Inernaional Journal of Economics and Finance; Vol. 9, No. 6; 2017 ISSN 1916-971X E-ISSN 1916-9728 Published by Canadian Cener of Science and Educaion VECM and Variance Decomposiion: An Applicaion o he Consumpion-Wealh Raio François De Paul Silachom 1 1 School for Graduae Sudies, SUNY-Empire Sae College, New York, USA Correspondence: François De Paul Silachom, School for Graduae Sudies, SUNY-Empire Sae College, 325 Hudson Sree 3 rd Floor, New York, NY 10013, USA. Tel: 1-646-230-1273. E-mail. Francois.Silachom@esc.edu Received: April 6, 2017 Acceped: May 19, 2017 Online Published: May 25, 2017 doi:10.5539/ijef.v9n6p188 URL: hps://doi.org/10.5539/ijef.v9n6p188 Absrac This sudy uses a variance decomposiion echnique, which doesn rely on he underlying economic heory, in order o implemen a permanen-ransiory variance decomposiion of he consumpion-wealh raio. We break down he wealh variable ino financial asses, angible asses, and human asses. Using quarerly daa over he las six decades, we rely on coinegraion analysis as he framework for he sudy, in order o assess he long-erm inerrelaion beween consumpion shocks, and hose from each of he above menioned wealh componens. Our resuls indicae ha wealh componens end o exhibi permanen shocks, while consumpion shocks appear o be ransiory. Moreover, he resuls also indicae a low conemporaneous correlaion beween shocks in consumpion and he ones from financial asses, and also beween shocks in consumpion and he ones from angible asses. In addiion, he variance decomposiion of consumpion shocks seems o indicae ha, over he ime a significanly increasing proporion of consumpion shocks is explained by financial asses. Keywords: coinegraion, error correcion model, variance decomposiion, consumpion-wealh raio 1. Inroducion In his sudy, we implemen a variance decomposiion echnique on a sysem of ime-series variables, in order o deermine which ones end o exhibi long erm permanen shocks, and which ones end o have ransiory shocks in he long run. One pariculariy of he echnique we use in order o achieve his variance decomposiion, is ha i doesn rely on any specific underlying economic heory. Our sysem of variables derives from he consumpion-wealh raio, from which we break down he wealh variable componen ino financial asses, angible asses, and human asses, in order o obain along wih he consumpion variable, a sysem of four ime-series variables o work wih. The sudy relies exensively on vecor auoregression analysis VAR, and more specifically on error correcion models ECM, o achieve he permanen-ransiory variance decomposiion beween he variables in he model. Gonzalo and Granger (1995), sugges a way of using error correcion model o implemen a permanen-ransiory variance decomposiion in a sysem of wo variables, and Gonzalo and Ng (2001), use he error correcion model o implemen a permanen ransiory decomposiion in a mulivariae conex wih a sysem of hree variables, in such a way ha he oucome doesn rely on he underlying economic heory. The main resuls of his sudy appear o indicae ha over he pas six decades covered by our daa, all wealh componens exhibi permanen shocks while consumpion shocks are ransiory. Moreover, he resuls indicae ha here s a low conemporaneous correlaion beween innovaions in consumpion and he ones from financial asses, and also beween innovaions in consumpion and he ones from angible asses. In addiion, he variance decomposiion of consumpion shocks indicaes ha over he ime, a significanly increasing proporion of consumpion shocks is explained by financial asses. A fac ha seem o sugges ha he consumpion-wealh linkage apparenly manifes iself essenially hrough financial asses. The res of he paper is srucured as follows: In he nex secion (secion 2) we presen a review of previous sudies relaed o his opic, hen in secion 3 we presen he heoreical framework of our work, and in secion 4 we presen our empirical framework. The main resuls, as well as he main implicaions of our findings are presened in secion 5, and finally he conclusion is presened in secion 6. 188
