusmen may or may no resore demand o absorb poenial oupu. Caskey and Fazzari (1992) develop an empirically calibraed model ha incorporaes hese effecs and find ha he desabilizing channels dominae he sabilizing channels, a poin amplified by Fazzari, Ferri, and Greenberg (1998) and Palley (2008). This work and recen hisorical experience srongly sugges ha wage and price adjusmen will no play he sabilizing role ha eliminaes demand consrains according o he mainsream neoclassical synhesis perspecive. 2 In his case, Say s Law fails no jus in he shor run bu over a longer horizon as well, and he quesion of wheher supply expansion is a sufficien condiion for economic growh becomes cenral. 3 The idea ha demand condiions affec long-erm growh has been a persisen heme in heerodox Keynesian research. Kregel (1980) reviews earlier lieraure; more recen conribuions are discussed by Foley and Michl (1999) and he volume edied by Seerfield (2010). This paradigm begins wih he seminal conribuion of Harrod (1939) which is closely relaed o he model discussed in he following secion. He presens a simple, inuiive approach o model how demand evolves over ime o arge a desired 1 Keynes and his followers discussed all of hese channels. In more modern lieraure, hese hree desabilizing channels have been emphasized, respecively, by Delong and Summers (1986), Tobin (1975), and Caskey and Fazzari (1987). 2 The los decade(s) in Japan provide perhaps he mos relevan modern example. Furhermore, he obvious desire of moneary auhoriies around he world o avoid nominal deflaion suggess ha hey have, a leas implicily, acceped he basic argumen ha falling prices are no sabilizing. While mainsream New Keynesian models coninue o emphasize nominal rigidiy as he reason ha demand may fall shor of poenial oupu, much pracical research has largely abandoned nominal adjusmen as he soluion o insufficien demand. In New Consensus models, he Taylor Rule or some form of inflaion argeing creaes a visible hand of moneary policy ha replaces nominal adjusmen as he cenral mechanism for eliminaing he real effecs of he demand. Recen experience wih boh he zero bound for nominal ineres raes and he inabiliy of less convenional quaniaive easing policies o iniiae susained recovery in he U.S. and elsewhere from he Grea Recession call ino quesions he effeciveness of moneary policy in his regard. Du (2010, p. 229) raises relaed quesions abou he effeciveness of moneary policy in generaing full employmen growh. 3 Palley (1996) also moivaes he imporance of demand effecs on growh and he Harrod model by referring o he incapabiliy of wage adjusmen o resore demand o a supply-deermined pah. 7

8 capial-oupu raio (or, equivalenly, a desired rae of capaciy uilizaion). Despie he inuiive appeal of is basic dynamic srucure, however, he Harrod model, is generally acceped o conain an anomaly or a problem, viz. he knife edge (Kregel, 1980, page 97; also see Boris, 1997, page 134, Palley, 1996, and Sko, 1989, chaper 6, and 2010). Simply pu, he seady-sae warraned growh pah of Harrod model is unsable; any disurbance from seady sae causes he growh pah o explode wihou bound or collapse oward zero, an empirically unrealisic predicion. A number of auhors have modified he Harrod model o address his knife-edge insabiliy. Shaikh (2009, p. 464), for example, proposes a simple and sensible dynamic adjusmen process ha renders he warraned pah perfecly sable. Sko (1989, 2008) also discusses mechanisms ha can make growh models wih a Harrod-like invesmen funcion sable in he long run. The insighs from his work are imporan. Noneheless, insabiliy of he warraned pah remains a persisen feaure in Keynes- Harrod growh models. 4 In he approach developed here, we embrace he knife-edge propery of he original Harrod model as a key feaure of he economy ha helps o explain long-erm growh. This approach sands in conras o he conclusion reached in much oher research ha he insabiliy of Harrod s warraned pah is an empirically unrealisic resul ha suggess a flaw in he model (Sko 1989 is an excepion). We draw moivaion from he conribuions of Hicks (1950) and Minsky (1959, 1982). These models are locally unsable bu conain globally explosive dynamics by inroducing ceilings and floors. While his echnique has been mainly applied wihin a business cycle perspecive (see Ferri and Greenberg, 1989, and Ferri and Minsky, 1992), we believe ha 4 Sko (1989, page 104) wries ha Harrod s insabiliy argumen is vindicaed despie feaures of an exended model ha may conain local insabiliy of he warraned pah in global limi cycles 8

