Productivity-Based Asset Pricing: Theory and Evidence

Transcription

1 Produciviy-Based Asse Pricing: Theory and Evidence Firs Presened: Ocober 2004 FMA Meeings, New Orleans. Curren Draf: April 22, 2005 Ronald J. Balvers Dayong Huang Division of Economics and Finance Division of Economics and Finance P.O. Box 6025 P.O. Box 6025 Wes Virginia Universiy Wes Virginia Universiy Morganown, WV Morganown, WV Phone: (304) Phone: (304) ABSTRACT This paper considers asse pricing from he producion side. I differs from earlier approaches o producion-based asse pricing in ha he pricing kernel is derived by replacing he marginal rae of ineremporal subsiuion wih an amended version of he marginal rae of ineremporal ransformaion in a complee markes economy. Relying on a general version of he radiional Real Business Cycle macro model we find ha he variables deermining he mean reurns of all financial asses are he produciviy shock as he sole facor ogeher wih he capial sock and lagged Solow residual (produciviy level) as condiioning variables. Sandard GMM esimaion finds ha our model improves on he complemenary consumpion-based and marke-based approaches and is compeiive wih he Fama-French hree-facor model. The model explains he size premium from differences in he uncondiional sensiiviy o produciviy shocks small firms are more sensiive o produciviy shocks and explains he value premium from differences in he condiional sensiiviy o produciviy shocks growh socks are more sensiive o produciviy shocks in good saes when he risk premium is low. JEL classificaion: G2; E44 Keywords: Cross-Secional Asse Pricing; Produciviy; Macro Facors; Producion-Based Asse Pricing

2 . Inroducion Ineremporal asse pricing heory encompasses hree complemenary approaches. Firs, he consumpion-based approach of Breeden (979), which involves a pricing kernel relaed o he marginal uiliy of consumpion. Iniial versions of he consumpion-based approach have no worked well empirically, bu more recen aemps by Campbell and Cochrane (999), Leau and Ludvigson (200, 2002), and Parker and Julliard (2005), are compeiive wih he empirically-moivaed hree facor model of Fama and French (992, 996). These papers respecively incorporae habi persisence, a condiional approach, and an alernaive approach o measuring fuure consumpion. A general drawback of he consumpion-based approach remains in ha consumpion and, more imporanly, is marginal uiliy are difficul o measure. A second complemenary approach o ineremporal asse pricing was developed earlier by Meron (973) and has as is pricing kernel he marginal uiliy of wealh. Is advanage is ha wealh is observable and ha changes in wealh can be relaed direcly o marke reurns. On he oher hand, he marginal uiliy of wealh is also affeced by sae variables ha summarize how valuable wealh is in differen saes. Bu he Meron model has lile o say abou which sae variables should be imporan; in general, any variables affecing fuure risk or risk aversion are candidaes. These would include a a minimum aggregae demand facors such as he variables governing habi persisence and he aggregae supply variables affecing produciviy. The hird complemenary asse pricing approach looks on he producion side insead of he consumpion side. I includes some quie differen conribuions. Based on he asse pricing Pekova and Zhang (2005) in a recen applicaion of he Meron approach reasonably pick he expeced marke risk premium as he sae variable. By condiioning he expeced marke risk premium on he erm spread, defaul spread, and lagged risk free rae hey are able o explain a subsanial componen of he value premium 2

3 models of Brock (982) and Lucas (978), respecively, Balvers, Cosimano, and McDonald (990) and Cechei, Lam, and Mark (990) argue ha aggregae oupu is equal or proporionae o aggregae consumpion and ha one could evaluae he marginal uiliy of consumpion a he observed level of oupu so ha aggregae oupu growh becomes he key asse pricing facor. The advanage is ha oupu growh is likely measured more accuraely han consumpion growh. 2 Wihin his hird approach, a differen producion-based perspecive is provided by Cochrane (99, 996) who explicily derives an expression for invesmen reurns and assumes ha hese can serve as a pricing kernel for asse reurns. Cochrane (996) finds ha invesmen reurns (using wo facors residenial and non-residenial invesmen growh as proxies) are significanly priced. Li, Vassalou and Xing (2003) use a more disaggregaed model and find ha a four-facor invesmen-growh approach increases he model fi dramaically. 3 While our paper fis wihin he hird asse pricing approach, i is fundamenally differen from he oher producion-based asse pricing papers. I derives a pricing kernel based on he 2 See Liew and Vassalou (2000) and Vassalou (2003) for recen applicaions of his approach o cross-secional asse pricing. 3 Peng and Shawky (999) employ Cochrane s (99) approach o sudy he equiy premium bu impose an ad hoc pricing kernel. A recen paper by Jermann (2005) develops a generalized version of Cochrane s (99) model o consider he size of he equiy premium. Addiionally, here are asse pricing models ha include a producion secor bu focus predominaely on explaining he size of he equiy premium. Jermann (998) argues ha we need boh adjusmen cos and habi persisence o mach he observed equiy premium. Boldrin, Chrisiano, and Fisher (200) emphasize limied inersecoral facor mobiliy and habi persisence in order o explain several aspecs of he equiy premium and key facs of he overall economy. Jermann (2003) provides an ineresing channel hrough which gains in produciviy push up he equiy premium given a concave producion funcion, heerogeneous size of he firm in erms of is labor inpus, and a small elasiciy of labor. The pah breaking model by Gomes, Kogan, and Zhang (2003) provides a srucural heory of he risk sensiiviies of firms differing by value and size aribues. These approaches focusing on he equiy premium belong o he consumpion-based approach, raher han he producion-based approach, as hey use he marginal rae of ineremporal subsiuion (wih or wihou a habi facor) as he pricing kernel. Kim (2003) provides a differen heoreical perspecive by using dualiy heory in Cochrane s (996) framework. Vassalou and Apedjinou (2003) empirically develop a corporae innovaion facor a scaled version of Solow s residual as considered in he presen paper showing ha his facor, when added o he marke facor, absorbs he momenum effec in cross-secional asse prices. 3

4 sae-coningen opimal reacions by firms o produciviy shocks. This kernel is shown o depend largely on facors deermining he marginal value of capial. Essenially, we ake advanage of he fac ha, in a compeiive economy wih complee financial markes, he marginal rae of ineremporal subsiuion is ied o a sochasic version of he marginal rae of ineremporal ransformaion. The former is he pricing kernel in he consumpion-based model; he laer becomes he pricing kernel in our model. The facors in he producion-based kernel are easily observable and are given unconroversially, a leas in he neoclassical radiion, by labor, capial and produciviy shocks. The assumpions in our model of a perfec compeiion, complee markes, neoclassical environmen where supply shocks in he form of produciviy shocks are imporan, brings us close o he canonical version of he Real Business Cycle (RBC) lieraure. Our resuls may be inerpreed as using alernaive evidence, semming from he cross-secion of financial reurns, on wheher produciviy shocks derived from he Solow residual are indeed a key source of macroeconomic flucuaions. If so, he produciviy shocks should be able o explain a significan fracion of cross-secional variaion in asse reurns. In our objecive of assessing how well he radiional RBC model explains he observed cross secion of asse prices we overlap wih Zhang (2005). He asks wheher a specific neoclassical model wih asymmeric capial adjusmen coss can explain he reurns of value and growh firms. The approaches are complemenary. On he one hand, our approach derives he pricing kernel in general equilibrium, endogenously generaing he appropriae risk premiums in he economy; on he oher hand, Zhang s approach allows a fully specified and calibraed general equilibrium framework, providing a more deailed look a firm-specific aspecs, endogenously 4

