Business Cycle Asymmetry in China: Evidence from Friedman s Plucking Model

Transcription

1 Business Cycle Asymmery in China: Evidence from Friedman s Plucking Model Tingguo Zheng a,b Yujuan Teng a Tao Song c a. The Wang Yanan Insiue for Sudies in Economics, Xiamen Universiy, Xiamen, Fujian, , PR China; b. Quaniaive Research Cener of Economics, Jilin Universiy, Changchun, Jilin, 13001, PR China; c. Insiue of Economics, Xiamen Universiy, Xiamen, Fujian, , PR China Absrac: Friedman s plucking model of business flucuaions suggess ha oupu canno exceed an upper limi, or ceiling level, bu i is occasionally plucked downward, wih deph and seepness, due o recessions. This paper invesigaes China s business flucuaions using he quarerly real GDP daa over he period Our resuls provide some suppor for he plucking model. We find ha here exiss he ceiling effec of real oupu, and he negaive asymmeric shocks affec he ransiory componen significanly, which herefore capures he plucking downward behavior during he recession from he idea of Friedman. In addiion, i is also suggesed by he resuls ha he basic asymmeric UC model is no appropriae for direcly modeling China s real oupu since he business cycle is inaccuraely measured, bu i works quie well when considering a srucural break a 199:Q. Key Words: business cycle; plucking model; asymmery; regime swiching; srucural break 1. Inroducion Asymmery in economic expansions and recessions is one of he naural feaures of business cycle in modern macroeconomics. In he earlier days, Michell (197) and Keynes (1936) noed ha recessions are shorer han expansions, and also more sudden and violen. Delong and Summers (1986), Sichel (1993), Ramsey and Rohman (1996), ec. furher repored ha recessions are deeper and seeper. They aribued recessions o occasionally ransiory shocks, while expansions o permanen shocks. In accordance wih Keynes observaions, Friedman (1964, 1993) also found he business cycle asymmery: The size of a recession grealy influences he size of he succeeding expansion, wih major expansions ending o follow major recessions, bu no vice versa. This led him o inroduce he plucking model of business flucuaions. In his model, here is anoher empirical regulariy ha real oupu shows an imporan ceiling effec; growh raes are on average below he ceiling rae, bu end back o i. If he ceiling level of oupu can be esimaed, we can no only deermine he size of he recession, bu also he gap beween real growh rae and rend growh rae. Boh he regulariies and heir heoreical discussions have imporan implicaions for business cycle analysis. The business cycle asymmery has been pu ino grea concern in boh economic heory and empirical research, on which exensive lieraures have been sudying, e.g. Nefcy (1984), Hamilon (1989), Diebold, Rudebusch and Sichel (1993). Friedman (1993) used a correlaion mehod o analyze he U.S. real GNP, 1

2 and found he evidence of he ceiling effec as well as he unidirecional relaionship beween he size of he recession and he subsequen expansion. Goodwin and Sweeney (1993) applied Friedman s correlaion mehod and a fronier producion approach o a se of eigh indusrial counries. They found ha alhough here is weak suppor for he hypohesis of seepness, here is subsanial suppor for he proposal ha he oupu ceiling plays a major role in business cycle flucuaions in Canada, France, Germany, Swizerland, and he Unied Saes. Razzak (001) applied a nonparameric es o a se of six indusrial counries and found ha Japan and Ausralia real GDP series show significan deph, while for New Zealand, here is only significan seepness in real GDP. Kim, Morley and Piger (005) exended he Hamilon s regime-swiching model wih a bounce-back erm, which links he lengh of each recession wih he srengh of he following recovery. They found a srong bounce-back effec for he Unied Saes and Ausralia. However, Friedman s and Goodwin and Sweeney s evidence on he plucking model is limied, in ha i is no based on a formal economeric model which can capure he asymmeric business cycle. Kim and Nelson (1999, hereafer KN99) firs proposed a formal economeric mehod describing Friedman s plucking model, which is able o esimae he size of negaive shocks and es he plucking hypohesis agains he symmeric rend-plus-cycle alernaive. They used he Markov regime-swiching sae space model o esimae he rend and cyclical componens for he Unied Saes and found ha recessions are periodic due o relaively large negaive shocks. Laer on, Mills and Wang (00), De Simone and Clarke (007) applied KN99 s mehodology o G7 counries and 1 indusrial counries, and heir resuls, o some exen, again suppored he fac ha he plucking model is an effecive mehod o analyze he business cycle asymmery. Recenly, Sinclair (009) furher proposed an asymmeric UC-UR model, which is he generalizaion of Morley, Nelson and Zivo s (003) correlaed unobserved componens model, allowing for asymmery. In recen years, Chinese scholars have done a lo of beneficial sudies on he asymmeric business cycle in China. Liu and Fan (001), and Xu, Zhu and Liu (005) applied he Hodrick-Presco filer and ime series mehods for rend decomposiion o sudy asymmeries and correlaions of China s business cycle, by esing and analyzing seepness and deph of cyclical componen. Chen and Liu (007) examined he asymmery and persisence of China s business cycle by uilizing a MSMV(3)-AR() model, and he resuls showed he asymmery and differen persisence in hree regimes from 1979:Q1 o 004:Q4. In addiion, Liu (003), Liu and Wang (003), Liu and Zheng (008) separaely idenified he business cycle phases beween recessions and expansions in China, using differen nonlinear mehods. In his paper, we will invesigae he rend and cyclical componens of China s real oupu, furher analyze he phases of business cycle and es he possible asymmery. Under he fac of business flucuaions since reform and opening up, we ake an empirical sudy on real oupu (GDP) using he quarerly daa from 1978 o 009. We will ake wo imporan concerns: he firs is o consruc an appropriae mehod o describe he feaures of China s business flucuaions, such as he possible srucural change since he 1990s, so as o achieve he applicabiliy of Friedman's plucking model effecively; he second is o idenify he phases and asymmeries of China s business cycle, and judge he deph and lengh of he recession.

3 Apar from he inroducion, he remainder of he paper is organized as follows. Secion is a brief review of China s business flucuaions. Secion 3 is abou he basic economeric model and is esimaion. Secion 4 presens he empirical resuls using China s quarerly real GDP daa from 1978 o 009, o describe he ceiling effec of oupu, o es he business cycle asymmery, and o analyze he deph and lengh of he recession. The las secion draws some conclusions.. Brief review of China s business flucuaions I has been widely acceped ha China s business flucuaions have gone hrough en complee cycles since 1953, wih five cycles before reform and opening-up, four cycles aferwards, and he las wo years are in he downward phases of he fifh cycle. Figure 1 repors he ime pah of China s real GDP and economic growh rae since 195. From he figure, i can be easily seen ha business flucuaion in China is obvious, and is periodiciy is also quie pronounced. 30% 1,300 1,00 1,100 1, % 10% 0% -10% -0% -30% LN(GDP)*100 GDP growh rae Figure 1. The log of real GDP and real GDP growh rae ( , annual daa) Noe: he solid bold line represens he log of real GDP 100, he solid hin line represens real GDP growh rae, and he verical line represens he locaion of roughs for he firs 9 business cycles; he 10h rough of he business cycle should be in 009. The base year for he GDP price index is year 000. The daa are obained from he CEI daabase a he China Economic Informaion Nework. From 1953 o he end of he Grea Culural Revoluion in 1976, he highes peaks of economic growh raes for he five cycles appear respecively in 1956 (15%), 1958 (1.3%), 1964 (18.3%), 1970 (19.4%) and 1975 (8.7%), and he lowes roughs of economic growh raes are in 1957 (5.1%), 1961 (-7.3%), 1967 (-5.7%), 197 (3.8%) and 1976 (-1.6%) respecively. All gaps beween peaks and roughs 3

4 are more han 10 percenage poins excep for he firs cycle, he gap of which is 9.9%, and here were hree violen ups and downs. Since 1978, he highes peaks of economic growh raes appear respecively, in 1978 (11.7%), 1984 (15.%), 1987 (11.6%), 199 (14.%) and 007 (13%); he lowes roughs of economic growh raes respecively in 1981 (5.%), 1986 (8.8%), 1990 (3.8%), 1999 (7.6%) and 009 (he rough of his cycle, is annual GDP growh rae is 8.7%. Based on he resuls of quarerly daa, his paper will show ha he las cycle has been compleed and he economic recovery began in he second quarer of 009). All gaps beween peaks and roughs are less han 8 percenage poins. Comparably speaking, afer he reform and opening up, China s business cycles have changed from a pah wih violen flucuaions and big peak-rough gaps, o a pah wih genle ups and downs and small peak-rough gaps, showing a high growh low flucuaion ype rend (Liu, ec. 005). In addiion, afer 1990, China s economy also shows a new feaure, ha is, he long sof landing period ( ) and he long sof expansion period ( ). During he ime, he cyclical flucuaions are obviously weakened and he sabiliies are markedly enhanced. In he following, we will deec his eviden change, and i will be regarded as a breakhrough in our analysis. 3. Model specificaion The empirical model used in his paper is mainly based on KN99 s mehod; however, i will be appropriaely adjused in our empirical analysis. The main advanage of KN99 s mehod is ha i allows he oupu o be decomposed ino a rend componen and a cyclical componen, boh of which can be inroduced a Markov discree variable, so ha i can capure he downward plucking behavior and he asymmeric cycle, along wih he ceiling oupu. 1 Consider he following asymmeric unobserved componens (UC) model of business flucuaions and assume ha he log of real GDP ( y ) is decomposed ino wo unobserved componens: y n c where n is he rend componen and c is he cyclical componen. = +, (1) In erms of Kim and Nelson (1999a), he cyclical componen is assumed o be an AR() process. To capure he regime swiching or asymmeric deviaion of real GDP from he rend, however, we assume ha he shock o he ransiory componen is a mixure of a symmeric shock ( shock ( π S u ) and an asymmeric, discree ). The asymmeric shocks can capure he plucking behavior and i is consisen wih he specificaion in Markov discree mixure-of-normal-disribuions suggesed by KN99 s mehod. Therefore, he cyclical componen is given by c = φc + φ c + πs + u, u ~ N(0, u( S )), () 1 1 where π is an asymmeric, discree shock, depending upon he unobserved variable S, and u is he S 1 Wha reflecs he business cycle feaure is he cyclical componen. If he cyclical componen has an asymmeric innovaion, hen he business cycle would have asymmeric feaure. 4

5 sandard symmeric shock, which is also assumed o be sae-dependen, i.e., ( S ) = (1 S ) + S. The discree variable,, depending on wheher he economy is in normal imes ( S = 0 ) or in recession S imes ( S = 1 ), is assumed o evolve according o he following firs-order Markov-swiching process as inroduced in Hamilon (1989): u u0 u1 Pr( S = 1 S 1 = 1) = q, Pr( S = 0 S 1 = 1) = 1 q (3) Pr( S = 0 S 1 = 0) = p, Pr( S = 1 S 1 = 0) = 1 p. (4) To idenify he saes of business flucuaions, we resric he discree, asymmeric shock parameer (π ) o be negaive, i.e. π < 0. Dur ing he recession imes ( = 1 ), he economy is hi by a ransiory shock wih negaive expeced value, and he cyclical componen ( c ) is plucked downward. During normal imes ( S = 0 ), he economy is in expansion or recovery, and he cyclical componen is enirely deermined by a symmeric AR() process, where he closer he sum of he auoregressive coefficiens φ 1+ φ o zero, he quicker of he economic recovery mus be. To deermine he sochasic rend componen (he rend ceiling componen), he poenial oupu, or he ceiling maximum feasible oupu, may be approximaed by a random walk wih all sors of disurbances, including he echnological disurbances sressed in he real business cycle lieraure, as suggesed by Friedman (1993). Therefore, he rend componen is wrien as: S n = μ + n 1 + v, v ~ N(0, v( S)), (5) I is noeworhy ha when he asymmeric parameer π is 0 (or π = 0 ), he model (1)-(3) would be reduced o he unobserved componens (UC-UR) specificaion of Morley e al. (003). 3 When he correlaion parameer, ρ = 0, he model (1)-(3) would be reduced o KN99 s specificaion. Moreover, when boh π = 0 and ρ = 0, he model becomes he radiional unobservable componen (UC-0) model. Therefore, he asymmery and he correlaion in his basic model can be esed hrough some suiable ess. The empirical model presened above can be rewrien as a Markov-swiching sae space model, so we can adop he approximae filer proposed by Kim (1994) and he approximae maximum likelihood esimaion mehod o esimae he unobserved sae vecors and he model parameers. For deails of Kim s approximae MLE mehod, readers are referred o Kim and Nelson (1999b). 4. Empirical resuls We selec China s quarerly real GDP daa from 1978:Q1 o 009:Q4,wih18 observaions in oal. Kim and Nelson (1999a) allowed for a drif wih a random walk process in he asymmeric UC model, which is consisence wih he specificaion of Clark (1987). This paper also ries o se he drif as a random walk process, bu he resul is unsaisfacory. In addiion, Sinclair (009) also showed if allowing for correlaion beween drif and oher disurbances, hen he correlaion coefficien may no be recognized, so she also recommended consan for he drif. 3 Morley, Nelson and Zivo (003) suggesed ha he UC-UR model wih correlaed innovaions can be equivalenly expressed o an ARIMA model, and he rend-cycle decomposiion based on UC-UR model is also equivalen o he Beveridge-Nelson (BN) decomposiion based on ARIMA model. 5

6 The daa afer 1994 are obained from he CEI daabase a he China Economic Informaion Nework, which is published by he Naional Bureau of Saisics. Since he official daa were no published unil 1994, we decompose China s annual real GDP daa from 1978 o 1993 ino quarerly daa following he same way as Chen and Liu (007) (for more deails see Abeysinghe and Gulasekaran, 004). Then, he series of real GDP are seasonally adjused wih he Tramo/Seas mehod. A las, he real oupu series are considered as 100 imes he naural log of real GDP, ha is, y = 100 log GDP, = 1,, K, T. In his secion, our empirical analysis will be carried ou in he following seps. Firsly, es he correlaion beween permanen and ransiory shocks using he UC-UR model. If here exiss, he correlaion in asymmeric UC model should also be aken ino accoun; bu no vice versa. Secondly, esimae he basic asymmeric UC model. Here, he real oupu is decomposed ino rend and cyclical componens, so ha we can es he asymmery and deermine wheher he resuls are consisen wih China s acual economy. Finally, consider an asymmeric UC model ha allows for a srucural break in model parameers. To accoun for ha, i is mainly based on he fac ha some changes have happened in China s business flucuaions since he 1990s, especially due o he sof landing and sof expansion Tesing for he correlaion Table 1 repors parameer esimaes and sandard errors (in parenhesis) for wo linear UC models, where Model 1 represens he radiional UC-0 model wih uncorrelaed innovaions, and Model is he UC-UR model wih correlaed innovaions. Here, we give special aenion o a es for he correlaion coefficien ρ, which can also be considered as an over-idenificaion es of he UC-UR model, where he null hypohesis is ρ = 0, i.e., here is no correlaion beween he innovaions, and he alernaive hypohesis is ρ 0, indicaing he exisence of he correlaion. Table 1. Parameer esimaes for linear UC models Parameers Model 1 Model AR(1) coefficien φ ** (0.0475) ** (0.0477) AR() coefficien φ ** (0.0467) ** (0.0470) Sandard deviaion of he permanen v ** (0.0508) ** (0.454) innovaion Sandard deviaion of he ransiory u ** (0.0678) ** (0.106) innovaion Correlaion beween he innovaions ρ uv (3.0879) Drif erm μ.3745 ** (0.0577).3738 ** (0.0495) Log Likelihood Noe: Sandard errors based on he negaive inverse Hessian are given in parenheses. ** denoes he rejecion of he null hypohesis a 5% level of significance. According o he log-likelihood values esimaed from Model 1 and Model, a likelihood raio saisic for esing ρ = 0 is 0.74, wih is corresponding p-value being I is obviously shown ha he null canno be rejeced, indicaing ha he UC-0 model is preferable. Nex, alhough he value of 6

7 correlaion coefficien in he UC-UR model is very close o 1, he p-value of a Wald-ype es saisic shows ha he correlaion coefficien is no significan. Therefore, boh he above ess for he significance of correlaion coefficien sugges ha we canno rejec he null of zero correlaion beween permanen and ransiory innovaions. Since he correlaion beween he innovaions was no found in he linear UC model, we can specify his coefficien wih a consrain ρ = 0 in he asymmeric UC model below, which is similar o he model specificaion in KN99 s paper, so as o avoid he problem of parameer over-idenificaion. 4.. Esimaion resuls of he basic asymmeric UC model Parameer esimaes and sandard errors for asymmeric UC models are repored in Table. Here, in Model 3, boh permanen and ransiory innovaions are sae-dependen on he discree variable ( S = 0 or 1), while in Model 4, he variances of he wo innovaions are assumed o be consans. In addiion, he laer has he same specificaion as Sinclair (009), bu he former is similar o Kim and Nelson (1999a). In he able, he resuls of log-likelihood values show ha Model 3 performs beer and reflecs more informaion han Model 4. The reason is ha he marginal log-likelihood value of Model 3 has increased by 7.0, relaive o ha of Model 4. On he oher hand, he asymmeric UC model is more suiable for modeling China s real oupu series han he linear UC model (Model 1). I can be seen ha he log-likelihood values of wo asymmeric UC models (Model 3 and Model 4) are grealy improved, and he likelihood-raio saisics are and 0.10 wih he corresponding p-value (boosrapping-p value based on 1000 simulaions) and 0.01, respecively. 4 The above resuls show ha he null of he linear UC model can be significanly rejeced. According o parameer esimaes, he resuls indicae he exisence of asymmery in he cyclical componen. I is repored in he able ha he asymmeric shock parameers for Model 3 and Model 4 are boh significanly less han 0; moreover, he larger he asymmeric parameer, he sronger he negaive shock in he recession mus be. As he sandard error ( u ) of he ransiory innovaion is almos 0, we can say ha he cyclical componen is only dependen on his asymmeric discree shock. Compared wih he linear UC model, he sum of auoregressive coefficiens (i.e., φ 1 + φ ) in he UC model is markedly reduced, indicaing ha he negaive shock decays very fas, relaively shor-lived. If here is no furher negaive shocks a he end of recession, economic recovery will come ino being due o he coupling of posiive shocks and negaive shocks; 5 once all influences of he negaive shocks disappear, he economy would reurn o he ceiling of oupu. In addiion, he ransiion probabiliies for measuring he probabiliy of self-mainenance in expansions or recessions show ha he self-mainenance of expansions is very srong wih expeced duraion of 1/ (1 p) = 36.5 quarers; bu i is very weak for recessions wih expeced duraion of abou 8 quarers. However, his resul could be no accurae, because i is no consisen wih he feaure of China s business flucuaions afer Since he es saisic is non-sandard for esing asymmery in he regime-swiching model, a parameer boosrap es is implemened. In more deails for boosrap mehods, readers are referred o MacKinnon (006). 5 Some papers also regard his sage as economic recovery of business cycle, such as Kim and Nelson (1999a), Kim, Morley and Piger (005). 7

8 Table. Parameer esimaes for linear asymmeric UC models Parameers Model 3 Model 4 AR(1) coefficien φ (0.1316) ** (0.1373) ** AR() coefficien φ (0.14) (0.165) Sandard deviaion of he permanen innovaion Sandard deviaion of he ransiory innovaion v (0.033) ** (0.0363) ** v (0.1475) ** u (0.0974) (0.1433) u (0.569) Drif erm μ.3056 (0.05) **.3499 (0.0570) ** Asymmeric parameer π (0.99) ** (0.588) ** Pr[ S = 0 = 0] p (0.0158) ** (0.0165) ** S 1 Pr[ S = 1 = 1] q (0.0655) ** (0.0653) ** S 1 Log Likelihood Noe: Sandard errors based on he negaive inverse Hessian are given in parenheses. ** denoes he rejecion of he null hypohesis a 5% level of significance. Nex, o invesigae he finess of he asymmeric UC model, as well as he inerpreabiliy for China s business flucuaions, we use parameer resuls in Table o esimae hese unobserved variables in Model 3. Figure 3 depics he rend componen ( ) which is he ceiling of oupu in Friedman s plucking model, n and he filered recession probabiliies ( P r( S 1 Y ) ), where Y represens all available informaion a = ime. I is cerain ha he rend of oupu is well consisen wih he ceiling level, describing wo imporan plucking periods: 1980:Q4 o 1987:Q1, and 1989:Q1 o 1995:Q1. From he recession probabiliies, moreover, we capure wo recession periods (1980:Q4 o 1983:Q3, and 1989:Q1 o 199:Q1, respecively) and one dae of he recession (1986:Q1). However, he resuls ploed by Figure 3 are no consisen wih he facs of China s economy. Alhough he figure can well describe acual business cycles before 199, i can hardly explain he periods afer 199, for example, he sof landing and sof expansion periods since Moreover, i also could no capure he apparen recession during he las wo years due o he recen worldwide financial crisis. In view of ha, i can be concluded ha he basic asymmeric UC model is no appropriae o describe China s business flucuaions accuraely. Therefore in he following, we inroduce an asymmeric UC model wih a srucural break afer 1990s, so as o beer es and verify he applicabiliy of Friedman s plucking model for China s business flucuaions. 8

9 1,10 1,080 1,040 1, LN(GDP)*100 Trend Probs(S=1 Y) Figure. Trend componen and recession probabiliies 4.3. Srucural break deecion and esimaion of he asymmeric UC model One drawback of KN99 s mehod is ha he asymmeric shock parameer ha measures he plucking downward behavior is assumed o be a consan. We noice ha i someimes canno well capure he changing ampliude of recession, especially when considering he enire hisorical period of business flucuaions, bu here could be a cerain srucural break ascribed o echnical innovaion, insiuional reforms, ec. Pu differenly, we canno use he same mehod o describe he srucural change in business flucuaions. Therefore, he basic asymmeric UC models (Model 3 and Model 4) are hen generalized o he models (Model 5 and Model 6 respecively) wih possible srucural breaks in parameers. For examples, if he asymmeric shock parameer π is changed, i implies ha he degree of business cycle asymmery has changed, and he recession paern may change accordingly; if he drif erm μ is changed, i implies ha he rend slope of real oupu has changed; if he auoregressive parameers φ 1 and φ are changed, hen he persisence of he recession changes; if he sandard deviaions of he permanen and ransiory innovaions, v and u, are changed, hen he shock srengh may change. In addiion, i is assumed ha ransiion probabiliies ( p and q ) are same before and afer he breakpoin, since we have only wo episodes of recessions afer 1990s, which may cause he esimaes o be imprecise. Now, we consider a case ha here is a srucural break in he asymmeric UC model (Model 3) since Assume ha each dae is possibly a breakpoin from he period of 1991:Q1 o 004:Q4, hen we need o esimae 60 asymmeric UC models wih differen breakpoins. From esimaed resuls, he dae 199: can be seleced as a breakpoin, since he model reaches is maximum log-likelihood value ( ). Compared o Model 3, as he log-likelihood value is grealy increased, i implies ha he asymmeric UC 9

10 model wih a srucural break performs beer han he basic asymmeric UC model. There could be some economic explanaions for his breakpoin 199:Q. From 1978 o 1991, he period from he reform and opening up o he esablishmen of marke economy, China s economic aciviies followed he planned economic sysem. A ha ime, macro-regulaion was no always cooperaed wih marke regulaion, so he ampliude of business flucuaions was very large. Afer 199, however, wih he evoluion of marke economic sysem, he basic role of marke in allocaing resources is improving, and he governmen s knowledge of economic rules has been grealy enhanced. Therefore, o some exen, he size of business flucuaions is reduced since 199. Table 3. Parameer esimaes for asymmery UC models wih he breakpoin a 199:Q Parameers Model 5 Model 6 AR(1) coefficien before 199 φ (0.0983) ** (0.0956) ** AR(1) coefficien afer 199 φ (0.1037) ** (0.1058) ** AR() coefficien before 199 φ (0.0884) (0.0893) AR() coefficien afer199 φ (0.094) ** (0.0943) ** Sandard deviaion of he permanen innovaion before 199 Sandard deviaion of he permanen innovaion afer 199 Sandard deviaion of he ransiory innovaion before 199 Sandard deviaion of he ransiory innovaion afer 199 v (0.1644) (0.1559) v (0.414) v (0.037) ** (0.064) ** v (0.0389) ** u (0.0903) ** (0.0660) ** u (0.1309) ** u (0.0880) (0.119) u (0.39) Drif erm before 199 μ (0.971) ** (0.69) ** Drif erm afer 199 μ (0.0891) ** (0.096) ** Asymmeric parameer before 199 π.491 (0.09) **.460 (0.075) ** Asymmeric parameer afer 199 π.3383 (0.0410) **.3436 (0.0400) ** Pr[ S = 0 = 0] p (0.0358) ** (0.0360) ** S 1 S 1 Pr[ S = 1 = 1] q (0.0389) ** (0.0399) ** Log Likelihood Noe: Sandard errors based on he negaive inverse Hessian are given in parenheses. ** denoes he rejecion of he null hypohesis a 5% level of significance. Table 3 repors parameer esimaes and sandard errors for asymmeric UC models wih he breakpoin a 199:Q, where in Model 5 he sandard deviaions of he permanen and ransiory innovaions are dependen on boh he discree sae variable and he breakpoin, while in Model 6 hey are only dependen on he breakpoin. Overall, he sandard deviaions of he innovaions in Model 5 are over-idenified, and oher parameer esimaes are close o each oher for Model 5 and Model 6. Firsly, he asymmeric parameer ( π ) is significanly less han 0 before and afer 199, bu he absolue value before 199 is 7 imes larger han ha afer 199, indicaing ha he ampliude of negaive innovaions or quarerly conracions is largely decreased. Secondly, he drif erm μ is around.4, implying ha he S 10

11 rend slope of real oupu is almos same, and China s annual rend growh rae is abou 9.6. Thirdly, for he sum of auoregressive parameers ( φ 1 + φ ), he persisence afer 199 is obviously sronger han ha before 199, implying lower decay of he negaive shock afer he srucural break, in accordance wih he fac of he sof landing period. Fourhly, compared o he basic asymmeric UC model he ransiion probabiliies change obviously, since he asymmeric UC model wih a srucural break can capure he acual business cycle afer 199. Here, he expeced duraion of expansions goes down o 1 quarers; and he expeced duraion of recessions increases o 10 quarers. In addiion, he ampliude of permanen and ransiory shocks is differen before and afer 199. The real oupu, before 199, is mainly affeced by ransiory shocks and asymmeric discree shocks, bu no he permanen shocks; while aferwards, i is mainly affeced by asymmeric discree shocks and permanen shocks, bu no ransiory shocks Trend, cycle and business cycle asymmery Based on he above resuls, we proceed o re-examine he business cycle behavior over he sample period, and evaluae he applicabiliy of Friedman s plucking model. We use parameer esimaes given in Table 3 o esimae he unobserved variables in Model 6, including he oupu rend ( ), he cyclical componen ( c ), and he recession probabiliies ( P r( S 1 Y ) ). According o Figure 3 and 4, we can obain he following imporan resuls: = n 1,10 1,080 1,040 1, LN(GDP)*100 Trend Probs(S=1 Y) Figure 3. Trend componen and recession probabiliies Firsly, recession probabiliies well describe he phases of China s business cycle. We noice ha if he probabiliy is greaer han 0.5, he economy is in recession. As is shown in Figure 4, we have capured five business cycles during , where he recession periods are respecively: 1980:Q4 o 1983:Q (he firs recession), 1986:Q1 (he second recession), 1989:Q1 o 1991:Q4 (he hird recession), 1997:Q3 o 11

12 006:Q1 (he forh recession) and he 008:Q1 o 009:Q1 (he fifh recession, which is mainly affeced by he worldwide financial crisis in 008. The conracions in 008:Q1 and 008:Q are mainly caused by Snow Disaser and Wenchuan Earhquake ). I is shown ha he marked downward siuaion has been basically reversed o he overall recovery since 009:Q, where he GDP growh rae arrived a 10.7% when 009:Q4. Therefore, he idenified business cycles are highly consisen wih China s economy, almos he same as he resuls repored by Zhang, ec. (005) based on annual daa. Secondly, oupu rend well explains he ceiling effec, and describes he plucking behavior. Figure 4 depics ha business flucuaions have experienced hree big plucking processes and wo small ones. The former hree processes include 1980:Q4 o 1985:Q, 1989:Q1 o 1994:Q4, 1997:Q3 o 007:Q1, while he laer wo ones refer o 1985:Q1 o 1985:Q4, 008:Q o presen (in progress). I is known ha in each process, he economy sill needs some ime o reurn o he normal rend or he ceiling of oupu afer going hrough a recession period Cycle Probs(S=1 Y) Figure 4. Cyclical componen and recession probabiliies Thirdly, and perhaps mos imporanly, he cyclical componen of real oupu effecively reveals he deph and lengh of he recession during differen periods, where he deph refers o he cumulaive value of negaive asymmeric shocks, and he lengh refers o he duraion of recession. As he duraion of negaive asymmeric shocks are longer, he recession becomes deeper. Figure 4 depics he deviaion of real oupu from he ceiling oupu in each cycle. I should be noed ha he greaer he deviaion, he deeper he recession mus be. We can see ha he deph and lengh of he five recessions since he reform and opening up are largely differen: he firs and hird are deeper, and i akes less ime o go down o he boom, meaning ha he negaive shocks are very large; he recession deph of he fourh cycle is less han ha of 1

13 he firs and hird ones, bu he duraion increases significanly, in accordance wih he fac of he sof landing and sof expansion periods afer 1993; he las recession is mainly caused by he worldwide financial crisis, and i is differen from all previous recessions since real oupu are largely deviaed from he ceiling a he beginning of his recession (007:Q4). 5. Discussions and conclusions Alhough Kim and Nelson s (1999a) mehodology can be used o es he business cycle asymmery under Friedman s plucking model of business flucuaions, wheher i is applicable for China remains unknown. In his paper, under he fac since reform and opening up, we conduc an empirical sudy on China s quarerly real GDP daa over he period The resuls show some evidence supporing Friedman s plucking model. We find ha here exiss he ceiling effec of real oupu and he negaive asymmeric shocks significanly affec he ransiory componen, which herefore capures he plucking downward behavior during he recession from he idea of Friedman. I is also shown ha he basic asymmeric unobservable componen (UC) model in KN99 is no suiable for modeling China s real oupu, bu he asymmeric UC model wih a srucure break in 199:Q can accuraely describe business flucuaions. We can find ha he basic asymmeric UC model canno explain he sof landing and sof expansion periods since 1990s, and i also canno capure a recession in 008 due o he worldwide financial crisis. However, hese unreasonable resuls do no consequenially mean a failure o suppor Friedman s plucking model, bu we should examine wheher here exiss a srucural break in business flucuaions. When a srucural break a 199:Q is aken ino accoun, we can no only accuraely measure he five business cycles since reform and opening up, bu also capure he significan change in he lengh and deph of he recession. According o he above resuls, here exis some differences in business flucuaions beween China and he counries like he Unied Saes. I can be briefly summarized in he following hree oulines. The firs is he ampliude of negaive asymmeric shocks. One similar sudy provided by Mills and Wang (00) shows ha he asymmeric shock parameers for G7 counries were (USA) 6, (UK), (Canada), (France), (Ialy), -1.8 (Germany) and (Japan), respecively. While for China, he ampliude of negaive shocks is relaively large before 199, almos larger han all he G7 counries, bu afer 199, i has been grealy reduced o a low level, which is very close o he Unied Kingdom and Japan. The second is he deph and lengh of a recession. The resuls repored by Kim and Nelson (1999a) and Sinclair (009) show ha he maximum deph of he U.S. recessions is beween -4 and -6, bu he lengh is quie shor. While for China, he dephs of he firs, second and hird recessions are relaively deeper, and he lengh is relaively longer, especially during he sof landing period. The las is he duraion of business cycle. I is mainly refleced in he difference of self-mainenance probabiliy or expeced duraion beween he phases of business cycle. As is poined ou by Hamilon (1989), he expeced duraion of 6 In oher lieraure, he resuls of he asymmeric shock parameer for U.S. real GDP are a lile differen from Mills and Wang (00), bu all less han -1. For example, he esimaed resuls given by Kim and Nelson (1999a), Sinclair (009) and De Simone and Clarke (007) are -1.11, -1.74, and -1.6 respecively. 13

14 recessions in U.S. is very shor, while ha of he expansion is so long. However for China, boh recession and expansion are quie long, due o he macro-conrol policy under he socialism marke economic sysem. Finally, he resuls in his paper reveal he fac ha China s economy begins o rise again since 009:Q, and hen he recession and he adverse effec due o he worldwide financial crisis are gradually and coninually being eliminaed. I is cerain ha he expansionary invesmen policy and he moderaely relaxed moneary policy a he end of 008 and during 009 have achieved some success, and China s economy is gradually geing ou of he shadow of he recession. However, i is essenial for China s governmen o ake furher posiive and effecive measures o avoid he sharp ups and downs, keep a moderae economic growh rae, and hus mainain a susainable developmen of he economy. References Abeysinghe, T. and Gulasekaran, R., 004, Quarerly Real GDP Esimaes for China and ASEAN4 wih a Forecas Evaluaion, Journal of Forecasing, 3, Chen, L.N. and Liu, H.W., 007, Empirical Invesigaion on he Asymmery and Persisence of Chinese Business Cycle, Economic Research Journal, 007(4), (In Chinese) Clark, P.K., 1987, The Cyclical Componen of U.S. Economic Aciviy, The Quarerly Journal of Economics, 10, De Long, J.B. and Summers, L.H., 1988, How Does Macroeconomic Policy Affec Oupu? Brookings Papers on Economic Aciviy, 1988(): De Simone, F.N., and Clarke, S., 007, Asymmery in Business Flucuaions: Inernaional Evidence on Friedman s Plucking Model, Journal of Inernaional Money and Finance, 6, Diebold, F.X., Rudebusch, G.D., Sichel, D.E., 1993, Furher Evidence on Business Cycle Duraion Dependence, In: Sock, J., Wason, M. (Eds.), Business Cycles, Indicaors and Forecasing. Universiy of Chicago Press, Chicago, Friedman, M., 1993, The Plucking Model of Business Flucuaions Revisied, Economic Inquiry, 31, Friedman, M., 1964, Moneary Sudies of he Naional Bureau, The Naional Bureau Eners is 45h Year. 44h Annual Repor. Goodwin, T.H. and Sweeney, R.J., 1993, Inernaional Evidence on Friedman s Theory of he Business Cycle, Economic Inquiry, 31, Hamilon, J., 1989, A New Approach o he Economic Analysis of Nonsaionary Time Series and he Business Cycle, Economerica 57, Keynes, J.M., 1936, The General Theory of Employmen, Ineres and Money, London, Macmillan. Kim, C.J., 1994, Dynamic Linear Models wih Markov-Swiching, Journal of Economerics, 60, 1-. Kim, C.J. and Nelson, C.R., 1999a, Friedman s Plucking Model of Business Flucuaions: Tess and Esimaes of Permanen and Transiory Componens, Journal of Money, Credi, and Banking, 31, Kim, C.J. and Nelson, C.R., 1999b, Sae-Space Models Wih Regime Swiching: Classical and Gibbs-Sampling Approaches wih Applicaions, The Mi Press. Kim, C.J., Morley, J. and Piger, J., 005, Nonlineariy and he Permanen Effecs of Recessions, Journal of Applied Economerics, 0, Liu, J.Q. and Fan, J.Q., 001, A Sudy of Asymmery and Relaiviy of China s Business Cyscles, Economic Research Journal, 001(5), (In Chinese) Liu, J.Q. and Wang, D.Y., 003, The Hypohesis of Growh Regimes and Tesing for Flucuaion Spillover Effec, Sudy of Finance and Economics, 003(5), 3-7. (In Chinese) 14

15 Liu, J.Q. and Zheng, T.G., 008, Recogniion of Phases of China s Business Cycle and Forecasing for he Growh Trend, China Indusrial Economics, 008(1), (In Chinese) Liu, S.C., 003, Analysis on he New Flucuaion Mode of China Economy Developmen, Economic Research Journal, 003(3), 3-8. (In Chinese) Liu, S.C., Zhang, X.J., and Zhang, P., 005, Smoohing he Business Cycles a a Moderaely High Aliude, Economic Research Journal, 005(11), (In Chinese) MacKinnon, J.G., 006, Boosrap Mehods in Economerics, The Economic Record, 8(Special Issue): S-S18. Mills, T.C. and Wang, P., 001, Plucking Models of Business Cycle Flucuaions: Evidence from G-7 Counries, Manuscrip. Loughborough Universiy. Michell, W.C., 197, Business Cycles: The Problem and is Seing, New York, Naional Bureau of Economic Research. Morley, J.C., Nelson, C.R. and Zivo, E., 003, Why Are he Beveridge-Nelson and Unobserved-Componens Decomposiions of GDP So Differen? The Review of Economics and Saisics, 85, Morley, J.C. and Piger, J., 009, The Asymmeric Business Cycle, Working Paper. Nefcy, S.N., 1984, Are Economic Time Series Asymmeric over he Business Cycle? The Journal of Poliical Economy, 9, Ramsey, J. and Rohman, P., 1996, Time Irreversibiliy and Business Cycle Asymmery, Journal of Money, Credi, and Banking, 8, 1-1. Razzak, W.A., 001, Business Cycles Asymmeries: Inernaional Evidence, Review of Economic Dynamics, 4, Sichel, D.E., 1993, Business Cycle Asymmery: A Deeper Look, Economic Inquiry, 31, Sinclair, T.M., 010, Asymmery in he Business Cycle: Friedman's Plucking Model wih Correlaed Innovaions, Sudies in Nonlinear Dynamics & Economerics, 14, forhcoming. Xu, D.F., Zhu, P.F., Liu, H., 005, "Abou he Business Cycle Asymmery in Chinese Economy", The Sudy of Finance and Economics, 005(4), (In Chinese) 15