9 i can also add o our undersanding of he role of aggregae demand over longer horizons. 5 Much recen heerodox growh lieraure has followed an alernaive pah o Harrod model based on he approach originaed by Kalecki. This research has pursued a wide variey of imporan issues, especially he impac of income disribuion on growh. The Kaleckian models, however, have a problemaic implicaion. The long-run rae of capaciy uilizaion is no deermined by a arge derived from firm behavior. Raher, seady-sae capaciy uilizaion emerges from oher feaures of he model, and firms are assumed o adjus heir behavior o accep he equilibrium uilizaion rae ha arises from he model soluion. Some auhors have pu forward mechanisms o faciliae his adjusmen. For example, firms may adjus heir arge rae of uilizaion in response o recen experience if such experience differs from he uilizaion rae firms would choose for echnological or sraegic reasons (see Du, 2010, page 235, for example). Or firms may accep a range of uilizaion raes as normal (Lavoie, 2010, p. 144), which allows oher facors o affec he long-run uilizaion rae, as long as i remains wihin he normal range. Noneheless, he invesmen decision is ulimaely made by he firm, and we herefore asser ha he firm s objecives should be he saring poin for undersanding invesmen dynamics. Tha is, he arge uilizaion rae should be chosen by firms, consisen wih Harrod s approach. 6 5 A differen approach has been suggesed by Aoki and Yoshikawa (2007), who also emphasize he link beween demand and growh. 6 For an overview of his issue and many furher references, see Blecker (2002), Sko (2010) and Lavoie (2010). Sko and Zipperer (2012) compare growh models empirically and find ha he implicaions of he Kaleckian models are no suppored by he daa. 9

10 2. Harrod s Model Revisied We begin wih he mos basic of Keynesian models. Oupu (Y ) is deermined by aggregae demand (AD ), which consiss of consumpion (C ) and invesmen (I ): Y = AD = C + I (2.1) We do no consider invenory dynamics and inernaional rade in his paper. The effec of including an auonomous componen of demand, such as governmen spending and resource consrains on producion is discussed in secion 3. As in Harrod, consumpion is proporional o income. Because we wan o race he acual, raher han he equilibrium, pah of demand and oupu hrough ime, we assume ha period consumpion depends on he expecaion of period income. I is convenien o represen hese expecaions in he form of a growh rae, so ha C = (1 s)(1+ Eg )Y 1 (2.2) where s is he consan propensiy o save and Eg is he expecaion of oupu and income growh beween period -1 and, condiional on informaion available a While specificaions such as equaion (2.2) are ofen criicized in he mainsream lieraure because hey lack opimizing microfoundaions, his specificaion leads o simple analyical resuls and links clearly o he lieraure sared by Harrod. 8 We noe ha equaion 2.2 can incorporae persisence ino he consumpion decision, as emphasized in 7 Expecaion errors could cause he ex pos saving-income raio o deviae from he arge s. Harrod assumes his possibiliy away by specifying curren consumpion as a funcion of curren income. Because curren income depends on curren consumpion, Harrod s model generaes an equilibrium pah for demand and oupu, wih he simple Keynesian muliplier resolved wihin each period. Our approach makes i easier o follow he dynamics of demand and oupu hrough ime, bu resuls are similar o hose of Harrod. 8 A linear consumpion rule such as equaion (2.2) can be derived from he firs-order condiions for ineremporal opimizaion of a represenaive consumer wih a reasonable uiliy funcion as in Aghion and Banerjee (2005, page 12). 10

11 life-cycle and permanen income models of consumpion, because he expeced growh rae may depend on longer lags of income or oher variables. To model invesmen, we firs make assumpions abou he firm s producion echnology. As in Harrod, producive capaciy is a linear funcion of he sock of capial. 9 We assume ha invesmen in period becomes effecive in period +1. Le v* denoe he desired capial-oupu raio for firms in he economy. Then he desired capial sock in +1 is K +1 = v * EY +1 = v *(1+ Eg ) 2 Y 1. (2.3) Assume ha capial depreciaes a rae δ (Harrod assumed δ =0). To reach his arge in +1, given ha he law of moion for capial is K = K 1 (1 δ) + I, (2.4) invesmen is I = v *(1+ Eg ) 2 Y 1 (1 δ)k. (2.5) Noe ha K is he capial sock a he beginning of ha arises from pas invesmen spending. Therefore, as is he case wih consumpion, invesmen in is deermined only by variables daed in earlier periods. Since gross invesmen canno be negaive, he invesmen enering ino equaion (2.1) is he maximum of 0 and he I given in equaion (2.5). This consrain is ignored in he following analyical discussion, bu i is incorporaed ino he simulaion model discussed in laer secions. Oupu in is given by 9 This echnology has also been resurreced in recen AK models of economic growh (see Aghion and Banerjee, 2005). 11

12 Y = C + I = (1 s)(1+ Eg )Y 1 + v *(1+ Eg ) 2 Y 1 (1 δ)k. (2.6) The oupu growh rae is g = (Y / Y -1 ) 1 and we equaion 2.6 divide by Y -1 o obain 1+ g = (1 s)(1+ Eg ) + v *(1+ Eg ) 2 (1 δ) K Y 1. (2.7) Equaion 2.7 gives he law of moion for growh, condiional on expeced growh. 10 All variables on he righ side of 2.7 are predeermined. This equaion provides he foundaion for he dynamic analysis o follow. The Warraned Rae We can solve equaion 2.7 for he seady-sae growh rae, which is he growh rae ha makes he acual growh rae in period equal o he expeced rae. 11 Seady sae also requires ha he capial-oupu raio, v = K / Y equal he arge level v*. 12 Denoe he seady sae growh rae by g*, and subsiue g* for Eg and v* for v. From 2.7, we obain he seady sae: " 1+ g* = (1 s)(1+ g*)+ v *(1+ g*) 2 (1 δ) K %" $ ' Y % $ ' # &# & Y = (1 s)(1+ g*)+ v *(1+ g*) 2 (1 δ)v *(1+ g*). (2.8) g* = s v * δ This seady-sae soluion is wha Harrod calls he warraned rae of growh. If firms and consumers expec he warraned rae o prevail, he dynamic law of moion delivers Y 1 10 A fully specified law of moion would require assumpions abou how expecaions evolve. This issue is discussed below. 11 See Sen (1970), Fazzari (1984) and Palley (1996) for similar inerpreaions of he warraned rae. Puu, Gardini and Sushko (2005) call his equilibrium a fixed growh poin. 12 These seady-sae condiions parallel he requiremens for equilibrium in boh flows and socks discussed by Hicks (1965, chaper 11). 12

