The Relationship between Consumption, Income and Wealth in Australia

Transcription

1 The Relaionship beween Consumpion, Income and Wealh in Ausralia Lance A. Fisher Glenn Oo School of Economics Universiy of New Souh Wales Sydney, Ausralia and Graham M. Voss Deparmen of Economics Universiy of Vicoria Vicoria, Canada Draf: Augus 2005 Preliminary and Incomplee Absrac This paper idenifies a long-run relaionship beween consumpion, labour income and wealh in Ausralian daa over he period 1976:4-2004:3. I also finds a long-run relaionship beween consumpion, labour income and he wo componens of wealh, namely, financial and non-financial wealh. The esimaed vecor-error correcion models show ha wealh and, principally non-financial wealh, adjuss he mos o resore he long-run coinegraing relaion among he variables in response o a ransiory shock. The ransiory componen of wealh, paricularly of non-financial wealh, is large relaive o he ransiory componen of consumpion and labour income. Since 2003, non-financial wealh has increased dramaically o levels above rend ha are unprecedened hisorically. A he same ime consumpion has no significanly moved above rend and his implies ha a downward adjusmen in non-financial wealh (ha is, a fall in housing prices) is expeced by households in he fuure o re-esablish he long-run relaionship among he series. Lance A. Fisher Glenn Oo School of Economics Universiy of New Souh Wales Sydney, NSW, 2053, Ausralia L.Fisher@unsw.edu.au G.Oo@unsw.edu.au Graham M. Voss Deparmen of Economics Universiy of Vicoria PO Box 1700 STN CSC Vicoria, BC V8W 2Y2, Canada gvoss@uvic.ca 1

2 1. Inroducion The recen srong growh in household wealh in many counries moivaes a number of sudies o examine he relaionship beween household consumpion and wealh. A key concern of such sudies is how household consumpion is likely o reac o variaions in household wealh, paricularly he possibiliy of subsanial declines in sock marke or housing asse values wih subsequen repercussions for aggregae consumpion. To his end, long run relaionships beween consumpion and wealh are ofen used as a guide o wealh effecs on consumpion. 1 These long run relaionships, however, mus be used wih some care. This poin is emphasised in a recen US sudy, Leau and Ludvigson (2004), which demonsraes ha much of he variaion in US household asse wealh, alhough highly persisen, is ransiory in naure eliciing lile or no response in household consumpion. Long run esimaes of wealh effecs hen oversae he adjusmen of consumpion o conjecured changes in asse wealh as he possible adjusmen o wealh iself is ignored. In general o undersand he relaionship beween consumpion and wealh requires a sysems approach: modelling he endogenous behaviour of boh consumpion and wealh, as well as idenifying economically inerpreable disurbances. This allows for a coheren daa-based assessmen of he likely behaviour of consumpion and wealh o underlying disurbances. This sudy re-evaluaes he wealh effec on consumpion in Ausralia using a sysems approach o modelling, a vecor error correcion model for consumpion, labour income and wealh. I follows Leau and Ludvigson (2004) by considering he permanen and ransiory shocks ha underlie he model and he relaive imporance hese shocks have for he series of ineres. Our sudy makes some addiional conribuions. As par of he empirical work, we explore in deail he long run relaionship beween consumpion, labour income, and wealh he underlying relaionship for sudies such as ours. Previous sudies, boh for Ausralia and he US, sugges ha he long-run relaionship beween hese series is no paricularly robus. As his maers for boh he long run and dynamic relaionships i is imporan o have a clear picure of he robusness of his relaionship. We also consider he individual behaviour of he componens of household wealh, financial and non-financial (housing) asses. In Ausralia, he non-financial asses represen abou sixy percen of household asses and he seep increase in wealh in recen years is largely explained by increases in housing prices (see for example Tan and Voss, 2003). In conras, much of he increase in US aggregae household wealh in recen years (specifically he 1990s) is explained by rising values of household equiy holdings (Poerba, 2000). 2 1 Leau and Ludvigson (2004) provide a summary of recen insances of wealh effecs calculaed from such long run relaionships. Poerba (2000) is an example for he US; Tan and Voss (2003) is an example for Ausralia. Oher recen relaed sudies are Hamburg e al. (2005) for Germany, Pichee and Tremblay (2003) for Canada, and Fernandez-Corugedo e al. (2002) for he UK. 2 Addiional evidence ha US household asse wealh is dominaed by equiy marke reurns is given in Leau and Ludvigson (2004), which noes a very high correlaion beween quarerly flucuaions in household ne worh and movemens in equiy reurns. I is possible, however, o oversress he dependence of household wealh in he US on financial asses. While his is cerainly rue in aggregae, he siuaion is 2

