Preference shocks in an RBC model with intangible capital

Transcription

1 Preference shocks in an RBC model wih inangible capial cr ip Kashif Zaheer Malik, Syed Zahid Ali, Ali Imiaz and Ammar Afab Acceped Manuscrip Version us This is he unedied version of he aricle as i appeared upon accepance by he journal. A final edied version of he aricle in he journal forma will be made available soon. M an As a service o auhors and researchers we publish his version of he acceped manuscrip (AM) as soon as possible afer accepance. Copyediing, ypeseing, and review of he resuling proof will be underaken on his manuscrip before final publicaion of he Version of Record (VoR). Please noe ha during producion and pre-press, errors may be discovered which could affec he conen. ed 2019 The Auhor(s). This open access aricle is disribued under a Creaive Commons Aribuion (CC-BY) 4.0 license. ce p Publisher: Cogen OA Journal: Cogen Economics & Finance Ac DOI: hp://dx.doi.org/ /

2 Preference shocks in an RBC model wih inangible capial 3- Ali Imiaz, PhD Associae Professor Bahria Universiy, Islamabad. Member Board of direcors CELL Foundaion Maasrich Universiy The Neherlands. 2-Syed Zahid Ali, PhD Professor, Deparmen of Economics, Lahore Universiy of Managemen Sciences, 4-Ammar Afab, PhD Texas A & M Universiy College Saion, Texas, USA. ammarafab@amu.edu an us cr ip 1- Kashif Zaheer Malik, PhD Assisan Professor Deparmen of Economics Lahore Universiy of Managemen Sciences kashif.malik@lums.edu.pk M Absrac In his paper we develop and simulae an RBC model ha includes inangible capial as a hird ed facor of producion. We sudy he effecs of inra-emporal preference shocks on economic aggregaes, employing he undeermined coefficien mehod of Chrisiano (2002) o solve he ce p model. Impulse response funcions o preference shocks reveal ha demand-side shocks are imporan in explaining he variaions in macroeconomic aggregaes. Key Words: Inangible Capial, Real Business Cycle, Preference/Demand Shocks Ac JEL Classificaion: E32, E37 1. Inroducion Pos-war U.S. daa suggess ha consumpion growh Granger-causes gross domesic produc (GDP) bu no vice versa, and ha GDP in urn Granger-causes business invesmen growh 2

3 bu no he oher way around (Wen, 2007). This resul suggess ha consumpion conains beer informaion abou he sources of shocks and ha oupu conains beer informaion han invesmen abou he sources of shocks. Sandard RBC models canno be used o explain hese causal relaionships since hey are based on he assumpion ha mos aggregae economic flucuaions are due o echnology (supply-side) shocks. 1 The seminal work of Kydland and Presco (1982) documened a key role for produciviy shocks in mimicking he majoriy of variaions in economic aggregaes such as oupu, consumpion, hours worked, real wages, and average produciviy. Their main findings are ha (i) invesmen is almos hree imes more volaile han oupu; (ii) nondurable consumpion is less volaile han oupu; (iii) hours worked and oupu are posiively correlaed; (iv) almos all macroeconomic variables are posiively correlaed wih oupu; and (v) movemens in macroeconomic variables show persisency (Rebelo, 2005). Kydland and Presco s (1982) resuls are suppored by Cooley and Presco (1995), Presco (1986), and King and Rebelo (1999). However, he asserion ha supply-side shocks are he main sources of economic flucuaions are challenged by Keynesian economiss. The Keynesian school argues ha economic flucuaions are a resul of demand-side shocks (Gali and Rabanal, 2005). For example, Gali s (1999) empirical sudy, which is based on an SVAR model esimaion wih shor-erm and long-erm resricions, shows ha condiional on a echnology shock, here exiss a negaive correlaion beween hours worked and produciviy and ha he Acceped Manuscrip conribuion of produciviy shocks in explaining variaions in economic aggregaes are quie weak. Gali and Rabanal (2004) argue ha he effecs of produciviy shocks on economic aggregaes are coningen upon he degree of price flexibiliy and he sysemaic response of moneary policy o he shock. They argue ha if he cenral bank accommodaes he produciviy 1 See Plosser (1989) for a comprehensive discussion of RBC models and heory. 3