13 an acual growh rae ha validaes expecaions. If here is no exogenous change in expecaions, growh should coninue a his rae. Bu wha happens if here is such a change? Consider a shock o expecaions. We can undersand he source of insabiliy in his model by looking a he derivaive of acual growh (g) wih respec o Eg, using he emporary law of moion, equaion (2.7), dg d(eg ) = [ 2v *(1+ Eg ) ] + (1 s) (2.9) If his derivaive is greaer han one, a shock o expecaions is magnified by he sysem dynamics. The derivaive exceeds one if Eg > s 1 (2.10) 2v * Along he warraned pah, Eg = g* = (s/v*) δ, so he condiion in 2.10 is always saisfied a he warraned growh rae. Tha is, a disurbance in he expeced growh rae along he warraned pah always generaes a deviaion in he acual growh rae away from he warraned rae larger han he size of he disurbance. This resul is cenral o he generic insabiliy of he model. The mahemaics behind equaions 2.9 and 2.10 is sraighforward, bu he economic inuiion is somewha suble. A casual look a he derivaive given by equaion 2.9 migh sugges ha insabiliy of he acual growh rae could be overcome in ways familiar from saic Keynesian models. The firs erm in brackes is an acceleraor effec: higher expeced growh induces more curren invesmen, more curren demand, and more acual growh. The second erm in brackes is he posiive effec of expeced 13

14 growh on consumpion ha also raises curren demand and acual growh. Weaken he acceleraor (reduce v*) or raise he saving rae (increase s) and he impac of a shock o expeced growh on acual growh ges smaller for a given level of expeced, consisen wih Keynesian inuiion. Bu such changes canno make he warraned pah sable because we canno deermine he sabiliy of he warraned pah by evaluaing condiion 2.10 a a given level of expeced growh. Changes in he demand parameers v* and s ha appear o sabilize demand dynamics have he opposie effec on he warraned growh rae ha mus be achieved along he seady-sae pah. For example, while raising s dampens he consumpion muliplier, i also requires a higher warraned rae of growh since seady-sae invesmen will have o be a higher share of oupu o absorb he exra saving. Alhough higher s raises he righ side of he inequaliy in 2.10, i also raises he relevan growh rae for evaluaing he sabiliy of he warraned pah on he lef side of 2.10, and by a larger amoun. This resul is key o undersanding why he warraned pah is unsable. Expecaions and Insabiliy The pah of he sysem following a disurbance o he warraned pah depends on how expecaions evolve. The derivaive in equaion 2.9 exceeds one for all values of Eg above g* and a large inerval of values below g*. 13 Thus, if he expeced growh rae deviaes from he warraned rae, acual growh will deviae from he warraned rae by an even larger amoun (in absolue value). Therefore, 13 For reasonable values of s and v*, he inequaliy in 2.10 fails only for large negaive expeced growh raes. In his case, he model can be sable, bu he dynamics do no converge o he warraned rae. Raher, he sysem goes o a growh rae of negaive 1 and zero oupu. 14

15 Eg Eg Eg > g* g = g* g < g* g > Eg < Eg = Eg (2.11) To race ou he dynamics of he sysem ou of seady sae, we need o specify how expecaions evolve. We hink of Eg as incorporaing all relevan informaion ino expecaions available a ime -1. Suppose ha he new informaion arriving a ime abou growh relaive o he previous expecaion (ha is, g relaive o Eg ) induces a change in he subsequen expeced growh rae (Eg +1 ) in he same direcion as he mos recen expecaion error. More formally, le he dynamics of expeced growh follow he simple rule g g g > Eg = Eg < Eg Eg Eg Eg > Eg < Eg = Eg. (2.12) Under his assumpion, equaions (2.11) and (2.12) show ha he warraned pah is always unsable. Indeed, because he only non-degenerae seady sae is given by he warraned pah, he model dynamics are always unsable. Growh rises wihou bound if growh expecaions are disurbed above g*, and oupu converges o zero if expecaions are disurbed below g*. 14 The insabiliy propery is generic o he Harrod model srucure. I does no depend on parameer values as long as he rule for expecaion formaion in equaion 2.12 holds (see Ferri e al., 2011, for a general discussion). And 2.12 seems reasonable. Suppose ha expeced growh is 3% in period 1 and acual growh in period 1 is 3.5%. 14 Also see Kregel (1980), Sen (1970), Fazzari (1984), and Palley (1996) for relaed inerpreaions of Harrod insabiliy. 15