5 generaing risk sensiiviies. Furher differences are ha we focus on explaining he mean excess reurns of any financial asse, no only he value premium, and in our specific explanaion of he value premium conrol for size. Our approach also allows convenional evaluaion of he model s performance agains ha of alernaive asse pricing models. In addiion, he resuls are no coningen on a specific parameerizaion bu apply o a large class of RBC models. The model generaes a simple produciviy-based asse pricing equaion wih he aggregae produciviy shock as he facor and he curren aggregae capial sock and level of produciviy as condiioning variables, capuring in essence he marginal value of capial. I performs exremely well agains he leading alernaives, suggesing no only ha he basic RBC framework is consisen wih he cross-secion of asse reurns bu also ha a producion-based pricing kernel may be preferable in pracice o he consumpion-based kernel (presumably because i is easier o measure capial and produciviy han i is o measure consumpion). The srong performance of he model in explaining he reurn difference among he 25 Fama-French porfolios sored by size and value arises because he uncondiional par of he model explains much of he dispersion of mean reurns by size class while he condiional par explains much of he dispersion of mean reurns beween value and growh firms. Smaller firms have higher exposure o produciviy risk on average while, for given size, value firms are mos risky in bad saes where he produciviy risk premium is high. 2. The Model (a) Derivaion of he producion-based pricing kernel Firs consider ha in sandard general equilibrium models, including he model we use 5

6 below, for every radable asse reurn, i r + : i u c, n n ) = β E [ r u ( c, n n )], () c ( + c + + where all subscrips (excep subscrip, indicaing ime) represen parial derivaives and β represens he discoun facor. For a sandard represenaive consumer, uiliy depends on consumpion c and leisure n n (he laer variable being ofen ignored in sandard cross-secional asse pricing models). Equaion () saes ha each asse is priced by he pricing kernel (or sochasic discoun facor), m + : m β u c, n n ) / u c, n n ). (2) + = c ( + + c ( We employ he sandard perfec compeiion, complee markes general equilibrium model ha is used as he work horse in radiional Real Business Cycle models. See for insance King and Rebelo (2000) for a survey. In his model he equilibrium is Pareo Efficien and a social planner approach can be used o analyze he model properies. The social planner maximizes: V ( k + + n, k +, θ ) = Max { u( c, n n ) + β E [ V ( k, θ )]} (3) Subjec o: θ = + H ( θ, ε + ), (4) c θ. (5) = F(, n, k ) k+ The life ime uiliy of he represenaive consumer is maximized subjec o a sandard producion funcion F θ, n, k ) ( where he inpus are (per-capia) labor n and capial 6 k, and where producion depends also on an exogenous echnology/produciviy level θ. The produciviy

7 level is assumed o follow a Markov process as given by equaion (4), wihε + represening he zero-mean, whie noise produciviy shock. Per-capia consumpion is given in equaion (5) as he par of per-capia producion ha is no used as nex period s capial sock. 4 The ime-o-build feaure of he model implies ha he capial sock is chosen a period before i becomes producive. Labor can be adjused insananeously. These assumpions imply ha here are exacly wo sae variables in he model: he curren per-capia capial level k and he curren produciviy level θ. Thus, he Bellman equaion of dynamic programming is as given in equaion (3), where V, θ ) represens he ( k indirec uiliy funcion he maximal lifeime value of uiliy for he represenaive consumer as dependen on he curren sae of he economy. The firs-order condiions for he capial and labor choices are: u u c ( k + + c, n n ) = β E [ V ( k, θ )], (6) n ( c n c, n n ) = u ( c, n n ) F ( θ, k, n ). (7) The envelope condiion is V k ( k c k, θ ) = u ( c, n n ) F ( θ, n, k ) (8) Updae equaion (8) by one period and and combine wih equaion (6) o yield: 4 Since we ignore adjusmen coss he undepreciaed par of he capial sock can be viewed as added o ne producion and hen aken ou again as par of he invesmen in he capial sock for he nex period. So we do no assume full depreciaion of he capial sock. 7

8 β uc ( c +, n n + ) u ( c, n n ) c = Vk ( k+, θ+ ) EVk ( k+, θ + ) Fk ( θ +, n +, k + (9) Thus, from equaions (2) and (9) we obain a producion-based pricing kernel: m = + + / k η F ( θ, n, k ), η V k, θ ) / E [ V ( k, θ )]. (0) = + k ( + + k + + Noe ha he producion-based kernel does no exacly equal he marginal rae of ineremporal ransformaion (MRIT). In he conex wihou adjusmen coss he MRIT equals / Fk ( θ +, n+, k+ ) and differs from he pricing kernel by a facor η + wih E = η +. The reason ha MRIS MRIT alhough markes are complee is ha here is an ineremporal risk ha even under perfec risk sharing canno be avoided given ime o build, he uncerainy abou he produciviy shock has real implicaions ha are unavoidable in he aggregae. The produciviy-based pricing kernel consiss of wo componens: he η + erm accouning for he fuure impac of unexpeced produciviy shocks, and he MRIT erm accouning for he curren impac of he produciviy shock. (b) Discussion and Asse Pricing Implicaions Our conribuion is ha we examine wheher he producion-based pricing kernel, derived from a model ha has been successful in characerizing key macroeconomic momens, is also useful in pricing he cross-secion of financial asses. We focus on he case of excess reurns for wo reasons. Firs, since he kernel is in real erms i prices in real erms and reurns need o be correced for inflaion. Raher han using some inflaion measure we subrac a benchmark asse 8

9 reurn ha is also in nominal erms so ha he resuling reurn is auomaically adjused for inflaion. Second, he pricing kernel for excess reurns (and more generally zero-invesmen porfolios) can be simplified, leading o a more parsimonious facor specificaion. The pricing equaion for excess reurns is: ie E[ r + Vk ( k+, θ + ) / Fk ( θ+, n+, k+ )] = 0, for all i, () where in his excess reurns formulaion we are able o eliminae he E V ( k, θ )] erm in he [ k + + pricing kernel. I is easy o see ha k + depends on he curren capial level k and he curren produciviy levelθ only, whereas n + depends on k + and θ +. The laer, in urn, depends on θ and he shock + ε as follows from equaion (4). Thus: m E + = Vk ( k+ + k = +, θ ) / F ( θ, n, k ) M ( k, θ, ε ). (2) Equaion (2) implies ha all reurns can be explained by k, θ, and ε +. Condiional on informaion a ime, only he produciviy shock ε + maers, so his is he only facor in pricing all asses. However, he exen o which ε + maers varies over ime depends on he sae of he economy and is deermined by k and θ. We have ignored invesmen adjusmen coss in he model formulaion o emphasize ha he resuls apply for he radiional RBC model and ha adjusmen coss are no necessary. Neverheless, i is no difficul o show ha a pricing kernel such as ha in equaion (2) arises in a larger class of models, including neoclassical models wih invesmen adjusmen coss such as 9

