Essays on China’s Macroeconomic Fluctuations

By Yueqing Jia

B.A in Economics, July 1995, Shandong University, China

M.A in Economics, January 1998, Shanghai University of Finance and Economics, China

M.A in Economics, January 2008, the George Washington University

A Dissertation submitted to

The Faculty of

The Columbian College of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy

January 31, 2012

Dissertation directed by

Tara M. Sinclair

Associate Professor of Economics and International Affairs

ii

The Columbian College of Arts and Sciences of The George Washington University certifies that

Yueqing Jia has passed the Final Examination for the degree of Doctor of Philosophy as of

November 14th, 2011 . This is the final and approved form of the dissertation.

Yueqing Jia

Dissertation Research Committee:

Tara M. Sinclair, Associate Professor of Economics and International Affairs, Dissertation Director

Frederick L. Joutz, Professor of Economics, Committee member

Maggie X. Chen, Associate Professor of Economics and International Affairs, Committee member

Essays on China’s Macroeconomic Fluctuations

iii

© Copyright 2011 by Yueqing Jia

All rights reserved

iv

Acknowledgements

I am grateful to my advisor Professor Tara Sinclair for her invaluable support and guidance

throughout my dissertation writing process, and want to express my great appreciation to the

other members of my dissertation committee: Professor Fred Joutz, Professor Maggie Chen,

and dissertation reader Professor Neil Ericsson and Dr. Mark DeWeaver for providing very

helpful comments and suggestions. My appreciation also extends to the participants and

discussants in the Southern Economist Association annual meeting and Georgetown Center

for Economic Research 2011 conference at Washington DC, for their insightful comments

and suggestions. I thank the Institute for International Economic Policy of GWU and GW-

CIBER for the support for my dissertation research.

v

Abstract of Dissertation

Essays on China’s macroeconomic fluctuations

The dissertation contributes to the understanding of the properties of China’s

macroeconomic fluctuations through applying advanced econometric methods to China’s

quarterly real GDP, which have been investigated little due to the shortage of data. The first

essay provides quarterly real GDP estimates for China from 1978q1-1991q4 using an

unobserved components approach. The approach imposes fewer prior restrictions on related

series and is more flexible than other disaggregation methods. The multivariate unobserved

components model with total trade and domestic credit as related series is selected as the best

fit model for temporal disaggregation of China’s real GDP. The estimated quarterly real GDP

data are then evaluated with univariate and multivariate time series analysis techniques. The

constructed quarterly data are shown to be of good quality and to provide valuable

information for the analyses of China’s macroeconomic fluctuations. I extend the study to the

macroeconomic linkages between China and other economies in the second and third essays.

In the second essay a two-country correlated UC model is applied to explore the relationships

between the real output fluctuations for the US and China over the period 1978q1-2009q4.

The two countries are found to share approximately half of their permanent and transitory

shocks. The third chapter investigates the relationships between the real output fluctuations

of China with those of developed countries over the period 1978q1-2009q4. The results

show that the correlations between the real output fluctuations of China and the developed

world are insignificant both in terms of permanent and transitory shocks. The analysis of this

dissertation with China’s quarterly data suggests that domestic factors may be the major

drivers of China’s macro-economic fluctuations during the sample period.

vi

Table of Contents

Acknowledgments…………………………………………………………………………..iv

Abstract of Dissertation…………………………………………………………..……...…..v

List of Figures……………………………………………………………………………...vii

List of Tables…………………………………………………………………….….……...x

Introduction………………………………………………………………………..………..1

Chapter 1 A New Look at China’s Output Fluctuations:

Quarterly GDP Estimation with an Unobserved Components approach………..6

Chapter 2 Permanent and Transitory Macroeconomic Relationships

between the US and China…………………………………..…………………70

Chapter 3 Permanent and Transitory Macroeconomic Relationships

between China and the Developed World……………………….....………….100

References…………………………………………………………………………..……..128

Appendices…………………………………………………………………………..…….143

Appendix 1-1: Literature review on studies of China’s macro data quality

Appendix1-2. the unobserved components decomposion model

Appendix1-3. Standard bivariate Blanchard-Quah model and decomposition

Appendix1-4: More results from the GVAR model estimation

with MUC and DdPS data.

vii

List of Figures

Figure1-1. China’s most recent revised official annual and quarterly real GDP

year on year growth rates (the shaded areas are “slowdown eras”)………………60

Figure 1-2a. The log quarterly real GDP (2000 as base year)

and the potential related series………...………………………………………….60

Figure1- 2b. Log annual data………………………………………………………………...61

Figure 1-2c: quarterly year on year growth rates of real GDP with

monetary related series (the shaded areas are “slowdown eras”)…………….61

Figure 1-2d: quarterly year on year growth rates of real GDP with

international trade related series (the shaded areas are “slowdown eras”) …....62

Figure1- 3: Disaggregation model selection:

Year on year quarterly growth rates (%) 1992-2008………..………….…..……62

Figure1- 4: Year on Year quarterly growth rate

(comparing with A&R from 1979-1991)……………………………..………….63

Figure1-5: Seasonal factors or China’s quarterly real GDP MUC

temporal disaggregation model and X12 seasonal adjustment method………....63

Figure 1-6: HP cycles with different value of λ……………………………………………64

Figure 1-7: Unobserved components decomposition: filtering and smoothing…………….64

Figure 1-8: HP and Christiano-Fitzgerald cycles of MUC temporal disaggregation

and A&R estimation of China’s quarterly GDP 1978-1992………………………65

viii

Figure1- 9: Linear in time residual, HP and BP cycles…………………………………..…65

Figure 1-10: HP, Christiano-Fitzgeral and UC cycles………………………………….…..66

Figure 1-11 a: Seasonal adjusted inflation (CPI) and real GDP level 1986-2010………….66

Figure1-11. b: First difference of log seasonal adjusted inflation

and real GDP 1986-2010………...…………………………………………………………..67

Figure1-12: Impulse responds functions on real output and inflation……………………...67

Figure1-13: Blanchard-Quah output gap with HP and Christiano-Fitzgerald cycles……….68

Figure 1-14: Blanchard and Quah cycles based on MUC data and A&R data ……………..68

Figure 1-15: The DdPS quarterly real GDP data and the MUC

estimated quarterly real GDP data ……………………………………………..69

Figure 2-1: Estimated permanent and transitory components………………………………94

Figure 2-1-1 : The US………………………………………………………...……………..94

Figure 2-1-2: China…………………………………………………………………..…..….95

Figure2- 2: Transitory Components Comparison………….…………………………..…...96

Figure 2-2-1: US Transitory Component: Comparing with HP Cycle……………………..96

Figure 2-2-2: China Transitory Components: Comparing with HP Cycle…………………96

Figure 2-3: US Transitory Component Comparing Different Information Sets…………..97

Figure 2-3-1: US Transitory Components Comparing: Univariate,

with China, with Inflation and with Oil price…………………………………..97

ix

Figure 2-3-2: US Transitory Component Comparing: with China vs. with Canada ……...98

Figure2- 4: China Transitory Components with Different Information Sets……………..99

Figure 3-1: Estimated permanent and transitory components……………………………123

Figure3-1.a: China Based on Bivariate Model with G7……………...…………………….123

Figure3-1.b: China Based on Bivariate Model with OECD……………………………….123

Figure3-1.c: G7 Based on Bivariate Model with China…………..………………………..124

Figure3-1.d: OECD Based on Bivariate Model with China………………………………..124

Figure 3-2: Comparing the Different Filtered Cycle Estimates:

Univariate and Bivariate Models………………………………….…………..125

Figure 3-3: Comparing the Different Cycle Estimates:

Univariate, Bivariate, and Trivariate Models………………………………………………125

Figure 3-4: Comparing the Cycle Estimates: DW aggregate,

Exports and Trade Balance………………………………….…………………126

.Figure3-5: 2007 – 2009 Chinese Real GDP and Permanent Component Estimates………126

Figure3- 6: 2007 – 2009 G7 and OECD Real GDP and

Permanent Component Estimates……………………………………………127

Figure 4A-1 Impulse response function: MUC data and DdPS data………………………155

x

List of Tables

Table 1-1: Unit root test results

(Augmented Dickey-Full Test on annual data 1978-2009)………….……..…….51

Table1-2: Johansen Co-integration test results of annual data……………………….….….52

Table1- 3: Disaggregation model selection………………………………………………….53

Table 1-4: China quarterly real GDP data: MUC model estimation,

A&R estimation and the official data (1978q1-2011q2)…………… …………….……..….54

Table 1-5: Correlations of year on year growth rates of quarterly real GDP

and potential related series……………………………………………………….57

Table 1-6: Temporal disaggregation parameter estimates---

MUC model with domestic credit and total trade (Log real GDP equation only);

Variance/correlation of cross series components for Log GDP

(final model: 1978q1-2009q4 with 1978q1-1991q4 real GDP missing) ……….....…57

Table 1-7: Unobserved component model parameter estimates (maximum likelihood)…....58

Table 1-8: Cointegration test of DdPS data and MUC data (1979q2-2003q4)……………....59

Table 1-9: Cointegrating analysis of GVAR modeling for China with MUC data

and DdPS original data (1979-2003, replicating of DdPS 2007)…… … ………59

Table2-1: Correlations of cycles of the US and China real GDP with HP,

BP decomposition and the growth rates Quarterly Data, 1978.1 – 2008.4………………..…92

Table 2-2: Estimation Results………………………………………………………………..92

Table 2-3: Standard Deviations of Shocks…………………………………………………..93

Table2- 4: Correlations of Permanent and Transitory Shocks………………………..……..93

Table 3-1: Correlations of Cycles for China and the Developed Country Aggregates……120

Table 3-2: Estimation Results……………………………………………………………..120

xi

Table3- 3: Standard Deviations of Shocks…………………………………………………121

Table 3-4: Within Series Correlations of Shocks…………………………………………..122

Table 3-5: Cross Series Correlations of Shocks……………………………………………122

Table 4A-1. Likelihood ration tests on the equality of cointegrating coefficients

estimated by GVAR modeling for China

with MUC data and DdPS original data………………………….…………...153

Table 4A-2: Short run error correction equation coefficients of GVAR

estimated based on MUC data and DdPS data …………………………………..………....154

1

Introduction

In the past three decades, China has emerged as one of the most important and

influential economies, with its remarkably rapid growth and integration into the world

economy. As the world’s second largest economy1, the largest exporter (since 2009) and the

world’s largest foreign exchange reserves holder, China’s economy, in the short and long

run, is more than ever the focus not only of academic research but also of policy makers and

stakeholders from inside and outside China. Although increasingly important, the properties

of China’s output fluctuations are not well understood. Very limited econometric analysis has

been conducted on China’s macroeconomic fluctuations. This is mainly due to the shortage

of high-frequency data. The complexity of China’s transitional economic and political

structures adds difficulties to the analysis. Lack of proper characterization of China’s output

trend and cycles may mislead the theoretical economic studies on Chinese economy as well

as the policy analysis. While the existing research relies mostly on the available annual data,

the study of low-frequency annual data obviously cannot fulfill the needs of economic

decision making in this fast changing world.

This dissertation contributes to the existing literature on empirical studies on China’s

macro economy in the following aspects: First, it provides a new temporal disaggregation of

quarterly real GDP data through the more flexible and general unobserved components (UC

hereafter) model framework. Second, the application of correlated UC model to China’s

quarterly real GDP data since 1978 adds to the limited existing empirical research on China’s

business cycle with advanced time series econometrics analysis. This dissertation provides

new evidence and policy implications for the understanding of China’s growth fluctuations in

1China passed Japan as the second largest economy in terms of nominal GDP in 2010.

2

terms of permanent and transitory shocks. Third, this study is the first application of

multivariate correlated UC model analysis of China’s quarterly real GDP with other

economies and external variables such as oil prices. With information from other economies

and external variables, I find that China’s macro-economic fluctuations are mainly driven by

domestic factors and economic policies.

The first essay of the dissertation provides temporal disaggregate estimates of China’s

quarterly real GDP data for the years 1978 through 1991, using multivariate unobserved

components models with state-space representation. China’s official quarterly real GDP data

are only available since 1992, which provides only 78 quarterly observations up to 2011 q2.

Small samples can limit the applicable methods and the quality of empirical analysis.

Extending the quarterly real GDP data from 1991 back to 1978 for China would provide a

complete sample of growth fluctuations for the economy since the beginning of the reforms

and thus a better understanding of the evolving properties of China’s macroeconomic

fluctuations along with the implementation of the reforms. Abeysinghe and Rajaguru (2004,

A&R hereafter), the only published study on the temporal disaggregation of China’s GDP

data, applies the original Chow-Lin (CL) related series technique to disaggregate China’s

annual real GDP data into quarterly data and provides quarterly real GDP growth rate

estimates from 1978Q1 to 1994 Q4. However, as I discuss in the first essay, the original CL

model based on univariate regression assumes a linear relationship among the related series

and does not consider the unit root properties of the series. Both assumptions may not be

proper in practice when choices of available related series are very limited.

In the first essay, I generalize the univariate and multivariate unobserved components

modeling for temporal disaggregation, and provides temporal disaggregate estimates of

3

China’s quarterly real GDP data for the years 1978 through 1991, using the selected

multivariate unobserved components model. The unobserved components approach is more

general than the Chow-Lin approach in dealing with unit root, seasonality and irregularity

properties. The method allows simultaneous disaggregation and seasonal adjustment of the

data, and imposes minimal prior restrictions on the data. It provides more flexibility for the

data selection, which is especially important for emerging countries whose high frequency

data are very limited. The multivariate unobserved components (MUC) model with domestic

credit and total trade as related series is selected as the best fit model based on the root mean

squared standard errors of the estimated data and the official published data over the

overlapping period. The estimated data from 1978-1991 with selected MUC model are more

efficient than the estimation from other temporal disaggregation methods.