3 The forma of he paper is follows. Secion 2 briefly reviews relaed lieraure and pus our work ino conex. In secion 3, we presen he empirical model and skech is relaionship o sandard heories of household consumpion. Secion 4 presens he empirical model esimaion including a variey of robusness checks on our principal conclusions. Finally, secion 5 summarizes our principal resuls and implicaions for policy makers concerning he behaviour of consumpion and wealh. 2. Relaed Lieraure: Theory and Exising Empirical Work In wo imporan papers, Leau and Ludvigson (2001, 2004) have reconsidered he relaionship beween consumpion, labour income and wealh for he Unied Saes. They idenify he permanen and ransiory componens in hese series and re-evaluae he imporance of he wealh effec on consumpion. They show ha mos of he variaion in wealh is ransiory and quie persisen and ha consumpion responds very lile o ransiory wealh flucuaions. As a resul, large movemens in wealh are esimaed o have a small impac on consumpion, much smaller han he esimaes repored in earlier U.S. sudies. They aribue mos of he variaion in wealh o flucuaions in sock marke wealh and correspondingly very lile o flucuaions in non-sock marke wealh, which is mainly housing wealh. Like consumpion, he ransiory componen of non-sock marke wealh is small whereas for sock marke wealh i is large. The imporance of he wealh effec on consumpion in Ausralia has recenly been invesigaed by Tan and Voss (2003). They find ha he wealh effec on consumpion is quaniaively imporan and ha consumpion responds more srongly o changes in non-financial wealh han o changes in financial wealh. However, heir analysis was conduced in a single-equaion framework which, as hey noe, assumes all of he adjusmen o changes in wealh occurs hrough consumpion changes and ha is likely o over-esimae he wealh effec on consumpion. Raher han focus on he wealh effec on consumpion, Fisher and Voss (2004) adop he approach of Leau and Ludvigson (2001) and evaluae he predicive conen of deviaions from he esimaed relaionship beween consumpion, labour income and wealh for consumpion growh, labour income growh and sock marke reurns in Ausralia. They find ha deviaions from he esimaed relaionship forecass nex period s reurn on he aggregae sock marke index bu no consumpion and labour income growh over nex period. Tha implies here is an imporan ransiory componen o sock marke wealh because sock reurns are predicable and an unimporan ransiory componen o consumpion as consumpion growh is no predicable, which has implicaions for he wealh effec on consumpion. The presen paper direcly esimaes he permanen and ransiory componen in consumpion, labour income and wealh, along he lines of Leau and Ludvigon (2004) and reconsiders he quesion of how imporan flucuaions in wealh are for consumpion changes in Ausralia. Moreover, he presen paper esimaes he permanen and ransiory componen in boh componens of wealh, financial and non-financial wealh, and evaluaes heir separae effec on consumpion. Mos of he ransiory variaion in wealh is aribuable o ransiory variaion in non-financial wealh hough ransiory variaion in somewha disored by he highly unequal disribuion of wealh in he US. For example, less han 10 percen of US households boh owned a home and held equiy worh more han he value of heir home in 1998 (Poerba, 2000). We reurn o his issue laer in he paper. 3

4 financial wealh is neverheless significan. There is lile response of consumpion and labour income o ransiory variaion in boh componens of wealh. Thus, i is expeced ha he large deviaion of wealh above is sochasic rend ha is observed in recen Ausralian daa will be correced by a downward adjusmen in wealh, principally nonfinancial wealh, raher han by any adjusmen in consumpion and labour income. The relaionship beween consumpion and wealh has also been invesigaed for some oher counries following he approach of Leau and Ludvigson (2001, 2004). Fernandez-Corugedo, Price and Blake (2002) find in U.K. daa a sizable ransiory componen o wealh and ha mos of he adjusmen o deviaions from he long-run relaion occurs hrough wealh. The resuls in his paper are quie similar o our own. Pichee and Tremblay (2003) consider he relaionship beween consumpion and wealh in Canada and find an imporan wealh effec on consumpion from flucuaions in housing wealh bu no from flucuaions in sock marke wealh. Hamburg, Hoffman and Keller (2005) find ha changes in wealh have virually no effec on consumpion in Germany and ha, unlike for Ausralia, he U.K. and Canada, he ransiory componen of wealh is small. In paricular, hey find ha deviaions from he long-run relaion beween consumpion, labour income and wealh are correced hrough adjusmens in labour income and no wealh. 3. Empirical Models In his secion, we lay ou he long-run models of consumpion and wealh ha form he basis of our empirical modelling in he following secion. We hen discuss how his long-run relaionship can be inerpreed in he conex of a dynamic sysem relaing consumpion, wealh and labour income. 3.1 Long run relaionship The basis for our empirical model is a long run relaionship beween consumpion, labour income, and household wealh ha arises from a sandard budge consrain for a represenaive agen economy. The relaionship is developed in Leau and Ludvigson (2001, 2004), building on earlier work by Campbell and Mankiw (1989) and is an approximaion o he budge consrain evaluaed around a seady share of consumpion o oal wealh. We exend he relaionship from hese papers in a sraighforward manner o include a decomposiion of oal wealh ino hree componens: human wealh, financial wealh and non-financial wealh. Tha is, W = H + Af + A n, where W is oal household wealh (beginning of period and in real per capia erms), H is human wealh, A f is financial wealh, and A n is non-financial wealh. In he following analysis we assume ha he shares of wealh for each of hese hree componens have sable seady sae values. We consider wo versions of he long run relaionship, wih and wihou he decomposiion of asse wealh ino financial and non-financial wealh. The wo relaionships are: c β β y β a = u (1) c γ γ y γ a γ a = v (2) f 3 n 4