4 shock by furher reducing he ineres rae, hen only hours worked will increase. In shor, hey argue ha a mere supply-side shock canno explain he observed daa. Subsequen work, such as Gali and Rabanal (2005) and Basu e al. (2006), suppors hese findings 2. Baxer and King (1991) also highligh he imporance of he demand-side shocks. Like Solow (1957), hey observe ha facor inpu growh is insufficien o explain he growh in oupu, and argue ha posiive exernaliies and increasing reurns o scale resolve his puzzle. They show ha a model wih increasing reurns o scale, which is driven by measured demandside shocks, mimics he acual flucuaions of business cycles in he U.S. They also find ha when preference shocks are combined wih produciviy shocks, boh he increasing reurns and he consan reurns models show daa consisen weak correlaion beween hours-worked and wages. Using sandard RBC models driven by demand shocks, Wen (2007) aemps o esablish a causal relaionship beween consumpion and oupu 3 and beween oupu and invesmen by assuming ha: (i) employmen and oupu canno respond o demand shocks immediaely; and (ii) invesmen canno immediaely respond o demand shocks. Wen (2007) surprisingly finds ha consumpion growh negaively causes oupu growh and also ha oupu growh negaively causes invesmen growh. Wen (2007) miigaes his problem by adding o he model capaciy uilizaion and mild producion exernaliies, and shows ha oupu growh Granger causes invesmen, bu fails o esablish he resul ha consumpion Granger causes oupu. Acceped Manuscrip Nakamura (2009), while quesioning he imporance of produciviy shocks, shows ha 2 Plosser (1989, p. 57) argued ha i is no always clear ha which shock should be classified as demand-side shock and which one is supply-side shock, since mos of he shocks generally affec demand and supply-side of he model a he same ime. 3 Cochrane (1994) argues ha since changes in consumpion predic changes in oupu, consumpion shocks are imporan o sudy business cycles. 4

5 moneary, cos-push, and preference shocks are also capable of replicaing business cycle flucuaions. Bencivenga (1992) assumes no ineremporal subsiuion and full depreciaion of he capial sock, and documens ha preference shocks are an imporan source of variaion in economic aggregaes.4 In paricular, she finds ha hours are more volaile han produciviy and ha consumpion is more volaile han oupu. She also finds a weak negaive correlaion beween working hours and produciviy. In his paper, we develop an RBC model wih inangible capial o invesigae he effec of preference shock (such as preference shocks o leisure demand) on economic aggregaes. To he bes of our knowledge, our work unique in analysing he effec of demand shocks in an RBC model wih inangible capial. We inroduce inangible capial in our model as a hird inpu in he producion funcion, along wih labor and physical capial. We assume hroughou ha, jus like any oher good, inangible capial is produced by means of labor and capial. Limied by muliple consrains, we assume hroughou ha firms always face a rade-off beween curren producion and fuure producion whenever hey increase he producion of inangible capial. Allocaing more labor and capial for curren producion means higher oupu and higher profis in he curren ime period. In conras, if he firm chooses o inves in he creaion of inangible capial, i will earn more profi in he fuure bu a he cos of low oupu and low profi in he curren ime period. Acceped Manuscrip Our model is a sandard RBC model wih he excepion of he inclusion of inangible capial in he producion funcion. We assume no governmen and ha all agens operae in compeiive 4 Bencivenga (1992) argues ha preference shocks may be inerpreed as resuling from shocks o household producion or from changes in relaive prices. 5

6 markes. To simplify our algebra and given he main focus of our paper, we assume ha all agens are homogenous, which helps us o develop our model using a single represenaive household and a single represenaive firm. The inclusion of inangible capial in he model is expeced o ake ino accoun crowding ou effecs, which generally occur in he even of demand-side shocks such as changes in governmen expendiure and exogenous shifs in consumpion. An increase in aggregae demand normally increases he real rae of ineres, which -- by crowding ou privae invesmen -- lessens he impac of he shock on key economic aggregaes. Many auhors in he recen pas aemped o overcome his problem by assuming habi persisen in consumpion and increasing reurns o scale in producion (see for example, Baxer and King, 1991 and Benhabib and Wen, 2004). We aemped in his paper o highligh he role of inangible capial in maerializing he demand-side shock effecs on real variables wihou appealing o consumpion persisence and increasing reurns o scale assumpions. Using our inangible capial augmened RBC model, we sudy impulse response funcions of macroeconomic aggregaes o a preference shock. We find ha demand-side shocks are imporan because hey can cause variaions in macroeconomic aggregaes. In paricular, we find ha a preference shock causes variaions in consumpion ha leads o variaions boh in oupu and invesmens. The findings of our sudy are consisen wih poswar U.S. daa. The res of he paper is organized as follows. The second secion discusses he model and is soluion and calibraion. The hird secion discusses resuls and he final secion concludes. Acceped Manuscrip 2. Model 6

7 In his secion we develop our model, which is releaed o ha of Malik e al. (2014). The novely of our model is in he inclusion of inangible capial in he producion funcion. We assume hroughou ha he economy comprises of wo ypes of agens: households and firms. We furher assume ha all agens are homogenous and operae in a compeiive environmen. As is he case in many sandard RBC models, we assume no governmen and ha agens form expecaions raionally. 2.1 Households The economy is populaed by a represenaive household ; all households are idenical, boh ex ane and ex pos. We assume ha agens live infiniely and ha a represenaive household wishes o maximize he following sum of presen and fuure discouned uiliy, derived from he consumpion of good and leisure: where β is a discoun rae, B measures preferences shocks. max Ε Σ β U( C,1 N, B ) (1) 0 = 0 C measures curren consumpion, N measures labor supply and We assume ha preferences shock follows a firs-order auoregressive process wih an iid error erm ( ε b ) and inerial coefficien 0< ρ b < 1: ln B Acceped Manuscrip b -1 b = ρ ln B + ε (2) To proceed furher and o derive resuls hrough model calibraions, we assume ha each labor endowed wih one uni of labor supply and her preferences can be mapped wih he following funcional form of he uiliy funcion: 7