The MUC estimated quarterly real GDP for China provides a better alternative of

China’s quarterly real output data for different univariate and multivariate time series

analyses. To evaluate the data quality, I apply different univariate trend cycle analyses, such

as Hodrick-Prescott filter (1997, HP filter hereafter), Band-Pass Baxer-King (1999) and

Christiano-Fizgerald (2003) filter and unobserved components decomposition method, and

structural multivariate analysis, such as Blanchard-Quah (1989) decomposition and Global

Vector Autoregression models (Dees et. al 2007, DdPS model hereafter) to the estimated

data. The analyses show that the extension of quarterly real GDP with the MUC model

provides valuable information for the understanding of the output fluctuations during the

sample period. Domestic factors and supply shocks are found to be the main driver of

China’s output fluctuations.

4

I extend the study to the macroeconomic fluctuation linkages using quarterly data

between China and other economies in chapter two2 and chapter three3 . Chapter two

contributes to the literature that applies the multivariate correlated unobserved components

model, a more general model with less restrictions and priors than the simple correlation and

VAR approaches, to investigate economic relationships of two economies at different

development levels and with more divergent economic structures. The relationship between

the macroeconomies of the US and China is explained through the permanent and transitory

components. The chapters also contribute to the limited literature on empirical studies of

properties of China’s macroeconomic fluctuations with a reasonably long sample of quarterly

data.

The model employed in the second chapter is a two-country correlated unobserved

components model based on the correlated unobserved component model proposed by MNZ

(2003) and extended by Sinclair (2009) and Mitra and Sinclair (2009). The model

specifically allows for the distinguishing of cross-country correlations driven by the

relationships between permanent innovations, caused by real shocks such as changes in

technology and economic and social institutions, from transitory or cyclical movements,

caused by changes in aggregate demand or monetary shocks in the two countries. The model

is also capable of exploring the role of information from the dynamics of each country in

identifying fluctuations in the other country.

The economic fluctuations of the US and China are found to be significantly

positively correlated for both permanent and transitory shocks. The two countries share about

2 The second chapter is based on joint work with Tara M. Sinclair that is currently under revision and resubmission to

the Journal of International Money and Finance. 3The third chapter is based on the joint work with Tara Sinclair prepared for the CESifo Venice Summer Institute

workshop on The Evolving Role of China in the Global Economy and to be published in a conference volume by MIT press.

5

half of the shocks both in the long run trend and short run movements. Estimates of China’s

permanent and transitory components do not change too much with information from the US

and alternative external information sets as well, which suggests that domestic factors may be

the major drivers of China’s real GDP fluctuations. The US transitory components estimated

with China data are very different from that estimated with other information sets such as

inflation, GDP of other developed countries and the oil price.

The third chapter investigates the relationships between the real output fluctuations of

China with those of developed countries over the period 1978q1-2009q4. The chapter

focuses on two measures of aggregate developed-country output: real GDP for the G-7

countries and real GDP for 25 OECD developed countries. The results of chapter three show

that the correlations between the real output fluctuations of China and the developed world

are insignificant both in terms of permanent and transitory shocks.

The results of analyses in all chapters, with bivariate unobserved components models,

Blanchard-Quah decomposition, and the GVAR models, are in agreement in that supply side

shocks and domestic factors play an important role in China’s real output movements.

Although China’s economy has been widely open to the world economy, outside shocks,

which may mainly be on the demand side, may have either not been as strong as that from

the domestic economic reforms and productivity changes, or have been effectively offset by

China’s macro-economic policies.

6

Chapter 1: A New Look at China’s Output Fluctuations: Quarterly GDP Estimation

with an Unobserved Components Approach

I. Introduction

“China moves to centre stage”

----Cover story, Economist, Oct. 30, 2008

In the past three decades, China has emerged as one of the most important and

influential economies, with its remarkably rapid growth and integration into the world

economy. China is the world’s second largest economy in 20104, the largest exporter (since

2009) and the world’s largest foreign exchange reserves holder. The recent financial crisis

pushed China to the frontier of world economic development. China’s economic

performance, in the short and long run, is more than ever the focus not only of academic

research but also of policy makers and stakeholders from inside and outside China.

Although increasingly important, the properties of China’s output fluctuations are not

well understood. Very limited econometric analysis has been conducted on China’s

macroeconomic fluctuations. This is mainly due to the shortage of high-frequency data. The

complexity of China’s transitional economic and political structures adds difficulties to the

analysis. Lack of proper characterization of China’s output trend and cycles may mislead the

theoretical economic studies on Chinese economy as well as policy analysis. While existing

research relies mostly on the available annual data, the study from low-frequency annual data

obviously cannot fulfill the needs of economic decision making in a fast-changing world.

4 China passed Japan as the second largest economy in terms of nominal GDP in 2010.

7

China’s official quarterly real GDP data are only available since 1992, which

provides only 78 quarterly observations up to 2011 q2. Small samples can limit the

applicable methods and the quality of empirical analysis. Just shortening the sample period

and ignoring the available annual observations before the quarterly data are available results

in losing important information for the properties of data generating process. Extending the

quarterly real GDP data from 1992 back to 1978 for China would provide a complete sample

of growth fluctuations for the economy since the beginning of the reforms and thus a better

understanding of the evolving properties of China’s macroeconomic fluctuations along with

the implementation of the reforms.

As to flow data such as real GDP, one way to solve the above problem is to

temporally disaggregate or interpolate the low frequency data into higher frequency data.

Using a proxy observed at higher frequency and estimating the real GDP with the production

function would be alternatives. However, for China, quarterly macro-economic data before

1992 are extremely limited. The only available series are from monetary and international

trade statistics. They are not sufficient to estimate the proxy and production function data

construction alternatives. Temporal disaggregation of annual real GDP to quarterly real GDP

with available related information thus becomes the only practical approach for the quarterly

GDP construction for the period. Temporal disaggregation is also a commonly used method

for resolving similar problems to other countries5 . Univariate methods, related series

univariate method or Chow-Lin method (Chow and Lin 1971, CL model hereafter) and

multivariate unobserved components (UC approach hereafter) methods are the three groups

5 For example the Eurostat (1999) documents that the temporal disaggregation method is used in the official statistics

agencies of the European countries.

8

of approaches that have been applied to temporal disaggregate macro-economic data in

literature.

Abeysinghe and Rajaguru (2004, A&R hereafter), the only published study on the

temporal disaggregation of China’s GDP data, applies the Chow-Lin related series technique

to disaggregate China’s annual real GDP data into quarterly data and provides quarterly real

GDP growth rate estimates from 1978Q1 to 1994 Q46. However, as I will discuss below, the

CL model based on univariate regression assumes a linear relationship among the related

series and does not consider the unit root properties of the series. Both assumptions may not

be proper in practice when choices of available related series are very limited.

My study generalizes the univariate and multivariate unobserved components

modeling for temporal disaggregation, and provides temporal disaggregate estimates of

China’s quarterly real GDP data for the years 1978 through 1991 using the selected

multivariate unobserved components model (MUC model hereafter). The unobserved

components approach is more general than the Chow-Lin approach in dealing with unit root,

seasonality and irregularity properties. The method allows simultaneous disaggregation and

seasonal adjustment of the data, and imposes minimum prior restrictions on the data. It

provides more flexibility for the data selection, which is especially important for emerging

countries whose high frequency data are very limited.

I temporally disaggregate China’s real GDP series using the unobserved components

models with different specifications of components and different combinations of related

series for model selection. The multivariate unobserved components (MUC) model with

6On their website (http://courses.nus.edu.sg/course/ecstabey/gdpdata.xls), the authors extended the series through

2007Q1, using quarterly year-on-year real GDP growth rates from the country data of Economist Intelligence Unit. The data resources of EIU country data for China are CEIC and National Bureau of Statistics of China (NBS).

9

domestic credit and total trades as related series is selected as the best fit model based on the

root mean squared standard errors of the estimated data and the official published data over

the overlapping period. The estimated data from 1978-1991 with selected MUC model are

more efficient than the estimation from other temporal disaggregation methods7.

The MUC estimated quarterly real GDP for China provides a better alternative of

China’s quarterly real output data for different univariate and multivariate time series

analyses. To evaluate the data quality, I apply different univariate trend cycle analyses, such

as Hodrick-Prescott filter (1997, HP filter hereafter), Band-Pass Baxer-King (1999) and

Christiano-Fizgerald (2003) filter and unobserved components decomposition method, and

structural multivariate analysis, such as Blanchard-Quah (1989) decomposition and Global

Vector Autoregression models (Dees et. al 2007, DdPS model hereafter) to the estimated

data. The analyses show that the extension of quarterly real GDP with the MUC model

provides valuable information for the understanding of the output fluctuations during the

sample period. Domestic factors and supply shocks are found to be the main driver of

China’s output fluctuations.

The purpose of this paper is to provide quarterly real GDP for China in consistency

with the official real output data. Thus, the availability and reliability of China’s official data,

the big concerns for China’s official GDP statistics, are carefully discussed before the data

construction.

There are six sections of this paper: Section II reviews the relevant literature on the

methodology of temporal disaggregation and the contribution of my paper in high frequency 7The comparison of the estimation of different approaches based on the root mean square errors is presented in section

V. The selected MUC estimation, including the observed annual levels in the estimation, fits the observed annual real growth rates better than the A&R estimation.

10

data construction; Section III presents the unobserved components or structural time series

models for the temporal disaggregation of China’s real GDP. Section IV addresses China’s

macroeconomic data problem. In Section V, the results of the data construction from

different model specifications are presented and evaluated. Section VI analyzes China’s real

GDP fluctuations with the constructed quarterly real GDP data using different univariate and

multivariate approaches and compares the results of permanent and transitory

macroeconomic fluctuations based on the constructed quarterly real GDP data. Section VII

concludes.

II. The literature

This study is related to the following strands of literature: first, the estimation of

missing high-frequency macro economic data from available low-frequency data, i.e.

interpolation and temporal disaggregation methods; second, the research on identifying

China’s output fluctuations and the commonly used univariate and multivariate aggregate

output trend and cycle decomposition methods. To evaluate the quality of the quarterly real

GDP data estimated in this paper, both univariate and multivariate methods are applied to the

estimated quarterly real GDP data for China. The unobserved components model is the key

modeling framework applied in this paper.

2.1 Literature on missing high frequency data and temporal disaggregation methods of

time series

Temporal disaggregation or interpolation has been extensively used by researchers

when high frequency data required by econometric analysis are not available. It is also a

routine practice for official statistical agencies to apply temporal disaggregation methods to

11

generate high frequency data, especially when direct estimation methods are unavailable or

information collection is costly (Proietti 2006, Eurostat, 1999).

Problems of time series disaggregation include interpolation of stock variables and

temporal disaggregation of flow variables. The estimation of China’s quarterly Gross

Domestic Product from the annual official data falls into the second category. There are

broadly three groups of methods that have been developed to temporally disaggregate lower

frequency data into higher frequency data:

1) univariate methods rely on the time series properties of the targeted series only.

For example, Stram and Wei (1986, 1990) derive smoothed estimation of unavailable high

frequency data based on the ARIMA structure of the series. Stram and Wei (1990) method

has been applied to the estimation of macroeconomic indicators by many official statistic

agencies (Eurostat 1999, part 6.45-6.46).

When the missing high frequency data period is short compared to the whole sample

period, a simple univariate interpolation is often convenient. However, when missing high

frequency data are for a relatively long period, the simple univariate interpolation, which

uses the time series properties of the target series itself (usually properties of the series

during more recent period when the high frequency data are available), is likely to distort the

results of high frequency analysis. Especially for the sample period when high frequency data

are missing. The problem may be more serious for data from emerging or transitional

economies. Their underlying economic structure and environment often change substantially.

More sophisticated methods that use more information to disaggregate data should be

considered.

12

2) Related series univariate models that were first proposed by Chow and Lin 1971

and extended by Fernandez (1981) and Litterman (1983) with a random walk and I (1) error

term respectively. Application of temporal disaggregation by the CL approach begins with

running OLS or GLS on a linear model of target series to the related series with low

frequency data. Assuming that the linear relationship of target series and related series is

consistent with low frequency and high frequency data, the estimated coefficients are then

used to predict the target series based on the high frequency related series data with

adjustment to match the annual aggregates. An AR (1) process for the error term is assumed

in the original CL model. To account for the non-stationary residuals, a random walk process

is assumed in the Fernandez model and I (1) in the Litterman model. Santos and Cardoso

(2001) and recently Proietti (2006) add lagged values of the dependent variable

(autoregressive distributed lag or ADL models) into the CL model. Harvey and Pierse (1984)

and Proietti (2006) present these groups of models in state space form and apply the Kalman

filter to estimate the missing observations.

The CL approach and its extension models use more information from observed

related high frequency data. Chen (1993) demonstrates with Monte Carlo simulated data that

the CL procedure is usually more efficient than the univariate only alternatives. The

convenience in application has made this method more popular in practice than the first

group of models. A&R (2004), the only published temporal disaggregation of China’s real

GDP, applies CL approach to the growth rates of GDP with the growth rates of M1 and total

trade as related series.

13

The major problem with this group of models is that the assumption of a linear

relationship between the target series and the related series is often difficult to verify with the

data (Proietti 2006, Moauro and Savio 2005).

As Harvey (1989 section 8.7) and Proietti (2006) mentioned, the univariate related

series models, although widely applied in practice, impose a strong assumption of

cointegrating relationship between targeted series and the related series and/or exogeneity of

the related series regressors. Moauro and Savio (2005) further proves that even with the

existence of cointegrating relationship, univariate with related series models, or CL method

will be efficient only when the constant and the autoregressive parameters are equal for all

included related series, or in terms of unobserved component model specification, the related

series are trend homogeneous. The assumptions are not likely to be verified in the true data,

especially when the choices of related series are very limited8.

The restriction of CL methods limits the choice of related series. The target series and

the sets of available “related” series may not have a linear relationship, but are usually

affected by the same economic environment and thus could provide valuable information and

improve the efficiency of the disaggregation. A&R, who use nominal M1 and the total trade

as related series, apply CL approach to the first-differences and the growth rates instead of

levels of the real GDP and related series to avoid the non-stationary and cointegration

problem. Even with the growth-rate approach, A&R did not find a significant linear

relationship between the growth rate of real GDP and M1, but found including M1 leads to

8 When choices of related series are limited, if no linear relationship is found among the series, there will be no

alternatives available.