5 All variables are in logarihms wih c oal consumpion, y afer ax labour income, a oal non-human wealh (ha is, boh financial and non-financial asses), a f financial wealh, and a n non-financial wealh. The wo error erms u and v are mean zero saionary variables. The wo consan erms arise from he linearizaion of he budge consrain. The slope coefficiens are seady sae share of wealh parameers and in principle β1+ β2 = 1 and γ 1 + γ 2 + γ 3 =1. 3 So, for example, β 2 = A / W, he seady sae raio of non-human asses in oal wealh. Labour income is inroduced ino he model as a means of measuring human asses; consequenly, β 1 = γ 1 = H /W. Under he assumpion ha c, y, a, a f, and a n are all firs difference saionary hen equaions (1) and (2) are coinegraing relaionships, which we use as he basis of our empirical models of consumpion and wealh. Before proceeding wih he esimaion, however, i is useful o briefly discuss a number of aspecs of equaions (1) and (2) ha bear on he esimaion and inerpreaion of he empirical resuls. Boh equaions are approximaions based upon he iner-emporal budge consrain of a represenaive agen wih no explici behavioural heory modelled oher han he imposiion of sandard ransversaliy condiions and he assumpions ha all asse markes are complee and wihou imperfecions. The equaions also assume ha human wealh can be measured, in logarihms, as he sum of curren labour income and a mean zero saionary process; see Leau and Ludvigson (2001) for deails. The error erms in equaions (1) and (2) are assumed o be mean zero saionary random variables. In general erms hey consis of expeced fuure log differences of consumpion and labour income (discouned) as well as expeced fuure ne reurns on he differen asse componens (also discouned). For (1) and (2) o represen coinegraing relaionships, hese variables mus be firs difference saionary. Finally, and mos imporanly, he log approximaions assume a sable seady sae raio of consumpion o oal wealh and sable seady sae shares of wealh componens in oal wealh. These bear on boh he predicion ha he errors in equaions (1) and (2) are saionary and ha he coefficiens in equaions (1) and (2) are sable. In he empirical work ha follows, here is a reasonable suggesion ha hese assumpions are no valid and conribue o weaknesses in he empirical resuls. The reason for his is easily anicipaed. As discussed earlier, here is some evidence ha consumpion has no growh as srongly as wealh in he las few years of he sample; moreover, here is evidence ha non-financial asses, primarily housing, have increased in value more rapidly han oher componens of household wealh. Boh of hese may be sufficien o cause (1) and (2) o fail as coinegraing relaionships. 3.2 Dynamic Sysem If eiher of he models (1) and (2) are found o represen valid coinegraing relaionships hen i is common o inerpre he coefficiens as long run elasiciies for consumpion relaive o labour income and wealh; in a similar manner, hey may also be 3 As noed in Leau and Ludvigson (2001), however, his only holds exacly if consumpion, which includes durables, is properly measured. As our measure of consumpion includes expendiure on durables raher han consumpion, we can expec he sum of hese coefficiens o differ from uniy. 5

6 used o consruc long run marginal propensiies o consume relaive o hese variables. Leau and Ludvigson (2004), however, sress ha such inerpreaions are poenially misleading. To see his, consider how we migh inerpre model (1). Suppose we inerpre he coefficien on wealh as he long run elasiciy of consumpion wih respec o wealh and argue ha a permanen rise in wealh gives rise o a cerain percenage increase (in his case β 2 ) in consumpion. While his is rue given (1), i is no a paricularly ineresing inerpreaion as i implicily reas wealh, and labour income, as exogenous variables when hey are in fac endogenous variables responding o underlying exogenous shocks, as is consumpion iself. To pu his in slighly differen erms, imagine a shock o wealh ha raises curren wealh by a cerain amoun and ask wha we migh infer from equaion (1) abou he response of consumpion. The answer is essenially nohing, boh for he shor run and long run response of consumpion. To deermine he response of consumpion we need o know how consumpion iself iniially responds o he underlying shock and how all of consumpion, labour income and wealh respond o he shock over ime ha is, we require a model of he adjusmen pahs ha resore he long run relaionship given in (1). This requires a dynamic sysem of equaions wih (1) or (2) providing he long run seady sae for he sysem, which, as is well known, is associaed he vecor error correcion model. A vecor error correcion model for equaion (1) assuming here are no shor-run dynamics is: c = µ + α ( c ˆ β y ˆ β a ) + ε c c c y = µ + α ( c ˆ β y ˆ β a ) + ε y y y a = µ + α ( c ˆ β y ˆ β a ) + ε a a a In his model i is he adjusmen coefficiens on he error correcion mechanism ha are of paricular ineres. They indicae how each of he hree variables in he sysem adjus o resore equilibrium following a shock o he error correcion mechanism. Leau and Ludvigson s work for he US indicaes he paern for he adjusmen coefficiens is αc = α y = 0 and αa 0. This implies ha when a shock o he economy disurbs he long run equilibrium relaionship for consumpion, labour income and wealh, i is he sock of wealh (and only he sock of wealh) ha adjuss o resore equilibrium. In his model all of he adjusmen o resore equilibrium following a disurbance o he long-run equilibrium is via changes in he sock of wealh. Thus, even if i can be esablished ha equilibrium relaionships of he form of (1) or (2) hold for he Ausralian economy, an undersanding of he adjusmen process requires ha we esimae he full error correcion sysem. Previous sudies of consumpion for Ausralia have eiher no done so or only enaively. 4 4 For example, Tan and Voss (2003) examine he effecs of permanen changes in he level of wealh using only a single equaion error correcion model for consumpion. This assumes ha all of he adjusmen o a change in he level of wealh occurs hrough consumpion, a poin he auhors noe bu do no explore. Fisher and Voss (2004) noe ha in he sample for which hey found enaive evidence for coinegraion, 6