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 2. Lieraure Hisory Several oher sudies explore issues relaed o hose considered here. Anhony Garra, Donald Roberson, and Sephen Wrigh (2004), sugges a mulivariae version of he Beveridge-Nelson Permanen-Transiory decomposiion, as a ool o assess wha are he economic mechanisms ha pull a given variable owards is rend. They show ha ransiory componens can be relaed direcly o he underlying saionary process ha drives he sysem. Campbell and Mankiw (1987); in Permanen-Transiory Componens and Economics Flucuaions, fail o rejec he hypohesis ha flucuaions in real GNP appear o represen only deviaions from he deerminisic rend. However, hey also consider he possibiliy ha his finding migh be due o he failure o disinguish he business cycle from oher flucuaions in real GNP. Gonzalo and Granger (1995), propose a new way of esimaing common long memory componens of large coinegraed sysems. John Cochrane (1994) in Permanen and Transiory Componens of GNP and Sock Prices, uses a wo-variable vecor auoregression framework, o characerize ransiory componens in GNP and sock prices. He finds ha shocks o GNP holding consumpion consan, are almos enirely ransiory, and accoun for large fracions of he variance of GNP growh. He finds also in he same sudy ha shocks o prices holding dividends consans, are almos enirely ransiory. Gonzalo and Ng (2001), propose a sysemaic framework for analyzing he dynamic effecs of permanen and ransiory shocks, on a sysem of n variables, using a wo-sep orhogonalizaion of he residuals of a VECM wih r coinegraing vecors. Marin Leau and Sydney Ludvigson (2003), in Undersanding Trend and Cycle in Asse Values: Reevaluaing he Wealh Effec on Consumpion, invesigae he wealh-consumpion linkage, in an aemp o explain why here are movemens in asse values ha ofen seem o be disassociaed wih imporan movemens in consumer spending. They find enough evidence o suppor ha only a small fracion of he variaion in household ne worh is relaed o variaion in aggregae consumer spending, wih he precision, hey coninue, ha his does no mean ha wealh has no effec on consumer spending, bu raher, ha only permanen changes in wealh are associaed wih movemens in consumpion. More recenly, Francis X. Diebold and Kamil Yilmaz (2011), in On The Nework Topology of Variance Decomposiion, combine VAR variance decomposiion heory and nework opology heory, o provide a way o assess measures of he connecedness among financial asse reurns and volailiies. Our curren sudy, parly follows on hese seps of Leau and Ludvigson (2003), in assessing he wealh-consumpion linkage, bu by decomposing he wealh elemen ino hree componens: financial asses, angible asses, and human asses, while relying on he variance decomposiion framework developed by Gonzalo and Granger (1995), and Gonzalo and Ng (2001). 3. Consumpion-Wealh Raio and Wealh Decomposiion. The mehodology we use in his sudy is ha of a represenaive agen economy in which all wealh, including human capial, is radable. The heoreical framework is based on he simple accumulaion equaion for aggregae wealh, wrien as: W 1 R )( W C ) (1) ( 1 w, 1 Where R is he ne reurn on aggregae wealh. w, 1 We use an adapaion of he derivaions by Campbell and Mankiw (1989), in Consumpion, Income, and Ineres Raes: Reinerpreing he Time Series Evidence, in Oliver Blanchard and Sanley Fischer, NBER Macroeconomics Annual: 1989, Cambridge, MA: MIT Press, 1989, pp. 185-216, and also hose from Campbell and Shiller (1986), in Dividend-Price Raio and Expecaions of Fuure Dividends and Discoun Facors, in order o ransform he accumulaion equaion for aggregae wealh (1), ino he following expression in which he consumpion-wealh raio is expressed as a funcion of expeced fuure reurns on wealh, and expeced fuure consumpion growh (in logarihms): i c w r c w w, i i1 (2) Where E is he expecaion operaor condiional on informaion available a ime. Now, considering he decomposiion of aggregae wealh ino financial, angible, and human asses, as W F T H, where: W = Marke Value of wealh a ime, F, T, and H, Marke value of financial, angible and human asses a ime, measured as he presen value a ime, of he sream of expeced fuure reurns from F, T, and H, respecively. The human asses here can consis of he raining, he experience, he knowledge, or any combinaion of hese ha an individual may poses, and is assumed here o have a markeable value of H a any ime, and is included in he aggregae wealh value i 189