16 Wha will happen o expeced growh for period 2? If he disurbance o growh is perceived as enirely emporary, perhaps expecaions for period 2 would remain a 3%. Bu if here is jus he slighes bi of uncerainy ha here may be some new informaion in he acual 3.5% growh rae ha prevails in period 1, expecaions for period 2 should rise above 3%. The increase in expeced growh may be small, bu a small move in he direcion of he mos recen expecaion error is all ha is required for insabiliy. Tha is, if expecaions for period 2 rise by a small incremen ε, acual growh in period 2 will be even higher han he 3.5% acual rae for period 1, by an incremen ha exceeds ε (his saemen is implied by 2.11). The expecaion updaing rule in 2.12 will herefore be validaed by he operaion of he acual model dynamics. 16

17 3. Conaining Insabiliy Explosive or implosive dynamics do no seem realisic. While we see insabiliy in modern developed economies, growh does no rise o infiniy or collapse o zero. Indeed, as discussed above, modern developed economies have demonsraed persisen, bu bounded growh over long sweeps of ime. I is herefore no surprising ha researchers should dismiss he inconvenien ruh of Harrods s knife-edge seady sae, eiher by rejecing he model or by ignoring dynamics off he warraned pah. We propose a differen response, one ha acceps he basic insabiliy of he model as a robus feaure of economic growh, bu wih addiional mechanisms o conain he insabiliy wihin realisic bounds. 15 Producive Capaciy: The Supply Side as a Ceiling A naural source for a ceiling on posiive insabiliy is a supply-side resource consrain (for a discussion, see Ferri, 1997). The model in secion 2 is driven enirely by demand under he implici assumpion ha all ha households and businesses wan o purchase can indeed be produced. Bu growh in demand a an increasing rae will evenually push he sysem oward he full employmen of is resources. Harrod called he exogenous growh rae of he labor force, possibly adjused for produciviy changes, he naural rae of growh, and his growh rae defines a pah of poenial oupu ha represens full employmen of labor. In deail, assume ha poenial oupu is iniially Y Our approach is closely relaed o he ceiling and floor model of Hicks (1950). In a commen ha almos direcly foreshadows he resuls of his secion, Asimakopulos (1997, p. 299) reviews Harrod s growh model and specifically menions ha upward deviaions in he acual growh rae would be conained by a ceiling deermined by shorages of producive capaciy and labor and downward movemens in growh bounded by a floor which is se by auonomous expendiures. 17

18 Labor supply and labor produciviy grow a a compound exogenous rae g N. Then, labor resources will consrain aggregae supply o be no greaer han Y s = Y s 1 (1+ g N ) = Y 0 (1+ g N ), (3.1) and acual oupu will be he minimum of aggregae demand and aggregae supply. 16 We do no impose capial limiaions on supply. There are wo reasons for his asymmery beween capial and labor. Firs, capial is produced while labor is no. The reason for invesmen as specified above is o accumulae capial o a level appropriae o produce anicipaed oupu. Second, empirical evidence suggess ha capial is hardly ever a binding consrain. This is no only because firms inves in capial in anicipaion of oupu growh, bu also because firms seem o operae wih excess physical capaciy. The U.S. capaciy uilizaion rae in manufacuring has averaged no much above 80 percen even in good economic imes (much lower in recessions); uilizaion has no been above 85 percen since he 1970s. A desired rae of capaciy uilizaion below 100 percen can be easily incorporaed ino he arge capial-oupu raio v*. The assumpion ha capial consrains do no bind resrics he relevance of our model o he moderae growh flucuaions of he kind observed in developed economies over recen years. A differen approach migh be needed in an excepional boom when capial consrains bind, bu he only hisorical case in recen U.S. hisory when such circumsances prevailed in he aggregae was World War 2. Fas-growing developing counries, however, may well 16 Also see Minsky (1982, page 260). Sko (1989) proposes a limi o insabiliy due o he rise in he srengh of labor relaive o firms caused by high employmen raes. Palley (1996, equaion 7) proposes a supply consrain on unsable demand dynamics. In his case, however, he consrain is ha acual growh is he minimum of demand growh and supply growh. In our case, we resric he level of oupu o be he minimum of he level of demand and supply. 18