7 4. Esimaion 4.1 Daa The daa we use are similar o Tan and Voss (2003) and Fisher and Voss (2004). The series used are: oal consumpion, c ; oal household ne wealh a, and is componens of ne financial asses a f and ne non-financial asses a n ; and afer-ax labour income y. The sample period is 1976:4 2004:3, which represens all of he available daa a he ime of he sudy. All variables are quarerly in real per capia erms and in logarihms. The consumpion deflaor is used o express all series in real erms. For calculaion of ne asses, household deb is disribued beween financial and nonfinancial asses proporionally (see Tan and Voss, 2003). The series used in esimaion are presened in Figure 1. The discussion in he previous secion idenified coinegraing relaionships beween he variables of ineres condiional on hese variables being firs difference saionary. Sandard augmened Dickey-Fuller ess esablish ha all of he variables of ineres are firs difference saionary a sandard significance levels. 4.2 Long Run Esimaes The firs ask is o esablish ha he long run relaionships in equaions (1) and (2) are coinegraing relaionships and o esimae he parameers of hese relaionships. To es for coinegraion, we esimae equaions (1) and (2) by OLS and apply various ess for a uni roo in he residuals; in each case, his is a es of a null hypohesis of no coinegraion. 5 The ess we apply o he residuals from coinegraing regressions are he augmened Dickey-Fuller (ADF) es and he Phillips-Perron (PP) and Phillips-Ouliaris ( Z τ ) ess. The ADF regression was esimaed wih four lags of he firs differenced residuals which was sufficien o ake accoun of serial correlaion in he residuals. To esimae he parameers of he relaionships, we use dynamic ordinary leas squares mehods (DOLS) due o Sock and Wason (1993). The resuls for he coinegraion ess and he DOLS esimaed parameers are repored in Table 1. For equaion (1), all he residual based ess rejec he null of no coinegraion a he five percen level. For equaion (2), he null of no coinegraion is rejeced by wo of he ess a he five percen level; he ADF es rejecs he null only a he en percen level. The evidence for coinegraion appears marginally sronger in he case of equaion (1) han equaion (2) bu in boh cases he evidence for coinegraion is srong. Having esablished ha (1) and (2) are coinegraing relaionships, efficien esimaes of he coinegraing parameers are obained from DOLS esimaion. The DOLS regressions augmen he OLS regressions wih k leads hrough o k lags of he firs difference of he righ-hand side variables. The choice of k is essenially arbirary. We repors parameer esimaes for k=4, alhough he parameer esimaes are broadly similar for k=2 and k=3. he esimaed adjusmen coefficiens in he vecor-error correcion model show ha wealh and no consumpion or labour income adjused o deviaions from he long-run relaion as in Leau and Ludvigson (2001, 2004). 5 Davidson and MacKinnon (1993) argue ha his procedure may have low power o rejec he null hypohesis of no coinegraion. If his is he case hen acually rejecing he null would seem o provide very srong evidence for coinegraion. 7

8 In addiion o finding suppor for coinegraion an imporan crierion for evaluaing models (1) and (2) is wheher he parameer esimaes repored in Table 1 are sensible. The log-linear approximaion o he budge consrain makes a srong predicion concerning he parameer values: hey are equal o he shares in oal wealh of human wealh (labour income as proxy) and non-human wealh or is componens. Unforunaely, hese share values are unobservable. We can, however, compare our resuls o Leau and Ludvigson (2004) for he US. Moreover, we do know ha he share of non-financial asses should be larger han he share of financial asses so his provides a furher check. Finally, he coefficiens should sum o one. The esimaes in Table 1 are broadly supporive of hese predicions. The sum of he coefficiens is very close o one for boh he hree and four variable model and as anicipaed he coefficien on non-financial wealh is larger han ha on financial wealh, hough by no much. The coefficien esimaes are also broadly consisen wih he US resuls in Leau and Ludvigson (2004). We can also compare he coefficiens across he wo models o see if hey are consisen. The sum of he wealh componen coefficiens in he four variable model should be equal o he coefficien on oal wealh in he hree variable model (since A /W = A f /W + A n /W ). And he coefficiens in Table 1 are broadly supporive of his predicion. The long run coefficien esimaes for models (1) and (2) define long run residuals, he error correcion erms ha are assumed saionary, based on he ess for coinegraion repored in Table 1. As a diagnosic check, we consider he behaviour of hese residuals, which are shown in Figure 2. Inspecion of hese residuals anicipaes some of he issues ha we examine in he dynamic sysem in he following secion. For boh models he end of he sample is characerized by large negaive residuals, relaively larger han a oher poins in he sample. This arises because of he large increase in wealh in he laer par of he sample, primarily bu no enirely due o increases in nonfinancial asses associaed wih he boom in housing prices. The large residual arises because neiher consumpion nor labour income adjuss over his period o offse he increases in wealh. The behavioural implicaions of he relaive responses of consumpion and wealh we consider in he nex secion. For now, we noe ha his residual may be an indicaion of specificaion problems wih our esimaed long run models. In paricular, i may be an arifac of srucural change in he long run model of which we have no aken proper accoun. These are imporan issues. For he momen, we proceed under he assumpion ha he full sample esimaes are he bes way o inerpre he daa. Subsequenly, we consider he issue of parameer sabiliy in greaer deail. To foreshadow he resuls from his robusness analysis, we do find evidence of insabiliy; however he conclusions of main analysis are unchanged. 4.3 Vecor Error Correcion Models Associaed wih he long-run models represened by equaions (1) and (2) are vecor-error correcion (VEC) models which characerize he dynamic adjusmen of he variables o deviaions from long-run equilibrium. The VEC represenaion is X = µ +Π X +Π X + K +Π X + ε, (3) k 1 k+ 1 8