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 W. Since he sock of human wealh is no direcly observable, we follow Ludvigson and Leau (2001), in Consumpion, Aggregae Wealh, and Expeced Sock Reurns JOF vol.56, by assuming ha he non-saionary componen of human capial, denoed H, can be well described by aggregae labor income, Y. Campbell (1996), in Undersanding Risk and Reurn, JPE vol. 104-2, considers labor income as he dividend on human capial. Considering he breakdown of he aggregae wealh variable, and under he addiional assumpion ha he aggregae wealh reurns R w, +1, can be considered as a weighed sum of he reurns from each individual wealh componens, our log consumpion wealh raio can be represened as follows: f y i1 w i c f y f 1 y c (3) f i Where he parameers α f, α τ, and α y are heoreically equal o he shares of financial asses, angible asses, and labor income in he log of aggregae wealh respecively, and ω f, ω τ, and (1 - ω f - ω τ ) heir respecive shares in he aggregae wealh reurn. Equaion (3) is a consumpion-based presen value relaion involving fuure growh of each componen of our wealh decomposiion, as well as fuure consumpion growh. This equaion suggess ha in case Δf, Δτ, Δy, and Δc are covariance saionary, hen consumpion, financial asses, angible asses, and labor income, are coinegraed. I also implies ha deviaions from heir common rend, represened by he lef-hand-side of (3), provide a raional growh forecas of any one of he four variables in he sysem, or of some combinaion of hem. The parameers α f, α τ, and α y represen he coinegraing coefficiens. 4. Empirical Framework: Model and Variables Descripion The main empirical approach in his sudy is he use of coinegraion o idenify permanen and ransiory componens beween consumpion, financial asses, angible asses, and labor income. We denoe by x c, f,, y )' he vecor of dependen variables in he model, represening respecively log of real ( consumpion expendiures, log of real ne financial asses, log of real angible asses, and log of real labor income respecively. The Augmened Dickey Fuller es is performed on hese four variables. Said and Dickey (1984) demonsrae ha he ADF es is asympoically valid in he presence of a moving average (MA) componen, provided ha sufficien lagged difference erms are included in he es regression. We choose o run he es wih he more general specificaion ha includes boh a consan and a linear rend, and wihou addiional exogenous variables. The sandard recommendaion is o choose a specificaion ha is a plausible descripion of he daa under boh he null and alernaive hypoheses, (Hamilon 1994, p. 501). In specifying he number of lagged difference erms o be added o he es regression, he usual recommendaion is o include a number of lags sufficien o remove serial correlaion in he residuals. The uni roos es on each variable in he sysem suggess ha all he variables conained in x are firs order inegraed, or I(1). To obain a correcly specified error-correcion model, we begin by esing for boh he presence and number of coinegraing relaions in x. Prior for doing ha, wo imporan issues needed o be invesigaed. Tha s wheher o include he rend and/or he drif parameers in he model, and wha is he appropriae lag lengh of he sysem. Johansen (1994) suggess ha: One should include a ime rend in he VECM if we suspec ha: The componens of he vecor 'X (or some combinaion of hem) are rend saionary, so ha hey veer apar. X is rend saionary raher han a mulivariae uni roo wih drif process. We may wan o es his hypohesis under he rend saionariy hypohesis ha he marix A ( 1) ' has full rank (n). One of Johansen's coinegraion ess, he race es, has his as alernaive hypohesis. Following hese recommendaions by Johansen (1994), he plo of all our four variables expressed in logs (Appendix B), suggess ha we should no include drif, nor rend in our analysis. The remaining issue which is he lag lengh, is deal wih by relying on he minimum value of he Akaike Informaion Crierion, AIC. The coinegraion es sugges he presence of a single coinegraing vecor; which we impose in he VECM i f i i 190
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 specifcaion from now on. The coinegraing coefficien on consumpion is normalized o one, and we denoe he single coinegraing vecor for x ( c, f,, y )', as (1, f,, y )'. We herefore consider from now on, he VECM represenaion specified below, using lower case for he sysem vecors of variables: x ' x ( L x e (4) x 1 ) 1 is he vecor of log firs differences, (,,, )', (γ c, γ f, γ τ, γ y )' is he (4 1) vecor of c f adjusmen coefficiens. I will be an imporan facor in elling us which variables subsequenly adjus o resore he common rend when a deviaion occurs. The Granger Represenaion Theorem saes ha, if a vecor x is coinegraed, a leas one of he adjusmen parameers, γ c, γ f, γ τ, or γ y mus be nonzero in he error-correcion represenaion (4). Thus if x j does a leas some of he adjusing needed o resore he long-run equilibrium subsequen o a shock ha disors his equilibrium, γ j should be differen from zero in he equaion for Δx j of he error-correcion represenaion. (L) is a finie order disribued lag operaor, and 1,,, )' is he y ( f y (4 1) vecor of coinegraing coefficiens. Throughou his paper, we use has o denoe he esimaed values of parameers. The erm ' x gives las period's equilibrium error, or coinegraing residual. 