19 have capial consrains on oupu and lile consrain on labor, which would require a differen approach o he one developed here. 17 The supply ceiling resricion creaes a disconinuiy in he sysem dynamics ha makes analyical resuls difficul and uninformaive when he acual pah his he ceiling. We analyze he behavior of he model in he neighborhood of he ceiling wih simulaions. In he simulaion model expeced growh adjuss adapively o acual growh according o Eg +1 = (1 α)g + αeg (3.2) wih a weigh (α) of 0.3 on lagged expeced growh (adjused as discussed below). The desired capial-oupu raio v* is 0.6 and he depreciaion rae is 0.1. Poenial oupu grows a 3 percen per year and he saving rae is calibraed o produce a 3 percen warraned rae of growh. (We discuss he possibiliy ha he naural and warraned raes of growh differ in secion 4.) The sysem is iniialized wih he warraned growh rae equal o he expeced and acual growh raes, wih 4% unemploymen of labor. Wha happens when a small posiive shock o expeced growh iniiaes unsable demand dynamics ha push oupu up agains he resource ceiling? As he sysem approaches he ceiling, acual and expeced oupu are growing faser han he naural rae of supply expansion. When he supply consrain binds, acual growh is limied o g N and demand falls quickly below he ceiling, and below expeced demand. The acual rae is now below he warraned rae. The sysem bounces off he ceiling ono an unsable declining growh pah. 17 Therefore, he relevan conex for our model is wha Sko and Zipperer (2012) label maure economies in which developmen has proceeded o he poin ha here is no an infiniely elasic supply of labor available ouside of he modern secor of he economy. 19

20 The basic inerpreaion is sraighforward. Upward demand insabiliy can drive demand o a level ha fully employs labor resources. Bu he full employmen pah is no sable. We shall reurn o discuss he role of he ceiling and momenary full employmen below in he conex of he full model. Auonomous Demand o Conain Downward Insabiliy In his subsecion, we demonsrae ha he presence of an auonomous componen of demand, one ha evolves independenly from he sae of he economy, is sufficien o conain downward insabiliy in growh. We denoe auonomous demand by F and consider below he effec of various specificaions for he ime pah of his variable. One can hink of F as governmen spending, bu i could also include auonomous componens of privae consumpion or invesmen. 18 Wih he addiion of F, demand (and oupu, as long as demand is less han poenial supply) becomes 2 ( 1 s)( 1+ Eg ) Y + v *( 1+ Eg ) Y 1 ( 1 δ ) K F Y = 1 +. (3.3) I is clear ha a posiive value of F prevens demand and oupu from collapsing o zero. The growh rae law of moion, condiional on expecaions, is: 1+ g = ( 1 s) ( 1+ Eg )+ v *( 1+ Eg ) 2 ( 1 δ) K + F. (3.4) Y 1 Y 1 18 Minsky (1982, page 260) imposes a similar floor condiion. In Hicks (1950) he auonomous demand floor comes from an auonomous componen of invesmen. 20

21 Inspecion of equaion 3.4 shows ha if g is on a downward pah oward negaive one, growh mus evenually urn posiive because as long as F does no decline (or a leas declines more slowly han Y ), shrinking Y -1 will evenually cause he final, always posiive, erm of 3.4 o dominae he deerminaion of growh. 19 To undersand hese dynamics more fully, we firs consider he condiions under which expecaions are realized in he model wih auonomous demand. Unless F grows a he same rae ha equaes acual and expeced growh, he model will no have a seady sae wih a non-zero growh rae. This is clear because he raio F / Y -1 in equaion 3.4 canno be consan unless F and oupu grow a he same rae. A any ime, however, we can define a growh rae ĝ such ha Eg = ĝ g = Eg. (3.5) Le v = K / Y denoe he acual capial-oupu raio and define f = F / Y. Then 3.4 and 3.5 imply ha 1+ g = ( 1 s) ( 1+ Eg ) + v *( 1+ Eg ) 2 ( 1 δ) K + F Y 1 Y 1 1+ g = ( 1 s) ( 1+ Eg ) + v *( 1+ Eg ) 2 ( 1 δ) ( 1+ g ) K ( )( 1+ ĝ ) + v *( 1+ ĝ) 2 ( 1 δ) 1+ ĝ ( ) + v *( 1+ ĝ ) ( 1 δ)v + f ( ) = s + ( 1 δ)v f 1+ ĝ = 1 s 1= 1 s v * 1+ ĝ Y ( )v + 1+ ĝ + ( 1+ g ) F Y ( ) f (3.6) ĝ = s f v * + ( 1 δ ) v v * 1 19 Firm invesmen behavior will srive o keep he capial sock in line wih oupu, hus he erm K / Y -1 will no grow wihou bound as Y -1 declines. If gross invesmen is bounded below by zero bu oupu coninues o shrink he capial sock will decline a rae δ, so if F is consan or growing, he final erm of 3.3 mus evenually dominae. 21

22 Noe ha ĝ will be ime varying in general because f and v change over ime. 20 Consider he behavior of ĝ along a negaive growh pah. Firs, suppose f equals zero as in he basic Harrod model discussed in secion 2. The dynamics of ĝ are hen driven enirely by he disequilibrium beween he acual and arge capial-oupu raios (if f is zero, v is he only ime-varying componen on he righ-hand side of equaion 3.6). Because he sysem is on an unsable negaive pah, g < Eg and he capial sock exceeds he arge level ex pos. This pushes v and ĝ upward while acual g declines. Because he g and ĝ pahs never cross, he downward dynamics of growh are never arresed and oupu converges o zero. This resul is simply a resaemen of he downward Harrod insabiliy discussed in he previous secion. Bu if F is consan (or growing), f grows as Y falls, pushing ĝ downward, oher hings equal. Will ĝ necessarily cach up wih g? The answer is yes. Suppose for he momen ha F = F for all ime. I is clear ha as he economy declines i will evenually reach a minimum level of oupu, since demand can never fall below F. Thus, even hough growh has been negaive along he declining pah, he acual growh rae mus evenually hi zero. If acual growh is zero wih negaive expeced growh, he acual rae exceeds he expeced rae and his implies ha ĝ has fallen below acual growh. (If F is growing over ime, f rises even faser, pushing ĝ down even more quickly. So he demonsraion 20 If he acual and expeced growh raes of demand are equal o g*, and he growh rae of F is se o g*, we can solve for a seady sae such ha f = f*and v = v*. In his case, equaion 3.2 implies ha g* = [(s - f*) / v*] - δ which could be viewed as a generalizaion of Harrod s warraned rae. Bu he exisence of his seady sae depends on he arbirary assumpion ha F grows a exacly g*. 22