14

better disaggregation9. Although the relationship of M1 and real GDP is not significant with

annual data, it provides information for quarterly GDP estimation that improves the

efficiency of the disaggregation.

3) Multivariate unobserved components (MUC) or structural time series models. The

application of UC models to temporal disaggregation was originated by Harvey and Pierse

(1984) and Harvey (1989)10. Harvey and Chung (2000), Moauro and Savio (2005) are

examples of the contributions of this group of models. MUC models set up a system of

unobserved components equations of the targeted and related series and estimate the models

in the system simultaneously. The approach allows cross series correlations for the

components and thus includes the quarterly information provided by the available related

series to the disaggregation of target series.

The MUC approach overcomes the limitation of CL methods. The MUC models are

capable of taking advantage of information from the available high frequency “related” time

series for the disaggregation, without putting prior restrictions on the specific relationship

between the series. Common trends, common cycles and common seasonalities among the

related series can be tested through MUC models (Moauro and Savio 2005). The MUC

approach is also flexible in handling both seasonally adjusted and non-seasonally adjusted

data and allows disaggregation and seasonal adjustment simultaneously. Proietti and Moauro

(2005) further show that the model is capable of handing seasonality very well. In addition,

with the Kalman smoothing estimation, the sample period can be extended to include the

information of the available high frequency observations of the targeted series in the later

9

A&R evaluates the disaggregation by comparing the quarterly data estimated from the model with the real data during

the overlapping period. 10 Harvey (1989) names his model “seemingly unrelated structural time series equation (SUTSE)”.

15

years. For example, China’s official quarterly real GDP data that are available since 1992 can

be included in the estimation of China’s real quarterly GDP during 1978-1991 in MUC

models. Since the time series property of a time series itself is usually stable over time, the

property of the observed high frequency data of the target series can help improving the

temporal disaggregation.

Since Harvey and Pierse (1984) first cast the univariate disaggregation methods into

state-space form and applied Kalman filter technique to estimate the missing high frequency

data, the state space approach has been regularly applied in the temporal disaggregation of

time series. Harvey (1989, section 6.3) proposed the method of using cumulator series to set

up the state space form over series of different time frequencies, where the missing high

frequency data is treated as missing observations, estimated with the Kalman smoothing

algorithm. The method provides more flexibility in modeling components of the series and

can be applied to both univariate and multivariate disaggregation models on both flow and

stock time series. Durbin and Quenneville (1997), Proietti (2006) generalized the state space

method applications to the CL model and its extensions. The related series are modeled as

exogenous regressors that enter into the measurement equation and/or transitory equation.

Cuche and Hess (1999) and Tasdemir (2008) disaggregate European and Turkish data using

the state space methods.

This paper further generalizes the models for the temporal disaggregation of flow

series with unobserved components stemming from Harvey (1989) and Moauro and Savio

(2005). I present the univariate and multivariate unobserved components models, with or

without cyclical components, in state space forms and estimate China’s quarterly real GDP

16

during 1978-1991 with Kalman smoothing algorithm. This paper is the first application of

temporal disaggregation of China’s real GDP with the unobserved components approach.

2.2 Literature on identifying and characterizing China’s output fluctuati ons

To evaluate the information provided by the quarterly real GDP levels of China from

1978-1991 estimated by the selected unobserved components model in this paper, I apply

different univariate and multivariate time series analytic methods to the data. Literature on

the measurement of China’s potential output or output gap is then closely related to this part

of study. The existing studies generally follow three approaches: the production function

approach, univariate trend-cycle decomposition approaches and multivariate time series

approaches or Vector autoregression approaches (VAR).

The trend of aggregate output is generally assumed to correspond to potential output

and the cycle is assumed to correspond to the output gap. Most of the studies on China’s

potential output estimation apply production function approach to annual data, which

estimates the Cobb-Douglas production function with potential capital and labor inputs11.

Decomposition of the aggregate output series into trend and cycle components has

been a common practice for aggregate output fluctuation analysis. Competing approaches

have been developed to decompose macroeconomic series such as the aggregate output into

“trend” and “cycle”, or permanent and transitory components. A number of studies (Morley

2008, Canova 1998, Zarnowitz and Ozyildrim 2006, Park 1996 and King and Rebelo 1993,

11

In this group of studies, Chow (1993 and 2002) intends to find the importance of capital formation and contributions of sectors, Heytens and Zebregs (2003) try to find the growth of Total Factor Productivity, Young (2003) focuses on alternative price levels, and Scheibe and Vine (2005) study the Phillips curve. Scheibe (2003) explores the production function with sector based estimation. This approach is also used for alternative GDP data constructions.

17

Gerlach and Yiu 2003) have shown that the revealed trend cycle properties are sensitive to

the detrending methods12.

For China’s real GDP, the Hodrick-Prescott (HP) filter is the widely used univariate

detrending method in the literature that models China’s business cycles (for example: Ha,

Fan and Shu 2003)13. Gerlach and Peng (2006) estimate annual Chinese output gap from

1982-2003 using the unobserved components (UC) model following Watson (1986) and

Clark (1987). They find that HP filter and UC approaches generate similar cyclical patterns.

Their estimation suffers from limitations due to the small sample size (21 observations) and

very broad confidence bands. Laurenceson and Rodgers (2010) use different frequencies of

cycles to identify the relative importance of demand and supply volatilities occurring at

China’s business cycle.

In recent years, several Chinese scholars applied nonlinear univariate methods such as

Markov-switching process to indentify the phases of business cycles in China (mostly

published in Chinese), examples of the studies include Chen and Liu (2007) Liu (2003, Liu

12

Canova (1998) examines the business cycle properties of US real macroeconomic time series data with seven different decomposition methods and finds that for aggregate output of the US, different decomposition methods generate cycles that differ in time duration and turning points. As for developing countries, Gerlach and Yiu (2003) compare output gaps with annual data for eight Asian economies (not including China) derived from four decomposition methods, and find gaps (cycle component) from HP, UC and BP decompositions are similar for these countries but the gaps derived by BN decompositions are different.

13 Although the production function approach uses more information for potential GDP estimation than the alternative

univariate approaches, it also introduces more potential problems. First, several assumptions are frequently made to set up the production function. Assumptions such as constant returns to scale in production, competitive markets for inputs and outputs may not be appropriate for China. There are no generally accepted potential levels of labor, capital inputs and total factor productivity growth for China. Secondly, the estimation needs capital and labor data, which faces similar data availability and reliability problems as well. Labor or employment data are even less available and reliable for China than GDP data. Missing capital and employment data have to be estimated before they are used in the potential GDP estimation. Third, the estimation must select proper price levels for different inputs and sectors (Young 2003), which are unavailable and have to be estimated. Finally, most research using this approach relies only on annual data due to the data availability problem. Because of the issues above, the results of production function estimations are not consistent among different studies.

18

and Zheng (2008), Zheng, Teng and Song (2010). Most of these researches suffer from small

sample problem.

In this paper, I apply the most widely used univariate methods include the Hodrick

and Prescott (1997, HP) filter, the Band-Pass filter (Baxter and King 1987, Christiano and

Fizgerald 2003, BP) filter, and the unobserved components models (Harvey 1985, Watson

1986, Clark 1987) to the estimated quarterly real GDP data to present the information

provided by the data.

Structural multivariate methods, on the basis of economic theories, introduce other

macroeconomic variables to identify the properties or the origins of output fluctuations.

These methods include the structural VAR, such as Blanchard-Quah (1989) approach and its

extensions (e.g. Clarida and Gali 1994) and multivariate system models such as the global

VAR approaches (Dees, Di Mauro, Pesaran and Smith 2007, DdPS hereafter). The current

applications of these approaches to China’s macroeconomic data suffer from shortage of long

time period quarterly GDP data. Among the limited published applications of Blanchard and

Quah to Chinese data, Zhang and Wan (2005) use real industrial output as a proxy for real

GDP for 1985-2000. Siklos and Zhang (2010), analyzing China’s inflation fluctuation with

the standard Blanchard and Quah framework and a tri-variate extension, have to limit their

analysis to the short sample period of 1990-2003. The original DdPS model estimation with

Chinese data use quarterly real output data that are derived from annual real GDP level by

evenly allocating the annual output to the four quarters of the year.

This paper applies the above univariate and multivariate time series analyses to the

estimated China’s quarterly real GDP and shows that the constructed data provide a better

19

high frequency and long period real GDP data alternative for the analyses of China’s output

fluctuations14.

III. Temporal disaggregation of China’s quarterly real GDP with unobserved

components model

3.1 the Model

The unobserved components models are set up in terms of components that have

direct interpretation of stylized features of the series. The models are capable of including

trend (or long run, permanent component), cycle (short run, transitory component), seasonal

components (if the data are not seasonal adjusted) and irregularities that represent the non-

systematic outlier observations or measurement errors.

Following Harvey (1989), the unobserved component models for temporal

disaggregation of China’s real GDP can be presented in multivariate state space form as

follows:

The measurement equation is:

ittititititit +εX)++γ+s+c=(τy β (1)

Or in a more general form:

ttttt +X+ZY Ε= βα (1’)

Where: Ttniyyy=y ntttit ,...,2,1 and ,...,2,1),,...,,( ,21 == ty1 is the target series (ty1 :

China’s real GDP) and ,...,,2 ntt yy are the related series for multivariate models. tZ is a

14

To focus on the evaluation of quarterly real GDP construction, in this paper I do not include the production function approach, which may involve data problems from capital and labor statistics.

20

mn× matrix, where m is the number of unobserved components, and N is the number of

dependent variables in multivariate models. tX is the matrix of assumed exogenous variables

or the “related variables” which will only be present in the univariate with related series

model15. β is the parameter vector of the explanatory variables. tα is 1×m the state vector

that contains the unobserved components that may include trend tτ , cycle tc , seasonality ts

, and irregularity tγ . tΕ is an 1×n vector of serially uncorrelated disturbances assumed with

mean zero and the covariance matrix tG , or 0)( =tE ε and tt GVar =)(ε

The transition equation is,

ttttt HT ηαα += −1 (2)

Where )' ( ttttt sc γτα = , tT is a mm× matrix, tH is mg × matrix ( mg = when all

components are defined as stochastic, g will not equal to m when some components are

defined as fixed or determinate). tη is a 1×g vector of serially uncorrelated disturbances with

mean zero and the covariance matrix, tQ , or 0)( =tE η and tt QVar =)(η

I use seasonally unadjusted data in the disaggregation models to avoid losing

information from such adjustments. The seasonal components generated through the

disaggregation will be compared with the seasonal factor generated from commonly used

seasonal adjustment procedure in the evaluation section of the paper.

15 I do not add explanatory variables to the unobserved components such as trend, cycles and/or seasonality. Adding

explanatory variables means adding assumptions on the relationship of the related series, which will reduce the generality of the model of data construction.

21

The disaggregation models are specified with choices for stochastic drift and

seasonality to capture the possible time variance of drift and seasonality16.

Disturbances of components within series are assumed uncorrelated from each other

in the disaggregate models following Harvey and Watson (1986), Harvey (1989) and Clark

(1987).

Putting observations with different timing intervals into the state space form is the

key step of using unobserved component model for temporal disaggregation. Harvey (1989,

section 6.3) introduced the technique of using a cumulator variable for mixed frequency data

in state space model. The cumulator variable for quarterly data is defined as following:

tct yy = , where 4),/,...(1,1)1( ==+−= ssnst ττ

11 ++ += ttct yyy

322 +++ ++= tttct yyyy

3213 ++++ +++= ttttct yyyyy ,

44 ++ = tct yy

545 +++ += ttct yyy

…

Where cty is the year up to date cumulated value of the quarterly level of the series,

and ty is the quarterly level of the series. For the years with only annual data available, only

cty 3+ , which equals the annual level of the series, is observable. For China’s real GDP, the

16 Fixed drift and seasonality are also tried for comparison.

22

cumulator variable cty is only observed once every 4 periods during 1978-1991. The series of

cumulator variable is considered as the target series (ty1 ) in all models. The unobserved

values of cty are then treated as missing observations to be estimated with smoothing

algorithms from the Kalman filter.

3.2 The unobserved components specification

The general UC model specification is capable of nesting the three categories of

interpolation models: Univariate models without related series, univariate models with

related series and multivariate unobserved components models. Different specifications of

the components are tried and the constructed quarterly data are evaluated.

The unobserved trend component can be specified as:

),0(~ , t1 τττ ηηµττ Qiidtttt ++= − (3)

There are two widely applied specifications of the slope of the trend: one is based on

Harvey (1985) and Watson (1986), which assumes that the trend is random walk with

constant drift, i. e., µµ =t ; the other is the Clark (1987) model, in which the trend is

assumed to follow random walk with a random walk drift, i.e. ttt ζµµ += −1 . Clark’s

assumption of a random walk with drift is capable of accounting for possible structure

breaks. To avoid losing information in the temporal disaggregation, the choice of time

varying or stochastic slope (the drift of trend) following Clark model is applied in the

disaggregation models with related series17.

17 Fixed slope of trend is also tried for comparison.

23

The estimation starts with general local linear trend (LLT) models, which do not

include cyclical component. The cyclical component is then introduced into the model and

assumed following 2nd order auto-regressive process or AR (2), as for most real output series

in the literature (Harvey 1985, Clark 1987 and Morley et. al. 2003). Harvey (1989) and

Durbin and Koopman (2001) suggest trigonometric expressions for cyclical components

which are not applied in this paper, because it may introduce arbitrary waves in the cyclical

components.

Thus when the unobserved cyclical component is included, the transition equation for

cyclical component is:

),0( ~ , ct2211 cctttt QNiidccc ηηϕϕ ++= −− (4)

The correlations between trend and cycle disturbance are assumed to be zero in the

temporal disaggregation models following Harvey and Watson (1986) and Clark (1987).

Since I will only take the Kalman smoothing estimation results of the missing observations

and not investigate the trend cycle decomposition from the temporal disaggregation, the

assumption of zero cross correlations will not affect the final result of the data construction18.