1 5. Main Resuls and Implicaions Table 1. Minimum informaion crierion Lag MA 0 MA 1 MA 2 MA 3 MA 4 MA 5 AR 0-11.78861-11.63212-11.57118-11.50699-11.4516-11.39751 AR 1-36.77828-36.69077-36.65201-36.7775-36.83518-36.87385 AR 2-36.99628-36.97361-36.88726-36.88588-36.86558-36.93982 AR 3-36.99651-36.9579-36.89507-36.886-36.83848-36.84815 AR 4-37.02186-36.95866-36.90829-36.80901-36.76287-36.78745 AR 5-36.98839-36.96623-36.87961-36.79413-36.812-36.75959 The es indicaes a number of lag lengh of 4 periods. Table 2. Coinegraion rank es using race H0: Rank=r H1: Rank>r Eigenvalue 5% Criical Trace Drif Value Drif in in ECM Process 0 1 2 3 0 1 2 3 0.1979 0.0406 0.0136 0.0114 60.8726 14.1274 5.3317 2.4329 39.71 24.08 12.21 4.14 NOINT Consan Table 3. Long-run parameer (alpha) esimaes when RANK=1 Variable consumpion 1.00000 financial asses 0.01237 angible asses -0.62314 labor income -0.45246 Table 4. Adjusmen coefficien (gamma) esimaes when RANK=1 Variable consumpion -0.00728 financial asses -0.01383 angible asses 0.00040 labor income 0.00388 191
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 The saionariy ess performed on all four variables of he sysem: C, f, τ, and y, respecively consumpion, ne financial asses, angible asses, and labor income, (all variables are in logs) sugges ha all four variables are I(1). The coinegraion es has been conduced using he coinegraing rank es and an AIC minimum value, wih a lag lengh of 4 periods (Table 1). They sugges he presence of a single coinegraing vecor, a a significance level of 5% (Table 2). The esimaes of he coinegraing vecor represened in his sudy by, is hen given by ˆ ' (1, 0. 0124, 0.6231, 0.4525) wih all he coefficiens normalized wih respec o consumpion (Table 3). Also, he esimaes of he unresriced long-run adjusmen coefficiens, whose vecor is represened by in his sudy, are given by ˆ' (-0.00728, -0.01383, 0.00040, 0.00388), for consumpion, ne financial asses, angible asses, and labor income, respecively (Table 4). Table 5. Error correcion model esimaes Dependen Variables c f cfy 1-0.00728-0.01383 0.00040 0.00388 -Value (-5.73) (-1.46) (0.19) (1.66) c 1 0.10524 0.00788 0.05397 0.42404 -Value (1.40) (0.01) (0.43) (3.10) c 2 0.04163 0.26677 0.24718 0.05106 -Value (0.54) (0.47) (1.92) (0.36) c 3 0.05568-0.31752 0.28290 0.34894 Value (0.73) (-0.56) (2.21) (2.51) f 1 0.03563 0.24421 0.31959 0.14881 -Value (0.86) (0.80) (4.59) (1.97) f 2-0.00616-0.13318 0.08784-0.09865 -Value (-0.15) (-0.43) (1.24) (-1.29) f 3 0.05148-0.25899 0.19258 0.09909 -Value (1.26) (-0.85) (2.80) (1.33) 1 0.03000 0.02724 0.02890 0.05001 -Value (3.21) (0.39) (1.84) (2.93) 2 0.01351 0.01344 0.02065 0.04764 -Value (1.42) (0.19) (1.29) (2.73) 3 0.01515 0.04952 0.00431 0.06503 -Value (1.58) (0.69) (0.27) (3.70) 0.04350-0.10332-0.07000-0.00097 y 1 -Value (1.09) (-0.35) (-1.04) (-0.01) y 2-0.00769-0.21282 0.00504 0.04764 -Value (-0.20) (-0.73) (0.08) (2.73) y 3-0.01337 0.16172-0.09533-0.14762 -Value (-0.35) (0.57) (-1.48) (-2.11) R-squared Pr > F 0.1549 0.0033 0.0143 0.9997 0.3167 <.0001 y 0.3408 <.0001 Resul #1: From his four-variables coinegraing sysem, he presence of a single coinegraing equaion suggess ha here are hree permanen componens and one ransiory componen, following Gonzalo and Ng. In order o deermine which are he common long-memory componens of he sysem of variables, we follow Gonzalo and Granger (1995), in idenifying he common facors. Since he las hree adjusmen coefficiens are no saisically significan (very low -saisics), Gonzalo and Ng (2001) recommend o resric hem o zero. When we impose ha resricion, our resriced vecor of adjusmen coefficien esimaes becomes, ˆ ' = (-0.00728, 0, 0, 0). We use hese values o obain he orhogonal marix ˆ, defined such ha ˆ ' ˆ 0. We hen implemen he permanen-ransiory decomposiion of he variables in he sysem. Our decomposiion indicaes ha he common facors, i.e hose variables ha exhibi a permanen shocks, are financial asses, angible asses, and 192
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 labor income. Consumpion shocks however are ransiory. This means, according o Engle and Granger (1987) inerpreaion, ha a deviaion from he common rend shared by consumpion, financial asses, angible asses, and labor income, can beer be described as ransiory movemens mosly in consumpion. This indicaes ha consumpion is he variable ha adjuss iself o push he sysem back o equilibrium afer a emporary move away from i. The finding ha consumpion shocks are ransiory, and wealh shocks are permanen, seems conrary o hose obained by Leau and Ludvigson (2003), where, wih a differen wealh decomposiion ino asses wealh and non-asses, hey found asses shocks essenially ransiory, whereas consumpion shocks were mosly permanen. One possible explanaion of he difference beween he wo resuls, could well be explained by he difference in he lag-lengh used in he VECM esimaion: Our lag-lengh es suggesed a four periods lag, which we have applied in he esimaion, while he oher uses one period lag. According o Gonzalo and Ng (2001), he number of lag-lengh periods included in he esimaion, has an imporan effec on he saisical significance of he adjusmen coefficiens; And he vecor of adjusmen coefficiens esimaes ˆ iself, is very imporan when implemening he permanen-ransiory decomposiion. As Ng and Gonzalo (2001) poin ou, he role of in any Permanen-Transiory decomposiion is very crucial since defines he permanen shocks. Our resuls however, are consisen wih he idea ha agens are expeced o adjus heir consumpion expendiures o changes in heir wealh wih a cerain ime delay which, we can refer o as he delay of consumpion adjusmen o wealh. Table 6. Cross correlaion of residuals Lag Variable cons f. asses. asses income 0 cons 1.00000 0.15901 0.14481 0.40638 f. asses 0.15901 1.00000 0.07427 0.09272. asses 0.14481 0.07427 1.00000 0.26512 income 0.40638 0.09272 0.26512 1.00000 1 cons -0.00218 0.00759-0.01546-0.01510 f. asses -0.01479-0.01249 0.00353-0.01339. asses 0.02537 0.03110-0.02087 0.00781 income -0.01378 0.00461-0.04739-0.04319 2 cons 0.00348 0.01026 0.00531-0.02468 f. asses -0.00818-0.00558-0.00363-0.00698. asses 0.02665 0.02665 0.01184-0.01523 income -0.00097 0.01615 0.03983-0.08706 3 cons 0.00968 0.00035 0.00848-0.04104 f. asses -0.00604 0.00561-0.00969-0.02101. asses 0.06782 0.03105 0.02225 0.05197 income 0.02765-0.00684 0.04418-0.02218 4 cons 0.00256-0.00918 0.07954 0.08651 f. asses 0.11887 0.05410 0.06566 0.15697. asses -0.03591-0.07988 0.06511-0.03898 income 0.06703 0.03993-0.02447 0.08475 Resul #2: From he able 6, we can also see ha here s a low conemporaneous correlaion beween innovaions in consumpion and innovaions in financial asses, 15.9%; also, a low conemporaneous correlaion beween innovaions in consumpion and innovaions in angible asses, 14.48%. This finding is consisen wih Leau and Ludvigson s finding ha, only a small fracion of he variaion in wealh is relaed o variaion in consumpion. However according o he generaed Cholesky variance decomposiion for consumpion growh residuals (Appendix A, Tables A1, and A2), his saemen appears o be rue only in a very shor horizon. Table A1 appears o indicae ha consumpion s variance is mosly explained by iself in a very shor horizon, and over he ime, a significanly increasing proporion of consumpion shock is explained by financial asses. The proporions of consumpion shocks explained by angible asses and labor income are relaively insignifican, boh a shor and long horizon ime periods. When he resricions are imposed on he adjusmen coefficiens (able A2), he proporion of he consumpion shocks explained by financial asses becomes even larger, and he one explained by angible asses and labor income becomes much smaller, compared o he resuls obained wihou resricion on he adjusmen coefficiens. 193
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 These ECM esimaes of he R-square are respecively, 0.1549 for consumpion, 0.0143 for financial asses, 0.3167 for angible asses, and 0.3408 for labor income (able 5). Their values seem o indicae ha, angible asses growh and labor income growh show srong reliance on he pas, consumpion growh shows a weak reliance on he hisory, while financial asses growh does no seem o rely on is pas. In oher words, i is no possible o rely on pas informaion o predic financial asses growh, his finding is somehow consisen wih he idea behind he efficien marke hypohesis. Table 7. Long-horizon growh of financial asses, angible asses, labor income, and consumpion, on cfy Horizon Variables Panel A Panel B Panel C Panel D f 2 h R 2 h R y 2 h R c 2 h R 1 2 3 4 5 6 7 8 12 inercep 0.06759 [1.56] -0.02771 [-2.34] 0.03255 [2.46] 0.01693 [2.65] cf 0.0087 0.0463 0.0164 0.0074 y 0.07844 [1.37] inercep 0.12947 [2.06] -0.05022 [-3.22] -0.06840 [-3.48] 0.03296 [1.89] 0.05596 [2.64] 0.01063 [1.26] 0.03026 [3.01] cf y 0.0151 0.0885 0.0170 0.0072 0.14927 [1.80] inercep 0.17928 [2.28] y -0.11739 [-4.54] -0.11499 [-4.29] 0.05376 [1.92] 0.07004 [2.43] 0.01648 [1.24] 0.04108 [3.10] cf 0.0181 0.1232 0.0123 0.0055 0.20407 [1.97] inercep 0.21055 [2.27] y -0.19228 [-5.45] -0.16930 [-5.08] 0.06220 [1.64] 0.08164 [2.31] 0.01898 [1.09] 0.04550 [2.81] cf 0.0172 0.1595 0.0096 0.0018 0.23419 [1.92] inercep 0.21938 [2.07] -0.27707 [-6.31] -0.22861 [-5.87] 0.06722 [1.44] 0.08990 [2.17] 0.01311 [0.61] 0.04807 [2.57] cf y 0.0133 0.1981 0.0072 0.0002 0.23450 [1.68] inercep 0.23131 [1.98] -0.36827 [-7.18] -0.28834 [-6.59] 0.06779 [1.24] 0.10852 [2.35] 0.00475 [0.19] 0.04688 [2.26] cf y 0.0115 0.2347 0.0084 0.0004 0.23905 [1.56] -0.45989 [-7.99] 0.08200 [1.35] -0.00846 [-0.31] inercep 0.23158-0.34317 0.13040 0.04810 [1.82] [-7.18] [2.56] [2.13] cf 0.0089 0.2660 0.0103 0.0018 y 0.22804 [1.36] -0.54480 [-8.66] 0.10041 [1.49] -0.01852 [-0.62] inercep 0.22934-0.39701 0.15775 0.05078 [1.68] [-7.72] [2.84] [2.10] cf 0.0069 0.2954 0.0136 0.0033 y 0.21371 [1.19] -0.62838 [-9.29] 0.12583 [1.72] -0.02672 [-0.84] inercep 0.34286-0.63520 0.20242 0.06112 [2.00] [-10.33] [2.88] [2.02] cf 0.0099 0.4272 0.0115 0.0105 y 0.31975 [1.42] -0.99130 [-12.27] 0.14461 [1.56] -0.05949 [-1.50] 194
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 x 20 h inercep 0.82346 [3.85] -0.91400 [-13.56] 0.26217 [2.88] 0.07289 [1.95] cf 0.0465 0.5829 0.0069 0.0371 y cfy, wih 0 1 h 0.86118 [3.07] h 1 2-1.45438 [-16.46] x x x... x h 0.14108 [1.18] -0.13697 [-2.79] Resul #3: In order o assess he predicive conen of he consumpion-wealh raio for fuure consumpion growh, he growh of fuure financial asses, fuure angible asses growh, and fuure labor income growh, we esimae long-horizons simple regressions of consumpion growh, c, financial asses growh h f, h angible asse growh, and labor income growh h y, agains he coinegraing residuals h cf y respecively. For his purpose, we make use he following specificaion: x h cfy, where 0 1 h x x x... x h 1 2 h. Since all he variables were shown o be I(1), boh our dependen and independen variables (expressed in differences) are saionary. Hence, we can rely on he regular -saisic o assess he saisical significance of he regression coefficiens. The regression resuls presened in Tables 2 appear o indicae ha: On one hand, here s no significan relaion beween fuure consumpion growh and he consumpion-wealh raio a shor horizons. However, a long-horizons he relaion appears o be significan (Table 7, Panel D). These resuls appear o sugges firs, ha he consumpion-wealh raio significanly predic he fuure consumpion growh only a a long horizon. Second, such an oucome would iself, be consisen wih he finding menioned earlier in Resul #1, ha when he sysem is ou of is equilibrium pah in shor horizon, consumpion is he variable ha will adjus gradually o allow he whole sysem o converge back o is long-horizon common rend. On he oher hand, we can observe from Table 7 Panel B, ha here s a significan negaive relaion beween fuure angible asses growh and he consumpion-wealh raio over he enire horizon considered. This seems o indicae ha: Firs, he consumpion-wealh raio does significanly predic he growh of fuure angible asses. Second, he negaive relaion beween he consumpion-wealh raio and he growh of fuure angible asses indicaes ha a high consumpion-wealh raio oday can be relaed o a low angible asse growh in he fuure, and vice-versa. Secondly, his also means, if we consider our daa se and, as far he US economy is concerned, ha he excess of saving implied by he delay of consumpion adjusmens o changes in wealh, has significanly and persisenly explained he growh of fuure angible asses over he enire horizon considered in his sudy, wih a much sronger effec as he ime horizon ges longer. However, here appears o be some weak and unsable relaion beween fuure financial asse growh and he consumpion-wealh raio (Table 7 Panel A), and no significan relaion beween fuure labor income growh and he consumpion-wealh raio over he enire horizon considered (Table 7 Panel C). 