10 Cochrane (996) and Zhang (2005). So he asse pricing model below derived from equaion (2) is consisen wih an invesmen adjusmen cos formulaion as well as he radiional RBC model. In principle, he producion-based pricing kernel in equaion (2) should price asses exacly as well as he consumpion-based pricing kernel in equaion (2). However, he consumpion-based kernel has no fared well in empirical work. The basic CCAPM of Breeden (979) performs poorly. More recen conribuions have refined he consumpion-based pricing kernel. Campbell and Cochrane (999) sugges ha lagged consumpion, represening exernal habi persisence, should be added o he pricing kernel; Leau and Ludvigson (200) add aggregae wealh as a condiioning variable; Balvers and Huang (2004) find ha real money balances affec he marginal uiliy of consumpion. Each of hese models performs beer han he basic CCAPM bu on he whole empirically falls shor of he performance of he Fama-French hree-facor model. These addiions do no even consider he effec of leisure/employmen which should also affec he marginal uiliy of consumpion, even in our simple model. Thus, applicaion of he consumpion-based pricing kernel is no sraighforward. In addiion, as poined ou clearly by Campbell (993), he necessary consumpion daa may no be ideal for esing he heory. For insance, in he saisics, durable aspecs on consumpion are no carefully separaed. This is imporan since any consumpion good ha is no fully depleed during one period should no be considered as fully consumed. Parker and Julliard (2005) deal wih his issue and effecively improve on he measuremen of curren consumpion growh by incorporaing fuure consumpion growh raes. Producion-side variables in comparison are more direcly recognizable in ha hey do no depend on subjecive uiliy funcion argumens bu insead on more sraighforwardly observable producion funcion componens. 0

11 We propose o evaluae he usefulness of he producion-based kernel empirically. While ohers have looked a producion-based asse pricing heir work is mehodologically very differen. Balvers, Cosimano, and McDonald (990) and Cechei, Lam, and Mark (990) merely replace consumpion by oupu and do no even consider cross-secional asse pricing implicaions. Cochrane (996) and Zhang (2005) impose a paricular producion-based pricing kernel exogenously. 5 (c) Empirical Implicaions Assume ha all reurns and he produciviy shock are joinly condiionally normally disribued. This assumpion is no essenial bu is sufficien o allow us o linearize he pricing kernel. From equaions () and (2), using he definiion of covariance: ie i E ( r + ) E[ M ( k, θ, ε + )] + Cov[ r +, M ( k, θ, ε + )] = 0. (3) Using Sein s Lemma (which applies here given he mulivariae normaliy assumpion): Defining: ie E[ M ε ( k, θ, ε + )] i E ( r + ) = Cov ( r +, ε + ), (4) E [ M ( k, θ, ε )] + b( k, θ ) = E[ M ε ( k, θ, ε E [ M ( k, θ, ε + + )], (5) )] and given E ( ε ) = 0 we have from equaion (4) ha + 5 Cochrane (996) explicily derives an expression for invesmen reurns and hen assumes ha a subse of he invesmen reurns can serve as he pricing kernel.

12 ie E{ r + [+ b( k, θ ) ε + ]} = 0, for all i. (6) Bu equaion (6) implies a mimicking linear pricing kernel ha prices all zero-invesmen asse porfolios equally as well as he original kernel in equaion (2): M * ( k,, ε + ) = + b( k, θ ) ε + θ, (7) sae variables: Following Cochrane (996), we make he simplifying assumpion ha b is linear in he 0 2 b( k, θ ) = b + b θ + b k, (8) which is a firs-order approximaion around he means of k, θ, ha are se o zero (meaning ha heir uncondiional mean impac is added o b 0 ). We focus empirically on he uncondiional implicaions of his condiional model. Take uncondiional expecaions in equaion (6) o obain ie E{ r + [ + b( k, θ ) ε + ]} = 0, for all i. (9) Subsiue equaion (8) ino (9) o derive he represenaion ha we es empirically. We now have he following uncondiional facors: ε +, kε +, θε +. Specifically, 0 ie ie 2 ie ) = b Cov( ε, r ) b Cov( θ ε, r ) b Cov( k ε, r ). (20) ie E ( r The covariances are proporionae o he (simple regression) beas for each of he hree facors. 2

13 The signs of he parameers in he linearized pricing kernel can be deermined by sraighforward comparaive saics analysis. Regreably, hese signs are generally ambiguous. The reason is he ypical opposing income and subsiuion effecs. For insance, he effec of a change in ε + in equaion (2) depends on how ε + affecs he marginal value of capial for he indirec lifeime uiliy of he represenaive consumer compared o how capial affecs curren producion a he margin. Boh effecs are posiive and are difficul o compare quaniaively. From equaions (2) and (2) we may insead look a how ε + affecs c +. Here he opposing effecs are more inuiive: One effec is a direc increase in producion for given inpus, leading via he income effec o higher consumpion and a lower marginal uiliy of consumpion. The second effec is he subsiuion effec of more producive invesmen, causing consumpion o fall for given producion. If he invesmen elasiciy is no oo large hen he income effec dominaes so ha higher ε + is associaed wih higher + c and lower marginal uiliy of consumpion. 6 This implies ha 0 b is negaive: excess reurns are discouned more srongly (valued less) in he face of produciviy risk because a posiive shock leads o more consumpion and a lower marginal evaluaion of reurns generaed in his case. The facor risk premium for produciviy risk hen is posiive and asses ha load heavily on he produciviy shock facor require high average reurns. The invesmen elasiciy, however, generally flucuaes wih he sae of he economy, which explains he role for he sae variables in affecing asse prices. In general he effec of he sae variables is quie complex and difficul o assess a priori. A reasonable chain of evens is ha 6 To simplify he inuiive discussion, we ignore here he effec ha leisure has on he marginal uiliy of consumpion. A posiive produciviy shock leads o increased labor demand and less leisure. This may increase or decrease he 3

14 improvemens in he sae of he economy increases in k and/or θ (discussed more precisely furher on, he sae is defined as b θ + b 2 k ), capuring he availabiliy and produciviy of resources, respecively raise k +, he capial sock for he upcoming period, so ha, ypically, he marginal uiliy of consumpion is expeced o be lower. The economy hen becomes less sensiive o ε +. In his scenario we expec in equaion (8) and uilizing equaion (7) ha 2 b, b > 0, so ha an improved sae implies ha b, θ ) is closer o zero. Thus he risk premium ( k on he produciviy facor varies over ime, wih improvemens in he sae of he economy miigaing he role of produciviy risk and lowering he risk premium. In addiion he sensiiviies of asse reurns o he produciviy shock generally are ime-varying because, depending on he paricular asse, he sae of he economy also affecs how he produciviy shock impacs paricular firms and indusries. In heory, he rue produciviy variables should ogeher explain asse reurns as well as he rue consumpion variables, even if we do no know exacly wha signs o expec for he parameers o be esimaed. For ha reason, we focus on he overall explanaory power of he model raher han he individual coefficien signs. 3. Empirical Evaluaion The model implies ha asse reurns are deermined by one sysemaic facor: he aggregae produciviy shock, wih he predeermined capial sock and level of produciviy (he Solow residual) as he condiioning variables. We discuss nex he mehodology, he daa, and he esimaion resuls for applying he model o explanaion of cross-secional reurn differences and marginal uiliy on consumpion depending on wheher leisure and consumpion are subsiues or complemens. 4

15 we provide a comparison wih oher asse pricing models in he lieraure. (a) Mehodology The mehod employed is he one-sage GMM esimaion of Hansen (982). We focus on one-sage GMM esimaion because as recommended by Alonji and Segal (996), Leau and Ludvigson (200b) and Cochrane (200), Hansen s opimal weighing marix is poorly esimaed when he cross secion of es asses is large relaive o he ime series of daa, which is he case in our sample. Jagannahan and Wang (2002) have shown ha he sochasic discoun facor (pricing kernel) approach is as efficien as he expeced reurn-bea approach and ha he sochasic discoun facor approach has higher power in deecing model misspecificaions. Furhermore, one-sage GMM esimaion enables us o focus on economically ineresing porfolios. We follow Cochrane (200) and formulae asse reurns in erms of he sochasic discoun facor and apply one-sage GMM o ge he esimaes of he sochasic discoun facor s loadings on he risk facors. Wih hese loadings, we hen compue he implied risk premia and heir significance via he dela mehod. 7 To evaluae he overall saisical significance of he model, we rely on Hansen s (982) JT saisic. To compare various leading asse pricing models we uilize several evaluaion crieria. A key diagnosic is he cross secional fi measured by adjused R-square calculaed from he acual reurns and prediced reurns. I is more appropriae han Hansen s JT saisic, if he quesion is no so much wheher he asse pricing model used is acually rue bu insead wheher he model explains a large fracion of cross-secional differences in asse reurns. Addiionally we presen he 7 The implied risk premia using one sage GMM are very close o hose obained from he Fama-MacBeh mehod. 5