The unobserved components models are capable of handling seasonal adjustment

simultaneously with the temporal disaggregation, with the underlying assumption that the

seasonality relationships of the disaggregated series are consistent or homogenous with the

related series along the sample period. There are two options of seasonality formulations in

the Structural Time Series Analyser, Modeller and Predictor package (STAMP 8, Koopman,

18 Assumption on the correlation of permanent and transitory shocks is critical to the estimation of permanent and

transitory compositions or the unobserved components. While the data construction only take the result of the estimation of the level of the series and not doing decomposition for the series, thus will not be affected by the assumption. The zero cross correlation assumption reduces the number of coefficients to be estimated and increases the degree of freedom, thus increases the chance of convergence especially for the multivariate models.

24

et al. 2007): trigonometric stochastic seasonality (Harvey 1989, 6.2), which allows for

changes of seasonality pattern along the sample time, and the fixed dummy seasonality. I

chose stochastic seasonality in the models, because it can track the possibility of changing of

seasonality during the time period and avoid losing information for the seasonality in the

constructed data19.

Measurement errors of the data can be a big concern for China’s macro-economic

data. Therefore I include irregularity term in the models. However, I do not find any

significant irregularities in any models.

3.3 Univariate and Multivariate models

Univariate models without related series

When 1=n , the model is a univariate UC model and contains the cumulated quarterly

real GDP level with missing observations only. The modeling starts with a Local linear

Trend (LLT) univariate model without cyclical components. For LLT model, the

measurement equation is simplified as:

tttt sy γτ ++= (5)

Univariate models with related series.

The univariate model with related series as exogenous explanatory variables without

cyclical component is comparable with Chow-Lin approach and its modifications (Harvey

1986). The explanatory variables enter into the measurement equation as:

��� � ��� � ��� � ��� � �� (6)

19 Fixed or determinant seasonality is also tried for comparison.

25

If the components are set as deterministic and tε as AR (1), the model is comparable

with the original CL model (Moauro and Savio 2005). When there is no cyclical component

included, the univariate with related series model with random walk drift is comparable with

modified CL method, also known as Fernadez (1981) model. To find the best model for

temporal disaggregation of China’s real GDP, I also try the models with AR (2) cyclical

component.

Multivariate unobserved components models

Temporal disaggregation using multivariate unobserved components models, as

reviewed in section II, uses the information from related macro-economic series and at the

same time avoids liner relationship assumption on the related series or the weakly exogenous

as in the Chow-Lin model and its extensions. As discussed in the literature section of this

paper, the multivariate UC models may be more appropriate if the cointegrating relationship

is hard to find between the available related series. The problem can be more likely for

emerging countries, where high frequency macro-economic data are very limited.

Another advantage of this framework is that it allows for simultaneous

disaggregation, seasonal adjustment and trend cycle decomposition. While not the focus of

data construction section of this paper, the common trends, cycles and seasonality among the

related series can be easily imposed and tested in the multivariate UC framework.

3.4 Logarithmic transform of the data

All series values are in natural logarithms to ensure positive estimation for real GDP

in the disaggregation models. First, due to the relatively small sample, a few large seasonal

troughs may cause the estimated quarterly real GDP to become negative when using levels of

26

the series20 . Logarithmic transformation of the data guarantees positive values of the

estimated quarterly data. Secondly, as Proietti 2006 shows, since logarithmic transformation

reduces the heteroscedasticity of the series and the underlying assumptions of the

multivariate disaggregation models include homoscedasticity on seasonality and variances

among series, it is more appropriate to use for those models.

The cumulated series of the logarithmic transformed target series can be expressed as:

)log( tct yly = , where 4),/,...(1,1)1( ==+−= ssnst ττ

)log( 11 ++ += ttct yyly

)log( 322 +++ ++= tttct yyyly

)log( 3213 ++++ +++= ttttct yyyyly ,

)log( 44 ++ = tct yly

)log( 545 +++ += ttct yyly

…

==+−=

=+= − otherwise ,1

4),/,....(1,1)1(,0),log( 1

ssnstyyy tt

ctt

ct

ττφφ (7)

Where ctly is the logged cumulated level of the real GDP, and c

ty is the cumulated

level of the real GDP.

20 Estimation of the models using levels of the series does generate a few negative results at certain seasonal troughs.

27

One concern about the logarithmic transformation on China’s data is the relatively

high growth of the series. As Banerjee et al. (1993) discussed about logarithmic

transformation of time series, changes in the logarithm approximately equal to the percentage

change of original levels of the series. When the changes are relatively large, logarithmic

transformation may dampen the growth patterns. However, comparing the results from

disaggregation with the real official data (the overlapping period 1991q1-2008q4) does not

show any significant effect on the magnitude of fluctuations.

IV. China macroeconomic data

My study aims to estimate China’s quarterly real GDP data in consistency with the

official quarterly published data since 1992. I focus on the real output fluctuations since

1978, when China embarked on the market-oriented and openness economic reform. The

annual and quarterly data used in this paper are from the National Bureau of Statistics of

China (NBS), the nation’s statistical authority21 , and official monetary authority and

international trade statistic agency.

4.1 The official GDP data

China’s National Accounts followed the Material Product System (MPS) of the

former Soviet Union from 1949 until 1985. China’s GDP estimation transitioned to follow

the guidance of United Nations System of National Account (SNA) in 1985 and formally

completed the process in 1992. The quarterly GDP data are officially published since 1992.

Empirical studies of the Chinese economy have been plagued by the problems of

availability and reliability of official Chinese macroeconomic data. Despite the data

21 The official data are published as cumulated year on year growth rate at comparable price. Data from 1992-2005 are

from the publication of National Bureau of Statistics of China (NBS 2008).

28

challenges, it is still worthwhile to study the features of China’s economy, the world’s 2nd

largest economy and the most populous country.

China’s official GDP have been criticized for having been overstated during 1980s

and 1990s (Rawski 2001, World Bank 2005, etc), understated in the middle of 2000s

(Economist May 1st 2008), and then overstated again during the most recent financial crisis.

Most recently, Huang (2011) argues that the true China’s GDP is likely to be much higher

than reported due to the understatement of consumption estimation. As a transitional

economy, China has undergone continuous changes, and has complex political, social and

economic structure. Despite the efforts made by NBS to improve and explain the GDP

estimates over the years, confidence in the accuracy of official data quality remains the

primary problem that must be addressed for empirical research on Chinese macroeconomic

issues22.

After carefully reviewing the literature on Chinese data quality and the national statistical

accounting system (Appendix 1-1), and comparing different data resources and data

construction methods23 , I agree with many researchers (Holz 2006, Chow 2006, Klein and

Ozmucur 2003) and most international organizations (OECD, IMF24). Although there are

weaknesses or short-comings in the statistical system that derives Chinese national accounts

22 A partial list of the recent media news and reports on China’s data problem includes (from the latest): “Reflating the dragon, can the world’s fastest-growing economy avoid a sharp downturn?” Economist Nov. 15th 2008,

which claims that China’s official growth fluctuations are smoothed” “An aberrant abacus—coming to terms with China’s untrustworthy economic numbers” Economist, May 1st 2008,

which ranks the reliability of Chinese statistics. 23 Besides the estimation with the data presented here, I apply the same methods to data covering shorter periods and

from other informal resources (the IMF World Economic Outlook dataset and Fudan University dataset). I compare the results and check if the data from different resources and the subsample data have significant different features.

24 The World Bank criticized the Chinese national account statistics and revised their GDP estimation for China upward for 34% from the officially reported number in 1993. In 1996, the World Bank accepted China’s reformed statistic system and the official GDP number again. But the World Bank revision and method of estimation was also questioned by many researchers.

29

estimation, Chinese official macroeconomic data after 1978 do not appear to be politically

manipulated or systematically biased. The official data can serve as “a reliable guide”

(OECD 2006) to the level and growth pattern of GDP, even though the margins of error are

“certainly larger than that of the most developed countries” (OECD 2006). Any other

alternative data series constructed or corrected by researchers has not been proven to be more

precise or reliable (Holz 2006). When I run the dissaggregation models in STAMP, I cannot

find the existence of any significant measurement errors or irregularity. Thus “Official

Chinese data should be the first port of call” (Scheibe 2003) for my study. The data resources

of my study, CEIC and IFS, both use the official data from China NBS as their final data

source.

The official quarterly real GDP year-on-year growths are shown in Figure 125. The

year-on-year real growth rates suggest that instead of “recessions” or negative growth rates at

the troughs of the cycles, China’s economy experienced “slowdowns” or “growth recessions”

at times but always had positive growth rates during the sample period. There are five major

slowdowns in year-on-year growth rates, which happened in 1980, 1984, 1989, 1996-1998

and most recently in 2008 (Chinese Academy Of Social Science, 2008-2010, Liu 2009). The

slowdowns in output growth in 1984 and 1996 were accompanied by hyperinflations. The

“Tiananmen Square” political chaos in 1989 significantly halted lots of the economic

activities across the country. The Asian financial crisis occurred in 1998 had an adverse

effect on the economic growth. In 2008, China’s economic growth dropped to 6.5% in the

last quarter, adversely shocked by the global financial crisis.

4.2 Related series

25

The data construction of this paper is based on log level data. The discussion in this section documents the information provided by the raw official real GDP data, which are published as year on year growth rates only.

30

The only available high frequency quarterly macro-economic data for the sample

period is monetary statistics and international trade statistics. To estimate the missing

quarterly real GDP data for China, I consider different combinations of monetary and trade

variables as related series in the multivariate UC modeling. The monetary series, including

domestic credit, international reserves, M1 and M2, are available quarterly since 1978;

International trade series include total exports and imports, total trade volume, which are

available quarterly since 1981. Domestic credit, international reserves, M1 and M2 are

nominal outstanding balance. Each series may carry different information associated with the

economic development and outputs fluctuations.

The monetary and trade data used in the temporal disaggregation of GDP are not only

available quarterly for the sample period, but also of good quality. According to the

Economist (2008) the quality of the related series’ data is among the top two most reliable

official macroeconomic data of China.

Figures 2.a and 2.b shows the log quarterly and annual real GDP and the potential

related series data used in the models. All data are not seasonally adjusted. The series appear

to follow similar upward trend in the long run. Figure 2.c and Figure 2.d present the year on

year growth rates26 of the available quarterly real GDP with the monetary and trade related

series respectively. Table1-5 documents the correlations of the year on year growth rates of

real GDP and the potential related series for the whole sample, data construction sample and

the fully available sample period.

26 The real GDP data construction of this paper is based on log level data rather than growth rates. However, the

relationships of series based on properties of growth rates, although they may be different from that based on the level data, provide useful information.

31

The correlations of the fluctuations of real GDP with most of the potential related

series appear to be high and stable except exports. The close to zero correlation of real GDP

and exports during 1978-1991 shows that the openness of China economy was very limited

during the period. With China’s expediting integration into the global economy in later years,

the correlation of economic growth with exports increased substantially. All joint tests of

cointegrating relationships between combinations of related series that include exports show

no evidence of cointegration (Table2).

V. Temporal disaggregation model selection and estimation results

This section presents the procedure of model selections and temporal disaggregating

estimation using the unobserved components model specified in section III.

5.1 Unit root and cointegration tests

The procedure starts with unit root test and cointegration test for the real GDP and

related series. The tests are important in finding whether Chow-Lin related series models are

valid or not. As I have discussed above, the estimation of univariate models with related

series (Chow-Lin method) will only be valid if there is a linear relationship between the

included related series and the target series. With nonstationary series, this assumption is

only valid when there is a cointegrating relationship among the series.

The stationarity of the annual logarithms level of the real GDP and related series is

tested using the Augmented Dickey-Fuller (ADF)27 . Table 1 reports the results of the ADF

tests. All series appear to have a unit root in the level and are stationary in first differences.

27

Other unit root tests methods lead to the same conclusion. The results are available upon request.

32

Thus, any temporal disaggregation methods, such as the original Chow-Lin model,

that not consider the nonstationarity of the series are invalid for Chinese real GDP level

disaggregation. The data must be first differenced before applying those methods. Or data

other than the real GDP level but stationary, such as the real growth rates used by A&R,

should be used. However, important information, especially on the level and trend, may be

lost during the first difference or using growth rates data. Plus the growth rates series may

have difference properties than the level data.

As I discussed in section III, the unobserved component approach is not only capable

of nesting the disaggregation of stationary series, but also capable of modeling the

nonstationarity with different specifications of the permanent component to capture the

property of the series.

I then use the Johansen cointegration test to check for a cointegrating relationship

among the different combination of the annual real GDP and related series. Table 2 presents

the results of the tests. The tests provide evidence in favor of cointegration among the annual

real GDP, total trade, imports and monetary indicators (domestic credit, M1 and M2). There

is no evidence of a cointegrating relationship when including exports in the system. Including

international reserves may introduce more than one cointegrating relation among the series.

The existence of a cointegrating relationship among the related series ensures that the Chow-

Lin method is applicable to the disaggregation of China real GDP with selected related

series. Thus the univariate with related series models should be included in the model

selection of temporal disaggregation.

5.2 Temporal disaggregation model selection and results

33

The unobserved components models for temporal disaggregation are estimated using

the STAMP8 program. The program applies the Kalman filter to obtain the components of

the series and uses maximum likelihood methods to estimate the parameters. Missing

quarterly data are generated with smoothing algorithm of the Kalman filter.

To select the model for disaggregation, I estimate the models with different

specifications of components and different combinations of related series. All models are

estimated with the full sample period from 1978q1-2009q4, but missing quarterly real GDP

from 1978q1-2008q4. Official quarterly real GDP for 2009 q1-q4 are used to initiate the

estimation, which is required by the STAMP program28. Once the estimations for 1978 q1 to

2008q4 are obtained, I calculate the root mean squared standard errors (RMSE) of the

estimated data and the official published quarterly data over overlapping period 1991q1-

2008q4. The best fit model for data disaggregation is then determined by the minimum

RMSE29. Based on the selected model, I estimated China’s real GDP series over the period

1978q1-1991q4. The RMSE criterion suggests the multivariate UC model including domestic

credit and total trade as related series with stochastic trend and AR (2) cyclical component

(Table 3). To further check the stability of the model, I replicate the model selection

procedure using subsample period from 1992-2009, when the quarterly real GDP are fully

observed. MUC model with domestic credit and total trade as related series is still the best fit

MUC model among all MUC combinations I have tried.