9 where X = ( c y a ) or X = ( c y af a n), is he firs difference operaor, µ is a vecor of inerceps, Π i is he marix of coefficiens on he ih lagged change in X and ε is a vecor of serially uncorrelaed random disurbances wih mean zero and covariance marix Ω. The marix Π provides informaion abou he long-run relaionships among he series. In paricular, Π = αβ where he coefficiens in he column vecor β are he DOLS esimaes of he coinegraing parameers and he coefficiens in he column vecor α are he adjusmen coefficiens or loadings on he error-correcion erm β X 1 in each equaion of he VEC model. We noe for fuure reference ha if he adjusmen coefficien or loading on he error correcion erm in an equaion of X is zero, hen he dependen variable of ha equaion is said o be weakly exogenous. Table 2 repors esimaes of he VEC models corresponding o equaions (1) and (2) for he full sample. Boh VEC models were esimaed wih hree lags which was he opimal lag lengh seleced by he AIC crierion and he log-likelihood raio saisic. Consider firs he resuls for he aggregae wealh model. The error correcion erm is saisically significan a he 5-percen level in he wealh equaion where i eners wih a posiive sign and is significan a he 10-percen level in he consumpion equaion where i eners wih a negaive sign. When privae saving is low (ha is, he error-correcion erm is high eiher because consumpion is high or labour income and wealh are low), consumpion is prediced o fall and household wealh o rise hereby resoring he longrun relaion. Consumpion adjuss more slowly han wealh since is adjusmen coefficien is considerably smaller (in absolue value) han i is for wealh. Labour income is weakly exogenous as he error-correcion erm is no saisically significan in he labour income equaion. In Ausralia, adjusmen o deviaions from he long-run relaionship occurs hrough boh consumpion and wealh changes whereas, in he U.S., he adjusmen occurs only hrough wealh changes (Leau and Ludvigson, 2004). Furher, lagged changes in wealh, in addiion o he error-correcion erm, predic curren changes in consumpion. Thus, he permanen income hypohesis is formally rejeced for Ausralia. Under his hypohesis, curren consumpion changes are unpredicable on he basis of any lagged informaion se. The permanen income hypohesis is also sricly rejeced for he U.S. as lagged changes in consumpion and household wealh conain predicive conen for curren consumpion changes (Leau and Ludvigson, 2004). Table 1 also shows ha curren changes in labour income are predicable on he basis of lagged changes in labour income and wealh, which is also he finding of Leau and Ludvigson (2004) in U.S. daa. Thus here is a ransiory componen in labour income even hough i is weakly exogenous in he VEC model. Turning o he disaggregaed wealh model, he error-correcion erm is no saisically significan in eiher of he wealh equaions, alhough is coefficien in he non-financial wealh equaion is very similar o ha in he aggregae wealh equaion. I is saisically significan a he 10-percen level in he consumpion equaion and eners wih a negaive sign as before and is no significan in he labour income equaion. Also, lagged changes in non-financial wealh have predicive power for curren changes in consumpion, labour income and non-financial wealh whereas curren changes in financial wealh appear unpredicable. The disaggregae wealh model appears o be less 9

10 precisely esimaed han he aggregae one. Neverheless, we can enaively conclude ha he adjusmen process is he same and of he wo componens of wealh i is nonfinancial wealh ha adjuss o deviaions from he coinegraing relaion. 4.4 Dynamic ineracions Dynamic ineracions among he variables can also be evaluaed in erms of he moving average represenaion of he VEC model. As shown in Johansen (1991), he VEC model (3) can be invered o obain he moving average represenaion for X : X = ρ + CL ( ) ε (4) i where ρ = C(1) µ, L is he lag operaor and C(1) = I + CL i 1 i = β γα =. Here 1 γ ( α β ) k 1 = Ψ, Ψ= I Π i= 1 i and he subscrip ( ) denoes a marix orhogonal o he original marix. In he conex of model (1), here is one shock which has ransiory effecs on he levels of he variables and wo socks which have poenially permanen effecs. This follows because here is one coinegraing relaion among hree variables (Sock and Wason, 1988). Similarly for model (2) here is one shock which has ransiory effecs and hree which have poenially permanen effecs on he levels of he series. There are several ways o ransform he shocks from he VEC model ino shocks which have permanen and ransiory effecs. Following Gonzalo and Ng (2001), define α G =. β The firs sep is o ransform he errors from he VEC model o obainu = Gε. I is sraighforward o show ha he shocks consruced as α ε have permanen effecs on he levels of he series while, in our case, he single shock β ε has only a ransiory effec. 6 However, he permanen and ransiory shocks are no necessarily orhogonal o one anoher. The second sep is o orhogonalize he permanen and ransiory shocks by applying he ransformaion v = 1 = 1 H u H G ε where H is he lower riangular marix such hahh = GΩ G. Once he permanen and ransiory shocks are made orhogonal, i is meaningful o show he response of each series o he shocks v and o calculae forecas-error variance decomposiions. Gonzalo and Ng (2001) recommend consraining saisically insignifican adjusmen coefficiens in esimaed α o zero before consrucing α because C (1) (which depends on α ) can be very sensiive o small variaions in esimaedα. Thus, in he empirical analysis ha follows, he VEC model is esimaed under he resricion ha labour income is weakly exogenous, a resricion no rejeced by he daa and i is from his model ha we form our esimae of α. Table 3 shows he decomposiion of he jh-sep ahead forecas error variance in he series ha comprise he wo models. As we are no concerned wih he inerpreaion 6 1 Specifically, he las column of he marix C(1) G, which gives he long-run impacs of he shocks u, is a column vecor of zeros, as required for a permanen-ransiory decomposiion. 10

11 of he permanen shocks individually, he able repors he percen conribuion of he permanen shocks combined o he forecas error variance ogeher wih he conribuion of he single ransiory shock. Consider he resuls of model (1) firs. The ransiory shock accouns for abou 37 percen of he forecas-error variance in consumpion a he onequarer horizon and declines o abou 10 percen a he four-quarer horizon. The wo permanen shocks ogeher correspondingly accoun for over 90 percen of he forecaserror variance in consumpion a horizons of four quarers and more. Almos all of he variabiliy in labour income is aribuable o he wo permanen shocks which accoun for over 93 percen of he forecas-error variance a all horizons. The ransiory shock is more imporan here for consumpion over shor horizons han i is in U.S. and U.K. daa (Leau and Ludvigson, 2004, Fernandez-Corugedo e al, 2002, respecively) and in all hree counries he ransiory shock explains a negligible amoun of he variabiliy in labour income. The findings are quie differen for household wealh. The ransiory shock accouns for abou 42 percen of he forecas error variance in wealh a an horizon of one quarer, 34 percen a four quarers and 25 percen a eigh quarers. Thus, he conribuion of he ransiory shock o he forecas-error variance in wealh is larger and more persisen han i is in consumpion. Is conribuion is also much smaller here han in U.S. daa where i accouns for over 90 percen of he variabiliy in wealh (Leau and Ludvigson, 2004) bu is of he same order of magniude as in U.K. daa (Fernandez- Corugedo e al, 2002). Turning o he resuls for model (2), he ransiory shock is jus as imporan in explaining consumpion variabiliy a shor horizons as i is in model (1). I also accouns for a negligible amoun of he variabiliy in labour income a all horizons. The mos ineresing feaure of he resuls is ha ransiory shock accouns for a considerably larger porion of he forecas-error variance in non-financial wealh han in financial wealh a all forecas horizons and, aken ogeher, he ransiory shock accouns for as much variabiliy in wealh as in model (1). I appears ha mos of he adjusmen in wealh o he ransiory shock occurs hrough non-financial wealh. Figure 3 shows he responses of he levels of he series in each model o a onesandard error ransiory shock along wih he responses of he esimaed coinegraing residual or error-correcion erm. Focusing on he responses in model (1) shown in par (a) of he figure, he ransiory shock leads o a sharp increase in wealh which gradually dissipaes over he nex 10 quarers. Thus he ransiory increase in wealh is quie persisen and is eliminaed only afer wo and a half years. By comparison, he consumpion and labour income responses are small. The response of labour income is somewha larger han consumpion o he ransiory shock bu boh responses are small by comparison o he wealh response. The response of he error correcion erm predominanly reflecs he response of wealh o he ransiory shock since i is wealh ha responds he mos and hus adjuss he mos o eliminae deviaions from he long-run relaionship. The responses o he ransiory shock in model (2) are shown in par (b) of he figure. The response of non-financial wealh is large and persisen being eliminaed only afer abou hree years. The response of financial wealh is less han half of ha of nonfinancial wealh and is less persisen dissipaing afer abou wo years. The responses of consumpion and labour income are small and pracically idenical o heir responses in 11