16 HJ disance measure based on Hansen and Jagannahan (997) which provides a measure of how far he closes pricing kernel ha exacly prices all asse mean reurns is from he pricing kernel implied by he model. 8 We furher use he KS raio measure based on Kandel and Sambaugh (995). Balvers and Huang (2005) show ha he KS raio provides a suiable crierion for ranking muli-facor models. The inerpreaion of his measure for a paricular model is ha for any specific risk level (porfolio variance) i corresponds o he average porfolio reurn ha a mean-variance invesor would aain in pracice by opimally applying he paricular model o guide porfolio choice. (b) The daa Our main es asses are he 25 porfolios sored by marke capializaion and book-o-marke raio. The reurns for hese asses are available from Kenneh French s websie. To consruc excess reurns, we subrac he hree-monh T-bill rae. We consruc he produciviy shock following King and Rebelo (2000). 9 In he aggregae producion funcion, labor inpus have a weigh of 2/3 and capial has a share of /3. We use GDP, Labor Hours and Gross Privae Invesmen daa from he Bureau of Labor Saisics and we infer he capial sock daa following Cochrane (99, 996). 0 Afer obaining he unexplained par of GDP growh, we firs remove a 8 To obain he HJ disance and make proper inferences for he case of excess reurns, we follow Cochrane (996) in resricing he expeced sochasic discoun facor o uniy, and proceed wih esimaion of a consan. The coefficien signs and magniudes for our produciviy-based model are qualiaively similar if we suppress esimaion of he consan in he sochasic discoun facor. 9 Solow s (957) measure of he aggregae produciviy shock gives us similar asse pricing resuls. Due o daa availabiliy, alernaive (and less common) measures for produciviy shocks for example, Jorgenson and Siroh (999), Basu e al. (2000) or produciviy shocks adjused for he effec of capial uilizaion, are no considered. 0 Specifically, we inerpolae he invesmen-capial raio and hen infer he capial sock daa assuming a 0% 6

17 rend using he Hodrick-Presco filer and hen fi an auoregressive process, AR(), o obain he produciviy shock. We use capial and he produciviy level (he Solow residual) as he condiioning variables. To ensure ha hese wo series are saionary, we use he demeaned deviaion from he Hodrick-Presco rend as he condiioning variable. (Oher filering, such as removing ime rend, provides qualiaively similar resuls). We employ per-capia daa hroughou, dividing by working-age populaion. Unless oherwise menioned, he daa are from he Federal Reserve Bank of S. Louis. Our sample sars a 965Q, resriced by he limied availabiliy of daa on labor hours, and ends a 2003Q. Table presens summary saisics for he produciviy shock and he condiioning variables for his sample period. The produciviy shock has no significan auocorrelaion bu has some negaive residual cross correlaion wih he lagged capial sock. The produciviy level and he capial sock display a large firs-order auocorrelaion and negaive bu insignifican cross correlaion. Also shown are he mean excess reurns of he 25 size and book-o-marke sored es asses for our 965Q-2003Q sample period. (c) Resuls for uncondiional models Table 2 repors he resuls for he uncondiional version of our model and for hree widely cied models: he CCAPM, he CAPM and he Cochrane (996) Invesmen-based CAPM. depreciaion rae. Given a ypical capial accumulaion equaion wihou adjusmen coss: k + = ( δ )( k + I ), i can be rewrien as i + = ( I + / I ) i /( δ )( + i ) where i is he invesmen-capial raio. Using he sample average of invesmen growh we firs compue he seady sae invesmen-capial raio and hen inerpolae he capial-labor raio for all daes imposing he 0% depreciaion rae. 2 The uncondiional model is he model in equaions 8 and 9 when b and b are zero; or, more generally from equaion 2 below, when he condiional produciviy shock risk premium is uncorrelaed wih he condiional produciviy shock sensiiviies of he es asse reurns. 7

18 According o he JT value, all models are rejeced (possibly due o poor esimaion of he specral densiy marix). Figure and Table 2 show ha he cross-secional fi of he produciviy-based model is 8.%, beer han he fi for wo of he uncondiional models. No surprisingly, as known from he previous lieraure, he CCAPM and CAPM perform poorly in explaining he cross secion of hese 25 size and book-o-marke sored asses. The implied risk premia for he CCAPM and he CAPM are no significan and he cross-secional fis are very low (wih adjused R-squares of 6.2% and 4.3%) while he Invesmen-based model has a cross-secional fi of 9.8%. Figure displays he fi for all models by showing he deviaions of each es asse s reurn from ha prediced by he model. This deviaion is he one-sage GMM pricing error discouned by he expecaion of he sochasic discoun facor. If here is no pricing error, he acual reurn equals he prediced reurn so ha all plos locae on he 45-degree line. The figure shows he cross-secional fi for each uncondiional model. Among he uncondiional models he performance of he produciviy-based model is close o ha of he Invesmen-based model and below he Fama-French 3-facor model (discussed in he following). (d) Resuls for he condiional models and he Fama-French model We now consider some condiional models and he Fama-French 3-facor model. The Fama-French model can be inerpreed as a version of he Meron-model. Two recen condiional consumpion-based models are included: he Leau and Ludvigson (200) cay model and he Campbell and Cochrane (999) habi persisence model. In addiion we consider our produciviy-based condiional model using equaions (8) and (9). 8

19 Table 3 shows ha our model has he lowes JT saisic (he Leau-Ludvigson model has he second-lowes), subsanially lower han ha of he Fama-French model. Figure 2 provides he adjused R-square which is 66.2% for our model compared o 75.8% for he Fama-French model. The Leau-Ludvigson and Campbell-Cochrane models have R-squares of 52.5% and 60.8% respecively. (e) Model evaluaion This secion repors various evaluaion saisics for each model. Consider firs he HJ disance for all candidae sochasic discoun facors. According o Hansen and Jagannahan (997), he disance beween any candidae sochasic discoun facor and he rue sochasic discoun facor is given by he square roo of he minimized Generalized Mehod of Momens (GMM) objecive, wih he second momen marix of asse reurns used o weigh he momen condiions. The HJ-disance is repored in Table 4 for each of he eigh models ogeher wih p-values for he null-hypohesis ha he disance is zero following Jagannahan and Wang (996) and Hodrick and Zhang (200). All models are rejeced when 25 asses are used bu our condiional model has he second lowes disance, afer he Fama-French 3 facor model. The rejecions are no surprising since Ahn and Gadarowski (2004) poin ou ha he HJ disance causes he correc model o be rejeced oo ofen for commonly used sample sizes. As recommended by Alonji and Segal (996) and Leau and Ludvigson (200b), we can eiher reduce he cross secion of asses or compue an alernaive disance measure using he ideniy marix insead of he HJ weighing marix as a parial remedy for he small sample bias problem regarding he HJ disance. In he firs approach, we use 0 size and book-o-marke sored 9

