A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 247

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1 Journal of Applied Economics, Vol. VI, No. 2 (Nov 2003), A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 247 A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION STEVEN COOK * Universiy of Wales Swansea Submied June 2000; acceped November 2001 The recenly examined durabiliy-asymmery hypohesis of Cook (1999) is re-evaluaed using he diagnosic ess of ime deformaion proposed by Sock (1987, 1988). An applicaion of hese ess o disaggregaed daa on U.S. consumers expendiure provides furher suppor for his hypohesis, wih he findings given an economic inerpreaion in erms of variables evolving a differing speeds over differen phases of he business cycle. Addiionally, building upon he sudies of Cover (1992), Karras (1996) and Rhee and Rich (1995), recen research by Arden e al. (2000) has shown he relaxaion of he assumpions of lineariy and symmery ypically employed in macroeconomeric models o resul in moneary policy having clear asymmeric effecs on he economy. In paricular i was shown ha expansionary moneary policy as given by a reducion in he ineres rae, has greaer effecs han conracionary policy (an increase in he ineres rae), and ha his becomes more apparen when he economy is in recovery raher han recession. The finding of nonlineariy in U.S. consumpion herefore has major implicaions for economeric modelling and policy analysis. JEL classificaion codes: C12; E32 Key words: ime deformaion; asymmery; non-lineariy; consumers expendiure I. Inroducion In recen research Cook (1999) has explored he possibiliy of a posiive * I am exremely graeful o an anonymous referee, he co-edior Mariana Cone Grand and he ediorial board for helpful commens which have improved he presenaion of he paper. However, he usual disclaimer applies. Correspondence should be addressed o Seven Cook, Universiy of Wales Swansea, Singleon Park, Swansea SA2 8PP, WALES, Tel: 44(0) , Tel: 44(0) , s.cook@swan.ac.uk.

2 248 JOURNAL OF APPLIED ECONOMICS relaionship beween he durabiliy of a good and he asymmeric, or nonlinear, behaviour i exhibis. The heoreical moivaion for he durabiliyasymmery hypohesis was wofold. Firs, he analysis of Caballero (1993) had explained he behaviour of expendiure on consumer durables using a ransacions cos model. In Caballero s model, expendiure on durables only reurns o he ime pah suggesed by he permanen income hypohesis when upper or lower rigger poins are reached. I was argued by Cook (1999) ha when he rigger poins are disribued asymmerically abou he permanen income pah, asymmeric behaviour will be exhibied. Second, as durable goods provide a sream of uiliy over ime, i was argued ha expendiure on durable goods is more closely relaed o he lieraure on invesmen raher han sandard consumpion heory. The analogy wih invesmen suppors he durabiliy-asymmery hypohesis as he opion value of waiing lieraure of Dixi (1992) and he endogenous delay model of Gale (1996) generae clear asymmeries in invesmen behaviour. To evaluae his hypohesis Sichel s (1993) ess of univariae business cycle asymmery were applied o daa on U.S. durable and non-durable consumers expendiure. Wih significan asymmery being found in durable goods alone, i was concluded ha supporive evidence for he durabiliy-asymmery hypohesis had been derived. The inenion of his noe is o re-evaluae he durabiliy-asymmery hypohesis using an alernaive, recenly proposed es. The es o be applied is he diagnosic es of ime deformaion due o Sock (1987,1988). Sock s ime deformaion ess are highly informaive, allowing he hypohesis of economic variables evolving a differen speeds during differen phases of he business cycle o be esed.via an applicaion o he original daa of Cook (1999) i will be seen ha furher supporive evidence for he durabiliyasymmery hypohesis is provided. An addiional reason for ineres in asymmeries and non-lineariies is provided by he recen research of Arden e al. (2000). Following he work of Cover (1992), where posiive and negaive moneary shocks are shown o have differing effecs on oupu in he US, a number of furher sudies have emerged also allowing he possibiliy of asymmeric effecs wihin reduced form models. Examples of hese include Karras (1996) for OECD economies, and Rhee and Rich (1995) also for he US. However, he research of Arden e al. (2000) exends his lieraure by incorporaing asymmeries wihin srucural