12 par (a). The adjusmen pah of he error correcion erm primarily reflecs he response of non-financial wealh and, o a lesser exen, financial wealh o he ransiory shock. Of he wo componens of wealh, i is non-financial wealh ha adjuss he mos o resore he long-run relaion following a ransiory shock. 4.5 Permanen and ransiory componens The moving average represenaion (4) can be summed o obain a represenaion for he levels of a variable as he sum of a permanen and ransiory componen. p s p s Specifically, X = X + X where he ih elemen of he vecors X and X is he permanen and ransiory componen of he ih variable a ime, respecively. The vecor of permanen componens is given by p X = X 0 + C(1) ( ε i + µ ), (5) i = 1 (see Johansen, 1991) where X 0 is he vecor of iniial permanen values and he vecor of s ransiory componens X is saionary by consrucion. 7 The permanen componen of he variable consruced from (5) can be hough of as he long-run forecas or rend componen of he variable and he ransiory componen as saionary deviaions of he variable from is rend. The hree panels of Figure 4 plo he permanen componen of consumpion, labour income and household wealh ogeher wih heir acual values. The permanen componens are calculaed from he esimaed VEC model according o equaion (5). 8 Consumpion is a very smooh series and is quie indisinguishable from is rend. Labour income has diverged from is esimaed rend a imes over he sample bu no for prolonged periods. Mosly recenly, labour income appears o have moved above is esimaed rend. Wealh has diverged considerably a imes from is esimaed rend and for prolonged periods. Thus wealh appears o rever more slowly o is rend han labour income. Since 2003, wealh has moved subsanially above is esimaed rend and his divergence is much larger and more pronounced han a any oher ime in he sample. Because here is very lile corresponding upward movemen in consumpion above rend, i appears ha he recen surge in wealh is viewed as ransiory and ha wealh is expeced o rever o back o is rend. A clearer picure is provided in Figure 5 which shows he ransiory componen in each series direcly as he difference beween he acual value of he series and is permanen componen. The mos sriking feaure of he figure is ha he ransiory componen of wealh is large, paricularly since 2003 and highly persisen: he firs-order auocorrelaion coefficien of ransiory wealh is 0.88 over he sample. The ransiory increase in wealh since 2003 is unprecedened hisorically. By conras, he ransiory 7 The vecor of permanen componens can also be expressed in erms of he orhogonal permanenransiory shocks as X = X + Γ (1) ( v + µ *) where Γ (1) = C(1) G H and µ * = H G µ. p 1 1 Boh 0 i = 1 i represenaions are equivalen and yield exacly he same decomposiion. 8 Recall ha he VEC model is esimaed under he resricion of weak exogeneiy of labour income. We esimae each iniial permanen componen in equaion (5) by forecasing 108 periods ahead beginning in 1977:4 from he esimaed VEC model and hen subracing off he deerminisic porion of he forecas. 12

13 componen in labour income is smaller and less persisen (he firs-order auocorrelaion coefficien is 0.55) and he ransiory componen of consumpion is pracically negligible. Since 2003 labour income has increased above rend while consumpion has increased o be slighly on rend. The lack of a large consumpion response o he recen surge in wealh suggess ha ransiory wealh will fall so ha wealh will rever o is rend hereby re-esablishing he long-run coinegraing relaion. Figure 6 shows he ransiory componen of each series in he four variable model. The ransiory componen in consumpion and labour income is very similar across he hree and four variable models. Transiory flucuaions in wealh are aribuable o he ransiory componen in boh financial and non-financial wealh. However, as figure 6 shows, i is he ransiory componen in non-financial wealh which is he more imporan. Increases in he ransiory componen of non-financial wealh observed in he figure are aribuable o he rapid rise in houses prices ha occurred in following financial deregulaion, , and more recenly since However, ransiory variaion in financial wealh has also been imporan, paricularly over , he period of he recen sock marke boom. Neverheless, he unprecedened surge in wealh since 2003 is chiefly due o he ransiory increase in nonfinancial wealh as a resul of a srong housing marke. 4.6 Sabiliy In his secion, we consider he possibiliy ha he coefficien esimaes in he coinegraing relaion show emporal insabiliy. This is of concern since he large residuals we observe since 2003 in figure 2 may eiher arise from a sequence of unusually large shocks o he variables or be indicaive of a changed relaionship beween consumpion, labour income and wealh ha invalidaes he conclusions from our economeric analysis. We address he issue of parameer insabiliy by reporing he resul of he SupF es for insabiliy in coinegraed regression models proposed by Hansen (1992). The null hypohesis of he es is ha he coefficiens in he coinegraing relaion are sable and he alernaive is ha here is a single srucural break of unknown break dae in he coefficiens of he coinegraing relaion. The es is essenially a sequence of Chow F-ess for srucural change in he coinegraing regression conduced for each break dae in a rolling window hrough he sample. The larges F-saisic obained is hen compared o he appropriae criical value abulaed in Hansen (1992). For our sample SupF = 47.3 for model (1) which far exceeds he 5 percen criical value of Thus, he es rejecs he null hypohesis of parameer sabiliy in model (1). The SupF saisic occurs a a break dae of 1998:3. While he es suggess insabiliy in he parameer esimaes, i is possible ha he insabiliy is no sufficienly large enough o invalidae he conclusions ha we have already drawn from he economeric analysis. Some insabiliy in he coefficien esimaes is expeced since in he las wo decades Ausralia has winessed a grea deal of srucural reform in financial markes ha may have alered he relaive imporance of non-human asses (and is componens) in oal wealh. In his case, we should observe changes in he long-run coefficien esimaes as well as he consan coefficien, all of which depend upon he relaive shares of wealh. To invesigae wheher our conclusions are robus in view of he finding of insabiliy and a break dae of 1998:3, we re-esimae 13