20 asses as he alernaive esing asses so ha we have a more precise esimaor of he HJ weighing marix. 2 As shown in Table 4, for he case of 0 asses, only he habi persisence model, marginally, and boh our uncondiional and condiional models survive. In he second approach, he disance is given by he square roo of he minimized GMM objecive using he ideniy marix as he weighing marix. The disance resuls for he ideniy-weighing marix are also repored in Table 4. Our condiional model, he cay model, he habi persisence model, and he invesmen-based model have a saisically insignifican disance. Similar o wha Leau and Ludvigson (200b) poin ou, even hough he Fama-French 3-facor model has he smalles disance when 25 asses are used, he disance is saisically significan. The produciviy-based model has he smalles disance in all cases (eiher HJ weighing marix or Ideniy weighing marix) when we consider 0 asses and second-smalles disance when we consider 25 asses (behind he Fama-French 3-facor model). Finally noe ha his equal-weighed disance is analogous o he RMSE of Cochrane (996) and is consisen wih he adjused R-square obained from a Fama-MacBeh (973) regression. The hird evaluaion approach presens he KS raio of Kandel and Sambaugh (995) and Balvers and Huang (2005) for each model. This raio, up o normalizaion depending on he risk level chosen by a mean-variance porfolio invesor, represens he mean porfolio reurn obainable from opimally using he model. When 25 asses are used, our condiional model is he second bes and is performance is very close o ha of he bes model (FF3). The case of 0 asses provides sill sronger suppor for our model wih even he uncondiional version beaing he FF3 model. 2 Asses, 5, 2, 25, 3, 35, 4, 45, 5, 55 of he 25 size and book-o-marke sored asses, wih he firs digi 20

21 (f) The JT difference es In his secion, we pu wo candidae models ogeher o generae an unresriced model. We repor he JT difference es saisic on he significance of removing a se of facors from he nesed model. The same groups of 25 and 0 porfolios are used. In he firs column of Table 5 we indicae he effec of removing our condiional producion-based model facors from he combinaion model. For insance, if he CCAPM is combined wih our model, hen removing our facors significanly raises he JT value by 8.4 (p-value of.0383). In Panel A, removing our model facors causes a significan increase in he JT saisic for all bu he invesmen-based model and he habi persisence model in he case of 25 es asses. In he 0 es asses case he JT saisic increase is significan in fewer cases since mos models do reasonably well in explaining hese 0 asses by hemselves. On he oher hand, he second column in Table 5 presens he effec of removing he alernaive model and leaving ours. For none of he models heir removal provides a significan increase in he JT saisic for he 0 asse case. For he 25 asse case only he FF3 model removal increases he JT saisic significanly. Panel B of Table 5 similarly describes he impac of excluding he produciviy facor from he condiional produciviy model (column ) and he impac of excluding he condiional facors from he condiional model (column 2, yielding he uncondiional model). Removing he produciviy shock causes a significan increase in he JT saisic for boh he 25 and 0 asse cases; removing he condiional facors causes a (marginally) significan increase only for he 0 asse case. capuring size from small o large and he second digi represening he book-o-marke variable from growh o value. 2

22 4. Inerpreaion and Comparison (a) Inerpreaion Equaion (6) gives direcly an expression for condiional mean excess reurns: ie i E ( r + ) = b( k, θ ) Cov ( r +, ε + ). (2) If we consruc a zero-invesmen posiion wih uni sensiiviy o he produciviy shock, is condiional expeced reurn equaion (2) i is given as ε E r + can be inerpreed as he produciviy risk premium. Applying ε E ( r + ) = b( k, θ ) Var( ε + ), (22) where he whie noise properies of ε + imply ha he uncondiional variance of ε + equals he condiional variance. Eliminaing b, θ ) from equaions (2) and (22) gives he bea ( k ie iε ε 0 2 formulaion E ( r + ) = β E ( r + ). Recall from equaion (8) ha b( k, θ ) = b + b θ + b k. Thus, E[ b( k b 0 ε, θ )] = and he uncondiional produciviy risk premium E( r + ) is from equaion ( + 0 (22) equal o b Var ε ) I is now easier o inerpre he coefficien esimaes in Tables 2 and 3. The uncondiional produciviy-model in Table 2 generaes an esimae of 0 b ha is negaive as prediced (given moderae invesmen elasiciy) bu no significanly so. I generaes a posiive quarerly risk premium of 0.26%. The condiional produciviy model in Table 3 yields an esimae of 0 b ha is again negaive as prediced bu now significan and implies a larger uncondiional expeced 22

23 ε 0 quarerly excess reurn E ) = b Var ε ) of 0.55%. The inuiion for he posiive ( r + ( + produciviy risk premium is ha posiive (negaive) produciviy shocks coincide wih high (low) aggregae producion and accordingly low (high) marginal valuaions of reurns generaed in ha siuaion. Asses wih posiive sensiiviy o he produciviy shock generae low (high) reurns when he marginal valuaion of hese reurns is high (low) and are hus risky. From equaion (22), he ime-varying aspec of he produciviy risk premium is capured by he sae: = (, θ ) [ (, θ )] = θ + k. Defining a good sae as s > 0 and a bad s b k E b k b b2 sae as s < 0, from equaion (22) good saes are associaed wih a low risk premium and bad saes wih a high risk premium. Alernaively, from equaion (6), good saes are associaed wih imes a which he pricing kernel is less sensiive o he produciviy shock and bad saes wih imes a which he pricing kernel is more sensiive o he produciviy shock. Empirically, from Table 3 he condiioning facors produce significanly posiive b and 2 b esimaes. Hence s depends posiively on θ and k. Since θ and k boh conribue posiively o aggregae producion here is a sochasic link beween he sae and producion: a good sae is linked o high aggregae oupu and a bad sae is linked o low aggregae oupu. The posiive coefficien signs for b and 2 b suppor he perspecive discussed in he heory secion ha higher θ and each miigae he effec of he produciviy facor by raising producion and he fuure capial sock and lowering he marginal value of produciviy shocks. Taking uncondiional expecaions in equaion (2) and using he definiions k 0 2 b( k, θ ) = b + b θ + b k and = b θ b k yields s

24 ie E ( r ie ie ) = b Cov( ε, r ) Cov[ s, Cov ( ε, r )]. (23) The uncondiional mean excess reurn consiss here of an uncondiional par and a condiional par. The uncondiional par is he premium based on he produciviy risk and asse risk sensiiviy in he average sae. The condiional par arises because of correlaion beween he produciviy risk premium and an asse s sensiiviy o he produciviy shock. If an asse s produciviy risk ie exposure is high high Cov ε +, r + ) ( when he risk premium is high low s i.e. here is a negaive covariance beween he wo, hen his conribues posiively o he asse s overall riskiness and produces a posiive condiional reurn componen. Figure 3 shows he prediced mean excess reurns for he 25 es asses and heir decomposiion ino he uncondiional and condiional componens. Panel A in Table 6 displays he individual excess reurn componens for he 0 asses consising of five size and wo value classes. All asses have a posiive uncondiional excess reurn. Given he negaive value for 0 b his implies ha all en asses load posiively on produciviy risk on average. This is inuiive since a posiive produciviy shock should direcly benefi mos firms. Panel A also shows ha all asses have negaive condiional excess reurn componens. This implies from equaion (23) ha, for insance, a good sae wih a lower risk premium on ε +, is associaed wih all asses having higher sensiiviy o ε +. An explanaion for why all asses are more (less) sensiive o he produciviy shock in good (bad) saes is relaed o he abiliy of firms o respond o such shocks. When θ and k are higher, producion is higher and he price of buying (or selling) a capial good is lower. Hence, in he absence of adjusmen coss, i is easier o ake advanage of a posiive produciviy shock as 24