23 ha ĝ caches up wih g wih consan F is sufficien o obain he same resul for rising F.) 21 The sae of he model afer ĝ falls below g is analogous o he Harrod insabiliy resul discussed in secion 2. Acual growh rises and oupu follows a locally unsable pah. Insabiliy is clear since he model is he same as Harrod s excep for he F erm in equaion 3.4. This erm is predeermined and herefore does no affec he derivaive of g wih respec o Eg ha proves insabiliy (see equaions 2.9 and 2.10). How far can oupu fall? Clearly he value of F is criical o answering his quesion. Suppose oupu his a local minimum value Y a some poin along is dynamic pah. A his ime, he acual growh rae approaches zero, and lagged oupu equals curren oupu. 22 From equaion 3.6 we have: 1+ g = ( 1 s) ( 1+ Eg ) + v *( 1+ Eg ) 2 ( 1 δ) 1+ g ( )v + 1+ g ( ) F Y ' and since acual growh is zero a Y, 21 Harrod (1939, pages 28-29) recognizes he possibiliy of a similar phenomenon: As acual growh depars upwards or downwards from he warraned level, he warraned rae iself moves, and may chase he acual rae in eiher direcions. The maximum raes of advance or recession may be expeced o occur a he momen when he chase is successful. In our conex he warraned rae ha is chasing he acual rae is analogous o ĝ and he maximum rae of recession occurs when ĝ = g. 22 Because he model is specified in discree ime, oupu may reach a minimum when growh is negaive bu swiches o posiive in he subsequen period. Noneheless, he analysis presened here for acual growh of zero provides a lower bound on oupu jus prior o he swich in he sign of acual growh. Furhermore, a growh cycle could occur wihou acual growh every becoming negaive. Insead falling, bu posiive, growh could swich o rising growh before oupu his a minimum. In his case, he analysis in he ex represens a non-binding lower bound on acual oupu jus prior o he swich in he direcion ha acual growh changes. 23

24 1= ( 1 s) ( 1+ Eg ) + v *( 1+ Eg ) 2 ( 1 δ)v + F Y ' Y ' = s 1+ Eg " # ( ) Eg v *( 1+ Eg ) 2 1 δ F ( )v $ % (3.7) This resul for he value of oupu a (or near) a local minimum of he dynamic business cycle is analogous o a saic Keynesian muliplier oucome, given he level of auonomous expendiure F. The firs erm in he denominaor of 3.7 is he marginal propensiy o save ou of an increase in lagged income. The brackeed erm in he denominaor is he marginal propensiy o inves ou of lagged oupu. 23 Equaion 3.7 shows ha he floor on oupu over ime rises wih he size of auonomous demand and any consumpion and invesmen demand induced by he presence of auonomous demand. Tha is, an economy wih a high propensiy o consume or inves (low s or high v*, respecively) will have a higher oupu floor ha conains is downside dynamics. Furhermore, for reasonable parameer values (paricularly a small value of s) he floor is much higher han auonomous demand iself. 24 Before leaving he discussion of F, we need o consider how he addiion of an auonomous componen of demand affecs he behavior of upward insabiliy. If his componen is large relaive o oal demand, i can consrain upward insabiliy before he sysem reaches he resource-consrain ceiling. The definiion of ĝ from equaion 3.6 helps explain his possibiliy. As he economy is on an upward growh pah f can decline 23 To simplify he inerpreaion of equaion 3.6 furher, suppose Eg is zero and v = v* a Y. Then he righ side of 3.6 reduces o F / (s - δv*). Because expeced growh is zero and capial is a he desired level, he gross propensiy o inves ou of lagged income is jus equal o depreciaion. 24 There is a similariy beween his resul and he supermuliplier model presened by Boris (1997). The supermuliplier models focus on poenial raher han acual oupu, bu auonomous expendiure plays an imporan role. Boris (page 153) wries auonomous expendiures ac as an engine which iniiaes he producion of consumpion and invesmen goods. 24