28

The initial value can be changed but the one year official quarterly data help in finding the convergence and reduce the length of iteration procedures.

29 Other statistic criteria are also shown in the table. Since the purpose of the modeling is not finding the best explanatory of GDP, the best fit of data disaggregation, or the RMSE is used to determine the selection of disaggregation model.

34

Table 6 presents the parameter coefficients and variances/correlations of components

estimates of the selected MUC domestic credit and total trade model, with full sample from

1978-2009 all quarterly real GDP observations missing, subsample from 1992-2009 with all

quarterly real GDP observations missing and the real temporal disaggregation model on full

sample with 1978-1991 quarterly real GDP to be estimated. The estimates of slope and AR

coefficients are very stable cross sample periods.

Figure 3 compares the year on year growth rate of official data, comparable Chow-

Lin methods and the MUC domestic credit and total trade model.

Using the selected model the final data construction estimation includes all available

official quarterly real GDP observations, leaving only 1978q1-1990q4 missing.

Figure 4 shows the year on year quarterly growth rates of the final results of

disaggregated real GDP, compared with series constructed by A&R. The MUC estimates has

similar but a little larger fluctuations than A&R estimation, except that the growth

accelerating started from 1981 peaked in 1984q4 in my estimation, while the A&R

estimation peaked 1 year later in 1985q4. Based on the annual official real growth data and

the official analysis from China NBS (Xu 2010), the MUC estimation is more reliable.

Bounded by the available annual level directly in the model estimation, the MUC estimates

follow the observed annual level better than A&R estimates. The multivariate structural

model analysis in the next section shows that this different affects the identification of the

property of shocks to China’s economy during this period. Both MUC estimation and A&R

estimation show a big drop in the last quarter of 1989. MUC estimate drops below zero.

VI. Univariate and multivariate time series analysis of China’s real GDP

fluctuations using the disaggregated quarterly data

35

To further evaluate the quality and information provided by the MUC temporal

disaggregated China quarterly real GDP data, I apply different univariate and multivariate

time series analysis techniques to the quarterly real GDP data from 1978q1-2010q4, with

data from 1978q1-1991q4 disaggregated from annual data by MUC model. The univariate

time series analytic methods include Linear in time functions, the Hodrick-Prescott (HP)

filter, the Band-pass or BP filter proposed by Baxter-King (1999) and Christiano and

Fitzgerald (2003), the unobserved components (UC) techniques. The multivariate structural

time series approaches are Blanchard-Quah decomposition (Blanchard and Quah 1989) and

the global vector autoregressive approach building on the work of Dees et al. (2007) (DdPS

approach hereafter). The MUC temporal disaggregated quarterly data provides a better

alternative of high frequency real output data that covers the whole period after China’s

economic reform and openness, and adds valuable information to the empirical investigation

on the properties of China’s output fluctuations.

6.1 Seasonal adjustment

Before conducting analysis, China’s quarterly real output data are seasonally adjusted

using the X-12 ARIMA method.

As discussed above, temporal disaggregation with the unobserved component

approach is capable of conduct seasonal adjustment simultaneously with the temporal

disaggregation. Figure 5 presents the seasonal components of the logged real GDP generated

from the MUC temporal disaggregation estimation and the seasonal factor based on X-12

ARIMA method. The two seasonal series are exactly the same, except slightly different at the

beginning of the sample period (5 observations). The seasonal adjustment through MUC

model appears to be convenient and reliable.

36

The X-12 ARIMA (2, 1, 2) and Tramo/seat (Time series Regression with ARIMA

noise, Missing Values and Outliers/Signal Extraction in ARIMA Time series) methods also

give similar results. The finding is consistent with Blades (2007), who performed similar

tests on current price quarterly GDP of China. The seasonal pattern of China’s quarterly real

GDP is regular and predictable.

The seasonally adjusted real GDP levels are then transformed to natural logarithms.

For calculation and explanation convenience, the natured log seasonally adjusted real GDP

level is annualized (multiplied by 4) and multiplied by 100.

6.2 Univariate statistical filters

Economic theories on economic fluctuations and growth, including real business

cycle theory, Keynesian theory and monetarism, all suggest that economies react differently

to permanent shocks with long-run effects than to transitory shocks whose effects dissipate in

the short run. Permanent or trend component of the real GDP is also considered as potential

output of a economy, while the transitory or cyclical component is used as measures of the

output gap. Understanding the relative role of permanent versus transitory movements in the

macroeconomic fluctuations of the countries is important for economists, forecasters, and

policy makers.

In contrast to the “classical business cycles” first defined by the Burns and Mitchell

(1946) as recurrent expansion, downturn, contraction and upturn in economic activity, the

“cycles” studying here follow the definition of “growth cycle”, which are “recurrent

fluctuations in the series of deviations from trend” (OECD Glossary). The later definition of

cycle is more appropriate for China’s real GDP fluctuations because the economy

experienced slowdowns in growth rates but the growth rates have always remained positive.

37

The contractions by definition should include slowdowns using a “growth cycle” definition

instead of only include absolute declines or recessions in economic activity. Morley and

Piger (2009) denote a more general “transitory-deviation definition” of the business cycle,

which are the short-run or transitory fluctuations in economic activity around the permanent

or “trend” level. The unobserved components (UC) techniques applied in this paper fit in the

“transitory-deviation” definition, while the cycles isolated from the series with a statistic

filter such as Hodrick-Prescott (HP) or Band-Pass (BP) filter fit in the traditional business

cycle or growth cycle definition.

Linear in time (LIT) in time

As benchmark for comparison, I begin the decompositions from the most naive linear

in time and polynomial in time models. The models assume a deterministic linear (or

polynomial) in time trend30. With the LIT estimation, I check for structural breaks by

applying Quandt-Andrews unknown breakpoint test to the constant and time coefficient with

trimmed 15% data and find that 1992q4 is a significant breakpoint during the sample

period31. The breakpoint is confirmed by Chow known breakpoint test. The Chow known

breakpoint test on linear in time model with official annual real GDP level confirms 1993 as

a significant (at 10% significant level) breakpoint during 1978-2009. There are evidences of

30 The linear and polynomial in time model specification is:

When n=1, the model is linear in time model. When n=2, it is quadratic in time model. The models are estimated with least squares method. The trend is the predicted value of yt and the cyclical component

is the residual from the estimation. The residuals are significantly auto-correlated. Although it is well known that LIT or polynomial in time models often fail to reveal the changes in slope or intercept of the trend over time, the estimations are simple and straightforward, thus still can be used as benchmarks. Since larger power polynomial in time model fit the data no better than the linear trend model, I use LIT result for comparison with results from other methods.

31 The test is conduct in Eviews. Same exercise using Pcgive package shows similar result, the recursive estimation breakpoint Chow test with the MUC quarterly data show evidence of breakpoint around 1992q3-1993q1.

38

breakpoint around the end of 1992 in both official annual data and the MUC quarterly data.

This breakpoint is mostly based on true underlying economic activity rather than the data

construction procedure.

In China’s economic development history, 1992q4 was the start of an era of stable

and high growth following the former leader Mr. Deng Xiaoping’s speech on his “Tour the

South of China” in early 1992. The speech re-affirmed the national policy of market oriented

economic reform and openness that was halted by the 1989 “Tiananmen” square political

chaos. This breakpoint thus is considered in the other trend cycle decomposition approaches

and the possible different properties of the economic fluctuations before and after 1992q4 is

investigated.

Hodrick-Prescott (HP) filter

HP filter is the most widely used approach of decomposition to obtain the smoothed

long term trend of China’s output (or potential output) and output gaps in the literatures so

far. The HP trend is determined by minimizing the weighted sum of the squared cycle and

changes in the growth rate of the trend32.

Although very popular and convenient, HP filter may generate artificial cycles when

applied to first-order integrated series. As shown by Cogley and Nason (1995) and Park

(1996), the HP filter is convenient but subject to several limitations: HP filter implicitly

assumes that the business cycle of the economy is symmetric during expansion and recession

32 I generate HP trend and cycle in E-views, where the HP filter chooses s to minimize:

λ is the smoothness control parameter that penalizes the fluctuations of trend. The HP filter get smoothed and stochastic

trend with is uncorrelated with the cyclical components. For quarterly data, the standard selection is λ=1600.

39

time, and the assumption of periodicity is sensitive to the end of the sample period. In

addition, the HP filter may generate artificial cycles when applied to first-order integrated

series. King and Rebelo (1993) pointed out the arbitrarily picked smooth parameter is based

on the observations of the US business cycles and may not be the optimal choice for other

economies. The HP filter also is criticized for lacking fundamental economic justification

and arbitrarily picking smooth parameter33. The cycle components are significantly sensitive

to the arbitrarily set smoothness control parameter λ. The standard choice of λ=1600, which

is based on the observations of US business cycles, leaves the duration of the cycles average

at 4-6 years. For China real GDP data, the average durations are above 8 years with λ=1600.

I tried different values for λs (8, 40) to check the sensibility of cycles (Figure 6). The

magnitudes of cycle appears much bigger with λ=1600, while similar when λ is set at 8 or 40.

However smaller λs make the cycle cross more frequently from the zero line. Since the λ

choices are arbitrary and there is no generally accepted criteria for choosing λ for China’s

quarterly real GDP, I use the standard λ=1600 result to compare with decompositions from

other approaches.

Band-Pass (BP) Baxer-King and Christiano-Fizgerald filter

Band-Pass (BP) filter, also called frequency filter (Sims 1974), isolates the cyclical

component of a time series by specifying a frequency band or a range of duration for cycles.

The filter takes a two-sided weighted moving average (Baxer and King 1999) of data where

cycles pass through the band that is arbitrarily selected. The BP procedure does not make

deterministic or stochastic assumption about the trend. The frequency of the cycle is the only

criteria used to identify trend and cycle. The selection of band is critical to the decomposition

33. See King and Rebelo(1993) for optimal conditions of HP filter.

40

results. The typical choice for quarterly data is usually set at between 6 to 32 quarters (fixed

length symmetric, Baxer and King 1999), which isolates all cycles that completed greater

than 6 quarters and less than 32 quarters into the cyclical component. Christiano and

Fitzgerald (2003) proposed a filter that considers the nonstationary and asymmetry of the

underlying data, thus is more proper for time series that have unit roots such as China’s real

GDP.

Unobserved component decomposition

As discussed above, the frequency filters impose assumptions that may generate

artificial cycles, thus may overstate the importance of the cyclical component. The statistical

filters provide very little information on the evolution of permanent or trend of the series,

which is important for a fast growing and transitional economy such as China. The fast

changes of China economic structure and gradually but continuously implemented economic

reforms may have impacts on the economy permanently or transitorily. To understand

China’s output fluctuations beyond the spurious statistical filters, I apply the structural time

series modeling or unobserved components modeling to further investigate the property of

permanent and transitory changes of China’s output.

Recent development of univariate time series econometric approaches favors “let the

data speak for itself”. The Unobserved Components (UC) models that I used for the temporal

disaggregation are also widely applied decomposition methods (Harvey 1985, Watson 1986

and Clark 1987). These methods explicitly account for the unit roots property of the series

without imposing any prior assumptions. By assuming a stochastic trend, the method capture

the property of the trend for aggregate output, which for most economies, grows or changes

over time and thus is not stationary in levels.

41

The unobserved component (UC) model, as discussed in the temporal disaggregation

part of the paper, assumes a stochastic trend and stationary cycle. Although theoretically the

temporal disaggregation and trend cycle decomposition can be done simultaneously with UC

models, only Kalman smoothing algorithm, which uses the information from the whole

sample, can be applied with missing quarterly observation of the real GDP series. Here I use

both Kalman smoothing and filtering algorithms on the full sample. The Kalman smoothing

calculations of China’s real GDP permanent and transitory components include information

from future data. The model specification is documented in appendix1- 2.

Figure 7 shows that the smoothing cycle is slightly larger in amplitude than the

filtering cycle. The turning points are also slightly different when using the future

information other than the historical information till the estimated point. The smoothing

estimates, including more information from the whole sample, usually fit the data better. The

filtering estimates is still very useful in forecasting when only historical information is

available.

The drift and parameters of AR terms can be estimated along with the decomposition

using maximum likelihood method. The parameter estimates of the models are reported in

Table 5. The estimated drift term, which can be interpreted as the average growth of the trend

or permanent component of China real output, is 2.46% quarterly or about 9.8% annually.

The estimated autoregressive coefficients, which represent the dynamics of the cyclical

components, are summed at 0.977, which implies that the fluctuations of the transitory

components are highly persistent.

42

Figure 8 shows the most commonly used HP and BP filtered cycles of China’s real

GDP with MUC and A&R disaggregated data. There are slight differences in the turning

pattern and magnitudes of cycles.

6.3 Comparison of output fluctuation results from different univariate time series

analytic methods.

HP and BP decompositions are similar in that both isolate low-frequency fluctuations

to the trend and keep certain high frequency fluctuations in the cycle. The methods impose

smoothness prior assumptions on the components and thus subject to restrictions of the

condition of properly using the priors. Both methods may distort the characteristics of trend

and cyclical components of integrated or I (1) series (Baxer-King BP filter). The LIT, HP, BP

Baxer-King and Christiano-Fitzgerald asymmetric BP filter cycles of China’s quarterly real

GDP generated from E-views are shown in Figure 9. The HP and BP Baxer-King cycles

appear to have similar cyclical patterns in peaks and troughs, while BP Baxer-King cycle is

smoother than HP cycle. Similar results have been found for output data of other countries.

(See Gerlach and Yiu 2003 for Asian economies, Park 1996 for the US). The identified

turning points of Christiano-Fitzgerald cycle are different from others for sample period after

1992q3. Christiano-Fitzgerald cycles turn earlier than other cycles. Christinao-Fitzgeral filter

considers the I(1) property and asymmetric length of cycles during the sample period. Based

on the shaded areas, which are peaks to troughs of real growth rates, the Christiano-

Fitzgerald cycle appears more reasonable. I use Christiano-Fitzgerald filter result for

comparison.

Figure 10 compares the estimated permanent and transitory components from HP, BP

Christiano and Fitzgerald filters and the UC model.

43

Different decomposition methods generate similar cyclical components before 1992

but different ones after 1992. The cycle periods appear shorter before 1992 (averaged at

about 4-6 years), while longer after (about 10 years for the cycle before the most recent

global financial crisis)34. Similar to the US economy, China experienced “moderation” in

economic fluctuation during the period. Explanation of this difference would be, during the

earlier period, the economy had to adapt to some fundamental economic reforms and transit

from full planned economy to a market oriented economic structure, and the lack of

adjustment mechanism result in stronger reactions to any shocks.

All approaches identify big transitory drops in 1982, when stimulating effects from

the first round of economic reforms faded, and a less negative gap in 1987, following the first

peak of inflation since the reform. The late 1989 drop was a combination of hyper-inflation

and political chaos. The most recent financial crisis period is first identified as spike in the

transitory components based on all methods, which shows the effects of stimulation package.

6.4 Structural multivariate analysis

The estimated China’s quarterly real GDP with selected multivariate UC model also

provide a better high frequency and long period real GDP data alternative for structural

multivariate analyses on China’s macroeconomic fluctuations. The following excises on

Blanchard-Quah approach and the global VAR method (Dees, Di Mauro, Pesaran and Smith

2007, DdPS hereafter) are two examples of the structural multivariate analyses using the

estimated China’s quarterly real GDP data35.

The structural VAR approach: Blanchard-Quah decomposition

34 Note that length of HP and BP cycles may just due to the choice of smoothness parameters. 35 Due to data limitation on quarterly capital investment and employment as I mentioned in earlier sections, production

function analysis cannot be conducted for the period before 2000 without data construction on those series.

44

Due to the shortage of long time period quarterly GDP data, the applications of

Blanchard and Quah method to Chinese quarterly data either use a very short sample period

of data (Siklos and Zhang 2010) or an alternative series as proxy for real output (Zhang and

Wan 2005). The MUC estimation of China’s real GDP fills this gap. Using the MUC

estimation of China’s quarterly real GDP data and inflation rate from IMF-IFS database, I

derive the demand component of China’s real output fluctuations using the standard

Blanchard and Quah bivariate structural VAR approach for 1986-201036. Compared with the

literature that uses other alternatives for aggregate output of China, the new real GDP data

provides more information for China’s macroeconomic fluctuation for a longer time period

and better coverage of the economy.

Blanchard and Quah (1989) identify structural supply shocks and demand shocks

with a structural vector autoregression method by assuming that the supply shocks, which are

usually driven by changes in productivity, affect the real output permanently whereas the

demand shocks only have temporary impacts on output. The original Blanchard and Quah

model uses the unemployment rate as the additional macroeconomic variable. Due to the

shortage of reliable employment data, application of the approach to China and other

emerging countries often use inflation as demand side related series (Bayoumi and

Eichengreen 1992, Bersch and Sinclair 2011). Following these literature, I use inflation rate

as additional macroeconomic series to identify supply and demand shock.

The unit root tests result indicates that the logged seasonal adjusted real GDP and

logged inflation rate are integrated of order 1. The Blanchard-Quah decomposition can be

applied to the bivariate VAR of first difference of logged seasonally adjusted real GDP (∆y)

36 The quarterly CPI data are available only since 1986.

45

and inflation rate (∆π). The data are presented in Figure11.a and 11.b. Appendix1-3 presents

the model specification. The lag length selection criteria suggest including six lags in the

VAR. The structural VAR is then set by imposing the Blanchard and Quah long-run

restriction, assuming the aggregate demand shocks do not have long-run effects on real

output.

Figure 11 shows the impulse response functions that trace out the impact on the levels

of real GDP and inflation by the identified supply and demand shocks. It shows that one unit

of positive demand shock increases the output by about 0.8 percent and the effect diminishes

in about 4 years. One unit of positive supply shock pushes the real output up by about 1.6

percent in the long run. A demand shock results in a sharp increase in inflation and a supply

shock leads to a slight drop in inflation first and then the effect quickly reverses upward. The

economy would face strong same direction price level changes from both demand and supply

shocks. It will be difficult for the central bank to control the inflation solely through

monetary policy which mainly affects the demand side. The impulse response function

results are in agreement with the results of previous studies (Zhang and Wan 2005).

The estimated forecast error variance decomposition of real output based on the MUC

data provides different information about China’s real output fluctuations than the

decomposition based on industrial production, an alternative proxy of real output used by

Zhang and Wan (2005). Based on MUC data, the output fluctuations are largely explained by

aggregate supply shock, while aggregate demand shocks are the main driver of inflation

changes. The share of supply shock to the variance of forecast error on real GDP is much

more stable (above 60% of the variance of output fluctuations) than the result of Zhang and

Wan (2005) indicated (increasing from 55% to 92% over 2 years forecasting horizon). Use

46

industrial production as proxy for the aggregate output can be problematic for China. The

share of industrial production in China’s aggregate output changes dramatically during the

sample period. As discussed in the data section, share of production from service sector, once

trivial during early 1980s, has greatly increased to over 40% of the total GDP in recent years.

Industrial production, which does not cover the service sector, could not reflect the overall

properties of the macroeconomic fluctuations.

The Blanchard-Quah output gap, defined as the accumulation of demand shocks on

output, can be derived using the estimated structural demand shocks and the noncumulative

impulse response function. By definition, the cyclical component of the real output should be

mean zero in the long run. Thus the gap is set to be closed at the mean of the Blanchard-Quah

demand components. Figure13 compares the Blanchard-Quah output with HP and Christiano

Fitzgerald cycles. The differences shall reflect the fluctuations caused by supply shocks

within the frequency band of the statistical filters.

Figure 14 compares the Blanchard-Quah output gaps based on MUC estimation and

A&R estimation. The Blanchard-Quah output gap of A&R data appears very similar to that

of MUC estimated data.

Global VAR

DdPS (2007) developed a multivariate system—a global VAR (GVAR) model—to

explore the international linkages among economies in an increasingly globalized world.

DdPS’s GVAR model for China includes the following country-specific variables as

dependent variables: real outputs, inflation, interest rates, and real exchange rates. Trade

weighted output, price level, equity price, interest rates and long run interest rates of the rest

of the world and the world oil price enter into the GVAR as exogenous variables. The model

47

includes two lags for all variables. The authors assume that all variables are integrated of

order one. To compare the estimation results with DdPS 2007, I replicate the model using

quarterly data of same sample period from 1979q2 to 2003q4.

A problem of the original DdPS model estimation with Chinese data is that the

quarterly real output data are derived from annual real GDP by evenly allocating the annual

output to the four quarters of the year. This simple disaggregation smoothes the quarter by

quarter changes of the series, thus loses the information on the quarterly macroeconomic

dynamics. I replicate the China DdPS GVAR model with the quarterly real GDP data

estimated by MUC model. The result of the replication shows that the new data provide

important information to the model. Simple disaggregaion of the data distorts the results37.

Figure 15 shows the level and the first difference of logged seasonal adjusted real

GDP estimated through the MUC model and the original DdPS data of logged real GDP38.

The MUC quarterly real GDP data introduce quarterly dynamics to the GVAR

system. The two real GDP series move within the boundary of the same annual real GDP

movement. Thus, they provide similar information on signs of the long run relationship of the

variables in the cointegrating vector. Table 8 shows the evidence of cointegration of the two

series (Erisson, Herdry and Tran 1994)39. However, the estimated effects of domestic

37 Note that the quarterly CPI data are available only since 1986. DpDS appear to construct the quarterly inflation data

based on annual inflation statistics. Same situation may exist for the interest rate data as well. In this analysis I focus on the discussion of real GDP data quality. To check the difference of the estimation based on the different real GDP data only, I keep the other series the same as the original DpDS dataset. However, there may be data construction problems to other series in DpDS estimation as well.

38 The level differences are due to the difference of base year setting. It will not affect the result of VAR estimation, which is based on the first difference of the series.

39 Ericsson, Hendry and Tran (1994) theoretically explain why seasonal adjusted and non seasonal adjusted data are cointegrated. The MUC real GDP and DdPS real GDP can be considered as seasonally adjusted through different procedures, thus should be cointegrated.

48

inflation and interest rates on real output based on the MUC data are much stronger than the

original DdPS data reveals40.

Table 9 presents the estimated cointegrating vector coefficients based on MUC

temporal disaggregated quarterly real GDP data and on the original DdPS data. The

estimation based on MUC data and original DdPS data both find that only domestic inflation

and short term interest rate are statistically significant. The high significance of domestic

inflation suggests the existence of a strong Phillips curve type relationship in China’s

macroeconomic fluctuations.

All foreign variables are insignificant for China’s macroeconomic fluctuations in the

long run based on both datasets. Although rapidly integrated into the world economy,

China’s economic fluctuations are still mainly driven by domestic factors rather than the

foreign and global factors during the sample period41.

Appendix 1-4 presents the results of short run coefficients and the graphs of impulse

response functions for each domestic variable in the GVAR system. The real GDP and

inflation appear to be exogenous based on the MUC data estimation. While based on the

original DdPS data, only inflation is exogenous. The plots of impulse response functions for

China’s real GDP based on the MUC data show that the economy recovers much quicker

than the original DdPS data estimated from shocks on other domestic variables. Seasonal

40 Table A4-1 in appendix 4 shows the result of likelihood ratio tests of equality of the coefficients estimated with MUC

data with the estimated coefficient original DdPS data. MUC coefficients are larger in absolute value but not significantly different from the DdPS estimated coefficients, and vise versa, which can be explained again based on Ericsson, Hendry and Tran (1994), that the two datasets can be considered as results of different seasonal adjustments and should show similar long run property of the underlying series.

41 This result is in agreement with the result of the other two papers I coauthored with Tara Sinclair using multivariate unobserved components model to investigate the relationship of China’s real output fluctuations with the US and the developed world economies using quarterly data from 1978-2009

49

dynamics introduced by the MUC data may cause these difference in short run analysis

(Ericsson et al. 1994)42.

VII. Conclusion

This paper provides quarterly real GDP estimates from 1978q1-1991q4 using

multivariate unobserved components models. The selected disaggregation model estimates

the quarterly real GDP levels of China from annual data with Kalman smoothing technique,

using information from the available quarterly domestic credit and total international trade

data without prior assumption of cointegration among the series. Although the traditional

Chow-Lin method of temporal disaggregation is valid for China data because of the evidence

of cointegration among the related series, the MUC model is found to be more efficient.

To evaluate the MUC model estimated China’s real quarterly GDP data, I apply the

temporal disaggregated quarterly real GDP series, lengthen by the temporal disaggregation

from 1978-2010, to different univariate and multivariate methods. The constructed quarterly

data are shown to be a better alternative than other proxies and estimations. The data provide

valuable information to the empirical study on China’s macroeconomic fluctuations.

The multivariate unobserved component temporal disaggregation approach could be

easily applied to the missing data problem of other macroeconomic indicators, and to the data

of other developing and transitional economies, where lack of high frequency data has been a

big obstacle of macroeconomic analysis.

Through evaluate the MUC model estimated China’s real quarterly GDP that covers

the 32 years since China started the economic reform and openness, the properties of China’s

42 Ericsson, Hendy and Tran (1994) provide analysis on the possibility of the difference in short run or error correction

modeling due to the difference in seasonal adjustment.

50

output fluctuations can be better understood. The results of unobserved components

decomposition, Blanchard-Quah decomposition, and the GVAR model suggest that supply

side shocks and domestic factors play an important role in China’s real output movements.

Although China’s economy has been widely open to the world economy, outside shocks,

which may mainly be on the demand side, may have either not been as strong as that from

the domestic economic reforms and productivity changes, or have been effectively offset by

China’s macro-economic policies.

Where is China’s economy today? Is it below or above potential output or trend? The

different trend cycle decompositions give different answers to this question: HP and

Blanchard-Quah decomposition find that China’s aggregate output since 2010 is slightly

below trend, while the Christiano Fitzgerald filter and UC model shows it still slightly above

permanent level. All methods of analyses show that China’s economy is now very close to

the potential level. The answer to whether the growth will speed up or slow down looks

ambiguous43. Given the importance of China in the global economy, this suggests further

research on China’s economy is clearly warranted.

43 Further research is desirable to better understand the features of China’s macroeconomic fluctuations. In Chapter two

and three I extend the study with multivariable unobserved components model on the relationship of output fluctuations with other macro-economic series. Other possible extension includes applying the multivariate approaches with inflation (the Philips curve), monetary policy indices and/or consumption.

51

Figures and Tables

Table 1-1: Unit root test results (Augmented Dickey-Full Test on annual data 1978-

2009)

Series test statistics a Lag-length

b Deterministic

c

Log GDP 3.608 2 Constant

log Export 7.391 0 none

Log Import 0.439 2 constant

Log Total trade 7.332 0 none

Log M1 4.480 1 none

Log M2 2.827 1 none

Log Domestic credit 3.489 1 none

Log international reserves 0.917 4 none

dLog GDP -4.002 *** 5 Constant

dlog Export -3.470 ** 5 constant

dLog Import -4.918 *** 1 constant

dLog Total trade -3.502 ** 0 constant

dLog M1 -5.744 *** 0 Constant

dLog M2 -3.547 ** 0 constant

dLog Domestic credit -4.288 *** 0 constant

dLog international reserves -4.344 *** 3 constant

Note: a. * , ** and ***denote rejection of the null hypothesis of a unit root at the10%, 5% and 1% significant levels critical values respectively; Critical values for the level series without constant are -1.954 and -2.653 for 5% and 1% significance levels respectively. Critical values with constant are -2.986 and -3.724 respectively. b. Optimal Lag length is determined by Akaike information criterion (AIC).

c. Deterministic components in the test are determined by AIC.

52

Table 1-2. Johansen Co-integration test results of annual data

Log GDP with selected combination of related series

Selection of

related series

in the system

Deterministic

components in

the cointegrating

equations a

Hypothesized

No. of CE(s)

Eigen-

value

Trace

Statistic Prob.

Max-

Eigen

Statistic Prob. c

M1,

Total trade

Constant

+trend

None * b 0.652 54.141 0.003 31.635 0.008

At most 1 0.463 22.506 0.124 18.634 0.064

At most 2 0.121 3.871 0.761 3.871 0.761

M2,

Total trade

Constant

+trend

None * 0.730 55.839 0.002 39.254 0.001

At most 1 0.387 16.585 0.447 14.663 0.213

At most 2 0.062 1.922 0.973 1.922 0.973

Domestic

credit,

Total traded

Constant

+trend

None * 0.630 49.016 0.011 29.792 0.014

At most 1 0.411 19.224 0.268 15.900 0.150

At most 2 0.105 3.324 0.836 3.324 0.836

Domestic

credit,

Exports

Constant

+trend

None 0.532 36.590 0.186 22.754 0.121

At most 1 0.297 13.836 0.671 10.583 0.557

At most 2 0.103 3.254 0.845 3.254 0.845

Domestic

credit,

Imports

Constant

+trend

None * 0.719 56.398 0.001 38.133 0.001

At most 1 0.408 18.265 0.326 15.708 0.158

At most 2 0.082 2.557 0.925 2.557 0.925

Intl.

Reserves,

Total trade

constant

+trend

None * 0.770 74.395 0.000 44.151 0.000

At most 1 * 0.515 30.244 0.013 21.678 0.023

At most 2 0.248 8.566 0.209 8.566 0.209

Note: a. The VAR systems all include a single lag and a linear trend (a constant and trend) on each variables, selected by the deterministic components in the cointegrating equation, chosen by Akaike Information Criteron (AIC) and Schwarz criteron (SC);

b. * denotes rejection of the null hypothesis at 5% significant level. The critical values for the 5% significant level on the Trace statistic are 42.915, 25.827 and 12.518 for the null hypothesis of no cointegrating equation, at most 1 cointegrating equation and at most 2 cointegrating equation respectively; the critical values for Maximun Eigen statistics for the 5% significant level on the Trace statistic are 25.823, 19.387 and 12.518 for the null hypothesis of no cointegrating equation, at most 1 cointegrating equation and at most 2 cointegrating equation respectively.

c. The p-values by MacKinnon-Haug-Michelis (1999) p-values; d. The combination of related series in the selected model of quarterly real GDP data estimation with

multivariate unobserved component approach.

53

Table1- 3: Disaggregation model selection

Note: a. The sample period covers 1978q1-2009q4, with only 2009 q1-q4 quarterly data observed as initiate

value; b. Stochastic slope: the slope is specified as random walk with drift c. RMSE: Root mean square errors of the estimated quarterly data with the published official quarterly data

over period 1991-2008 d. The cyclical component choice may change to find convergence

Explanatory

variable

Model specification Model comparison criterion

Slope Seasonality Cyclical

component

Log

Likelihood

Akaike

Inform

ation

Criteri

on

(AIC)

Bayesian

Schwartz

Criterion

(BIC)

DW

test RMSE

c

Univariate

models

M1-1 Stochastic b Stochastic No cycle 107.85 -8.21 -8.08 1.950 0.0143

M1-2 Stochastic Stochastic AR(2) 111.03 -9.54 -9.40 1.998 0.0144

M1-3 fixed fixed AR(2) 112.09 -9.52 -9.38 1.998 0.0144

Univariate

models with

Explanatory

variables a

M1, TR

[Chow-Lin

comparable ]

fixed Stochastic

AR(1)

94.95 -7.15 -7.01 1.885 0.0721

M1,

TR[Fernandez

1981 A&R

comparable ]

Stochastic Stochastic

No cycle

99.26 -8.60 -8.43 1.422 0.0134

DC, TR Stochastic Stochastic AR(2) 97.56 -9.12 -8.74 1.713 0.0139

M2 TR Stochastic Stochastic AR(2) 98.04 -8.63 -8.46 1.687 0.0130

M2 IM EX Stochastic Stochastic AR(2) 96.08 -8.72 -8.52 1.623 0.0133

DC IM Stochastic Stochastic AR(2) 97.99 -8.85 -8.67 1.581 0.0142

Multivariate

models d

M1, TR Stochastic Stochastic No cycle 768.98 -8.45 -8.32 1.806 0.0163

M1, TR Stochastic Stochastic AR(2) 773.31 -8.44 -8.30 1.815 0.0162

DC TR Stochastic Stochastic AR(2) 806.56 -9.74 -9.61 1.986 0.0128

M2 TR Stochastic Stochastic no cycle 796.86 -8.40 -8.27 1.981 0.0148

DC EX Stochastic Stochastic AR(2) 810.41 -9.17 -9.04 1.995 0.0147

DC IM Stochastic Stochastic AR(2) 760.95 -9.33 -9.20 1.906 0.0207

DC TR M1 Stochastic Stochastic AR(2) 1234.03 -8.90 -8.77 1.683 0.0249

DC TR IR Stochastic Stochastic no cycle 1051.56 -8.59 -8.46 1.978 0.0168

DC IM EX Stochastic Stochastic no cycle 1067.73 -9.06 -8.92 1.950 0.0196

54

Table1- 4: China quarterly real GDP data: MUC model estimation, A&R estimation

and the official data (1978q1-2011q2)

Continue:

Quarter

MUC estimated

quarterly real

GDP level (2000

as base year)

Standard

Errors a

MUC

estimated

year on

year real

growth

rates

A&R

estimates

year on

year

growth

rates

Official year

on year real

growth rates

(updated

2011 Q2) b

Official published

cumulated year on

year real growth

rates (updated 2011

Q2) c

Official

annual

growth rates

Annual

real GDP

level(2000

as base

year)

1978-1 267.4 0.03216

1978-2 310.0 0.02482

1978-3 317.5 0.03308

1978-4 412.0 11.7 1306.8

1979-1 286.2 0.04353 7.0 6.4

1979-2 332.7 0.03545 7.3 7.3

1979-3 340.9 0.03704 7.4 7.9

1979-4 446.3 8.3 9.1 7.6 1406.1

1980-1 306.5 0.01653 7.1 7.5

1980-2 359.4 0.04006 8.0 8.4

1980-3 367.5 0.05357 7.8 8.2

1980-4 482.4 8.1 7.2 7.8 1515.8

1981-1 327.4 0.03612 6.8 4.8

1981-2 380.1 0.04336 5.8 4.1

1981-3 384.6 0.05673 4.7 3.9

1981-4 502.5 4.2 4.9 5.2 1594.6

1982-1 345.6 0.03061 5.6 6.9

1982-2 407.7 0.03837 7.3 7.8

1982-3 422.4 0.04840 9.8 9.3

1982-4 564.0 12.3 9.0 9.1 1739.7

1983-1 377.0 0.02947 9.1 7.8

1983-2 449.1 0.03604 10.2 9.0

1983-3 471.0 0.04526 11.5 12.1

1983-4 632.2 12.1 13.7 10.9 1929.4

1984-1 421.4 0.02753 11.8 14.9

1984-2 509.4 0.03365 13.4 14.2

1984-3 542.8 0.04210 15.2 14.0

1984-4 749.0 18.5 15.3 15.2 2222.6

1985-1 485.4 0.02550 15.2 16.3

1985-2 586.4 0.03114 15.1 16.3

1985-3 610.6 0.03886 12.5 15.8

1985-4 840.2 12.2 16.8 13.5 2522.7

1986-1 542.9 0.02325 11.8 7.3

1986-2 650.4 0.02841 10.9 10.6

1986-3 663.9 0.03538 8.7 8.9

1986-4 887.4 5.6 8.6 8.8 2744.7

1987-1 593.9 0.02077 9.4 11.0

1987-2 717.8 0.02539 10.4 10.7

1987-3 749.6 0.03158 12.9 11.9

1987-4 1001.6 12.9 13.4 11.6 3063.0

1988-1 666.0 0.01794 12.1 11.4

1988-2 812.3 0.02196 13.2 12.5

1988-3 836.9 0.02728 11.6 11.8

1988-4 1094.0 9.2 9.5 11.3 3409.2

55

Continue:

1989-1 729.6 0.01460 9.6 6.2

1989-2 866.2 0.01790 6.6 5.4

1989-3 862.8 0.02219 3.1 3.2

1989-4 1090.4 -0.3 0.2 4.1 3548.9

1990-1 757.6 0.01025 3.8 2.1

1990-2 891.0 0.01259 2.9 2.3

1990-3 900.8 0.01553 4.4 4.4

1990-4 1134.4 4.0 7.3 3.8 3683.8

1991-1 797.1 5.2 8.6

1991-2 957.1 7.4 8.2

1991-3 1017.9 13.0 9.7

1991-4 1250.6 10.2 10.3 9.2 4022.7

1992-1 905.5 13.6 13.6

1992-2 1082.0 13.1 13.3

1992-3 1153.2 13.3 13.3

1992-4 1453.2 16.2 14.2 14.2 4593.9

1993-1 1042.3 15.1 15.1

1993-2 1239.4 14.5 14.8

1993-3 1308.2 13.4 14.3

1993-4 1642.6 13.3 14.0 13.9 5232.5

1994-1 1176.7 12.9 12.9

1994-2 1387.9 12.0 12.4

1994-3 1470.4 12.4 12.4

1994-4 1882.9 14.6 13.1 13.1 5917.9

1995-1 1317.9 12.0 12.0

1995-2 1528.8 10.2 11.0

1995-3 1616.0 9.9 10.6

1995-4 2100.2 11.5 10.9 10.9 6563.0

1996-1 1461.6 10.9 10.9

1996-2 1678.4 9.8 10.3

1996-3 1769.1 9.5 10.0

1996-4 2310.3 10.0 10.0 10.0 7219.3

1997-1 1613.6 10.4 10.4

1997-2 1846.7 10.0 10.2

1997-3 1920.1 8.5 9.6

1997-4 2510.4 8.7 9.3 9.3 7890.7

1998-1 1736.2 7.6 7.6

1998-2 1973.2 6.9 7.2

1998-3 2074.5 8.0 7.5

1998-4 2722.4 8.4 7.8 7.8 8506.2

1999-1 1894.2 9.1 9.1

1999-2 2123.0 7.6 8.3

1999-3 2235.1 7.7 8.1

1999-4 2900.3 6.5 7.6 7.6 9152.6

2000-1 2064.7 9.0 9.0

2000-2 2310.1 8.8 8.9

2000-3 2434.0 8.9 8.9

2000-4 3112.7 7.3 8.4 8.4 9921.5

2001-1 2240.2 8.5 8.5

2001-2 2489.0 7.7 8.1

2001-3 2624.3 7.8 8.0

2001-4 3391.5 9.0 8.3 8.3 10744.9

56

Notes: a. The standard errors are for the estimated log cumulated year up to date levels estimated by the MUC model.

b. Calculated by the author based on the official published cumulated year on year quarterly growth rates. c. The official year on year real growth rates from 1992-2004 are from Historical data on china Quarterly

GDP estimator 1992-2005 (National Bureau of Statistics of china, 2008). Data from 2005-2011 are from the website of the NBS (http://www.stats.gov.cn/tjsj/jidusj/). All data include official revisions up to date.

.

2002-1 2439.6 8.9 8.9

2002-2 2710.5 8.9 8.9

2002-3 2880.0 9.7 9.2

2002-4 3692.8 8.9 9.1 9.1 11722.7

2003-1 2703.1 10.8 10.8

2003-2 2946.6 8.7 9.7

2003-3 3191.4 10.8 10.1

2003-4 4054.0 9.8 10.0 10.0 12895.0

2004-1 2984.2 10.4 10.4

2004-2 3281.2 11.4 10.9

2004-3 3504.0 9.8 10.5

2004-4 4428.1 9.2 10.1 10.1 14197.4

2005-1 3318.4 11.2 11.2

2005-2 3636.2 10.8 11

2005-3 3899.2 11.3 11.1

2005-4 4948.0 11.7 11.3 11.3 15801.7

2006-1 3729.9 12.4 12.4

2006-2 4135.8 13.7 13.1

2006-3 4377.4 12.3 12.8

2006-4 5565.5 12.5 12.7 12.7 17808.5

2007-1 4252.1 14.0 14

2007-2 4754.1 15.0 14.5

2007-3 4999.9 14.2 14.4

2007-4 6331.4 13.8 14.2 14.2 20337.3

2008-1 4732.5 11.3 11.3

2008-2 5264.3 10.7 11

2008-3 5493.8 9.9 10.6

2008-4 6799.1 7.4 9.6 9.6 22289.7

2009-1 5040.2 6.5 6.5

2009-2 5696.5 8.2 7.4

2009-3 6008.8 9.4 8.1

2009-4 7572.7 11.4 9.1 9.1 24318.1

2010-1 5639.9 11.9 11.9

2010-2 6288.5 10.4 11.1

2010-3 6592.1 9.7 10.6

2010-4 8302.5 9.6 10.3 10.3 26823.0

57

Table1-5. Correlations of year on year growth rates of quarterly real GDP and

potential related series

Sample period

Domestic

credit M1 M2 Exports Imports

Total

trade

1978-2009 0.35 0.43 0.38 0.19 0.49 0.43

1978-1991* 0.43 0.42 0.32 -0.02 0.56 0.51

1992-2009 0.32 0.47 0.56 0.35 0.38 0.40

Note: * official quarterly GDP real growth rates are not available during this period. Annual growth rates are used to get the correlations.

Table1-6. Temporal disaggregation parameter estimates---MUC model with domestic

credit and total trade (Log real GDP equation only)

1978q1-2009q4

(all quarterly real

GDP missing)

1992q1-2009q4

(all quarterly real GDP

missing

1978q1-2009q4

(1978q1-1991q4

real GDP missing)

Log

likelihood 805.566 479.22 1063.98

coefficients

Slope 0.024 0.020 0.025

(0.000) (0.000) (0.000)

AR(1)+AR(2) 0.999 0.999 0.973

Variances of components

Level 0.0000000 0.0000000 0.0000000

Slope 0.0000000 0.0000042 0.0000000

Seasonal 0.0000001 0.0000000 0.0000000

ARs 0.0000161 0.0000053 0.0000000

Irregular 0.0000000 0.0000000 0.0000000

Note: standard errors in parentheses.