8 UC (, N) = ln C+ Bη(1 N) (3) Where he parameer η is he relaive weigh of leisure ( L = 1 N ) in he consumer uiliy funcion. We may use equaion (3) o show ha BηC is he marginal rae of subsiuion beween consumpion and leisure. 5 In each period, he represenaive household has hree sources of income: (i) labor income ( wn ) afer supplying N number of hours a he real wage rae w ; (ii) renal income ( rk ), where r is renal rae and K is physical capial; and (iii) profi income π. In each period he household consumes ( C ) and invess ( I ) in physical capial. Using he above informaion, we may wrie he represenaive household budge consrain as: C + I = wn + rk + π (4) We furher assume ha invesmen I augmens he capial sock over he ime as follows: K = 1 I + (1 + δ) K (5) where δ (0,1) is he rae of depreciaion of physical capial. To rule ou Ponzi schemes, we assume a suiable ransversaliy condiion. Equaions (4) and (5) can be combined o yield a single budge consrain: C+ K+ 1 = wn + rk + (1 δ) K+ π (6) Acceped Manuscrip 5 dc From (3) i can be shown ha = BηC < 0 i.e. o increase one uni of leisure he household is willing o forgo dl an amoun Bη C in consumpion. The reader may noe here ha in case of preference shocks, he consumer is willing o sacrifice more consumpion o ge one uni of exra leisure. 8

9 Using equaions (3) and (6) he Bellman equaion for he household uiliy maximizaion problem can be wrien as follows 6 : Vk E c B N EVk ' ( ) = max ln + η(1 ) + β ( ) cnk,, ' s.. C + K' = w N + rk + (1 δ) K + π Which yields he following Euler equaions commonly known as firs order condiions of uiliy maximizaion when he household chooses C, N,and K + 1, : 1 C Bη 1 N Acceped Manuscrip = λ (7) = wλ (8) β EV ( k ') = λ (9) V = (1 + r δ) λ (10) We can combine equaions (7) o (10) o yield he following equaions: k CBη w = (11) 1 N C 1 = βe ' + (1 C' ( r δ) Equaion (11) and (12) can be solved o deermine he ime pah of consumpion and labor supply (or leisure) which are subjec o shif as B, δ, and β changes. (12) 2.2 Firms 6 ' Where K = K + 1 9

10 We assume ha o produce he final good ( Y) he represenaive firm hires labor ( N ), rens physical capial ( K ), uses inangible capial ( Z ) and operaes under condiions of perfec compeiion. The firm s producion funcion is defined as follows, where we assume a consan reurns o scale echnology: Y e ( A s N ) ( s K ) Z = (13) ln θ φ 1 φ τ τ N K In equaion (13) inangible capial is added as a hird facor of producion ha is produced wih he help of labor and physical capial. Accordingly, s N and sk denoe respecively he fracion of labor and physical capial which he firm allocaes o produce he final good ( Y ). The remainder of he labor and physical capial, (1 S N ) and (1 SK ) respecively, is used by he firm o produce inangible capial ( Z ). In equaion (13) we also model wo shocks: a permanen echnology shock ( A ) and a ransiory produciviy shock ( θ ). The dynamics of boh hese shocks are defined by equaions (14) and (15) respecively, where parameer ρ and ρ θ measure persisen in he shocks and he parameer v a measures a drif process: a a 1 a ln A = ν + ρ ln A + ε (14) ln θ ρ ln θ ε + 1 θ θ, + 1 Acceped Manuscrip a = + (15) The sock of inangible capial available in period +1 depends on he amouns of labor and physical capial devoed o he producion of inangible capial in he curren period and as well as he sock of inangible capial produced in period 1 for period ( Z ): μ 1 μ 1 ω ω + 1 = ( (1 N) ) ((1 K) ) Z A s N s K Z (16) 10

11 Following Bankard s (2000) organizaional forgeing idea, we assume ha knowledge depreciaes wih ime as he economic environmen goes hrough various ransformaions. The parameer ω (0,1) capures he conribuion of pas inangible capial, which he decays he furher back in ime i was creaed. ω = 1 implies ha inangible capial is consan over ime. In conras, ω = 0 implies ha inangible capial decays fully in he curren period and makes no conribuion o inangible capial in fuure periods. The produciviy shock A, which appears boh in equaion (13) and equaion (16), ensures a balanced growh pah where increases in labor produciviy over ime occur in boh he final good and inangible capial good secors. I can be shown ha μ(1 ω) measures he elasiciy of labor hours ha are used in he curren period o + 1 creae inangible capial wih respec o inangible capial in he nex period Acceped Manuscrip dln Z dln N. In he case of μ = 1, physical capial is no used in he creaion of inangible capial. On he oher hand, μ = 0 implies ha he firm allocaes only labor o producion of he final good( Y ). 2.3 Normalizaion In order o solve he model for he seady sae and o sudy he opimum choices of represenaive agens we normalize all he variables of he model o a permanen echnology shock ( A ) such ha he ransformed sysem does no exhibi growh 7. Our ransformed variable 7 Normalizaion of he variables in RBC models is done for reasons such as (i) he ransformed sysem does no exhibi growh, (ii) seady sae should be compued in normalized variables since seady sae assume no occurrence of shock, and (iii) simulae he deerminisic dynamic sysem (Malik e al., 2014, page 35) 11