6. Conclusion In his sudy, we invesigae some aspecs of he relaionship beween wealh componens and consumpion. More specifically we decompose wealh ino financial asses, angible asses, and human asses, and, along wih consumpion, we firs ry o idenify which variables exhibi permanen shocks and which ones exhibi ransiory shocks. In order o achieve his, we use he model derived by Campbell and Mankiw (1988) and, apply our wealh decomposiion o obain a raional expecaion ineremporal linear expression, relaing he curren consumpion-wealh raio o expeced fuure consumpion growh, expeced fuure financial asses growh, expeced angible asses growh, and expeced human asse s growh. Second, we rely on some of he resuls obained from he above invesigaion, o ry o assess he cross correlaions, as well as he predicabiliy of each of hese variables by he consumpion-wealh raio. We make he assumpion ha he value of each wealh componen reflecs he sum of he presen values of he sream of revenues expeced from hese asses. The human asse s value is proxied by labor income. Our main resuls in his sudy indicae ha all wealh componens exhibi permanen shocks, while consumpion shocks are ransiory. They also indicae ha here s a low conemporaneous correlaion beween innovaions in consumpion and financial asses, and also beween innovaions in consumpion and angible asses. However, a 195
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 variance decomposiion of consumpion shocks indicaes ha, over he ime a significanly increasing proporion of consumpion shocks is explained by financial asses. This paricular aspec of our findings seems o sugges ha he consumpion-wealh linkage in his sudy manifess iself essenially hrough financial asses. Finally, we find ha he consumpion-wealh raio persisenly and significanly predics fuure angible asses growh. This las resul appears o indicae ha over he enire ime horizon considered in his sudy, he excess of savings resuling from he delay of consumpion adjusmen o changes in wealh, has mos likely and consisenly, been convered ino angible asses. References Alvarez, F., & Urban, J. (2001). The Size of The Permanen Componen of he Asse Pricing Kernels. NBER, w8360. hps://doi.org/10.3386/w8360 Ang, A., & Geer, B. (2005). Sock Reurn Predicabiliy: Is i There? NBER, Sepember. Bekaer, G., Eric, E., & Seven, G. (2006). Socks and Bonds Reurns wih Moody Invesors. NBER, w12247. Bekaer, G., Eric, E., & Yuhang, X. (2006). Risk, Uncerainy and Asse Prices. NBER, w12248. hps://doi.org/10.3386/w12248 Bernanke, B., & Mark, G. (2000). Moneary Policy and Asse Price Volailiy. NBER, w7559. hps://doi.org/10.3386/w7559 Blanchard, O. J., & Danny, Q. (1988). The Dynamic Effecs of Aggregae Demand and Supply Disurbances. NBER, w2737. hps://doi.org/10.3386/w2737 Boudoukh, J., Mahew, R., & Rober, F. W. (1994). Inducry Reurns and he Fisher Effec. Journal of Finance, 49(5). hps://doi.org/10.1111/j.1540-6261.1994.b04774.x Campbell, J. Y. (1988). Asse Prices, Consumpion, and he Business Cycle. NBER, w6485 March. Campbell, J. Y. (1990). A Variance Decomposiion for Sock Reurns. NBER wp3246. hps://doi.org/10.3386/w3246 Campbell, J. Y. (1991). A Variance Decomposiion for Sock Reurns. Economeric Journal, 101(405). hps://doi.org/10.2307/2233809 Campbell, J. Y. (1996). Undersanding Risk and Reurn. Journal of Poliical Economy, 104(2). hps://doi.org/10.1086/262026 Campbell, J. Y. (2000). Commen on Low Inflaion: The Behavior of Financial Markes and Insiuions. Journal of Money, Credi and Banking, 32(4), 1088-1092. hps://doi.org/10.2307/2601161 Campbell, J. Y., & Gregory, N. M. (1987). Permanen and Transiory Componens in Macroeconomic Flucuaions. NBER, w2169. hps://doi.org/10.3386/w2169 Campbell, J. Y., & Gregory, N. M. (1989). Consumpion, Income, and Ineres Raes: Reinerpreing he Time Series Evidence. NBER, w2924. hps://doi.org/10.1086/654107 Campbell, J. Y., & John, A. (1993). Wha Moves he Sock and Bond Markes? A Variance Decomposiion for Long-Term Asses Reurns. Journal of Finance, 48(1), 3-37. hps://doi.org/10.1111/j.1540-6261.1993.b04700.x Campbell, J. Y., & Pierre, P. (1991). Pifalls and Opporuniies: Wha Macroeconomiss should know abou uni roos. NBER w0100. hps://doi.org/10.3386/0100 Campbell, J. Y., & Rober, J. S. (1988). Inerpreing Coinegraing Models. NBER, w2568, April. Cochrane, J. (2005). Financial Markes and he Real Economy. Graduae School of Business, Universiy of Chicago, Sepember. hps://doi.org/10.3386/w11193 Cochrane, J. H. (1994). Permanen and Transiory Componens of GNP and Sock Prices. The Quarerly Journal of Economics, 109(1), 241-265. hps://doi.org/10.2307/2118434 Cochrane, J. H. (2001). Asse Pricing. Princeon Universiy Press. Collard, F., Parick, F., & Imen, G. (2006). Predicabiliy and Habi Persisence. JEDC, 30. hps://doi.org/10.1016/j.jedc.2005.06.016 Diebold, F. X., & Yilmaz, K. (2011). On The Nework Topology of Variance Decomposiions: Measuring The Connecedness Of Financial Firms. NBER, w17490. hps://doi.org/10.3386/w17490 196