3 A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 249 models. I is shown ha he relaxaion of he assumpions of lineariy and symmery ypically employed in macroeconomeric specificaions leads o moneary policy having clear asymmeric effecs. More precisely, i was found ha he presence of non-lineariies and asymmeries resuled in moneary policy having differen effecs depending upon (i) he sign of he moneary shock (expansionary or conracionary) and (ii) he phase of he business cycle he economy was in a he ime of he shock (recovery or recession). In paricular i was seen ha he effecs of expansionary moneary policy in he form of ineres rae cus are greaer han hose of conracionary moneary policy (increase ineres raes). I was furher found ha he effecs of expansionary moneary policy are greaer when he economy is in recovery han when i is in recession. The discovery of asymmery or non-lineariy in consumers expendiure herefore has major implicaions for boh economeric modelling and policy analysis. To achieve is objecive his noe will proceed as follows. In he following secion he noion of ime deformaion and diagnosic ess for is presence will be oulined. Secion III will presen he resuls of he applicaion of his es o daa on U.S. consumer durables and non-durables, wih secion IV concluding. II. Time Deformaion Sock (1987) inroduces he noion of ime deformaion models which are based upon he disincion beween an economic, or operaional, ime scale (s) wihin which variables evolve, and he calendar ime scale from which observaions are drawn (). A coninuous laen process evolving in economic ime, ξ(s), is hen relaed o he observaion of his process in calendar ime by s = g(). A variable of ineres, x, observed a discree poins in calendar ime can hen be relaed o he laen process by: x = ξ (g()) (1) Despie he novely of he above framework, he use of alernaive ime scales does have a precursor in he phase averaging procedures employed a he Naional Bureau of Economic Research. The use of phase averaging,

4 250 JOURNAL OF APPLIED ECONOMICS where daa are averaged across differen phases of he business cycle, has a long hisory wih Burns and Michell (1946) and Friedman and Schwarz (1982) being early and more recen applicaions of his approach. In conras o phase averaging, he wo forms of ime scale ransformaion considered here are based upon he use of Nefci s (1984) swiching, or indicaor, variable. The firs form, cyclical expansion/conracion, relaes o changes in he variable of ineres. For cyclical expansion-conracion he relevan indicaor variable, z, is defined as: z 1 if x 0 = 0 if x < 0 (2) where x in his insance represens each of he consumpion series in urn. The second form of ime scale ransformaion, cyclical growh expansion/ conracion, relaes o changes in he variable of ineres in relaion o is average rae of change. For cyclical growh expansion/conracion he relevan indicaor variable, z, is defined as: z 1 if x x = 0 if x < x (3) These forms of ime deformaion herefore consider asymmery or nonlineariy arising due o differen speeds of evoluion during recessionary and recovery periods. For cyclical expansion/conracion, he possibiliy of differing behaviour is permied when he variable of ineres is eiher increasing or decreasing over he business cycle. For growh expansion/ conracion, he differing behaviour is permied depending upon wheher curren growh is above or below a long-run average growh rae. Despie he compuaionally demanding naure of he esimaion of ime deformaion models (see Sock, 1988), i is relaively sraighforward o implemen diagnosic ess for he presence of ime deformaion. When he variables of ineres possess sochasic rends, Sock (1987) proposes he use of he following models:

5 A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 251 wih he presence of ime deformaion examined via significance esing of he coefficiens (α i, β i ) and (α * i, β* ). The relevan null hypoheses, H : α = β i 0 i i = 0 in (4) and H * : 0 α* i =β* = 0 in (5), are ha ime deformaion is no presen. i III. Resuls τ ( ) i ( ) τ 1 i= 1 i i = 1 i i i (4) x = µ + λ x + α z z + β z z x + ε τ ( ) i ( ) (5) τ µ λ α β ε 1 i= 1 i i = 1 i i i x = + x + z z + z z x + The daa used in his noe are he same seasonally adjused, quarerly observaions in 1992 dollars from 1959(1) o 1998(1) of U.S. consumers expendiure on durables and non-durables employed by Cook (1999). 1 The noaion cd and cnd will herefore represen he naural logarihms of he durables and non-durables series respecively. Before presening he resuls of esing for ime deformaion, i was noed in he previous secion ha regressions of he form of (4) and (5) are appropriae when he variables under analysis have sochasic rends. Applicaion of fifh order Augmened Dickey-Fuller ess confirmed he findings of Cook (1999) ha boh cd and cnd are I(1) processes. 2 The resuls obained from applying he models (4) and (5) o he consumpion daa are given in Table 1. Repored in his able are he asympoic marginal significance levels (p-values) for he F-ess of he significance of he cyclical expansion/conracion coefficiens (α i, β ) and he cyclical growh i expansion/conracion coefficiens (α *, i β* ). Given ha he daa used are i quarerly, wo alernaive lag lenghs of one and four periods (τ = 1, 4) were chosen for he funcions of he swiching variables z and z. The resuls show ha ime deformaion of he cyclical expansion/conracion form is presen for durables using boh lag lenghs, wih he resuls for he longer lag lengh being highly significan. This is he only evidence of ime deformaion, as durables do no exhibi ime deformaion of he cyclical growh form and non-durables display no evidence of ime deformaion of eiher form. 1 Daasream codes USCNDURBD and USCNNONDD. 2 Applicaion of hese uni roo ess replicaed he resuls repored in Cook (1999).