14 our models for he sample ha ends in 1998:3 and see wheher we can draw he same conclusions, paricularly concerning ransiory variaion in consumpion and wealh, as we did previously. Table 4 repors he resuls of he coinegraion analysis for he sample 1976:4-1998:3. For he hree variable model, here is evidence for coinegraion a he 5 percen level on he basis of all he ess. For he four variable model, he ADF es rejecs he null of no coinegraion only marginally above he 5 percen level while he oher wo ess clearly rejec he null a he 5 percen level. Compared o he full sample resuls, he evidence for coinegraion is somewha sronger in he sub-sample. The DOLS esimaed coefficiens in boh models are srikingly similar o heir corresponding full sample esimaes. Thus he esimaed long-run coefficiens appear remarkably robus, nowihsanding ha here was some evidence for a srucural break in he coinegraing relaion for he aggregae wealh model a 1998:3. Esimaes of he adjusmen coefficiens in he VEC models for he sub-sample are also shown in able 4. For he hree variable model, he esimaed coefficien on he error correcion erm in he consumpion and wealh equaions is highly significan and is abou wice as large as ha esimaed for he full sample. Thus, consumpion and wealh boh adjus more quickly in he sub-sample han in he full sample o deviaions from he long-run coinegraing relaion. For he four variable model, he coefficien on he error-correcion erm appears o be more precisely esimaed in he consumpion equaion and in boh wealh equaions han in he full sample. The adjusmen coefficien for consumpion is significan a he 5 percen level and for non-financial and financial wealh, i is significan a he 10 and 11 percen levels, respecively. Thus he evidence is sronger in he sub-sample ha consumpion and boh componens of wealh adjus o deviaions from he long-run relaionship. The error-correcion erm is no significan in he equaion for labour income in boh models and, as in he full sample, labour income is weakly exogenous and plays no par in he adjusmen process. Table 5 shows he decomposiion of he forecas-error variance in he variables when boh VEC models are esimaed over he sub-sample. 9 The forecas error variance decomposiions for he sub-sample are pracically he same as for he full sample. The only noable difference is ha he ransiory shock accouns for a slighly larger percenage of he forecas-error variance in financial wealh a shor horizons. Figure 7 shows he responses of he variables o he ransiory shock over he sub-sample. For boh he hree and four variable models, he responses are qualiaively he same as for he full sample repored in figure 3. The larges response o he ransiory shock occurs in wealh and, more specifically, in non-financial wealh. The response of financial wealh is also large up o horizons of four quarers bu is somewha less han half as much as he response of non-financial wealh and dissipaes more quickly. The response of consumpion and labour income o he ransiory shock is small. Thus, as in he full sample, i is he adjusmen in wealh ha primarily resores he long-run coinegraing relaions following a ransiory shock. Up o his poin he conclusions we draw from he economeric analysis are essenially he same irrespecive of wheher he models are esimaed over he sub-sample 9 As for he full sample, he forecas error variance decomposiions and he responses o he ransiory shock are repored for he VEC models esimaed under weakly exogenous labour income and wih hree lags. 14