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ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 Bureau of Economic Analysis. The oher wealh variables -Toal wealh is household ne worh in billions of curren dollars, measured a he end of he period, no seasonally adjused. - Tangible Asses are measured in his sudy as Real esae + Equipmens and sofware + Consumer durable goods. - Financial Asses are made of oal financial asses from households and non-profi organizaions, in billions of dollars, and non-seasonally adjused. All hese oher wealh variables are deflaed in his sudy, by he GDP deflaor in order o have heir values in real erms. The source for hese daa is he Board of Governors of he Federal Reserve Sysem. A complee descripion of hese daa may be found a hp://www.federalreserve.gov/releases/z1/curren/ Appendix A Variance Decomposiion of consumpion shocks (he ransiory shocks), over a 30 (quarers) periods horizon Table A1 Period S.E. C FA TA Y 1 0.004512 100.0000 0.000000 0.000000 0.000000 2 0.007039 97.49167 1.844834 0.509162 0.154329 3 0.009213 94.70941 4.176935 1.012008 0.101643 4 0.011388 90.65578 7.179819 2.097801 0.066604 5 0.013484 85.50411 11.73058 2.713336 0.051965 6 0.015437 81.79405 15.01648 3.147360 0.042105 7 0.017245 79.06731 17.37070 3.527853 0.034135 8 0.018916 76.81313 19.36574 3.792643 0.028488 9 0.020460 75.05660 20.94725 3.970185 0.025957 10 0.021901 73.66154 22.17704 4.136156 0.025260 11 0.023251 72.49765 23.17743 4.298538 0.026383 12 0.024530 71.50181 24.00775 4.461275 0.029166 13 0.025755 70.62963 24.70254 4.633975 0.033861 14 0.026937 69.84271 25.29502 4.822981 0.039291 15 0.028086 69.11665 25.80806 5.030060 0.045226 16 0.029210 68.43211 26.25993 5.256710 0.051246 17 0.030313 67.77677 26.66316 5.502818 0.057251 18 0.031400 67.14301 27.02546 5.768608 0.062926 19 0.032473 66.52507 27.35339 6.053321 0.068219 20 0.033536 65.91888 27.65213 6.355929 0.073053 21 0.034589 65.32221 27.92503 6.675310 0.077450 22 0.035635 64.73334 28.17472 7.010548 0.081388 23 0.036675 64.15102 28.40355 7.360524 0.084903 24 0.037709 63.57436 28.61341 7.724214 0.088015 25 0.038740 63.00274 28.80585 8.100642 0.090763 26 0.039767 62.43566 28.98227 8.488908 0.093169 27 0.040792 61.87272 29.14389 8.888123 0.095264 28 0.041815 61.31364 29.29183 9.297457 0.097075 29 0.042837 60.75820 29.42705 9.716117 0.098626 30 0.043859 60.20626 29.55045 10.14335 0.099939 Noe. Cholesky Ordering: Consumpion, Fin. Asses, Tan. Asses, Labor income. 198
ijef.ccsene.org Inernaional Journal of Economics and Finance Vol. 9, No. 6; 2017 Table A2 Period S.E. C FA TA Y 1 0.004491 100.0000 0.000000 0.000000 0.000000 2 0.006986 97.36353 1.987846 0.516301 0.132320 3 0.009127 94.32370 4.571205 1.023987 0.081103 4 0.011274 89.92244 7.914164 2.106371 0.057026 5 0.013352 84.32064 12.93961 2.698294 0.041453 6 0.015289 80.32090 16.56864 3.076910 0.033548 7 0.017088 77.40388 19.18546 3.379109 0.031552 8 0.018756 75.00008 21.41931 3.549925 0.030678 9 0.020304 73.11799 23.23106 3.623954 0.026991 10 0.021754 71.59974 24.70318 3.673529 0.023544 11 0.023119 70.30953 25.96240 3.706911 0.021159 12 0.024418 69.18617 27.06507 3.728146 0.020619 13 0.025668 68.18540 28.04627 3.745536 0.022792 14 0.026880 67.27053 28.93822 3.763899 0.027343 15 0.028060 66.41883 29.76219 3.784719 0.034264 16 0.029217 65.61228 30.53534 3.809109 0.043271 17 0.030354 64.83989 31.26871 3.837139 0.054267 18 0.031476 64.09542 31.96856 3.869157 0.066865 19 0.032584 63.37394 32.64025 3.904894 0.080920 20 0.033680 62.67192 33.28791 3.943936 0.096239 21 0.034767 61.98746 33.91391 3.985887 0.112741 22 0.035844 61.31906 34.52016 4.030495 0.130277 23 0.036914 60.66543 35.10838 4.077404 0.148786 24 0.037977 60.02559 35.67989 4.126328 0.168186 25 0.039034 59.39874 36.23582 4.177013 0.188427 26 0.040085 58.78415 36.77716 4.229252 0.209437 27 0.041132 58.18119 37.30480 4.282838 0.231171 28 0.042175 57.58930 37.81953 4.337599 0.253572 29 0.043215 57.00798 38.32206 4.393373 0.276595 30 0.044251 56.43679 38.81300 4.450019 0.300192 Noe. Cholesky Ordering: Consumpion, Fin. Asses, Tan. Asses, Labor Income. One can noice ha from boh ables here s a gradual increase along wih he horizon, of he proporion of he consumpion variance explained by financial asses, whereas he proporion explained by angible asses and labor income respecively are relaively sable. Appendix B Variables plo 7 6 5 4 3 2 55 60 65 70 75 80 85 90 95 00 05 10 15 consumpion financial asses angible asses labor income Copyrighs Copyrigh for his aricle is reained by he auhor(s), wih firs publicaion righs graned o he journal. This is an open-access aricle disribued under he erms and condiions of he Creaive Commons Aribuion license (hp://creaivecommons.org/licenses/by/4.0/). 199