25 if F grows more slowly han oupu. If he auonomous demand is a large share of oal demand (f is large) his effec can dominae he dynamics of ĝ, so ha ĝ caches up wih g before oupu reaches he full-employmen limi. In his case, expeced growh exceeds acual growh, and expeced growh declines. Thus, he presence of auonomous demand can preven upward insabiliy from pushing he sysem o full employmen. We will discuss he condiions under which his siuaion arises in more deail in he nex secion. 4. Paerns of Growh The model presened in he previous secions leads o hree qualiaively differen kinds of growh pahs ha we describe nex. Excess Demand There is nohing in our model ha prevens he floor level of oupu defined in equaion 3.6 from becoming arbirarily large (le s approach zero, for example). I is herefore possible for he floor on demand o approach and exceed he resource consrain ceiling from equaion 3.1. In his case, he resource consrain is always binding, and here is persisen excess demand. Oupu grows along he supply-deermined pah. Noe ha downward insabiliy described in secion 2 does no occur, even briefly, because he floor on oupu is so high. Equaion 3.7 shows ha he demand floor exceeds exogenous poenial supply if eiher auonomous demand is high or he saic Keynesian muliplier is large. This possibiliy relaes in an ineresing way o he classic problem, idenified by Harrod, ha he seady-sae warraned growh rae may no be equal o he naural rae of supply 25

26 growh. If he warraned pah were an appropriae proxy for acual oupu, hen a low warraned rae would sugges indefiniely rising unemploymen. Bu, as we have seen, he warraned rae, if i exiss a all, is no a sable equilibrium for he sysem and herefore should no be viewed as a heoreical proxy for acual growh. Indeed, a low warraned rae corresponds o a low saving rae and a high invesmen rae (high value of v*), boh of which raise he oupu floor induced by auonomous demand and make he siuaion of excess demand in which labor resources are persisenly fully employed more likely. In his sense, he dynamics of our model exhibi a paradox of hrif (also see Harrod, 1939, pages 30-31). While persisen excess demand and a full-employmen growh pah are possible oucomes of our simple model, his siuaion does no seem o describe empirical growh pahs in modern developed counries. Momens of srong full employmen seem o be fleeing and generalized excess demand is almos never observed. 25 A deailed explanaion for why his is he case is beyond he scope of his paper, bu we offer hree observaions here. Firs, as he economy approaches a sae of excess demand, endogenous forces could lead o an acceleraion of he naural rae of growh. Boh profi opporuniies and sources of funding for invesmen will expand as he resul of srong economic performance associae wih high demand. These condiions could spur innovaion ha raises produciviy and relaxes supply consrains. This favorable oucome may be mos likely if excess demand is modes so ha innovaion induced by a high-uilizaion economy can expand capaciy before severe supply bolenecks or 25 In he U.S., he only clear siuaion of generalized excess demand seems o be during World War 2. Alhough acceleraing inflaion wih very low unemploymen in he middle 1960s suggess ha he growh pah may have approached excess demand. 26

27 inflaionary pressures arise. A second possibiliy, likely of relevance in recen decades, is ha fear of acceleraing inflaion as unemploymen falls leads o moneary ighening ha chokes off demand. Third, he financing of high raes of demand growh could raise financial fragiliy, as discussed exensively by Minsky (1986). This fragiliy could curail srong invesmen and consumpion. The resul would be a decline in he demand floor o levels ha eliminae excess demand and open he door o downward insabiliy. We leave exploraion of hese issues for furher research. Cyclical Demand-Driven Expansion A more realisic growh paern arises when he dynamic floor for oupu lies below he supply-deermined ceiling. In his case, he acual growh pah prediced by he model cycles in a bounded range. If boh he resource consrain and he auonomous demand variable are growing over ime (no necessarily a he same rae), he bounds ha conain he acual pah of he economy will expand as well. Because he economy occasionally ouches he growing resource consrain, acual oupu will exhibi secular growh, consisen wih observed acual growh pahs in developed economies, as discussed in he inroducion. This growh pah is fundamenally differen from resuls generaed by mos oher growh models. The oupu pah does no converge o a full-employmen seady sae; i follows an endogenous cyclical pah beween he floor and ceiling. Full employmen consrains growh emporarily for brief momens of ime, bu demand deermines oupu and growh a almos all poins. In addiion, he lower bound on he oupu pah is enirely demand deermined according o ypical Keynesian logic. The floor defined by equaion 3.7 rises oward he resource consrain ceiling as auonomous demand becomes 27

28 larger or as parameers change ha cause he consumpion and invesmen induced by auonomous demand o increase. Figure 1 presens a simulaed growh pah produced by he model. Recognizing ha demand will flucuae for a variey of reasons no capured by he basic model laid ou in secion 2, we added sochasic shocks o expeced growh wih a sandard deviaion of one percenage poin per year. The sochasic shocks make he cycles irregular, and hence more realisic han he smooh cycles he model produces in he absence of shocks. Noe how oupu occasionally ouches or closely approaches he full-employmen poenial pah, bu does no say here. As he relaive share of auonomous demand declines, or as he Keynesian muliplier falls, he gap beween floor and ceiling widens, which allows oupu pah o wander furher away from he poenial pah. For example, he average deviaion beween he poenial and acual pah in figure 1 is 5.6 percen wih auonomous demand iniially se o 30 percen of oal demand. If auonomous demand is iniially 28 percen, he average gap widens significanly o 13.7 percen (holding all else consan, including he sequence of sochasic shocks o expeced growh). 26 Thus, he dynamic characerisics of he growh pah appear o be quie sensiive o he size of auonomous demand. 26 The simulaion model used o generae figure 1 has he benchmark parameers described earlier in he ex. Poenial oupu and auonomous demand boh grow a 3 percen per year. The saving rae is calibraed o 0.378, which produces a 3 percen warraned rae of growh. (A warraned rae exiss because poenial oupu and auonomous demand are se o grow a he same rae.) Noe ha he saving rae mus be high enough o accommodae boh invesmen and auonomous demand in seady sae. If auonomous demand is governmen spending, i would be appropriae o inerpre par of wha appears as saving in his model as income axes imposed a a consan marginal rae. 28