25 more producive capial can cheaply be acquired. When a negaive produciviy shock occurs, he lower price of capial magnifies he negaive impac since he revenue from selling unused capaciy is lower. Thus he implicaions of he produciviy shock are more exensive in a good sae, even hough consumers can bear risk more easily in his sae. In a bad sae, when θ and are lower, a posiive produciviy shock has less pervasive effecs since producion is lower and capial more expensive so i is difficul o ake advanage of he posiive shock. When he shock is negaive in his sae, he effec is miigaed because he less producive capial can be sold a a decen price. 3 k (b) Explanaion of he size and value premiums Why does our condiional produciviy-based model explain he value and size-sored porfolio means beer han an uncondiional produciviy-based model and as well as he Fama-French hree-facor model designed specifically o explain hese mean reurns? The uncondiional excess reurn componen is posiive for all es asses all have posiive exposure o he produciviy facor on average. However, here is a clear paern in ha smaller firms have considerably higher sensiiviy o he produciviy shock. Thus, he uncondiional componen does well in explaining he size effec. The condiional componen is negaive for all es asses. I represens he fac ha, for all 3 Alernaive inuiion is on based on equaion (20): asses ha load posiively on θ ε + or k ε have lower risk + (for given loading on ε ) and hence have lower average reurns. The reason is ha, since in a good sae he price of + risk is lower, wo asses wih idenical average sensiiviies o ε, he one asse ha has he higher sensiiviy o + ε + when he sae is good (ha is, loads posiively on θ ε + or kε ) has is highes sensiiviy when he price of risk is + lowes and herefore has a lower average reurn. 25

26 ie asses, Cov ε +, r + ) he excess reurn s sensiiviy o he produciviy shock is higher when ( he sae of he economy b θ + b 2 k is beer. Bu a beer sae implies a smaller risk premium on he produciviy facor, so expeced excess reurns are lower as equaion (9) implies. The key observaion in Figure 3 is ha he reducion in he mean excess reurns based on he condiional componen is larges for growh firms. Therefore, he condiional componen does well in explaining he value premium: growh firms are on average abou as sensiive o produciviy shocks as are value firms, bu heir sensiiviy is high for saes in which he price of risk is low and consequenly hey require a lower expeced reurn on average han do value firms. Table 6 provides addiional deail for his explanaion of he value and size premiums. Panel A shows numerically wha may also be apparen from Figure 3 ha he explanaion for he size effec is due o smaller firms having higher sensiiviy o produciviy shocks on average; alhough here is also a smaller condiional componen. The explanaion for he value premium is purely based on he condiional effec which arises because, compared o value firms, growh firms have heir highes risk exposure when risk premiums are lower or negaive, hus requiring lower reurns on average. For each of he size classes he uncondiional reurn componen differences beween value and growh firms are no significan; bu in conras he condiional reurn componen differences beween value and growh firms are significan for each size class. To check he condiional explanaion for he value premium, in Panel B we consider he produciviy beas he loadings on he produciviy shock for he value and growh firms in he five size classes. All firms have higher beas in he good sae when he price of risk is low, as is consisen wih he negaive condiional reurn componens in Panel A. For each size class, growh firms are significanly riskier han value firms in good saes when he price of risk is lower or 26

27 negaive; value firms are significanly riskier in bad saes when he price of risk is higher. This is consisen wih he condiional reurn componen for he growh firms being more negaive han ha of value firms, and, given he similar uncondiional reurn componens, wih he reurns of value firms being higher on average han he reurns of growh firms. The above explanaions for he size and value premiums are no complee unless we can also explain why small firms have higher exposure o produciviy shocks on average and why he exposure o produciviy shocks changes more for growh firms as he sae changes. Here our macro-based model is a a disadvanage relaive o he recen conribuions of Gomes, Kogan, and Zhang (2003), Zhang (2005), and ohers who provide specific models of how facor sensiiviies change over ime for classes of firms. We can speculae as o plausible causes for he differences in facor exposures ha may explain he size and value premiums in our model bu he model is no designed o explain hese differences. A possible reason for why small firms have higher produciviy-facor loadings may be because small firms end o be of more recen vinage. They herefore may rely more on recen echnology or may be more dependen on new opporuniies and looking for niches; each of which are sensiive o produciviy/echnology flucuaions. Growh firms are riskier in good saes, s > 0. This explains he value premium bu he model does no ell us why growh firms are riskier in good saes. A plausible explanaion is relaed o he observaion ha he good sae implies a lower price of capial (boh higherθ and k raise k +, lowering he price of capial in he period ha he produciviy shock occurs). For all firms, invesmen is more sensiive o produciviy shocks if he price of capial is lower (as is confirmed in Table 6, panel B). Bu he growh firms, which are reasonably characerized by boh 27

28 higher and more sensiive invesmen, in a beer sae benefi more from a posiive produciviy shock which renders he invesmen more producive a a ime when i is also cheaper; or suffer more from a negaive produciviy shock making invesmen less producive. 4 In a beer sae value firms benefi less from a posiive produciviy shock since hey can ake less advanage of he low price of capial; bu hey are similarly no affeced as much when a negaive shock occurs. Zhang (2005) emphasizes ha he value premium exiss because value is riskier han growh in bad imes when he price of risk is high and in his sense his accoun coincides wih ours. His ineresing explanaion is ha, due o asymmeric coss of adjusmen, in bad imes value firms canno dispose of heir excess capial wihou considerable cos. This explanaion clashes wih our empirical resuls (Panel B of Table 6) ha boh value firms and growh firms are less risky in bad imes; and ha growh firms are he riskies in good imes. The apparen conflic likely arises because he sae is defined differenly in our work and because Zhang s pricing kernel does no include capial. His exclusion of capial is of noe since, in our findings, capial accouns quaniaively for a subsanially (facor en) larger par of he condiional reurn componen han does he produciviy level. (c) Alernaive ses of es asses and managed porfolios While we discuss he performance of our model in explaining he size and book-o-marke sored porfolios, he size and value premium puzzles are no our focus. We would like o argue ha he produciviy-based model should do well in explaining oher ses of es asses as well. We 4 I is more difficul o explain why he beas of growh firms urn negaive in bad saes, as is shown in Table 6, Panel B. The firs-order approximaion in equaion (8) may be responsible as i leads o quaniaively larger errors a he exremes. 28

29 employ a represenaive se of oher groupings of U.S. equiies based on hose available from Kenneh French s web sie. Consider firs he 0 porfolios sored by size and book-o-marke raio for which we discussed some resuls earlier. I is imporan o check more specifically he resuls for his grouping wih he same size and book-o-marke variables o sor porfolios because i conains fewer asses so ha he GMM esimaion mehod may be more reliable. As Table 7 shows, he resuls now are even sronger in favor of our model. An alernaive soring crierion considers grouping by indusry. We look a 48 porfolios and once more a 0 porfolio case sored by indusry characerisics. The condiional produciviy-based model is again comparable o Fama-French 3 facor model, he Leau and Ludvigson cay model and he consumpion-based CAPM wih habi persisence. We furher examine 0 porfolios sored by dividend-price raio. Resuls are again similar and confirm our conclusion ha he producion-based perspecive is a leas compeiive wih exising approach based on he consumpion-based perspecive and wih he Fama-French model. Lasly, we scale he reurns of, respecively, 0 and 6 size and value sored porfolios by sandard condiioning variables: he erm premium and he dividend-price raio. Cochrane (200) poins ou ha such scaling corresponds o evaluaing he reurns of porfolios acively managed o exploi he expeced reurn responses o changes in he condiioning variables. As Table 7 shows he condiional produciviy-based model again performs well. Wih 0 asses and wo condiioning variables, we have a oal of 30 managed asses and we achieve an R-square of 77.7% and wih 6 asses we have 8 managed asses in oal and an R-square of 83.2%, boh exceed he performance of he Fama-French 3-facor model. 29