12 is defined by he following equaions, where a ilde is placed over each of he normalized variables 8 : 2.4 Firm opimizaion C + a' K ' = wn + rk + (1 δ) K + π (17) I = ak ' ' (1 δ ) K (18) ' C a E ( r ' (1 ) = β + δ C ' Acceped Manuscrip (19) lnθ φ 1 φ τ Y = e ( s N) ( s K) Z τ (20) N 1 Z ' a' = (1 s ) N N (1 sk) K Z K ω ( ) ( ) μ μ ω Facing wo consrains in each period (he producion funcion for oupu in equaion (13) and he producion funcion for inangible capial equaion 16), he firm maximizes he presen value of is real profis. The firm s opimizaion problem can be wrien as: 1 ω 1 τ μ μ φ φ τ ω V( Z) = Max EU( s N) ( s K) Z wn rk + βv( Z') + λ (1 s ) N (1 s ) K Z Z' a' c N K N K N, K, sn, sk, z' (22) The firs order opimizaion condiions for he above problem are: wu c (21) ( ) ( ) βev ( ') = λa' (23) z Y (1 ) a' Z ' U μ ω c φ λ = N + N (24) 8 To normalize he variables we divide each equaion by A and define A + where a = A ' 1 C = and A C C+ 1 C+ 1 A+ 1 ' ' = = Ca, A A A

13 φy λμ(1 ω) a' Z ' Uc = s N 1 s N (25) ru The envelope condiion is as follows: c U Y (1 μ)(1 ω) a' Z ' = (1 φ τ) λ K + N c (1 φ τ) Y λ(1 μ)(1 ω) a' Z ' = sk 1 sk Y Z ' Vz = U c τ λ ωa' Z + Z Subsiuing equaion (28) ino equaion (23) gives equaion (29), which represens he marginal value of an exra uni of inangible capial: Y ' Z '' β Uc τ λ' ωa'' λa' Z + = ' Z ' We noe ha due o he inclusion of inangible capial in he producion funcion, firms are no equaing he marginal produciviies of labor and capial o heir respecive facor prices. I is ineresing o noe here ha equaions (24) and (25) imply ha firm allocaes capial and labor o he producion of inangible capial in such a way ha marginal decreases in he oupu of he final good offse he marginal increase in inangible capial available o he firm. Formally, (26) (27) Acceped Manuscrip combining equaion (26) wih (24) and equaion (27) and (25) resuls in he following equaions: (28) (29) Y 1 w= φ = MP (30) N s N s N N 13

14 Y 1 r = (1 φ τ) = MP K (31) s K s K K Since 0< s N < 1 and 0< s K < 1, i is clear from he above wo equaions ha facor prices exceed heir marginal produc in he producion of he final good. 9 Proposiion 1: In he presence of inangible capial, facor prices exceed heir respecive marginal produciviies. Equaion (32) capures invesmen in inangible capial: Combining equaions (30), (31), and (32) gives: I z Y I wn ( 1 s ) rk ( 1 s ) = + (32) z N K 1 s N 1 s K = φ+ (1 φ τ ) sn sk Equaion (33) implies ha invesmen in inangible capial is increasing in oupu bu decreasing in he shares of facors of labor and capial. The firm s profi in he presence of inangible capial is\ ]: Acceped Manuscrip (33) π = Y wn rk (34) Using equaions (30), (31) and (33) in equaion (34) gives us he following relaionship beween profi and inangible capial invesmen: π = τy I (35) z 9 Labor and capial shares ac as a ime-varying wedge beween facor prices and marginal producs. 14

15 Equaion (35) depics a rade-off beween he curren period s profi ( π ) and invesmen in inangible capial ( I z ). The above discussion gives us our second proposiion. Proposiion 2: Firms sacrifice heir presen profi o creae inangible capial for fuure producion. 2.5 The Seady Sae In he seady sae, all variables are invarian o ime changes i.e. C' = C, Y ' = Y, K '' = K ' = K, and Z '' = Z ' = Z. We can use equaion (12) o solve for he seady sae value of he real rae of ineres ( r ) as follows: Similarly, while using equaion (29) we can show ha: a r = ( 1 δ ) (36) β UY c λaz = βτ 1 βω and by using equaion (37) in (24), (25), (26) and (27) we ge he following expressions: Y μ(1 ω) βτ w = φ + N 1 βω Y (1 μ)(1 ω) βτ r = (1 φ τ) K + 1 βω Acceped Manuscrip ( s ) 1 N μβτ(1 ω) = s φ(1 βω) N ( s ) 1 K βτ (1 μ)(1 ω) = s (1 φ τ )(1 βω) K (37) (38) (39) (40) (41) 15