29 Cyclical Peaks Below he Poenial Pah As discussed in secion 3, i is possible ha he presence of auonomous demand imposes an endogenous demand ceiling on he growh cycle below he level of he resource-consrain ceiling. Figure 2 shows his siuaion. The parameer values and shocks are he same as hose ha generaed figure 1 wih hree excepions. Firs, auonomous demand grows a 2 percen, less han he 3 percen growh of resources. Second, he iniial share of auonomous demand is higher, 40 percen raher han 30 percen, so ha he F / Y -1 erm in equaion 3.3 plays a relaively larger role in he dynamics. Third, o offse he effec of higher auonomous demand on he level of he floor, he saving rae is raised by 10 percenage poins. These changes sar he demand 29

30 floor and resource-consrain ceiling a approximaely he same place hey were for figure 1, bu auonomous spending is a bigger share of iniial demand and grows more slowly. The peaks of he cycle do no reach he poenial pah. The gaps ge larger as ime proceeds. In his case he growh pah is enirely demand deermined and here is no endogenous mechanism ha drives demand high enough o absorb he economy s resources. (The cycle is also more regular because he endogenous dynamics dominae he sochasic shocks.) This growh paern, like he excess demand case discussed above, seems somewha unrealisic. Modern economies do seem o have occasional momens of full employmen. We conclude ha he cyclical pah ha reaches poenial, such as he one 30

31 depiced in figure 1, is he mos empirically relevan. Bu we mus recognize ha he dynamics in figure 2 remain possible. 5. Conclusion: Demand and Growh In he model presened here, demand drives growh a almos all poins in ime. Of course, growh canno persis indefiniely wihou expanding supply. Bu in he mos realisic cases produced by our model, he growh pah is usually consrained by demand, no supply. Tha said, supply can deermine he upper envelope of he growh pah. Wih some ses of parameer values, he oupu pah occasionally pushes up agains resource consrains, bu full employmen is no a dynamic equilibrium. The source of secular demand growh is he fundamenal upward insabiliy of he dynamics of invesmen and consumpion, as idenified decades ago by Harrod. Because our model does no rely on a price mechanism ha drives demand oward poenial oupu, i avoids he unrealisic neoclassical synhesis assumpion, implici in radiional neoclassical growh heory, ha disinflaion or deflaion necessarily pushes aggregae demand o full employmen levels in he shor run. This resul shifs he inerpreaion of Harrod s insabiliy. In much of he lieraure ha followed Harrod, he dynamic insabiliy of he model was reaed as a heoreical problem, because real-world economies do no have knife-edge properies. For example, Boris (1997, page 134) rejecs Keynesian growh models of he Harrod ype because hey imply oo high a degree of insabiliy. In conras, insabiliy helps align he predicions of our model wih broad empirical facs because i is he source of endogenous demand growh ha is necessary o generae long-erm growh pahs 31

32 consisen wih observed hisories of modern economies (also see Sko, 1989 in his regard). 27 Harrod s insabiliy, however, operaes in boh direcions. I is naurally limied on he high side by resource consrains. To conain downward insabiliy, we inroduce an auonomous componen of demand, like auhors such as Hicks (1950), Minsky (1959, 1982), and Asimakopoulos (1997) before us. We have shown ha auonomous demand has a profound effec on he model dynamics. I induces a floor ha urns around negaive dynamics oward growh. If auonomous demand is a large share of oal demand, is presence can also consrain he upward insabiliy, so i is possible ha demand and oupu never reach he full-employmen pah. We focus on demand-led dynamics ha ransmi oucomes in period o demand in period +1, an approach ha leads o he basic Harrod resuls. By adding auonomous demand, however, he model reveals a feaure analogous o he saic Keynesian heory. The floor on he growh dynamics a a minimum poin of he business cycle is he value of auonomous spending imes a muliplier ha depends on marginal propensiies o spend in a familiar way. In his sense, he model merges aspecs of saic and dynamic Keynesian heory. One could inerpre hese resuls o infer ha demand does no affec he longerm growh rae ha occurs beween he poins when he economy occasionally his he supply-deermined ceiling. From an empirical poin of view, he resul could hardly be oherwise. If, as a maer of fac, economies occasionally nudge up agains full use of 27 Sources of upward insabiliy beyond he invesmen dynamics analyzed in his paper could also explain demand growh. For example, commodiy booms could be imporan, paricularly for emerging marke counries. 32