15 or full sample. However, he quesion arises as o wha he esimaed sub-sample models say abou he size of he ransiory componens in he series no only over he esimaion period bu also for he period 1998:4-2004:3. To address his quesion, he permanen componens in boh he hree and four variable models are calculaed according o equaion (5), where he respecive VEC models are esimaed over he sub-sample under he resricion of weak exogeneiy of labour income and wih hree lags. This gives he permanen componen in he series for each model, respecively, from 1977:4-1998:3. To obain he permanen componen in he series for he remainder of he sample, he onesep ahead forecas of he variables from each VEC model is obained and subraced from he acual values of he variables o give ou of sample residuals from 1998:4-2004:3. Placing hese ou of sample residuals in equaion (5) provides esimaes of he permanen componen in he series of each VEC model from 1998:4-2004:3. Thus, we can obain he ransiory componen in he series for each VEC model over he esimaion and ou of esimaion samples. Figures 8 and 9 show he ransiory componen in he series for he hree and four variable models, respecively. These plos are remarkably similar o he corresponding plos obained from full sample esimaion shown in figures 5 and 6. In paricular, on he basis of he sub-sample esimaion, he ransiory componen in wealh is prediced o be large and posiive from 2003 moving wealh above rend o hisorically unprecedened levels. Labour income is also prediced o increase srongly above rend from 2003 while consumpion is relaively unchanged. Figure 9 shows ha he prediced ransiory increase in wealh from 2003 is mainly aribuable o he prediced increase in non-financial wealh, alhough he ransiory increase in financial wealh prediced over 2003 also conribues imporanly. We conclude ha irrespecive of wheher he esimaion period is for he sub-sample or full sample, he inferences from he esimaed VEC models are he same: from 2003 o he end of he sample, wealh, and in paricular non-financial wealh, has increased o hisorically unprecedened levels above rend while consumpion remains close o rend necessiaing, in he near fuure, a downward adjusmen in wealh and specifically, in non-financial wealh. Because he inferences from he sub-sample models are unchanged from hose from he full-sample models, whaever insabiliy in he parameer esimaes ha ess for srucural sabiliy may sugges, parameer insabiliy does no appear o be large enough o aler our inferences. 5. Conclusions This paper shows ha here is a long-run relaionship beween consumpion, labour income and wealh in Ausralian daa. I also shows ha here is a long-run relaionship beween consumpion, labour income, financial wealh and non-financial wealh. The long-run relaions imply ha here is boh a permanen and a ransiory componen in he series. For consumpion and labour income, he ransiory componen is small. However, he ransiory componen in wealh and, paricularly non-financial wealh, is large. Transiory movemens in financial and non-financial wealh are largely unrelaed o consumpion spending because consumpion is dominaed by permanen componens. This is paricularly apparen owards he end of he sample where nonfinancial wealh has increased o unprecedened levels above is rend while a he same ime consumpion has moved only slighly around is rend resuling in large deviaions from he long-run relaionships. Thus, o re-esablish he long-run relaionships, i is 15

16 wealh and principally non-financial wealh ha is expeced o adjus downwards, albei somewha slowly as is ransiory componen is quie persisen, so ha a downward correcion in housing prices is expeced. Wih respec o policy implicaions, he Reserve Bank should no be unduly concerned abou he poenial impac on inflaion of large swings in asse values since hey do no ranslae ino large swings in consumpion spending, he larges componen of aggregae demand. 6. References Campbell, J.Y. (1996), Undersanding Risk and Reurn, ' Journal of Poliical Economy 104, Campbell, J.Y. and N.G. Mankiw (1989), Consumpion, Income and Ineres Raes: Reinerpreing he Time Series Evidence, in O.J. Blanchard and S. Fischer, eds., NBER Macroeconomics Annual: Cambridge, MA: MIT Press, Davidson, R. and J.G. MacKinnon (1993), Esimaion and Inference in Economerics, Oxford Universiy Press, Oxford. Fernandez-Corugedo, E., S. Price, and A. Blake (2002), The Dynamics of Consumer Expendiures: The U.K. Consumpion ECM redux, Working paper, Bank of England. Engle, R.F. and C.W. Granger (1987), Co-Inegraion and Error Correcion: Represenaion, Esimaion, and Tesing, Economerica 55(2), Gonzalo, J. and S. Ng (2001), A Sysemaic Framework for Analyzing he Dynamic Effecs of Permanen and Transiory Shocks, Journal of Economic Dynamics and Conrol 25, Fisher, L.A. and G.M. Voss (2004), Consumpion, Wealh and Expeced Sock Reurns in Ausralia, The Economic Record 80(251), Hamburg, B., Hoffman, M., and J. Keller (2005), Consumpion, Wealh and Business Cycles in Germany, CESIFO Working Paper Hansen, B. E. (1992), Tess for Parameer Insabiliy in Regressions wih I(1) Processes Journal of Business and Economic Saisics 10, Johansen S. (1991), Esimaion and Hypohesis Tesing of Coinegraion Vecors in Gaussian Vecor Auoregressive Models, Economerica 59, Leau, M. and S.C. Ludvigson (2001), Consumpion, Aggregae Wealh, and Expeced Sock Reurns, The Journal of Finance 66(3) June, Leau, M. and S.C. Ludvigson (2004), Undersanding he Trend and Cycle in Asse Values: Reevaluaing he Wealh Effec on Consumpion, American Economic Review 94(1), Pichee, L. and D. Tremblay (2003), Are Wealh Effecs Imporan for Canada? Bank of Canada Working Paper Poerba, J.M. (2000), Sock Marke Wealh and Consumpion, Journal of Economic Perspecives 14(2), Sims, C.A. (1980), Macroeconomics and Realiy, Economerica 48,

17 Sock, J.H. (1987), Asympoic Properies of Leas Squares Esimaors of Coinegraing Vecors, Economerica 55, Sock, J.H. and M. Wason (1993), A Simple Esimaor of Coinegraing Vecors in Higher Order Inegraed Sysems, Economerica 61, Tan, A. and G. Voss (2003), Consumpion and Wealh in Ausralia, The Economic Record 79(244),

18 Table 1 Tess for coinegraion and long-run esimaes: sample 1976:4-2004:3. Tess for coinegraion ADF(4) PP Z τ 5% C.V. 10% C.V. c β0 β1y β2a c γ 0 γ1y γ2af γ3an DOLS Esimaes (k =4) β 0 β 1 β 2 AR(1) c β β y β a (-40.00) (14.99) (19.21) γ 0 γ 1 γ 2 γ 3 AR(1) c γ 0 γ1y γ2af γ3an (-14.03) (12.07) (11.55) (5.15) Noes: This able repors residual based ess for coinegraion based on he OLS esimaes of he parameers in he coinegraing regressions. ADF(4) is he adjused Dickey-Fuller -saisic from he coinegraing regression, including four lags of he firs differences of he OLS residuals. PP and Z τ are he Phillips-Perron and Phillips-Ouliaris -saisics, respecively. In each case, he auocovariance funcion is runcaed a four lags. The criical values are aken from Hamilon (1994), Table B.8. The number of leads and lags of changes in he righ-hand side variables in he DOLS regressions is k=4. AR(1) is he firs-order auocorrelaion coefficien of he esimaed residuals from he DOLS regressions. 18