16 Equaions (38) o (41) reveal ha he seady sae wage rae, ren on physical capial, and income shares of boh labor and capial are all independen of inangible capial. We can summarize his resul as follows: Proposiion 3: In he seady sae, he wage rae ( w ), renal on physical capial ( r ), income share of labor, and income share of capial are all independen of he sock of inangible capial. The facor shares of labor and capial in he seady sae can easily be recovered from equaions (34) and (35). Plugging equaions (40) and (41) ino equaion (33), we ge he seady sae inangible invesmen o oupu raio as: I z βτ(1 ω) = Y 1 βω We can noe in equaion (42) ha he raio of invesmen in inangible capial o oupu of final goods depends on parameersτ and ω, where τ is he key parameer ha measures he elasiciy of he final good o inangible capial (see equaion (13) above). One can noe in equaion (42) ha here exiss a proporional relaionship beween he inangible invesmen-oupu raio andτ 10. The share of labor income o oal oupu can be derived from equaion (38) as: wn μ(1 ω) βτ = φ Y + 1 βω Acceped Manuscrip Similarly, using equaion (33), we can solve for he capial-oupu raio as: (42) (43) 10 From (42) i can be shown ha dln( I / Y) z = 1. d lnτ 16

17 K Y 1 (1 μ)(1 ω) βτ = (1 φ τ) r + 1 βω (44) Equaion (44) implies ha he capial o oupu raio decreases as μ (he elasiciy of inangible capial o labor used in he producion of inangible capial, as seen in equaion (16)) increases 11. However, he increase in he same parameer increases he share of labor income in oal oupu (see equaion (43)). From equaion (16) we can see ha he permanen echnology shock is increasing in labor. In his siuaion, an increase in μ furher increases he abiliy of he shock o creae more inangible capial for a given amoun of labor. On he oher hand, from equaion (44) we can see ha an increase in τ decreases he share of physical capial bu he share of he capial good in he producion of he final good increases (see equaion (13) above). The above discussion leads us o our nex proposiion: Proposiion 4: Invesmen in inangible capial is of higher value o he producer han invesmen in physical capial. Finally, we can wrie he following equaion for inangible capial in he seady sae: ( ) ( ) 1 1/1 μ μ Z = (1 s ) N N (1 sk) K a We can use equaion (45) o eliminae Z in he producion funcion (see equaion (20) above). Since he capial-oupu raio is already deermined; equaion (39) can be used o solve for oupu Acceped Manuscrip of he final good in he seady sae. Once oupu is deermined, capial can be calculaed. Given he seady sae oupu, wage can be deermined using equaion (43). Similarly, consumpion can ω (45) be esimaed from he goods marke equilibrium condiion ( Y = C + I ). Profi in he seady sae 11 rk From (46) we can deermine he capial share in oal oupu as follows: Y (1 μ)(1 ωβτ ) = (1 φ τ) + 1 βω 17

18 can be esimaed using equaion (34). Since he seady sae values of capial, labor, and income shares of facor of primary inpus are already deermined, he sock of inangible capial and invesmen in inangible capial can be deermined while using equaions (45) and (32) respecively. 2.6 Sochasic Model We employ Chrisiano s (2002) mehod of undeermined coefficiens o solve our dynamic model. We can use he wo Euler equaions from he household problem o sudy he ime pah of key variables in he even of preference shocks. The sysem of equaions ha describe he problem of he firm can be furher simplified by using equaion (26) in equaions (24), (25), (26) and (29). This helps us o reduce he model ino four equaions ha can be solved simulaneously for four endogenous variables: capial, inangible capial, he income share of labor, and he income share of capial. The relaionship beween he income share of capial and labor is as follows: s N φ(1 μ) sk = μ(1 φ τ)(1 s ) + φ(1 μ) s K Acceped Manuscrip In equaion (46) we noe ha he income share of labor ( s N ) is non-linearly relaed o he income share of capial ( s K ). Since sn is known, he oupu of he final good can be wrien as follows: K (46) Y = f( K, N, s, s, Z) (47) N K 18

19 Likewise, he real wage rae ( w) can be deermined as follows: Y w = φ (48) s N The above equaion suggess ha he oupu of he final good depends boh on labor as well as he income share of labor: w= f( Y, N, s N ). We can also deermine he renal rae (r) by using equaion (44): Y φ(1 μ)(1 sn ) r = (1 φ τ) K + μsn Equaion (49) suggess ha he renal rae of physical capial is a funcion of oupu, capial, and he facor share of labor: r= f( Y, K, s N ). N Consumpion in a dynamic equilibrium can be deermined eiher using he budge consrain or goods marke clearing condiion: Acceped Manuscrip (49) C = Y a' K ' + (1 δ ) K (50) To summarize he above discussion, we can show ha he dynamic sysem as laid ou in our model consiss of four equaions ha could be solved using he feedback par of he sochasic model. 12 Two equaions are based on he household problem and he oher wo are based on he firm problem: CBη w = (51) 1 N 12 The feedback par characerizes he impac of he endogenous sae variables on he curren period endogenous variables. For furher reference see Chrisiano (2002). 19

20 ' C a E ( r ' (1 ) = β + δ C ' (52) ω ( ) ( ) 1 Z ' a' = (1 s ) N N (1 sk) K Z μ μ ω ' CY ' s N μ(1 ω) τ (1 sn) β 1 + ω ' = CY ' (1 sn ) φ sn Equaions (51) o (54) are he equilibrium condiions ha can be used in our calibraion exercise in he nex secion. 3. Model Calibraion 3.1 Choice of Parameer Values Parameers β η δ φ τ μ ω Values (53) (54) We calibrae eleven parameers: β, η, δ, ρ, φ, τ, μ, ω, ρ, ρ and v a. Since his is an b exension of a sandard RBC model, some of he parameers are easy o pin down, for insance he discoun rae is assumed o be β = 0.99, which is consisen wih a one-percen nominal rae of ineres. Similarly, we assume a capial depreciaion rae ( δ ) of 0.025, hese values are idenical o Jack and Lin (2013). The elasiciy of labor (φ ) is se a and he elasiciy of capial (1 φ τ ) is assumed o be These parameer values are sandard in he lieraure Acceped Manuscrip (see, for example, Plosser 1989). Inclusion of inangible capial necessiaes a choice of variables slighly differen from he sandard RBC model. For example, Mc-Graan and Presco (2010) ρ b a θ ρ a ρ θ v a assume an income share of capial of 0.26, which is on he lower side. The household ineremporal condiion is used o pin down he value of uiliy parameer ( η = ). 20

21 Since his model includes inangible capial, hree parameers are of special imporance: τ, μ,andω. We aler he values of hese parameers in beween he maximum and minimum ha are used in he lieraure o see how i affecs he overall performance of he model. We also analyze how hese changes affec he facor share allocaion of labor and capial o he oupu producion and creaion of inangible capial. The value of τ used in he paper is The minimum value is 0.076, which is used McGraan and Presco (2010). This value resuls in a higher seady sae value for boh labor and capial shares allocaed o producion. However, a lower value of τ resuls in an invesmen o oupu raio of approximaely 32 percen, which is very high. The raio of inangible invesmen o angible invesmen is 23 percen, which is almos 50 percen less han wha McGraan and Presco (2010) repor. We have chosen 0.33 as he maximum value of τ. The higher value of τ resuls in lower labor and capial resources divered owards oupu producion and more used o produce inangible capial. A higher value of τ brings he invesmen o oupu raio o less han 14 percen, which means ha consumpion is more han 85 percen of oupu. This higher value also resuls in a very high raio of invesmen in inangible capial o physical capial and oupu, which does no seem o be consisen wih expecaions. The second imporan parameer is μ. We have used a value ha is close o he maximum value available in he lieraure. We have seleced a minimum value of 0.4. The minimum value of μ Acceped Manuscrip increases he labor share in producion and decreases he capial share, as expeced. Less labor is used in inangible capial creaion and more capial is engaged in he creaion of inangible capial. The minimum value of μ also increases he invesmen o oupu raio o 30 percen, which is very high in a closed economy model wih no governmen. We have seleced a median 21

22 value of 0.62, which resuls in a higher labor share in producion. The value of his parameer is very sensiive o he conribuion of labor in he producion and creaion of inangible capial. The median value can only increase he invesmen o oupu raio o 28 percen, which is sill very high. The inangible invesmen o physical invesmen raio is around A higher value for μ keeps he seady sae raios close o he daa. The las parameer is ω. If ω =1, his means ha inangible capial is consan over ime and a value of zero implies ha curren inangible capial does no conribue o produce inangible capial in he nex period. We picked a minimum value of 0.30 and a maximum value of A minimum value does significanly affec he capial and labor share allocaion. I basically implies ha curren inangible capial is no conribuing much o fuure creaion. This number does no aler he seady sae raios, however; he raio of inangible o angible capial increases. A very high value of ω increases boh he share allocaion however, he increase is no more han 3 percen, and slighly increases he invesmen o oupu raio. Overall, changes in he values of ω is no very sensiive o he seady sae raios. Finally, we choose wo seady sae raios ha are imporan for our model: he inangible invesmen o oupu raio and he invesmen in inangible capial o invesmen in physical capial raio. In he exising lieraure, a number of differen values are used. For example, see McGraan and Presco (2010), Corrado e al (2006) and Hou and Johri (2009). We assume an inangible invesmen o oupu raio of The invesmen in inangible capial o invesmen Acceped Manuscrip in physical capial raio is assumed o be 0.68, which is higher han he raio of 0.42 assumed by McGraan and Presco (2010), bu lower han he value assumed by Corrado e al. (2006) and Hou and Johri (2009). 22