6 252 JOURNAL OF APPLIED ECONOMICS Table 1. Time Deformaion Tess Asympoic marginal significance levels z τ = 1 τ = 4 τ = 1 τ = 4 z * cd * ** cnd Noes: * denoes significance a he 5% level. ** denoes significance a he 1% level. Therefore wih posiive resuls found for durables alone, he durabiliyasymmery hypohesis is re-confirmed and given an inerpreaion in erms of variables evolving a differen speeds during recessionary and recovery periods. IV. Conclusion In his noe he recenly proposed posiive relaionship beween he durabiliy of consumer goods and he asymmeric behaviour hey exhibi has been re-evaluaed. In conras o he previous sudy which applied he ess of business cycle asymmery proposed by Sichel (1993), diagnosic ess of ime deformaion have been employed as hey are more informaive of he source of any asymmery deeced. In an applicaion o U.S. consumers expendiure on durables and non-durables, previous findings of excessive asymmery in durables have been suppored, and in doing so an inerpreaion has been provided for hem in erms of variables evolving a differing speeds during recessionary and recovery periods. Recen sudies such as Arden e al. (2000), Cover (1992), Karras (1996) and Rhee and Rich (1995) have shown asymmeries o have a major impac on he influence of economic policy. In paricular, Arden e al. (2000) shows ha he relaxaion of he symmery and lineariy assumpions ypically imposed in macroeconomeric specificaions leads o clear asymmeries in he effecs of moneary policy, boh in erms of he sign of he shock (posiive or negaive) and he phase of he business cycle a he ime of he shock (recovery or recession). In ligh of hese sudies, he presen findings of asymmery and non-lineariy have major implicaions for boh economeric modelling and policy analysis.

7 A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 253 References Arden, R., Cook, S., Holly, S. and P. Turner (2000), The Asymmeric Effecs of Moneary Policy: Some Resuls from a Macroeconomeric Model, The Mancheser School 68: Burns, A.F. and W.C. Michell (1946), Measuring Business Cycles, New York, Naional Bureau of Economic Research. Caballero, R.J. (1993), Durable Goods: An Explanaion for heir Slow Adjusmen, Journal of Poliical Economy 101: Cook, S. (1999), Cyclicaliy and Durabiliy: Evidence from U.S. Consumers Expendiure, Journal of Applied Economics 2: Cover, J. (1992), Asymmeric Effecs of Posiive and Negaive Money Supply Shocks, Quarerly Journal of Economics 107: Dixi, A. (1992), Invesmen and Hyseresis, Journal of Economic Perspecives 6: Friedman, M. and A.J. Schwarz (1982), Moneary Trends in he Unied Saes and Unied Kingdom: Their Relaion o Income Prices and Ineres Raes, , Chicago, Universiy of Chicago Press. Gale, D. (1996), Delay and Cycles, Review of Economic Sudies 63: Karras, G. (1996), Are he Oupu Effecs of Moneary Policy Asymmeric?, Oxford Bullein of Economics and Saisics 58: Nefci, S.N. (1984), Are Economic Series Asymmeric over he Business Cycle?, Journal of Poliical Economy 92: Rhee, W. and R. Rich (1995), Inflaion and he Asymmeric Effecs of Money on Oupu Flucuaions, Journal of Macroeconomics 17, Sichel, D. (1993), Business Cycle Asymmery: A Deeper Look, Economic Inquiry 31: Sock, J.H. (1987), Measuring Business Cycle Time, Journal of Poliical Economy 95: Sock, J.H. (1988), Esimaing Coninuous Time Processes Subjec o Time Deformaion: An Applicaion o Pos-War GNP, Journal of he American Saisical Associaion 83: