A New Look at China s Output Fluctuations: Quarterly GDP Estimation with an Unobserved Components Approach

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1 A New Look a China s Oupu Flucuaions: Quarerly GDP Esimaion wih an Unobserved Componens Approach Yueqing Jia Deparmen of Economics The George Washingon Universiy Washingon, DC yqjia@gwmail.gwu.edu RPF Working Paper No hp:// December 10, 2011 RESEARCH PROGRAM ON FORECASTING Cener of Economic Research Deparmen of Economics The George Washingon Universiy Washingon, DC hp:// Research Program on Forecasing (RPF) Working Papers represen preliminary work circulaed for commen and discussion. Please conac he auhor(s) before ciing his paper in any publicaions. The views expressed in RPF Working Papers are solely hose of he auhor(s) and do no necessarily represen he views of RPF or George Washingon Universiy.

2 A New Look a China s Oupu Flucuaions: Quarerly GDP Esimaion wih an Unobserved Componens Approach Yueqing Jia 1 Deparmen of Economics The George Washingon Universiy Washingon, DC yqjia@gwmail.gwu.edu This Draf: December 2011 JEL Classificaion: C53; E32 Key words: Business cycle, economic growh, emporal disaggregaion unobserved componens, China Absrac This paper provides quarerly real GDP esimaes for China from 1978q1-1991q4 using an unobserved componen approach. The approach imposes fewer prior resricions on relaed series and is more flexible han oher disaggregaion mehods. The mulivariae unobserved componens model wih oal rade and domesic credi as relaed series is seleced as he bes fi model for emporal disaggregaion of China s real GDP. The esimaed quarerly real GDP daa are hen evaluaed wih univariae and mulivariae ime series analysis echniques. The consruced quarerly daa are shown of good qualiy and provide valuable informaion for he analyses of China s macroeconomic flucuaions during he period. 1. George Washingon Universiy, Deparmen of Economics, 2115 G Sree, NW Monroe Hall 340, Washingon, DC 20052, yqjia@gwmail.gwu.edu, Tel (m) The auhor hanks he Insiue for Inernaional Economic Policy and GW-CIBER for suppor for his research projec and appreciaes my disseraion commiee members: Professor Tara Sinclair, Fred Jouz, Neil Ericsson, Maggie Chen, Dr. Mark Deweaver; Professor James Morley and he paricipans in he Souhern Economis Associaion annual meeing and Georgeown Cener for Economic Research 2011 conference a Washingon DC for very helpful commens and discussions. The remaining errors are my own. 1

3 I. Inroducion China moves o cenre sage ----Cover sory, Economis, Oc. 30, 2008 In he pas hree decades, China has emerged as one of he mos imporan and influenial economies, wih is remarkably rapid growh and inegraion ino he world economy. China is he world s second larges economy in , he larges exporer (since 2009) and he world s larges foreign exchange reserves holder. The recen financial crisis pushed China o he fronier of world economic developmen. China s economic performance, in he shor and long run, is more han ever he focus no only of academic research bu also of policy makers and sakeholders from inside and ouside China. Alhough increasingly imporan, he properies of China s oupu flucuaions are no well undersood. Very limied economeric analysis has been conduced on China s macroeconomic flucuaions. This is mainly due o he shorage of high-frequency daa. The complexiy of China s ransiional economic and poliical srucures adds difficulies o he analysis. Lack of proper characerizaion of China s oupu rend and cycles may mislead he heoreical economic sudies on Chinese economy as well as policy analysis. While exising research relies mosly on he available annual daa, he sudy from low-frequency annual daa obviously canno fulfill he needs of economic decision making in a fas-changing world. China s official quarerly real GDP daa are only available since 1992, which provides only 78 quarerly observaions up o 2011 q2. Small samples can limi he applicable mehods and he qualiy of empirical analysis. Jus shorening he sample period and ignoring he 2 China passed Japan as he second larges economy in erms of nominal GDP in

4 available annual observaions before he quarerly daa are available resuls in losing imporan informaion for he properies of daa generaing process. Exending he quarerly real GDP daa from 1992 back o 1978 for China would provide a complee sample of growh flucuaions for he economy since he beginning of he reforms and hus a beer undersanding of he evolving properies of China s macroeconomic flucuaions along wih he implemenaion of he reforms. As o flow daa such as real GDP, one way o solve he above problem is o emporally disaggregae or inerpolae he low frequency daa ino higher frequency daa. Using a proxy observed a higher frequency and esimaing he real GDP wih he producion funcion would be alernaives. However, for China, quarerly macro-economic daa before 1992 are exremely limied. The only available series are from moneary and inernaional rade saisics. They are no sufficien o esimae he proxy and producion funcion daa consrucion alernaives. Temporal disaggregaion of annual real GDP o quarerly real GDP wih available relaed informaion hus becomes he only pracical approach for he quarerly GDP consrucion for he period. Temporal disaggregaion is also a commonly used mehod for resolving similar problems o oher counries 3. Univariae mehods, relaed series univariae mehod or Chow-Lin mehod (Chow and Lin 1971, CL model hereafer) and mulivariae unobserved componens (UC approach hereafer) mehods are he hree groups of approaches ha have been applied o emporal disaggregae macro-economic daa in lieraure. Abeysinghe and Rajaguru (2004, A&R hereafer), he only published sudy on he emporal disaggregaion of China s GDP daa, applies he Chow-Lin relaed series echnique o disaggregae China s annual real GDP daa ino quarerly daa and provides quarerly real GDP 3 For example he Eurosa (1999) documens ha he emporal disaggregaion mehod is used in he official saisics agencies of he European counries. 3

5 growh rae esimaes from 1978Q1 o 1994 Q4 4. However, as I will discuss below, he CL model based on univariae regression assumes a linear relaionship among he relaed series and does no consider he uni roo properies of he series. Boh assumpions may no be proper in pracice when choices of available relaed series are very limied. My sudy generalizes he univariae and mulivariae unobserved componens modeling for emporal disaggregaion, and provides emporal disaggregae esimaes of China s quarerly real GDP daa for he years 1978 hrough 1991 using he seleced mulivariae unobserved componens model (MUC model hereafer). The unobserved componens approach is more general han he Chow-Lin approach in dealing wih uni roo, seasonaliy and irregulariy properies. The mehod allows simulaneous disaggregaion and seasonal adjusmen of he daa, and imposes minimum prior resricions on he daa. I provides more flexibiliy for he daa selecion, which is especially imporan for emerging counries whose high frequency daa are very limied. I emporally disaggregae China s real GDP series using he unobserved componens models wih differen specificaions of componens and differen combinaions of relaed series for model selecion. The mulivariae unobserved componens (MUC) model wih domesic credi and oal rades as relaed series is seleced as he bes fi model based on he roo mean squared sandard errors of he esimaed daa and he official published daa over he overlapping 4 On heir websie (hp://courses.nus.edu.sg/course/ecsabey/gdpdaa.xls), he auhors exended he series hrough 2007Q1, using quarerly year-on-year real GDP growh raes from he counry daa of Economis Inelligence Uni. The daa resources of EIU counry daa for China are CEIC and Naional Bureau of Saisics of China (NBS). 4

6 period. The esimaed daa from wih seleced MUC model are more efficien han he esimaion from oher emporal disaggregaion mehods 5. The MUC esimaed quarerly real GDP for China provides a beer alernaive of China s quarerly real oupu daa for differen univariae and mulivariae ime series analyses. To evaluae he daa qualiy, I apply differen univariae rend cycle analyses, such as Hodrick- Presco filer (1997, HP filer hereafer), Band-Pass Baxer-King (1999) and Chrisiano-Fizgerald (2003) filer and unobserved componens decomposiion mehod, and srucural mulivariae analysis, such as Blanchard-Quah (1989) decomposiion and Global Vecor Auoregression models (Dees e. al 2007, DdPS model hereafer) o he esimaed daa. The analyses show ha he exension of quarerly real GDP wih he MUC model provides valuable informaion for he undersanding of he oupu flucuaions during he sample period. Domesic facors and supply shocks are found o be he main driver of China s oupu flucuaions. The purpose of his paper is o provide quarerly real GDP for China in consisency wih he official real oupu daa. Thus, he availabiliy and reliabiliy of China s official daa, he big concerns for China s official GDP saisics, are carefully discussed before he daa consrucion. There are six secions of his paper: Secion II reviews he relevan lieraure on he mehodology of emporal disaggregaion and he conribuion of my paper in high frequency daa consrucion; Secion III presens he unobserved componens or srucural ime series models for he emporal disaggregaion of China s real GDP. Secion IV addresses China s macroeconomic daa problem. In Secion V, he resuls of he daa consrucion from differen model specificaions are presened and evaluaed. Secion VI analyzes China s real GDP flucuaions 5 The comparison of he esimaion of differen approaches based on he roo mean square errors is presened in secion V. The seleced MUC esimaion, including he observed annual levels in he esimaion, fis he observed annual real growh raes beer han he A&R esimaion. 5

7 wih he consruced quarerly real GDP daa using differen univariae and mulivariae approaches and compares he resuls of permanen and ransiory macroeconomic flucuaions based on he consruced quarerly real GDP daa. Secion VII concludes. II. The lieraure This sudy is relaed o he following srands of lieraure: firs, he esimaion of missing high-frequency macro economic daa from available low-frequency daa, i.e. inerpolaion and emporal disaggregaion mehods; second, he research on idenifying China s oupu flucuaions and he commonly used univariae and mulivariae aggregae oupu rend and cycle decomposiion mehods. To evaluae he qualiy of he quarerly real GDP daa esimaed in his paper, boh univariae and mulivariae mehods are applied o he esimaed quarerly real GDP daa for China. The unobserved componens model is he key modeling framework applied in his paper. 2.1 Lieraure on missing high frequency daa and emporal disaggregaion mehods of ime series Temporal disaggregaion or inerpolaion has been exensively used by researchers when high frequency daa required by economeric analysis are no available. I is also a rouine pracice for official saisical agencies o apply emporal disaggregaion mehods o generae high frequency daa, especially when direc esimaion mehods are unavailable or informaion collecion is cosly (Proiei 2006, Eurosa, 1999). Problems of ime series disaggregaion include inerpolaion of sock variables and emporal disaggregaion of flow variables. The esimaion of China s quarerly Gross Domesic Produc from he annual official daa falls ino he second caegory. There are broadly hree 6

8 groups of mehods ha have been developed o emporally disaggregae lower frequency daa ino higher frequency daa: 1) univariae mehods rely on he ime series properies of he argeed series only. For example, Sram and Wei (1986, 1990) derive smoohed esimaion of unavailable high frequency daa based on he ARIMA srucure of he series. Sram and Wei (1990) mehod has been applied o he esimaion of macroeconomic indicaors by many official saisic agencies (Eurosa 1999, par ). When he missing high frequency daa period is shor compared o he whole sample period, a simple univariae inerpolaion is ofen convenien. However, when missing high frequency daa are for a relaively long period, he simple univariae inerpolaion, which uses he ime series properies of he arge series iself (usually properies of he series during more recen period when he high frequency daa are available), is likely o disor he resuls of high frequency analysis. Especially for he sample period when high frequency daa are missing. The problem may be more serious for daa from emerging or ransiional economies. Their underlying economic srucure and environmen ofen change subsanially. More sophisicaed mehods ha use more informaion o disaggregae daa should be considered. 2) Relaed series univariae models ha were firs proposed by Chow and Lin 1971 and exended by Fernandez (1981) and Lierman (1983) wih a random walk and I (1) error erm respecively. Applicaion of emporal disaggregaion by he CL approach begins wih running OLS or GLS on a linear model of arge series o he relaed series wih low frequency daa. Assuming ha he linear relaionship of arge series and relaed series is consisen wih low frequency and high frequency daa, he esimaed coefficiens are hen used o predic he arge series based on he high frequency relaed series daa wih adjusmen o mach he annual 7

9 aggregaes. An AR (1) process for he error erm is assumed in he original CL model. To accoun for he non-saionary residuals, a random walk process is assumed in he Fernandez model and I (1) in he Lierman model. Sanos and Cardoso (2001) and recenly Proiei (2006) add lagged values of he dependen variable (auoregressive disribued lag or ADL models) ino he CL model. Harvey and Pierse (1984) and Proiei (2006) presen hese groups of models in sae space form and apply he Kalman filer o esimae he missing observaions. The CL approach and is exension models use more informaion from observed relaed high frequency daa. Chen (1993) demonsraes wih Mone Carlo simulaed daa ha he CL procedure is usually more efficien han he univariae only alernaives. The convenience in applicaion has made his mehod more popular in pracice han he firs group of models. A&R (2004), he only published emporal disaggregaion of China s real GDP, applies CL approach o he growh raes of GDP wih he growh raes of M1 and oal rade as relaed series. The major problem wih his group of models is ha he assumpion of a linear relaionship beween he arge series and he relaed series is ofen difficul o verify wih he daa (Proiei 2006, Moauro and Savio 2005). As Harvey (1989 secion 8.7) and Proiei (2006) menioned, he univariae relaed series models, alhough widely applied in pracice, impose a srong assumpion of coinegraing relaionship beween argeed series and he relaed series and/or exogeneiy of he relaed series regressors. Moauro and Savio (2005) furher proves ha even wih he exisence of coinegraing relaionship, univariae wih relaed series models, or CL mehod will be efficien only when he consan and he auoregressive parameers are equal for all included relaed series, or in erms of unobserved componen model specificaion, he relaed series are rend homogeneous. The 8

10 assumpions are no likely o be verified in he rue daa, especially when he choices of relaed series are very limied 6. The resricion of CL mehods limis he choice of relaed series. The arge series and he ses of available relaed series may no have a linear relaionship, bu are usually affeced by he same economic environmen and hus could provide valuable informaion and improve he efficiency of he disaggregaion. A&R, who use nominal M1 and he oal rade as relaed series, apply CL approach o he firs-differences and he growh raes insead of levels of he real GDP and relaed series o avoid he non-saionary and coinegraion problem. Even wih he growhrae approach, A&R did no find a significan linear relaionship beween he growh rae of real GDP and M1, bu found including M1 leads o beer disaggregaion 7. Alhough he relaionship of M1 and real GDP is no significan wih annual daa, i provides informaion for quarerly GDP esimaion ha improves he efficiency of he disaggregaion. 3) Mulivariae unobserved componens (MUC) or srucural ime series models. The applicaion of UC models o emporal disaggregaion was originaed by Harvey and Pierse (1984) and Harvey (1989)8. Harvey and Chung (2000), Moauro and Savio (2005) are examples of he conribuions of his group of models. MUC models se up a sysem of unobserved componens equaions of he argeed and relaed series and esimae he models in he sysem simulaneously. The approach allows cross series correlaions for he componens and hus includes he quarerly informaion provided by he available relaed series o he disaggregaion of arge series. 6 When choices of relaed series are limied, if no linear relaionship is found among he series, here will be no alernaives available. 7 A&R evaluaes he disaggregaion by comparing he quarerly daa esimaed from he model wih he real daa during he overlapping period. 8 Harvey (1989) names his model seemingly unrelaed srucural ime series equaion (SUTSE). 9

11 The MUC approach overcomes he limiaion of CL mehods. The MUC models are capable of aking advanage of informaion from he available high frequency relaed ime series for he disaggregaion, wihou puing prior resricions on he specific relaionship beween he series. Common rends, common cycles and common seasonaliies among he relaed series can be esed hrough MUC models (Moauro and Savio 2005). The MUC approach is also flexible in handling boh seasonally adjused and non-seasonally adjused daa and allows disaggregaion and seasonal adjusmen simulaneously. Proiei and Moauro (2005) furher show ha he model is capable of handing seasonaliy very well. In addiion, wih he Kalman smoohing esimaion, he sample period can be exended o include he informaion of he available high frequency observaions of he argeed series in he laer years. For example, China s official quarerly real GDP daa ha are available since 1992 can be included in he esimaion of China s real quarerly GDP during in MUC models. Since he ime series propery of a ime series iself is usually sable over ime, he propery of he observed high frequency daa of he arge series can help improving he emporal disaggregaion. Since Harvey and Pierse (1984) firs cas he univariae disaggregaion mehods ino sae-space form and applied Kalman filer echnique o esimae he missing high frequency daa, he sae space approach has been regularly applied in he emporal disaggregaion of ime series. Harvey (1989, secion 6.3) proposed he mehod of using cumulaor series o se up he sae space form over series of differen ime frequencies, where he missing high frequency daa is reaed as missing observaions, esimaed wih he Kalman smoohing algorihm. The mehod provides more flexibiliy in modeling componens of he series and can be applied o boh univariae and mulivariae disaggregaion models on boh flow and sock ime series. Durbin and Quenneville (1997), Proiei (2006) generalized he sae space mehod applicaions o he 10

12 CL model and is exensions. The relaed series are modeled as exogenous regressors ha ener ino he measuremen equaion and/or ransiory equaion. Cuche and Hess (1999) and Tasdemir (2008) disaggregae European and Turkish daa using he sae space mehods. This paper furher generalizes he models for he emporal disaggregaion of flow series wih unobserved componens semming from Harvey (1989) and Moauro and Savio (2005). I presen he univariae and mulivariae unobserved componens models, wih or wihou cyclical componens, in sae space forms and esimae China s quarerly real GDP during wih Kalman smoohing algorihm. This paper is he firs applicaion of emporal disaggregaion of China s real GDP wih he unobserved componens approach. 2.2 Lieraure on idenifying and characerizing China s oupu flucuaions To evaluae he informaion provided by he quarerly real GDP levels of China from esimaed by he seleced unobserved componens model in his paper, I apply differen univariae and mulivariae ime series analyic mehods o he daa. Lieraure on he measuremen of China s poenial oupu or oupu gap is hen closely relaed o his par of sudy. The exising sudies generally follow hree approaches: he producion funcion approach, univariae rend-cycle decomposiion approaches and mulivariae ime series approaches or Vecor auoregression approaches (VAR). The rend of aggregae oupu is generally assumed o correspond o poenial oupu and he cycle is assumed o correspond o he oupu gap. Mos of he sudies on China s poenial oupu esimaion apply producion funcion approach o annual daa, which esimaes he Cobb- Douglas producion funcion wih poenial capial and labor inpus 9. 9 In his group of sudies, Chow (1993 and 2002) inends o find he imporance of capial formaion and conribuions of secors, Heyens and Zebregs (2003) ry o find he growh of Toal Facor Produciviy, Young (2003) focuses on alernaive 11

13 Decomposiion of he aggregae oupu series ino rend and cycle componens has been a common pracice for aggregae oupu flucuaion analysis. Compeing approaches have been developed o decompose macroeconomic series such as he aggregae oupu ino rend and cycle, or permanen and ransiory componens. A number of sudies (Morley 2008, Canova 1998, Zarnowiz and Ozyildrim 2006, Park 1996 and King and Rebelo 1993, Gerlach and Yiu 2003) have shown ha he revealed rend cycle properies are sensiive o he derending mehods 10. For China s real GDP, he Hodrick-Presco (HP) filer is he widely used univariae derending mehod in he lieraure ha models China s business cycles (for example: Ha, Fan and Shu 2003) 11. Gerlach and Peng (2006) esimae annual Chinese oupu gap from using he unobserved componens (UC) model following Wason (1986) and Clark (1987). They find ha HP filer and UC approaches generae similar cyclical paerns. Their esimaion suffers from limiaions due o he small sample size (21 observaions) and very broad confidence bands. Laurenceson and Rodgers (2010) use differen frequencies of cycles o idenify he relaive imporance of demand and supply volailiies occurring a China s business cycle. price levels, and Scheibe and Vine (2005) sudy he Phillips curve. Scheibe (2003) explores he producion funcion wih secor based esimaion. This approach is also used for alernaive GDP daa consrucions. 10 Canova (1998) examines he business cycle properies of US real macroeconomic ime series daa wih seven differen decomposiion mehods and finds ha for aggregae oupu of he US, differen decomposiion mehods generae cycles ha differ in ime duraion and urning poins. As for developing counries, Gerlach and Yiu (2003) compare oupu gaps wih annual daa for eigh Asian economies (no including China) derived from four decomposiion mehods, and find gaps (cycle componen) from HP, UC and BP decomposiions are similar for hese counries bu he gaps derived by BN decomposiions are differen. 11 Alhough he producion funcion approach uses more informaion for poenial GDP esimaion han he alernaive univariae approaches, i also inroduces more poenial problems. Firs, several assumpions are frequenly made o se up he producion funcion. Assumpions such as consan reurns o scale in producion, compeiive markes for inpus and oupus may no be appropriae for China. There are no generally acceped poenial levels of labor, capial inpus and oal facor produciviy growh for China. Secondly, he esimaion needs capial and labor daa, which faces similar daa availabiliy and reliabiliy problems as well. Labor or employmen daa are even less available and reliable for China han GDP daa. Missing capial and employmen daa have o be esimaed before hey are used in he poenial GDP esimaion. Third, he esimaion mus selec proper price levels for differen inpus and secors (Young 2003), which are unavailable and have o be esimaed. Finally, mos research using his approach relies only on annual daa due o he daa availabiliy problem. Because of he issues above, he resuls of producion funcion esimaions are no consisen among differen sudies. 12

14 In recen years, several Chinese scholars applied nonlinear univariae mehods such as Markov-swiching process o indenify he phases of business cycles in China (mosly published in Chinese), examples of he sudies include Chen and Liu (2007) Liu (2003, Liu and Zheng (2008), Zheng, Teng and Song (2010). Mos of hese researches suffer from small sample problem. In his paper, I apply he mos widely used univariae mehods include he Hodrick and Presco (1997, HP) filer, he Band-Pass filer (Baxer and King 1987, Chrisiano and Fizgerald 2003, BP) filer, and he unobserved componens models (Harvey 1985, Wason 1986, Clark 1987) o he esimaed quarerly real GDP daa o presen he informaion provided by he daa. Srucural mulivariae mehods, on he basis of economic heories, inroduce oher macroeconomic variables o idenify he properies or he origins of oupu flucuaions. These mehods include he srucural VAR, such as Blanchard-Quah (1989) approach and is exensions (e.g. Clarida and Gali 1994) and mulivariae sysem models such as he global VAR approaches (Dees, Di Mauro, Pesaran and Smih 2007, DdPS hereafer). The curren applicaions of hese approaches o China s macroeconomic daa suffer from shorage of long ime period quarerly GDP daa. Among he limied published applicaions of Blanchard and Quah o Chinese daa, Zhang and Wan (2005) use real indusrial oupu as a proxy for real GDP for Siklos and Zhang (2010), analyzing China s inflaion flucuaion wih he sandard Blanchard and Quah framework and a ri-variae exension, have o limi heir analysis o he shor sample period of The original DdPS model esimaion wih Chinese daa use quarerly real oupu daa ha are derived from annual real GDP level by evenly allocaing he annual oupu o he four quarers of he year. 13

15 This paper applies he above univariae and mulivariae ime series analyses o he esimaed China s quarerly real GDP and shows ha he consruced daa provide a beer high frequency and long period real GDP daa alernaive for he analyses of China s oupu flucuaions 12. III. Temporal disaggregaion of China s quarerly real GDP wih unobserved componens model 3.1 he Model The unobserved componens models are se up in erms of componens ha have direc inerpreaion of sylized feaures of he series. The models are capable of including rend (or long run, permanen componen), cycle (shor run, ransiory componen), seasonal componens (if he daa are no seasonal adjused) and irregulariies ha represen he non-sysemaic oulier observaions or measuremen errors. Following Harvey (1989), he unobserved componen models for emporal disaggregaion of China s real GDP can be presened in mulivariae sae space form as follows: The measuremen equaion is: y (1) i =(τi+ci+si+γi )+ X+εi Or in a more general form: Y Z + X+ (1 ) 12 To focus on he evaluaion of quarerly real GDP consrucion, in his paper I do no include he producion funcion approach, which may involve daa problems from capial and labor saisics. 14

16 Where: yi = ( y1, y2,,..., yn), i 1,2,..., n and 1,2,..., T y 1 is he arge series ( y 1 : China s real GDP) and y2,,..., yn are he relaed series for mulivariae models. Z is a n m marix, where m is he number of unobserved componens, and N is he number of dependen variables in mulivariae models. X is he marix of assumed exogenous variables or he relaed variables which will only be presen in he univariae wih relaed series model 13. is he parameer vecor of he explanaory variables. is m 1he sae vecor ha conains he unobserved componens ha may include rend τ, cycle c, seasonaliy s, and irregulariy. is an n 1vecor of serially uncorrelaed disurbances assumed wih mean zero and he covariance marix G, or E( ) 0 and Var ( ) G The ransiion equaion is, T 1 H (2) Where ( c s )', T is a m m marix, H is g m marix ( g m when all componens are defined as sochasic, g will no equal o m when some componens are defined as fixed or deerminae). is a g 1vecor of serially uncorrelaed disurbances wih mean zero and he covariance marix, Q, or E( ) 0 and Var ( ) Q I use seasonally unadjused daa in he disaggregaion models o avoid losing informaion from such adjusmens. The seasonal componens generaed hrough he disaggregaion will be compared wih he seasonal facor generaed from commonly used seasonal adjusmen procedure in he evaluaion secion of he paper. 13 I do no add explanaory variables o he unobserved componens such as rend, cycles and/or seasonaliy. Adding explanaory variables means adding assumpions on he relaionship of he relaed series, which will reduce he generaliy of he model of daa consrucion. 15

17 The disaggregaion models are specified wih choices for sochasic drif and seasonaliy o capure he possible ime variance of drif and seasonaliy 14. Disurbances of componens wihin series are assumed uncorrelaed from each oher in he disaggregae models following Harvey and Wason (1986), Harvey (1989) and Clark (1987). Puing observaions wih differen iming inervals ino he sae space form is he key sep of using unobserved componen model for emporal disaggregaion. Harvey (1989, secion 6.3) inroduced he echnique of using a cumulaor variable for mixed frequency daa in sae space model. The cumulaor variable for quarerly daa is defined as following: y y, where s( 1) 1, 1,...( n/ s), s 4 c y y y c 1 1 y y y y c y y y y y, c y y c 4 4 y y y c Where c y is he year up o dae cumulaed value of he quarerly level of he series, and y is he quarerly level of he series. For he years wih only annual daa available, only c y, 3 which equals he annual level of he series, is observable. For China s real GDP, he cumulaor variable c y is only observed once every 4 periods during The series of cumulaor 14 Fixed drif and seasonaliy are also ried for comparison. 16

18 variable is considered as he arge series ( y 1 ) in all models. The unobserved values of c y are hen reaed as missing observaions o be esimaed wih smoohing algorihms from he Kalman filer. 3.2 The unobserved componens specificaion The general UC model specificaion is capable of nesing he hree caegories of inerpolaion models: Univariae models wihou relaed series, univariae models wih relaed series and mulivariae unobserved componens models. Differen specificaions of he componens are ried and he consruced quarerly daa are evaluaed. The unobserved rend componen can be specified as: 1, ~ iid (0, Q ) (3) There are wo widely applied specificaions of he slope of he rend: one is based on Harvey (1985) and Wason (1986), which assumes ha he rend is random walk wih consan drif, i. e., ; he oher is he Clark (1987) model, in which he rend is assumed o follow random walk wih a random walk drif, i.e. 1. Clark s assumpion of a random walk wih drif is capable of accouning for possible srucure breaks. To avoid losing informaion in he emporal disaggregaion, he choice of ime varying or sochasic slope (he drif of rend) following Clark model is applied in he disaggregaion models wih relaed series 15. The esimaion sars wih general local linear rend (LLT) models, which do no include cyclical componen. The cyclical componen is hen inroduced ino he model and assumed following 2 nd order auo-regressive process or AR (2), as for mos real oupu series in he lieraure (Harvey 1985, Clark 1987 and Morley e. al. 2003). Harvey (1989) and Durbin and 15 Fixed slope of rend is also ried for comparison. 17

19 Koopman (2001) sugges rigonomeric expressions for cyclical componens which are no applied in his paper, because i may inroduce arbirary waves in he cyclical componens. Thus when he unobserved cyclical componen is included, he ransiion equaion for cyclical componen is: c 1c 1 2c 2 c, c ~ iid N(0, Qc ) (4) The correlaions beween rend and cycle disurbance are assumed o be zero in he emporal disaggregaion models following Harvey and Wason (1986) and Clark (1987). Since I will only ake he Kalman smoohing esimaion resuls of he missing observaions and no invesigae he rend cycle decomposiion from he emporal disaggregaion, he assumpion of zero cross correlaions will no affec he final resul of he daa consrucion 16. The unobserved componens models are capable of handling seasonal adjusmen simulaneously wih he emporal disaggregaion, wih he underlying assumpion ha he seasonaliy relaionships of he disaggregaed series are consisen or homogenous wih he relaed series along he sample period. There are wo opions of seasonaliy formulaions in he Srucural Time Series Analyser, Modeller and Predicor package (STAMP 8, Koopman, e al. 2007): rigonomeric sochasic seasonaliy (Harvey 1989, 6.2), which allows for changes of seasonaliy paern along he sample ime, and he fixed dummy seasonaliy. I chose sochasic seasonaliy in he models, because i can rack he possibiliy of changing of seasonaliy during he ime period and avoid losing informaion for he seasonaliy in he consruced daa Assumpion on he correlaion of permanen and ransiory shocks is criical o he esimaion of permanen and ransiory composiions or he unobserved componens. While he daa consrucion only ake he resul of he esimaion of he level of he series and no doing decomposiion for he series, hus will no be affeced by he assumpion. The zero cross correlaion assumpion reduces he number of coefficiens o be esimaed and increases he degree of freedom, hus increases he chance of convergence especially for he mulivariae models. 17 Fixed or deerminan seasonaliy is also ried for comparison. 18

20 Measuremen errors of he daa can be a big concern for China s macro-economic daa. Therefore I include irregulariy erm in he models. However, I do no find any significan irregulariies in any models. 3.3 Univariae and Mulivariae models Univariae models wihou relaed series When n 1, he model is a univariae UC model and conains he cumulaed quarerly real GDP level wih missing observaions only. The modeling sars wih a Local linear Trend (LLT) univariae model wihou cyclical componens. For LLT model, he measuremen equaion is simplified as: y s (5) Univariae models wih relaed series. The univariae model wih relaed series as exogenous explanaory variables wihou cyclical componen is comparable wih Chow-Lin approach and is modificaions (Harvey 1986). The explanaory variables ener ino he measuremen equaion as: (6) If he componens are se as deerminisic and ε as AR (1), he model is comparable wih he original CL model (Moauro and Savio 2005). When here is no cyclical componen included, he univariae wih relaed series model wih random walk drif is comparable wih modified CL mehod, also known as Fernadez (1981) model. To find he bes model for emporal disaggregaion of China s real GDP, I also ry he models wih AR (2) cyclical componen. Mulivariae unobserved componens models 19

21 Temporal disaggregaion using mulivariae unobserved componens models, as reviewed in secion II, uses he informaion from relaed macro-economic series and a he same ime avoids liner relaionship assumpion on he relaed series or he weakly exogenous as in he Chow-Lin model and is exensions. As discussed in he lieraure secion of his paper, he mulivariae UC models may be more appropriae if he coinegraing relaionship is hard o find beween he available relaed series. The problem can be more likely for emerging counries, where high frequency macro-economic daa are very limied. Anoher advanage of his framework is ha i allows for simulaneous disaggregaion, seasonal adjusmen and rend cycle decomposiion. While no he focus of daa consrucion secion of his paper, he common rends, cycles and seasonaliy among he relaed series can be easily imposed and esed in he mulivariae UC framework. 3.4 Logarihmic ransform of he daa All series values are in naural logarihms o ensure posiive esimaion for real GDP in he disaggregaion models. Firs, due o he relaively small sample, a few large seasonal roughs may cause he esimaed quarerly real GDP o become negaive when using levels of he series 18. Logarihmic ransformaion of he daa guaranees posiive values of he esimaed quarerly daa. Secondly, as Proiei 2006 shows, since logarihmic ransformaion reduces he heeroscedasiciy of he series and he underlying assumpions of he mulivariae disaggregaion models include homoscedasiciy on seasonaliy and variances among series, i is more appropriae o use for hose models. The cumulaed series of he logarihmic ransformed arge series can be expressed as: 18 Esimaion of he models using levels of he series does generae a few negaive resuls a cerain seasonal roughs. 20

22 c ly log( y ), where s( 1) 1, 1,...( n/ s), s 4 ly log( y y 1) c 1 ly log( y y y 3) c 2 2 c ly log( y y y y 3), ly log( y 4) c 4 ly log( y y 5) c 5 4 y c c 0, s( 1) 1, 1,...( n / s), s 4 log( y 1 y ), (7) 1, oherwise Where of he real GDP. c ly is he logged cumulaed level of he real GDP, and c y is he cumulaed level One concern abou he logarihmic ransformaion on China s daa is he relaively high growh of he series. As Banerjee e al. (1993) discussed abou logarihmic ransformaion of ime series, changes in he logarihm approximaely equal o he percenage change of original levels of he series. When he changes are relaively large, logarihmic ransformaion may dampen he growh paerns. However, comparing he resuls from disaggregaion wih he real official daa (he overlapping period 1991q1-2008q4) does no show any significan effec on he magniude of flucuaions. IV. China macroeconomic daa 21

23 My sudy aims o esimae China s quarerly real GDP daa in consisency wih he official quarerly published daa since I focus on he real oupu flucuaions since 1978, when China embarked on he marke-oriened and openness economic reform. The annual and quarerly daa used in his paper are from he Naional Bureau of Saisics of China (NBS), he naion s saisical auhoriy 19, and official moneary auhoriy and inernaional rade saisic agency. 4.1 The official GDP daa China s Naional Accouns followed he Maerial Produc Sysem (MPS) of he former Sovie Union from 1949 unil China s GDP esimaion ransiioned o follow he guidance of Unied Naions Sysem of Naional Accoun (SNA) in 1985 and formally compleed he process in The quarerly GDP daa are officially published since Empirical sudies of he Chinese economy have been plagued by he problems of availabiliy and reliabiliy of official Chinese macroeconomic daa. Despie he daa challenges, i is sill worhwhile o sudy he feaures of China s economy, he world s 2 nd larges economy and he mos populous counry. China s official GDP have been criicized for having been oversaed during 1980s and 1990s (Rawski 2001, World Bank 2005, ec), undersaed in he middle of 2000s (Economis May 1s 2008), and hen oversaed again during he mos recen financial crisis. Mos recenly, Huang (2011) argues ha he rue China s GDP is likely o be much higher han repored due o he undersaemen of consumpion esimaion. As a ransiional economy, China has undergone coninuous changes, and has complex poliical, social and economic srucure. Despie he effors 19 The official daa are published as cumulaed year on year growh rae a comparable price. Daa from are from he publicaion of Naional Bureau of Saisics of China (NBS 2008). 22

24 made by NBS o improve and explain he GDP esimaes over he years, confidence in he accuracy of official daa qualiy remains he primary problem ha mus be addressed for empirical research on Chinese macroeconomic issues 20. Afer carefully reviewing he lieraure on Chinese daa qualiy and he naional saisical accouning sysem (Appendix 1), and comparing differen daa resources and daa consrucion mehods 21, I agree wih many researchers (Holz 2006, Chow 2006, Klein and Ozmucur 2003) and mos inernaional organizaions (OECD, IMF 22 ). Alhough here are weaknesses or shorcomings in he saisical sysem ha derives Chinese naional accouns esimaion, Chinese official macroeconomic daa afer 1978 do no appear o be poliically manipulaed or sysemaically biased. The official daa can serve as a reliable guide (OECD 2006) o he level and growh paern of GDP, even hough he margins of error are cerainly larger han ha of he mos developed counries (OECD 2006). Any oher alernaive daa series consruced or correced by researchers has no been proven o be more precise or reliable (Holz 2006). When I run he dissaggregaion models in STAMP, I canno find he exisence of any significan measuremen errors or irregulariy. Thus Official Chinese daa should be he firs por of call (Scheibe 2003) for my sudy. The daa resources of my sudy, CEIC and IFS, boh use he official daa from China NBS as heir final daa source. 20 A parial lis of he recen media news and repors on China s daa problem includes (from he laes): Reflaing he dragon, can he world s fases-growing economy avoid a sharp downurn? Economis Nov. 15h 2008, which claims ha China s official growh flucuaions are smoohed An aberran abacus coming o erms wih China s unrusworhy economic numbers Economis, May 1s 2008, which ranks he reliabiliy of Chinese saisics. 21 Besides he esimaion wih he daa presened here, I apply he same mehods o daa covering shorer periods and from oher informal resources (he IMF World Economic Oulook daase and Fudan Universiy daase). I compare he resuls and check if he daa from differen resources and he subsample daa have significan differen feaures. 22 The World Bank criicized he Chinese naional accoun saisics and revised heir GDP esimaion for China upward for 34% from he officially repored number in In 1996, he World Bank acceped China s reformed saisic sysem and he official GDP number again. Bu he World Bank revision and mehod of esimaion was also quesioned by many researchers. 23

25 The official quarerly real GDP year-on-year growhs are shown in Figure The yearon-year real growh raes sugges ha insead of recessions or negaive growh raes a he roughs of he cycles, China s economy experienced slowdowns or growh recessions a imes bu always had posiive growh raes during he sample period. There are five major slowdowns in year-on-year growh raes, which happened in 1980, 1984, 1989, and mos recenly in 2008 (Chinese Academy Of Social Science, , Liu 2009). The slowdowns in oupu growh in 1984 and 1996 were accompanied by hyperinflaions. The Tiananmen Square poliical chaos in 1989 significanly haled los of he economic aciviies across he counry. The Asian financial crisis occurred in 1998 had an adverse effec on he economic growh. In 2008, China s economic growh dropped o 6.5% in he las quarer, adversely shocked by he global financial crisis. 4.2 Relaed series The only available high frequency quarerly macro-economic daa for he sample period is moneary saisics and inernaional rade saisics. To esimae he missing quarerly real GDP daa for China, I consider differen combinaions of moneary and rade variables as relaed series in he mulivariae UC modeling. The moneary series, including domesic credi, inernaional reserves, M1 and M2, are available quarerly since 1978; Inernaional rade series include oal expors and impors, oal rade volume, which are available quarerly since Domesic credi, inernaional reserves, M1 and M2 are nominal ousanding balance. Each series may carry differen informaion associaed wih he economic developmen and oupus flucuaions. 23 The daa consrucion of his paper is based on log level daa. The discussion in his secion documens he informaion provided by he raw official real GDP daa, which are published as year on year growh raes only. 24

26 The moneary and rade daa used in he emporal disaggregaion of GDP are no only available quarerly for he sample period, bu also of good qualiy. According o he Economis (2008) he qualiy of he relaed series daa is among he op wo mos reliable official macroeconomic daa of China. Figures 2.a and 2.b shows he log quarerly and annual real GDP and he poenial relaed series daa used in he models. All daa are no seasonally adjused. The series appear o follow similar upward rend in he long run. Figure 2.c and Figure 2.d presen he year on year growh raes 24 of he available quarerly real GDP wih he moneary and rade relaed series respecively. Table 5 documens he correlaions of he year on year growh raes of real GDP and he poenial relaed series for he whole sample, daa consrucion sample and he fully available sample period. The correlaions of he flucuaions of real GDP wih mos of he poenial relaed series appear o be high and sable excep expors. The close o zero correlaion of real GDP and expors during shows ha he openness of China economy was very limied during he period. Wih China s expediing inegraion ino he global economy in laer years, he correlaion of economic growh wih expors increased subsanially. All join ess of coinegraing relaionships beween combinaions of relaed series ha include expors show no evidence of coinegraion (Table2). V. Temporal disaggregaion model selecion and esimaion resuls This secion presens he procedure of model selecions and emporal disaggregaing esimaion using he unobserved componens model specified in secion III. 24 The real GDP daa consrucion of his paper is based on log level daa raher han growh raes. However, he relaionships of series based on properies of growh raes, alhough hey may be differen from ha based on he level daa, provide useful informaion. 25

27 5.1 Uni roo and coinegraion ess The procedure sars wih uni roo es and coinegraion es for he real GDP and relaed series. The ess are imporan in finding wheher Chow-Lin relaed series models are valid or no. As I have discussed above, he esimaion of univariae models wih relaed series (Chow- Lin mehod) will only be valid if here is a linear relaionship beween he included relaed series and he arge series. Wih nonsaionary series, his assumpion is only valid when here is a coinegraing relaionship among he series. The saionariy of he annual logarihms level of he real GDP and relaed series is esed using he Augmened Dickey-Fuller (ADF) 25. Table 1 repors he resuls of he ADF ess. All series appear o have a uni roo in he level and are saionary in firs differences. Thus, any emporal disaggregaion mehods, such as he original Chow-Lin model, ha no consider he nonsaionariy of he series are invalid for Chinese real GDP level disaggregaion. The daa mus be firs differenced before applying hose mehods. Or daa oher han he real GDP level bu saionary, such as he real growh raes used by A&R, should be used. However, imporan informaion, especially on he level and rend, may be los during he firs difference or using growh raes daa. Plus he growh raes series may have difference properies han he level daa. As I discussed in secion III, he unobserved componen approach is no only capable of nesing he disaggregaion of saionary series, bu also capable of modeling he nonsaionariy wih differen specificaions of he permanen componen o capure he propery of he series. 25 Oher uni roo ess mehods lead o he same conclusion. The resuls are available upon reques. 26

28 I hen use he Johansen coinegraion es o check for a coinegraing relaionship among he differen combinaion of he annual real GDP and relaed series. Table 2 presens he resuls of he ess. The ess provide evidence in favor of coinegraion among he annual real GDP, oal rade, impors and moneary indicaors (domesic credi, M1 and M2). There is no evidence of a coinegraing relaionship when including expors in he sysem. Including inernaional reserves may inroduce more han one coinegraing relaion among he series. The exisence of a coinegraing relaionship among he relaed series ensures ha he Chow-Lin mehod is applicable o he disaggregaion of China real GDP wih seleced relaed series. Thus he univariae wih relaed series models should be included in he model selecion of emporal disaggregaion. 5.2 Temporal disaggregaion model selecion and resuls The unobserved componens models for emporal disaggregaion are esimaed using he STAMP8 program. The program applies he Kalman filer o obain he componens of he series and uses maximum likelihood mehods o esimae he parameers. Missing quarerly daa are generaed wih smoohing algorihm of he Kalman filer. To selec he model for disaggregaion, I esimae he models wih differen specificaions of componens and differen combinaions of relaed series. All models are esimaed wih he full sample period from 1978q1-2009q4, bu missing quarerly real GDP from 1978q1-2008q4. Official quarerly real GDP for 2009 q1-q4 are used o iniiae he esimaion, which is required by he STAMP program 26. Once he esimaions for 1978 q1 o 2008q4 are obained, I calculae he roo mean squared sandard errors (RMSE) of he esimaed daa and he official published 26 The iniial value can be changed bu he one year official quarerly daa help in finding he convergence and reduce he lengh of ieraion procedures. 27

29 quarerly daa over overlapping period 1991q1-2008q4. The bes fi model for daa disaggregaion is hen deermined by he minimum RMSE 27. Based on he seleced model, I esimaed China s real GDP series over he period 1978q1-1991q4. The RMSE crierion suggess he mulivariae UC model including domesic credi and oal rade as relaed series wih sochasic rend and AR (2) cyclical componen (Table 3). To furher check he sabiliy of he model, I replicae he model selecion procedure using subsample period from , when he quarerly real GDP are fully observed. MUC model wih domesic credi and oal rade as relaed series is sill he bes fi MUC model among all MUC combinaions I have ried. Table 6 presens he parameer coefficiens and variances/correlaions of componens esimaes of he seleced MUC domesic credi and oal rade model, wih full sample from all quarerly real GDP observaions missing, subsample from wih all quarerly real GDP observaions missing and he real emporal disaggregaion model on full sample wih quarerly real GDP o be esimaed. The esimaes of slope and AR coefficiens are very sable cross sample periods. Figure 3 compares he year on year growh rae of official daa, comparable Chow-Lin mehods and he MUC domesic credi and oal rade model. Using he seleced model he final daa consrucion esimaion includes all available official quarerly real GDP observaions, leaving only 1978q1-1990q4 missing. Figure 4 shows he year on year quarerly growh raes of he final resuls of disaggregaed real GDP, compared wih series consruced by A&R. The MUC esimaes has similar bu a lile larger flucuaions han A&R esimaion, excep ha he growh acceleraing 27 Oher saisic crieria are also shown in he able. Since he purpose of he modeling is no finding he bes explanaory of GDP, he bes fi of daa disaggregaion, or he RMSE is used o deermine he selecion of disaggregaion model. 28