23 3.2 Dynamic Effecs of Preferences Shocks In his secion we sudy he impulse responses of oupu, consumpion, invesmen, inangible capial, and inangible invesmen o a preference shock ( B ). From equaion (1) we noe ha a preference shock is expeced o increase leisure and lower consumpion, due o he inheren rade-off beween hem. I is expeced ha -- as consumpion decreases -- oupu decreases, which in urn resuls in lower physical as well as inangible capial. I is also expeced ha he inra-emporal preference shock produces co-movemen beween consumpion and oupu, and beween oupu and employmen, as observed in real-world daa. Under he RBC model, he characerisic equaion of labor supply capures he difficuly for consumpion and employmen o move ogeher unless echnology changes a he same ime. Technically, an increase in B funcionally plays a similar role as changes in echnology. Wha is needed o obain comovemen beween consumpion and hours worked is for eiher he labor demand or he supply curves o shif for a reason oher han a pure wealh effec. An increase in pure wealh increases consumpion bu lower hours worked. The preference shock ends o change hours worked for a reason oher han a wealh effec. Closely relaed o our asserion, Bencivenga (1992) argues ha preference shocks may be inerpreed as resuling from shocks o household producion or from changes in relaive prices. The impulse responses of normalized variables o a preference shock are shown in Figure Acceped Manuscrip 1m where we have generaed he ime pah of key economic aggregaes by giving a one sandard deviaion shock o leisure ( B ). As expeced, he increase in leisure causes a decrease in consumpion. The fall in consumpion is due o he marginal rae of subsiuion beween consumpion and leisure, as noed in Secion 2. The decrease in consumpion led o a decrease in 23

24 oupu. This is an imporan resul as is observed in he US daa (see, for example Wen, 2007). Wen (2007) aemped o rack he co-movemen beween consumpion and oupu (consumpion Granger causes oupu) by giving a demand-shock bu concludes ha business cycle heory remains behind business cycle measuremen. In oher words, changes in produciviy are he real cause of flucuaions in economic aggregaes, raher han demand shocks. In conras, our resuls show ha in he presence of inangible capial, changes in consumpion do cause changes in oupu. The fall in oupu has a negaive impac on he employmen of boh labor and physical capial, as can be seen in Figure 1. Likewise, we noe ha hours and capial devoed o he creaion of inangible capial also decrease. The co-movemen beween oupu and physical invesmen is also observed in pos-war U.S. daa. I is ineresing o noe here ha our model wih inangible capial mimic hese resuls in he even of preference shocks, which a sandard RBC model is expeced o replicae coningen on produciviy shocks bu no on demand shocks (Wen, 2007). The change in oupu is probably due o facor price movemens in he even of he shock. From equaions (30) and (31) we noe ha facor prices are higher han heir respecive marginal produciviies, which enails a less han proporional decrease in inpu prices in he even of fall in oupu. Firms are herefore lef wih no choice bu o decrease oupu of final goods and invesmen in inangible capial. Acceped Manuscrip 24

25 To summarize our above discussion, we may conclude consumpion is imporan because i predics changes in oupu, which in urn predic changes in invesmen. This is consisen wih he conclusion of Cochrane (1994). 4. Conclusionn Impulse Response funcion o Preference Shocks-Normalized variables ha sudy of changes in In his paper we develop and simulae an RBC model ha includes inangible capial as a hird facor of producion. We assume ha in each period, he firm choosess o devoe a cerain fracion of labor and physical capial o he producion of inangible capial, which becomes an inpu in he producion of final good in he forhcoming period. However, allocaion of some Acceped Manuscrip resources o he producion of inangible capial negaively affecs curren producion and profi. We sudy he ime pah of consumpion, oupu, physical capial, and inangible invesmen in he even of preferencee shock. 25

26 In he developmen of our model, we learn ha due o inclusion of inangible capial a perfecly compeiive firm paying inpu prices more han heir respecive produciviies. Similarly, in he seady sae we learn ha he wage rae, renal on physical capial, income shares of boh labor and capial are all independen of inangible capial. Our model calibraions indicae ha demand-side shocks such as reference shock causes an increase in leisure bu a decrease in consumpion. The decrease in consumpion causes a decrease in oupu, hours-worked, and capial formaion. These resuls are very similar o hose depiced in pos-war USA daa, which reveals ha changes in consumpion cause changes in oupu and ha changes in oupu cause changes in invesmen. The novely of our resul is ha we mimic hese resuls by calibraing he RBC hrough demand-side shocks, which goes agains he predicion of sandard RBC models ha major flucuaions in economic aggregaes are due o echnology shocks. References Basu, S., Fernald, J., and Kimball, M., Are Technology Improvemens Conracionary? American Economic Review 96(5): Baxer, M., and Rober., G., Producive exernaliies and business cycles. Discussion Paper / Insiue for Empirical Macroeconomics 53, Federal Reserve Bank of Minneapolis. Benhabib, J., and Wen, Y., Indeerminacy, aggregae demand, and he real business cycle. Journal of Moneary Economics, 51(3), Benkard, L., Learning and Forgeing: The Dynamics of Aircraf Producion. American Economic Review 90(4), Acceped Manuscrip Bencivenga, V., An Economeric Sudy of Hours and Oupu Variaion wih Preference Shocks. Inernaional economic review. Vol. 33, N0. 2, pp Chrisiano, L., Eichenbaum, M., and Vigfusson, R., Wha happens afer a echnology shock? NBER Working Paper

27 Chrisiano, L., Eichenbaum, M., and Evans, L., Nominal Rigidiies and he Dynamic Effecs of a Shock o Moneary Policy. Journal of Poliical Economy, Vol. 113, No. 1, pp Chrisiano, L., Solving Dynamic Equilibrium Models by a Mehod of Undeermined Coefficiens. Compuaional Economics 20(1-2), Cochrane, J., Shocks. Carnegie-Rocheser Conference Series on Public Policy, December 41, pp Cooley, F., and Presco, E., Economic Growh and Business Cycles, in Froniers of Business Cycle Research, pp: 1 38, ed. Thomas F. Cooley, Princeon: Princeon Universiy Press Corrado, C., Hulen, C., and Sichel, D., Inangible Capial and Economic Growh. Finance and Economics Discussion Series , Board of Governors of he Federal Reserve Sysem. Favilukis, Jack & Lin, Xiaoji, "Long run produciviy risk and aggregae invesmen," Journal of Moneary Economics, Elsevier, vol. 60(6), pages Francis, N., and Ramey. V., Is he Technology-Driven Real Business Cycle Hypohesis Dead? Shocks and aggregae flucuaions revisied. Journal of Moneary Economics 52(8), Gali, J., Technology, Employmen, and he Business Cycle: Do Technology Shocks Explain Aggregae Flucuaions? American Economic Review 89(1), Gali, J., and Rabanal, P., Technology Shocks and Aggregae Flucuaions: How Well Does he Real Business Cycle Model Fi he Poswar U.S. Daa? in NBER Macroeconomics Annual 2004, edied by Mark Gerler and Kenneh Rogoff, Cambridge, MIT press. Hashmi, R., Inangible Capial and Inernaional Income Differences. Macroeconomic Dynamics 17(3), Hou, K., and Johri, A., Inangible Capial, Corporae Earnings and he Business Cycle. McMaser Universiy Deparmen of Economics Working Paper No Jinnai, R Inangible Capial, Asse Prices, and Business Cycles. Unpublished paper, Deparmen of Economics, Princeon Universiy. Malik., K., Ali., S., and Khalid., A., Inangible capial in a real business cycle model. Economic Modelling, 39, (C), King, R., and Rebelo, S., Resusciaing Real Business Cycles, in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, chap. 14, Elsevier, Amserdam Acceped Manuscrip Kydland, E. and Presco, E., Time o Build and Aggregae Flucuaions. Economerica, Vol. 50, No. 6, pp McGraan, R., and Presco, E., Unmeasured Invesmen and he Puzzling US Boom in he 1990s. American Economic Journal: Macroeconomics 2(4),

28 Nakamura, E., Deconsrucing he Success of Real Business Cycles, Economic Inquiry Vol. 47, No.4, pp Plosser, C., Undersanding Real Business Cycles. The Journal of Economic Perspecives, Vol. 3, No. 3, pp Rebelo, S., Real Business Cycle Models: Pas, Presen, and Fuure. NBER Working Paper hp:// Presco, E., Theory Ahead of Business-Cycle Measuremen, Carnegie-Rocheser Conference Series on Public Policy, 25, Solow, M., Technical Change and he Aggregae Producion Funcion. The Review of Economics and Saisics, Vol. 39, No. 3, pp Wen, Y., Granger causaliy and equilibrium business cycle heory. Federal Reserve Bank of S. Louis. 89(3), pp Acceped Manuscrip 28

29 Abou he Auhor Kashif Zaheer Malik, PhD, is an Assisan Professor a Economics Deparmen in Lahore Universiy of Managemen Sciences. Dr. Malik is a Fulbrigh Scholar and has a Masers and PhD degree in Economics from Florida Sae Universiy. Dr. Malik is an economis wih over welve years of experience in he areas of applied macroeconomics, economerics and economic analysis. His research area includes Applied Macro-Economics, Time-Series Economerics and Developmen Economics. His recen sudies have been published in acclaimed journals such as Economics Modelling, Elsevier. Dr. Malik has recenly been awarded gran by Innovaion for Povery Acion (IPA) o conduc field experimens (Randomized Conrol Trials) on Lease-Based Microfinance Conracs for Micro-Enerprises in Pakisan. The research is being implemened in collaboraion wih Universiy of Oxford and Akhuwa (A microfinance insiuion). Public Ineres Saemen The aricle shows ha in he presence of inangible capial, preference shocks such as leisure can also help explain movemens in macroeconomic aggregaes. This an imporan resul since i enails ha demand shocks in he economy also play an imporan role in explaining shor-erm business cycle flucuaions. An imporan conclusion is ha demand side shocks are also relevan in explaining aggregae flucuaions in macroeconomic variables which goes agains he predicion of sandard Real Business Cycle models ha major flucuaions in economic aggregaes are due o echnology shocks. Table : Choice of Parameers value Parameers β η δ φ τ μ ω Values Acceped Manuscrip ρ b ρ a ρ θ v a 29

30 Impulse Response funcion o Preference Shocks-Normalized variables Acceped Manuscrip 30