30 5. Conclusion We sudy he cross secion of asse reurns from he producion side of he economy and argue ha asse reurns are deermined by a one facor model wih wo condiioning variables. The facor is he aggregae produciviy shock, he impac of which is condiional on he sae of he economy. In he conex of our model a sandard real business cycle model he sae of he economy is fully characerized by he capial sock and he curren level of produciviy (he Solow residual). The resuls srongly suppor our model compared o exising heoreical models in he lieraure and is a leas compeiive empirically wih he Fama-French hree-facor model. Thus, he cross-secion of asse prices provides suppor for he canonical RBC model from a differen perspecive. The model provides a beer inegraion beween finance and macroeconomics. Furhermore, i appears ha he speculaed improved measuremen from using producion variables insead of consumpion variables indeed provides a beer explanaion of he cross-secion of asse prices. The produciviy-based model does well across a variey of differen es asses. The explanaions for he mean reurns of he challenging 25 Fama-French es asses sored by size and value is ha small firms have higher mean reurns han big firms mosly because heir average sensiiviies o produciviy risk are higher; value firms have higher mean reurns han growh firms, in spie of having approximaely he same average sensiiviy o produciviy risk, because he risk premiums and risk sensiiviies vary wih he capial sock and produciviy level: As he sae variables, capial sock and/or produciviy level, increase, he risk premium falls while risk 30

31 sensiiviies o he produciviy shock increase. Bu he risk sensiiviies of he growh firms increase more rapidly wih he sae variables han hose of he value firms so ha growh firms have heir highes risk when he produciviy risk premium is low or negaive, implying lower reurns on average. The reason ha growh firms are more sensiive o changes in he sae may be ha he price of capial varies inversely wih he sae. Thus, growh firm values vary more dramaically wih produciviy shocks in a good sae, as posiive shocks are complemened wih a low price of capial enabling hese firms o benefi from he posiive shocks cheaply. 3

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33 Cochrane, John H., 200, Asse Pricing, Princeon Universiy Press, New Jersey. Consaninides, George, 990, Habi formaion: A Resoluion of he Equiy Premium Puzzle, Journal of Poliical Economy 98, Consaninides, George M., and Darrell Duffie, 996, Asse pricing wih heerogeneous consumers, Journal of Poliical Economy 04, 29{240. De Bond, Werner F. M. and Richare H. Thaler, 987 Furher Evidence on Invesor Overreacion and Sock Marke Seasonaliy." Journal of Finance 42, Fama, Eugene F., and Kenneh R. French, 992, The Cross-Secion of Expeced Sock Reurns, Journal of Finance 47, Fama, Eugene F., and Kenneh R. French, 993, Common risk facors in he reurns on socks and bonds, Journal of Financial Economics 33, Fama, Eugene F., and Kenneh R. French, 996, Mulifacor explanaions of asse pricing anomalies, Journal of Finance 5, Fama, E. F. and J. D. MacBeh, 973, Risk Reurn and Equilibrium: Empirical Tess, Journal of Poliical Economy 7, Ferson E. Wayne, Sergei Sarkissian and Timohy T. Simin, 2003, Spurious Regressions in Financial Economics? Journal of Finance 58, Gomes, Joao, Leonid Kogan, and Lu Zhang, 2003, Equilibrium Cross Secion of Reurns, Journal of Poliical Economy, Goval Ami, and Ivo Welch, 2004, A comprehensive Look a he Empirical Performance of Equiy Premium Predicion, NBER working paper Hansen, Lars Peer, 982, Large Sample Properies of Generalized Mehod of Momens Esimaion, Economerica 50, Hansen, Lars Peer, and Ravi Jagannahan, 997, Assessing Specificaion Errors in Sochasic Discoun Facor Models, Journal of Finance 52, Hansen, Lars Peer, and Kenneh J. Singleon, 982, Generalized Insrumenal Variables Esimaion of Nonlinear Raional Expecaions Models, Economerica 50, Hodrick, R. and X. Zhang (200). "Evaluaing he Specificaion Errors of Asse Pricing Models." Journal of Financial Economics 62,

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36 Table. Summary saisics on he produciviy level θ, capial level k, and produciviy shock ε. The daa are from 965Q o 2003Q. Trends are removed using he Hodrick-Presco filer wih 600 as smoohing parameer. The figure shows he excess reurn of 25 porfolios sored by size and book o marke raio obained from Kenneh French s websie. sands for he smalles size and smalles book-o-marke quinile; 5 represens he larges size and book-o-marke quinile. Summary Saisics θ k ε Sandard Deviaion Cross-Correlaion θ k ε Auocorrelaion lag lags lags lags Mean Reurn of 25 Asses 0.04 Acual Quarerly Reurn Value Size 2 36

37 Table 2. GMM one-sage esimaes for he pricing kernel loadings on he sysemaic facors (he b i parameers), he implied risk premiums and heir -values, Hansen s JT saisics, and implied R-squares. Models -4 (PROD, CCAPM, CAPM and INV) are, respecively, our uncondiional produciviy-based asse pricing model, he CCAPM, he CAPM and Cochrane s (996) invesmen-based ass pricing model. The -saisics are based on Newey-Wes esimaors using 5 lags. The daa are from 965Q o 2003Q. PROD Consan ε b JT saisics p-value 0.00% Risk Premium % R-Square 8.% -saisics.89 CCAPM Consan C b JT.7 -saisics p-value 0.00% Risk Premium % R-Square 6.2% -saisics CAPM Consan Mk b JT saisics p-value 0.00% Risk Premium % R-Square 4.3% -saisics INV Consan Inv Non-Inv b JT saisics p-value 0.00% Risk Premium % R-Square 9.8% -saisics

38 Table 3. GMM one-sage esimaes for he pricing kernel s loadings on he sysemaic facors (he b i parameers), he implied risk premiums and heir -values, Hansen s JT saisics, and implied R-squares. Models 5-8 (PROD-θk; FF3; CCAPM-CAY; CCAPM-C) are, respecively, our produciviy-based model condiioned on he Solow residual and capial wih rend removed by a Hodrick-Presco filer; he Fama and French (996) 3-facor model; he Leau and Ludvigson (200) condiional (cay as condiioning variable) Consumpion CAPM, and he Consumpion CAPM wih habi persisence. The -saisics are based on Newey-Wes esimaors using 5 lags. The daa are from 965Q o 2003Q. PROD-θk Consan ε ε.θ ε.k b JT saisics p-value.34% Risk Premium % R-Square 66.2% -saisics FF3 Consan Mk Smb Hml b JT saisics p-value 0.00% Risk Premium % R-Square 75.8% -saisics CCAPM-CAY Consan cay C C.cay b JT saisics p-value 0.2% Risk Premium % R-Square 52.5% -saisics CCAPM-C Consan C(-) C() C(). C(-) b JT saisics p-value 0.00% Risk Premium % R-Square 60.8% -saisics

