Equity Market or Bond Market Which Matters the Most for Investment? Revisiting Tobin s q Theory of Investment

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1 Technology and Invesmen, 01, 3, hp://dx.doi.org/10.436/i Published Online November 01 (hp:// Euiy Marke or Bond Marke Which Maers he Mos for Invesmen? Revisiing Tobin s Theory of Invesmen Willi Semmler, Lebogang Maeane Deparmen of Economics, New School for Social Research, New School Universiy, New York, USA semmlerw@newschool.edu, mael36@newschool.edu Received Augus, 01; revised Sepember, 01; acceped Sepember 10, 01 ABSTRACT Recen experience seems o have shown ha credi markes are more imporan han euiy markes for invesmen and macrodynamics. This paper examines he effec of Tobin s euiy and bond on invesmen. More specifically we sudy he role of Tobin s euiy (usual), average and bond for aggregae invesmen over he period 1953: Q4-011: Q1. Employing bond and euiy, or alernaively bond and average, shows ha hese variables are very relevan in explaining invesmen. Ye, he ime scale maers oo. Examining he relaionship of hese variables over a long ime scale, a low freuencies, we can show ha he combinaion of bond and average are he mos significan deerminans of aggregae invesmen. Moreover, for he longer ime scale he wo variables, bond and average, resul in he highes goodness of fi demonsraing good in-sample forecasing properies. As o he individual deerminans of aggregae invesmen over he period 1953: Q4-011: Q1, bond is by far he mos influenial variable a all freuencies since i always has he highes correlaion wih invesmen and his correlaion is always saisically significan. Similarly, he greaer significance of average, as compared o euiy, is probably an oucome of he financing insrumens for invesmen. Keywords: Euiy Marke; Bond Marke; Tobin s Theory of Invesmen 1. Inroducion In macroeconomics one of he mos conenious issue is he heory and empirics of invesmen. Tobin s seminal work ha invesmen is guided by he value of he asse of he firm in he sock marke has become he sandard heory of invesmen. I is based on some measure of he sock marke value of he firm (value of corporae euiy) relaive o he replacemen cos of is exising capial. This measure is denoed as Tobin s in he lieraure, and as a resul Tobin s is used as a main deerminan of a firms invesmen decision. Numerous heoreical and empirical sudies on his issue have been conduced, bu as has also been noed, for example by [1,], he relaion beween Tobin s and invesmen has been uie an empirical failure. Amongs oher reasons, his may reflec ha he marke valuaion of a firm s asses is very volaile and here seem o be oher relevan facors deermining invesmen. Numerous aricles have been published ha showed, hose facors such as expecaions, he disincion beween invesmen decisions and invesmen spending 1, credi and financing consrains are imporan as well. In 1 Differences beween invesmen decisions, invesmen spending, and he ime lag beween he wo, are discussed in Kaleckian approaches. a simplisic view, o finance an invesmen projec a firm could consider he following: 1) Using reained profis (inernal finance); ) Issuing a deb insrumen for example a bond (exernal finance); 3) Selling euiy or shares (exernal finance) and 4) Obaining loans from a bank or financial insiuion (exernal finance). Alhough a firm may have financing opporuniies and even if i faces no financing consrain, here are sill more facors ha may be aken in o consideraion before underaking an invesmen projec. Moreover, he decision on he ype of exernal financing is a facor. A firm may aim a obaining or issuing a deb insrumen. By issuing a deb insrumen, his allows a firm o fully benefi from he ne profis or ax advanages. On he oher hand, a firm may inend o issue shares (euiy). Issuing shares has he downside of paying ou profis, bu i has he upside of spreading he risk in he even ha a projec is no profiable. Recenly he major issue has become o wha exen firms invesmens are deermined by he value of euiy or by condiions of he credi markes (bond issuing and loans from banks). One can sae hose alernaive invesmen rules by saying: Wha drives invesmen? Is i Tobin s euiy or Tobin s bond? In addiion, we would wan o explore which deerminans are relevan on differen ime scales.

2 04 The radiional heory of invesmen provides an elegan represenaion of a firms decision problem, relaing invesmen o he value of he euiy of a firm. In addiion, he heory yields a simple invesmen rule derived from a firms decision problem. This paper examines wheher he deerminans of invesmen are bond and euiy. We will also use a less convenional measure, namely an average. As a resul, we will employ alernaively euiy and average. Using bond and euiy or bond and average, allows us o ake in o accoun oher facors beyond sock marke valuaion as being he key facor deermining invesmen. As o he ime scale of he link beween he differen s and invesmen we examine he relaion beween invesmen, bond and euiy and he relaion beween invesmen, bond and average, whereby all he variables are evaluaed a higher and lower freuencies. The remainder of he paper is organized as follows: Secion presens an ouline of he sandard heory of invesmen. Secion 3 discusses he mehodology and daa sources. Secion 4 presens he esimaion resuls and Secion 5 concludes he paper.. The Sandard Theory of Invesmen Model In his secion, we presen a modified neoclassical invesmen model ha characerizes he represenaive firm s decision problem and we use his o derive he relaion beween invesmen and Tobin s. The modificaion we inroduce is in he form of adjusmen coss and based on he derivaion, we express a regression euaion ha we esimae. We follow a similar framework o ha oulined by [3]. In addiion, we employ Ponryagin s maximum principle and also evaluae he local sabiliy properies around he seady sae of each variable of ineres. The objecive of he represenaive firm is o deermine invesmen ha maximizes he presen value of is ne profi over an infinie horizon, and his is presened as follows: r max e π Kk I CI d I =0 s.. I k () where is he presen value of he firms ne profi over an infinie horizon, πk is he real flow of profis for he firm per uni of capial, and k is he firm s capial sock. In line wih [3], we assume he discoun rae r is consan and ha K he indusry wide capial sock rajecory is aken as given by each firm and each firm chooses is invesmen over ime o maximize for a given K. The real flow of profis for he firm, π K, are inversely relaed o K. We also assume ha (1) here is a zero depreciaion rae and in line wih [4] we also assume ha he purchase price of a uni of invesmen good is one and hence he cos of purchasing an invesmen good is I. In oher sudies such as [5], he adjusmen coss of invesing are a convex funcion of he invesmen rae. In line wih [4], we assume ha adjusmen coss are a convex funcion of he level of invesmen and are given as I CI, 0, where CI I 0 (for all I 0 ) and C I 0. To solve he problem ha he represenaive firm faces we employ Ponryagin s maximum principle and formulae he curren value Hamilonian. The curren value Hamilonian is expressed as follows: Hck, I (3) π Kk I CII, where e r and denoes he marke value of a uni of capial. Subsiuing he explici adjusmen coss funcion in he curren value Hamilonian resuls in he following: H k, I c I Kk I I π. (4) The firs order condiions derived from (4) are as follows: H k, I c I also expressed as: 0 1 I 0 1 I 1 I. The law of moion for he co-sae variable is: H ( k, I ) c k r r π K. The ransversaliy condiion can be wrien as follows: r lim e k 0. Euaion (5) implies an invesmen rule which is ha firms inves unil he oal cos of an addiional uni of capial is eual o he marke value of a uni of capial. Euaion (5) can also be inerpreed as he marke value of a uni of capial is also eual o he marginal value of an addiional uni of capial. We show his alernaive inerpreaion in he Appendix (A1) by using he Hamilon-Jacobi-Bellman mehod o solve he firm s maximizaion problem and his yields he same resul as shown in Euaion (5). Alhough Euaion (6) is he law of moion for he co-sae variable, i also implies ha he mar- (5) (6)

3 05 ginal revenue of capial is eual o is opporuniy cos. Using Euaion (5) allows us o deermine he opimal invesmen level ha maximizes he curren value Hamilonian and his is represened as follows: 1 1I I 1 I 1. (7) Using Euaion (5) we can now reach he following opimal invesmen rules: 1) When 1 I 0, ) when 1 I 0 and 3) when 1 I 0. In he lieraure, he sandard measure of Tobin s is he raio of a firm s sock marke valuaion relaive o he replacemen cos of is physical asse. Using his approach, if is greaer han one, hen a firm should underake an invesmen projec because he marke values he firm s asses beyond he cos associaed wih aking on an invesmen projec. Even wih he implied invesmen rule based on he derivaion of Euaion (5), [,6] noe ha he criical variable which is marginal and in his conex as derived in Euaion (5) is unobservable. As a resul, empirical work based on he heory of invesmen is based on is average measure, where he average measure is used as a proxy for marginal. Moreover, [] noe ha he average measure as a proxy is used wih sock marke valuaions only under sringen condiions which are linear homogeneiy of he profi and adjusmen cos funcion. Neverheless, he sandard invesmen model assumes ha all firms in an indusry are idenical. As a resul, if here are N firms in he indusry, i follows ha economy wide capial accumulaion is expressed as follows: K Nk NI I K. (8) N I 1 From Euaion (5) we have ha and CI I which is hen expressed as K C I 1 bu from (8), I and hence we N have he following: K C 1 I, (9) N which is a monoonic funcion, is a one-o-one funcion and is an ono funcion. As a resul, and as noed by [7] he inverse exiss, ha is C 1 exiss which hen allows Using a cos funcion ha is uadraic in he invesmen rae e.g. 1 I CI, k a k, yields a non-inuiive and difficul o explain k K. Defining he inverse in a N general funcional form resuls in he following: 1 us o have C 1 1 1, (10) 1 C f and from his we obain he following: K f 1 K Nf 1 N. (11) Euaion (11) allows us o observe he relaion beween economy wide capial accumulaion and Tobin s. The funcion f 1 is a monoonic funcion and i preserves he properies of he original funcion C I 1. As a resul, we have he following: K K N N C I C C I 0. (1) Similarly because f 1 preserves he properies of he original funcion, we hen have he following: 1 C 10, (13) 1 1 K C 1 f 1 0. π r K (14) Using Euaions (6) and (11) we hen have a sysem of wo differenial euaions which are derived from he firms opimizing sraegy. The sysem of wo differenial euaions is as follows: K Nf 1., (15) (16) We now proceed o deermine he seady sae values of he sysem and hen analyze local sabiliy around he seady. The seady sae is deermined as follows: π K 0 (17) r and using Euaions (8) and (16) we hen have ha when 1k 0, and K 0 and f 0 0. The differenial euaions are non-linear because we do no have he explici form of he funcion πk, and also do no have he explici form of he funcion f 1. As a resul, we linearize he sysem of differenial euaions. The linearized forms of Euaions (15) and (16) are expressed as follows: r K K K, (18) firs order condiion for he following: π H k c r πk r I. As a resul, ha is why for k he purposes of his paper, we employ a cos funcion ha is uadraic in he level of invesmen and no uadraic in he invesmen rae. K Nf 1, (19) which in marix form can be expressed as follows:

4 06 r π K K 1 0 K Nf π K K r 1 Nf (0) The Jacobian marix analyzed a he seady sae is as follows: r πk J. 1 0 Nf The race of he Jacobian marix a seady sae is Trace J r 0 and he deerminan of he Jacobian marix a seady sae is Deerminan De J π K Nf 1 0 π K 0 where 1 0 and Nf. As a resul, he syse m exhibis saddle pah sabiliy. 3. Mehodology and Daa In his secion we presen he mehodology we use o esimae he relaion beween invesmen, Tobin s euiy and bond. In addiion, we explain he daa ha we use in our analysis. The analysis in he paper is for he U.S. economy. We esimae an euaion using a paricular represenaion and ransformaion of he firs order condiion expressed in Euaion (7). We esimae an euaion beween he invesmen rae, Tobin s and bond and we use wo forms of observable Tobin s, namely euiy (usual) and also average. In line wih [1,], we esimae he following euaions using OLS wih Newey- Wes HAC consisen sandard errors. The euaions are as follows: I 0 1B 1 E 1, (1) K I 0 1 K B 1A 1. () The ransformaion in relaion o (7) is consisen wih empirical esimaions and as a resul we use he inves- I men rae denoed as, as a dependen variable and K no he level of invesmen. For our empirical analysis, Tobin s euiy is denoed as E, and is defined as he raio of he marke value of corporae euiy o ne worh 3 Link o he daa is hp:// 4 To compile bond, daa on Moody s Baa index is denoed in monhly form. As a resul, o be consisen wih all oher series, we conver he daa ino uarerly daa by using an eually weighed moving average. The link o he daa series for bond is hp://research.slouisfed.org/fred. (oal asses minus oal liabiliies). Average, is denoed as A, and is defined as he raio of he sum of he marke value of corporae euiy and oal liabiliies o oal asses. The daa for consrucing average and euiy is derived from he Federal Reserve Board s Flow of Funds accoun Z1 saisical release for March 8h, The values are no seasonally adjused and are for Nonfinancial Corporae business. Bond, which is also referred o as he relaive price of corporae bonds is compued in r 10 line wih [1,] as B where r Baa 0.1 y is he 10 year reasury consan mauriy rae and y Baa is Moody s Baa Corporae bond yield. The daa for compuing bond is derived from he Board of he Federal Reserve Sysem (FRED) 4. For invesmen and capial sock, we use he series on privae non-residenial fixed invesmen in euipmen and srucures and he corresponding curren cos of ne capial sock from he Bureau of Economic Analysis Esimaion Resuls In his secion we presen he esimaion resuls of Euaions (1) and (). In addiion we presen he esimaion resuls of Euaions (1) and () using he low freuency componen of each variable. The low freuency componen is he rend componen of each variable, which we consruc using a HP filer 6. We use he rend componen of each variable so as o capure he relaionship beween he variables when hey are analyzed a low freuency which should reflec long run rends. Table 1 repors he sandard regression resuls for Euaions (1) and (). The Wald join coefficien es indicaes ha joinly, bond and euiy (usual) have an effec on he invesmen rae. Similarly, based on he Wald join coefficien es, boh bond and average have an effec on he invesmen rae. Over he period 1953: Q4-011: Q1, using eiher average or euiy and aking ino accoun serial correlaion wih a four uarer moving average, he percenage poin responsiveness of he invesmen rae wih respec o bond is approximaely he same. In addiion, he 5 The curren cos of ne capial sock is denoed annually and daa is in year-end esimaes. As a resul, we use he year end value of he previous period and divide i by four. We do no use he divided series as a proxy for he uarerly daa, insead we ake each year end esimae which is divided by four, hen compile a uarerly series hrough linear inerpolaion beween each year end esimae raher han use he whole year end esimae as a proxy for uarer 1 of he following period because his would oversae he value. As a resul, each year end esimae is divided by four and is hen used as a proxy for he following year uarer one series, hen linear inerpolaion is used hrough he variables ha are proxies so ha a series for uarer and uarer 3 can be consruced for each year from 1953: Q1-011: Q1. 6 We use he maximum sandard value for so ha we can generae a smooh rend series.

5 07 Regression Oupu (P-value in parenhesis) Regressors: Bond and Euiy (usual) Residual Diagnosics Wald Tes: Join Coefficien Tes Regressors: Bond and Average (usual) Residual Diagnosics Wald Tes: Join Coefficien Tes Table 1. Sandard regression oupu 1953: Q4-011: Q1. α 0 α 1 α R S.E. of regression (0.07) (0.00) (0.67) Auocorrelaion: LM (4) = Heeroske-dasiciy: Normaliy: JB Sa = Sric exogeneiy 1 : (0.00) ARCH (4) = (0.00) (0.961) Orhogonaliy is saisfied = α = α = 0 H ( 0.06) (0.00) (0.034) Auocorrelaion: LM (4) = Heeroske-dasiciy: Normaliy: JB Sa = 0.41 Sric exogeneiy 1 : (0.00) ARCH (4) = (0.00) (0.8) Orhogonaliy is saisfied = α = α = 0 H 0 1 χ () = (0.00) χ () = (0.00) Euaions (1) and () adjused for auocorrelaion wih MA (4) erms and Newey-Wes HAC consisen sandard errors. goodness of fi is relaively he same where bond and average or bond and euiy explain 63% of he variaion in he invesmen rae. This resul of he goodness of fi is fairly similar wih [1,] resuls over heir full sample periods which are 1953: Q3 o 007: Q and 195: Q1-009: Q4, respecively. Anoher similar resul o ha of [1,] is ha in boh he regressions using eiher bond and average or bond and euiy, bond is more correlaed wih he invesmen rae as compared o he oher regressors. Furhermore bond is always saisically significan a all levels of significance and he sriking similariy is also capured in he regression where bond and euiy are used, where in his conex euiy has no explanaory power. Table repors he regression resuls for Euaions (1) and () conduced wih heir respecive rend variables. The Wald join coefficien es indicaes ha joinly, he rend of bond and rend of euiy have no effec on he invesmen rae. In addiion, he percenage poin responsiveness of he invesmen rae wih respec o bond and he percenage poin responsiveness of he invesmen rae wih respec o euiy are individually saisically insignifican when using he rend componens of he variables. This resul probably shows and capures he low variaion in eiher one of he variables because of he smoohness of he rend. On he oher hand, he Wald join coefficien es shows ha joinly he rend of bond and he rend of average have an effec on he rend of he invesmen rae. In addiion, he percenage poin responsiveness of he invesmen rae wih respec o bond and percenage poin responsiveness of he invesmen rae wih respec o average are individually uaniaively and saisically significan when using he rend componen of he variables. Furhermore, he percenage poin responsiveness of he rend of he invesmen rae wih respec o he rend of bond and he rend of average are he highes as compared o any oher coefficiens and he goodness of fi of 8% is also he highes showing good in sample forecasing properies. Based on Tables 1 and, here is evidence ha joinly, bond and euiy or bond and average have an effec on he invesmen rae. In addiion, his is suppored by he goodness of fi. Even wih hese findings, an analysis of he rend componen of he respecive variables shows ha i is average and bond, raher han euiy and bond, which joinly and individually affec he invesmen rae. This is consisen wih he inerpreaion ha over he long erm, bond and average raher han bond and euiy deermine aggregae invesmen. The resul ha he bond is so dominan for invesmen in he shorer as well longer run may need some ualificaions. For example, oher liabiliies raher han corporae euiy also have an imporan role in he financing of invesmen projecs. Of paricular ineres, is also ha a low freuency bond and average reveal he highes goodness of fi and by implicaion his shows good in-sample forecasing properies. 5. Conclusion This paper finds evidence ha boh, bond and euiy, and alernaively bond and average have a srong impac on invesmen. Ye, an analysis of he ime scales of he economic relaionships high and low freuency movemens of he daa shows ha i is average and bond, raher han euiy and bond, ha joinly and individually deermine he invesmen rae. Moreover, using he low freuency componen of bond and average, resuls in he highes goodness of fi and his implies good in-sample forecasing properies. Based on hese findings, using he rend componen of he variables, over he long erm bond and average raher han bond and euiy deermine invesmen. In some sense, our resuls replicae earlier sudies ha euiy value

6 08 Regression Oupu (P-value in parenhesis) Table. Regression wih rend componen of each variable 1953: Q4-011: Q1. α 0 α 1 α Regressors: Trend Bond and Trend Euiy (usual) (0.03) (0.6) (0.93) Residual Diagnosics Wald Tes: Join Coefficien Tes Auocorrelaion: LM (4) = Heerosked-asiciy: ARCH 5.39 (0.00) (4) = 17.3 (0.061) H 0 = α 1 = α = 0 χ () = 0.6 (0.87) R S.E. of regression Normaliy: JB Sa = Sric exogeneiy 1 : (0.79) Orhogonaliy is saisfied Regressors: Trend Bond and Trend Average (0.43) (0.0) (0. 01) Auocorrelaion: LM (4) = Heerosked-asiciy: ARCH Normaliy: JB Sa = 1.4 Sric exogeneiy 1 : Residual Diagnosics 9.84 (0.00) (4) = (0.005) (0.5) Orhogonaliy is saisfied Wald Tes: Join Coefficien H Tes 0 = α 1 = α = 0 χ () = (0.00) Euaions (1) and () wih rend componen of each variable adjused for auocorrelaion wih MA (4) erms and Newey-Wes HAC consisen sandard errors. appears o be a oo noisy variable o conclusively show is impac on invesmen in he shorer run. If anyhing i will show up as a relevan facor for invesmen in he longer run. The credi marke and bond marke seem o be more imporan. Thus oher liabiliies, raher han corporae euiy, such as bonds, loans and oher deb insrumens may be used and may have an imporan role in he financing of an invesmen projec. REFERENCES [1] T. Philippon, The Bond Markes, Quarerly Journal of Economics, Vol. 14, No. 3, 009, p p doi:10.116/jec [] M. Gallegai, J. Ramsey and W. Semmler, Bond Prices : Wih or wihou Euiy Marke s? New School Universiy, New York, 011, pp [3] D. Romer, Advanced Macroeconomics, 3rd Ediion, McGraw-Hill, New York, 006. [4] M. Kao, M. Ofori and W. Semmler, Tobin s and Invesmen in a Model wih Muliple Seady Saes, In: T. Asada and T. Ishikawa, Eds., Time and Space in Economics, Springer, Berlin, 007, pp doi: / _4 [5] L. H. Summers, Inflaion, Taxaion and Corporae Invesmen: A Q Theory Approach, Naional Bureau of Economic Research Working Paper, Vol. 600, No. 604, 1980, pp [6] F. Hayashi, Tobin s Marginal and Average : A Neoclassical Inerpreaion, Economerica, Vol. 50, No. 1, 198, pp doi:10.307/ [7] A. C. Chiang and K. Wainwrigh, Fundamenal Mehods of Mahemaical Economics, 4h Ediion, McGraw-Hill, New York, 005.

7 09 Appendix A1: Solving he Model Using he Hamilon-Jacobi-Bellman Mehod In he ouline of he modified neoclassical invesmen model, Euaion (5) implies an invesmen rule which is ha firms inves unil he oal cos of an addiional uni of capial is eual o he marke value of a uni of capial. Euaion (5) is derived using Ponryagin s maximum principle. We now use he Hamilon-Jacobi-Bellman mehod o solve he firm s maximizaion problem so ha we can show ha he marke value of a uni of capial is eual o he marginal value of an addiional uni of capial. Using he Hamilon-Jacobi-Bellman mehod we have he following value funcion: V r k max e π K k I C I d, (A1) I 0 s.. I k I, and where CI. The Hamilon-Jacobi-Bellman euaion for (A1) has he following form: max π rv k K k I C I V k I (A) I Differeniaing he Hamilon-Jacobi-Bellman euaion wih respec o he conrol variable resuls in he firs order condiion which is as follows: rv k 1CIVk0, I which is also expressed as follows: 1 V k C I. (A3) Using he explici adjusmen coss funcion, ai CI, hen CI I and Vk1 I. From he curren value Hamilonian and Euaion (5) we have ha 1 I Vk. This resul shows ha he marke value of a uni of capial, which is, is also eual o he marginal value of an addiional ich is V k. uni of capial wh