39 Table 4. GMM disance ess using he inverse of he second momen marix of asse reurns (he HJ-marix) and he ideniy marix (he I-marix) as he weighing marices for Models -8. The daa are from 965Q o 2003Q. The p-values for he weighed χ 2 saisic of Jaganahan and Wang (996) o es for he significance of he disance measure (for boh weighing marices) are based on 0,000 simulaions. The es asses are he 25 porfolios sored by size and he book-o-marke raio from Kenneh French s websie and a group of 0 porfolios ha is a subse of he above-menioned 25 asses (for each size quinile, we pick he porfolio wih he lowes book-o-marke raio and highes book-o-marke raio). The boom rows presen he generalized KS raios of Balvers and Huang (2005) o represen he mean porfolio reurn ha maximally could be obained from using each misspecified model. HJ Weighing Marix Ideniy Weighing Marix KS Raio 25 Asses 0 Asses 25 Asses 0 Asses 25 Asses 0 Asses HJ-dis. p-value HJ-dis. p-value HJ-dis. p-value HJ-dis. p-value PROD % % % % CCAPM % % % % CAPM % % % % INV % % % % PROD-θk % % % % FF % % % % CCAPM-CAY % % % % CCAPM-C % % % %

40 Table 5. In Panel A we apply he JT difference es o compare our condiional produciviy-based model (PROD-θk, wih he Solow Residual and capial as condiioning variables) o he following alernaives: CCAPM, MKT, INV, FF3, CCAPM-C and CCAPM-CAY. For boh panels he numbers lised are he JT difference saisic (Diff-JT) and is p-value for he null hypohesis ha he difference in comparing he unresriced model conaining he facors of wo models agains he resriced version conaining he facors of one model is zero. All condiioning variables are Hodrick-Presco filered. The firs column excludes he facors from he condiional produciviy-based model; he second column excludes he facors from he model indicaed by ha row. In Panel B we apply he JT difference es o compare he condiional produciviy-based model (PROD-θk) o boh he uncondiional model (PROD) and he condiioning variables by hemselves (STATE). Panel A JT 25 Asses 0 Asses Excluding: PROD-θk Alernaive PROD-θk Alernaive CCAPM p-value 3.83% 89.59% 5.92% 8.92% CAPM p-value 0.9% 37.29% 0.50% 99.58% INV p-value 75.55% 39.8% 20.05% 8.64% FF p-value 0.00% 0.35% 84.97% 98.00% CCAPM-C p-value 68.74% 43.9% 6.03% 96.96% CCAPM-CAY p-value 0.34% 23.73% 58.08% 84.73% Panel B JT 25 Asses 0 Asses Excluding: PROD Sae PROD Sae PROD-θk p-value 0.56% 6.47% 0.06% 7.8% 40

41 2 Table 6. The sae of he economy is measured by s = b θ + b k. We have a good (bad) sae when s > 0 ( < 0). The price of risk is low (high) in a good (bad) sae. Panel A shows he uncondiional and condiional excess reurn componens for value and growh and value minus growh porfolios for each size quinile of he 25 porfolios consruced by size and he book-o-marke raio. Panel B displays he produciviy beas on he same porfolios condiioned on he good and bad saes. Panel A: Reurn Decomposiion Uncondiional Reurn Componen Condiional Reurn Componen Value Growh HML Value Growh HML Small 4.95% 4.93% 0.02% -0.33% -2.69% 2.36% -value Semi-Small 4.07% 4.44% -0.37% -0.49% -2.50% 2.0% -value Medium 3.80% 3.92% -0.2% -0.48% -2.39%.9% -value Semi-Big 3.63% 3.43% 0.9% -0.69% -.88%.9% -value Big 2.67% 2.82% -0.5% -0.30% -.42%.2% -value Panel B: Condiional Beas Good Sae Bad Sae Value Growh HML Value Growh HML Small value Semi-Small value Medium value Semi-Big value Big value

42 Table 7. Cross-secional R-squares for all eigh models, using differen es asses. 0BEME represens 0 porfolios from he 25 porfolios sored by size and book-o-marke raio: we pick hose wih he highes and he lowes book-o-marke raio for each size quinile. 48IND indicaes 48 porfolios sored by indusry characerisics; 0IND indicaes 0 porfolios sored by indusry characerisics; 0DP indicaes 0 porfolios sored by dividend price raio. Using 6 porfolios sored by size and book-o-marke raio, 2 managed porfolios are consruced employing he once-lagged erm premium and dividend yield as he condiioning variables. This gives a oal of 8 porfolio reurns (8Managed). A similar approach using he 0BEME porfolios generaes a oal of 30 porfolio reurns (30Managed). All daa from 965Q o 2003Q are obained from Kenneh French s websie. 0 BM 48 Indusry 0 Indusry 0 DP 30 Managed 8 Managed PROD 4.2% 2.2% 0.3% 20.4% 3.% 35.3% CCAPM 32.8% 2.5% 9.% 28.5%.% 0.2% CAPM 25.2% 3.0% 0.2% 23.9% 4.9% 0.5% INV 9.0% 6.5% 23.5% 49.9% 3.5% 33.5% PROD-KS 86.4% 5.8% 35.6% 45.3% 77.7% 83.2% FF3 73.9% 9.5% 9.0% 26.5% 7.9% 80.7% CCAPM-CAY 55.0% 6.4% 28.6% 63.4% 38.6% 39.4% CCAPM-C 7.5% 5.4% 3.5% 28.6% 57.% 68.8% 42

43 Figure. Acual reurns and prediced reurns for Models -4 (PROD, CCAPM, CAPM and INV) which are, respecively, he uncondiional produciviy-based asse pricing model, he CCAPM, he CAPM and Cochrane s (996) invesmen-based ass pricing model. See Table for model deails. The wo-digi numbers denoe he Fama-French 25 porfolios. The firs digi refers o he size quinile (from, small, o 5, large) and he second digi refers o he book-o-marke quinile (from, low book-o-marke, o 5, high book-o-marke). 5 PROD 5 CCAPM 4 R2: 8.% 4 R-2: 6.2% prediced excess reurn % prediced excess reurn % acual excess reurn % acual excess reurn % 5 CAPM 5 INV 4 R-2: 4.3% 4 R-2: 9.8% prediced excess reurn % prediced excess reurn % acual excess reurn % acual excess reurn % 43

44 Figure 2. Acual reurns and prediced reurns for Models 5-8 (PROD-θk; FF3; CCAPM-CAY; CCAPM-C) are, respecively, our produciviy-based model condiioned on he Solow residual and capial; he Fama and French (996) 3-facor model; he Leau and Ludvigson (200) condiional (cay as condiioning variable) Consumpion CAPM, and he Consumpion CAPM wih habi persisence. See Table 2 for model deails. The wo-digi numbers denoe he Fama-French 25 porfolios. The firs digi refers o he size quinile (from, small, o 5, large) and he second digi refers o he book-o-marke quinile (from, low book-o-marke, o 5, high book-o-marke). 5 PROD-θk 5 FF3 4 R-2: 66.2% 4 R-2: 75.8% prediced excess reurn % prediced excess reurn % acual excess reurn % acual excess reurn % 5 CCAPM-CAY 5 CCAPM-C 4 R-2: 52.5% 4 R-2: 60.8% prediced excess reurn % prediced excess reurn % acual excess reurn % acual excess reurn % 44

45 Figure 3. Decomposiion of reurns ino heir uncondiional upper lef panel and (he negaive of) condiional risk premium upper righ panel componens for he 25 porfolios sored by size and book-o-marke raio. The lower lef panel shows he sum of he uncondiional and condiional reurn componens and he lower righ panel shows he acual mean reurns of he 25 porfolios. 45