58

Variance /correlation of cross series components for Log GDP (final model: 1978q1-

2009q4

With 1978q1-1991q4 real GDP missing)

log GDP

(var)

LDCq

(correlations) LTRq(correlations)

level

0.000000 0.022340 0.096930

Slope

0.000013 0.870300 0.998500

Seasonal

0.000003 0.426000 0.280800

AR(1)

0.000000 0.000980 0.002656

AR(2)

0.000000 0.005417 0.014180

Irregular

0.000000 0.000000 0.000000

Table1-7. Unobserved component model parameter estimates (maximum likelihood)

Drift(μ) Phi1(φ1) Phi2 (φ2)

S.E of

permanent

shocks

S.E of

transitory

shocks

Log

likelihood

2.460 1.876 -0.899 0.937 0.227 -188.684

(0.087) (0.147) (0.151) (0.094) (0.210)

59

Table 1-8: Cointegration test of DdPS data and MUC data (1979q2-2003q4)

hypotheses

Trace

test [ Prob]

Max

test [ Prob]

r=0 21.4 [0.005]** 21.39 [0.002]**

r≤1 0.01 [0.921] 0.01 [0.921]

Note: The tests are Johansen trace eigenvalue test and maximul eigenvalue test. ** denote the rejection of hypotheses at 1% critical value. Rejection of r=0 is evidence in favor of the existence of at least one cointegrating vector.

Table1- 9. Cointegrating analysis of GVAR modeling for China with MUC data and

DdPS original data (1979-2003, replicating of DdPS 2007)

Note: Note: *. **,*** indicate the rejection (at the 10%, 5% and 1% critical values) of the null hypothesis that a particular coefficient is zero. The tests are based on the likelihood ratio statistic that are asymptotically distributed as Chi^2 (1).

MUC data

estimates DdPS estimates

Variables β Standard

Errors(SE) Chi^2(1) Prob β

Standard

Errors(SE) Chi^2(1) Prob

Endogeous variables

China GDP 1 1

China inflation 13.267 (2.180) 18.313 [0.0000]*** 6.791 (1.058) 22.720 [0.0000]***

real exchange rates 0.303 (0.229) 0.916 [0.3386] 0.083 (0.129) 0.258 [0.6118]

ST interest rate of China -43.895 (8.714) 15.464 [0.0001]*** -23.011 (4.286) 20.406 [0.0000]***

Exogenous variables

foreign aggregate GDP 2.887 (2.749) 0.930 [0.3350] 1.747 (1.406) 1.561 [0.2116]

foreign inflation 4.998 (8.738) 0.242 [0.6230] 1.464 (4.327) 0.091 [0.7626]

foreign real equity price -0.114 (0.258) 0.157 [0.691] -0.096 (0.142) 0.462 [0.4968]

foreign ST interest rates 21.501 (12.191) 1.580 [0.2088] 9.835 (5.986) 1.442 [0.2298]

foreign LT interest rates -24.928 (23.187) 1.103 [0.3140] -7.452 (11.557) 0.368 [0.5442]

oil price 0.211 (0.170) 1.466 [0.2260] 0.076 (0.085) 0.730 [0.3929]

TREND -0.049 (0.024) 2.647 [0.1037] -0.038 (0.012) 5.849 [0.0156]**

Figure 1-1. China’s most recent revised official

on year growth rates (the shaded areas are “slowdown eras”

Figure1-2a. The log quarterly real GDP (2000 as base year) and the potential related

series.

0

2

4

6

8

10

12

14

16

181

97

8.1

19

79

.2

19

80

.3

19

81

.4

19

83

.1

19

84

.2

19

85

.3

60

. China’s most recent revised official annual and quarterly real GDP year

the shaded areas are “slowdown eras”)

. The log quarterly real GDP (2000 as base year) and the potential related

19

86

.4

19

88

.1

19

89

.2

19

90

.3

19

91

.4

19

93

.1

19

94

.2

19

95

.3

19

96

.4

19

98

.1

19

99

.2

20

00

.3

20

01

.4

20

03

.1

20

04

.2

20

05

.3

20

06

.4

Annual growth Quarterly growth

quarterly real GDP year

. The log quarterly real GDP (2000 as base year) and the potential related

20

06

.4

20

08

.1

20

09

.2

20

10

.3

61

Figure 1-2b. Log annual data

Figure1-2c: quarterly year on year growth rates of real GDP with monetary

related series (the shaded areas are “slowdown eras”)

-10

0

10

20

30

40

50

1980 1985 1990 1995 2000 2005 2010

Real GDP (show annual growth rate when quarterly not available)domestic creditM1M2

62

Figure 1-2d: quarterly year on year growth rates of real GDP with international

trade related series (the shaded areas are “slowdown eras”)

Figure 1-3. Disaggregation model selection: Year on year quarterly growth rates

(%) 1992-2008

Note: Year on Year quarterly growth rates are calculated as g=log(Yt)-Log(Yt-4)

-40

-20

0

20

40

60

1980 1985 1990 1995 2000 2005 2010

Real GDP (show annual growth rate when quarterly not available)ExportsImportsTotal trades

4

6

8

10

12

14

16

18

92 94 96 98 00 02 04 06 08

official real GDP MUC Chow-Lin Fernandez1981

63

Figure1-4. Year on Year quarterly growth rate (comparing with A&R from 1979-1991)

Figure1-5 Seasonal factors or China’s quarterly real GDP MUC temporal

disaggregation model and X12 seasonal adjustment method

-4

0

4

8

12

16

20

79 80 81 82 83 84 85 86 87 88 89 90 91

MUC estimatesA&RAnnual growth

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1980 1985 1990 1995 2000 2005

X12 seasonal factorMUC seasonality

64

Figure 1-6. HP cycles with different value of λ

Figure 1-7. Unobserved components decomposition: filtering and smoothing

-8

-6

-4

-2

0

2

4

6

1980 1985 1990 1995 2000 2005 2010

HPCYCLE HP_40 HP_8

-6

-4

-2

0

2

4

6

700

800

900

1,000

1,100

1980 1985 1990 1995 2000 2005 2010

UC trend filteringUC trend smoothingUC cycle filteringUC cycle_smoothing

65

Figure 1-8. HP and Christiano-Fitzgerald cycles of MUC temporal disaggregation and

A&R estimation of China’s quarterly GDP 1978-1992

Figure 1-9. Linear in time residual, HP and BP cycles

-8

-6

-4

-2

0

2

4

6

1978 1980 1982 1984 1986 1988 1990 1992

HPCYCLE_MUC HPCYCLE_AR

-6

-4

-2

0

2

4

6

1978 1980 1982 1984 1986 1988 1990 1992

BPCYCLE_MUC BPCYCLE_AR

-10

-8

-6

-4

-2

0

2

4

6

8

1980 1985 1990 1995 2000 2005 2010

LIT residualBP Baxer-King cycleChristiano-Fitzgerald cycleHP cycle

66

Figure 1-10. HP, Christiano-Fitzgeral and UC cycles

Figure 1-11 a. Seasonal adjusted inflation (CPI) and real GDP level 1986-2010

1-11. b. First difference of log seasonal adjusted inflation and real GDP 1986-2010

-8

-6

-4

-2

0

2

4

6

1980 1985 1990 1995 2000 2005 2010

UC cycleHP cycleChristiano-Fitzgerald cycle

20

40

60

80

100

120

1990 1995 2000 2005 2010

seasonal adjusted CPI level

600

650

700

750

800

850

900

1990 1995 2000 2005 2010

log seasonal adjusted real GDP*100

67

Figure1-12 Impulse responds functions on real output and inflation

Figure1-13. Blanchard-Quah output gap with HP and Christiano-Fitzgerald cycles

-2

0

2

4

6

8

10

86 88 90 92 94 96 98 00 02 04 06 08 10

first difference of log real GDPfirst difference of log CPI

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

5 10 15 20 25 30 35 40

Output response to demand shockInflation response to demand shock

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

5 10 15 20 25 30 35 40

Output response to supply shockInflation response to supply shock

68

Figure 1-14 Blanchard and Quah cycles based on MUC data and A&R data

Figure 1-15. The DdPS quarterly real GDP data and the MUC estimated quarterly real

GDP data

-8

-6

-4

-2

0

2

4

6

1980 1985 1990 1995 2000 2005 2010

HP cycleBlanchard-Quah cycleChristiano-Fitzgerald cycle

-8

-6

-4

-2

0

2

4

6

88 90 92 94 96 98 00 02 04 06 08 10

Blanchard-Quah cycle A&R dataBlanchard-Quah cycle MUC data

69

Note: The difference of levels is due to the difference of the base year setting of the two datasets. It will not

affect the VAR analysis, which uses first difference of the series.

2

3

4

5

6

7

8

9

78 80 82 84 86 88 90 92 94 96 98 00 02

Log real GDP_DdPSLog real GDP_MUC

-.01

.00

.01

.02

.03

.04

.05

.06

78 80 82 84 86 88 90 92 94 96 98 00 02

First difference of quarterly real GDP_MUCFirst difference of quarterly real GDP_DdPS

70

Chapter2. Permanent and Transitory Macroeconomic Relationships between the US

and China44

I. Introduction

In the midst of the recent global financial crisis, economic linkages between the US

and China, the largest developed country and the largest developing country respectively,

have become an especially hot topic in the media and among policy makers from both

countries. The nominal GDP of the US and China together accounted for 30% of total world

output in 2008 according to the World Bank Global Economic Monitor estimation. Terms

such as “Chimerica” (Ferguson and Schularick 2007) and “G2” were introduced recently to

describe the ties between the US and Chinese economies and the importance of their

relationship not only to each other, but also to the world economy.

Although bilateral trade and the macroeconomic imbalances experienced by both

countries have been more discussed in the relationship of the US and China, linkages

between these two economies are now substantial in many respects. The two countries have

mutually benefitted from cross-country trade and investment. Concerns, however, have

arisen for both countries due to their close economic linkages. Questions from the US

include: Is China a threat to the US economy? Will the growth of China hurt the

competitiveness of the US? (US Congress research report 2007).45 Questions for China

might be: How is its economic performance affected by the US business cycle and economic

44 The second chapter is based on joint work with Tara M. Sinclair that is currently under revision and resubmission to

the Journal of International Money and Finance. 45 Although the US is still near the top of the list according to the Global Competitiveness Report (World Economic

Forum 2009), China has quickly climbed into the top 30. The US lost its top competitiveness ranking in the World Economic Forum’s Global Competitiveness Report 2009-2010 to Switzerland. The US dropped to second due to the impact of the financial crisis on its financial markets and macroeconomic stability. China inched up from 30 to 29 in the 2009 report.

71

policy? Are the high growth rates China experienced since the economic reform sustainable?

Maintaining a relatively high and stable growth rate is considered to be the top priority for

successful economic reforms and political stability in China. A better understanding of how

the two economies react and interact with respect to macroeconomic shocks is important to

answer the above questions for stake holders from both nations.

Economic theories on economic fluctuations and growth, including real business

cycle theory, Keynesian theory and monetarism, all suggest that economies react differently

to permanent shocks with long run effects than to transitory shocks whose effects dissipate in

the short run. Understanding the relative role of permanent versus transitory movements in

the macroeconomic fluctuations of these two countries and the connections between them is

thus important for economists, forecasters, and policy makers. This paper investigates the

relationships between the macroeconomic fluctuations of the US and China. We do this by

estimating the permanent and transitory components for each country’s real GDP while

allowing for within and cross-country correlations between the permanent and transitory

shocks.

Different economies may experience different types of shocks as well as react

differently to those shocks. Shocks can be shared or transmitted across countries through

trade and financial linkages, through similar economic experiences, or through “contagion”46,

where shocks appear to be transmitted across countries even though there is no fundamental

reason for the transmission. Proper identification and better understanding of the relationship

of the permanent and transitory components of the economic dynamics between the

economies is thus important for proper long term and short term strategy and policy making

46 http://www1.worldbank.org/economicpolicy/managing%20volatility/contagion/definitions.html

72

on the economic relationships between the economies. The issue is of particular importance

for the study of macroeconomic relationships between the US and China. An improved

understanding of the patterns of long term competitiveness and productivity and short term

fluctuations may lead to different domestic and foreign economic and political policies which

influence not only the economic development and future relationships of the two giants but

also the rest of the world.

The model employed in this paper is a two-country correlated unobserved

components model based on the correlated unobserved component model proposed by

Morley, Nelson and Zivot (2003, hereafter MNZ) and extended by Sinclair (2009) and Mitra

and Sinclair (2009). It is estimated with quarterly real GDP data of the two countries from

1978 through 2008. The model specifically allows us to distinguish cross-country

correlations driven by the relationships between permanent innovations, caused by real

shocks such as changes in technology and economic and social institutions, from those

between transitory or cyclical movements, caused by changes in aggregate demand or

monetary shocks in the two countries. The model also allows us to explore the role of

information from the dynamics of each country in identifying fluctuations in the other

country. Bivariate models with alternative information sets are estimated for comparison

purposes.

The structure of the rest of the paper is as following: Section II reviews the related

literatures. Section III presents the econometric models and methods applied. Section IV

discusses the data used in this paper. Section V presents the results of the model estimation.

Section VI concludes.

II. Literature Review

73

2.1 Literature on the Method

Empirical studies examining the macroeconomic relationships across economies

generally apply one of three major approaches. The first method estimates correlations of the

time series of macroeconomic variables or correlations of their filtered cyclical and/or trend

components. The second widely used approach applies vector auto regression (VAR) models

to investigate the co-movement of economic fluctuations among the economies. The third

approach is to use a factor model to capture the correlation among economies in a common

factor or factors.

The first method is the simple correlation method, based either on classical

correlation, which estimates a static correlation between time series, or dynamic correlation

(Croux et al 2001), which takes into consideration the frequency of the business cycles. This

method is very limited and depends heavily on the decision on how to handle the

nonstationarity which is regularly found in macroeconomic time series data. Competing

econometric tools have been developed to decompose macroeconomic series such as the

aggregate output into “trend” and “cycle”, or permanent and transitory components. Among

them, the most widely used univariate methods include the Hodrick and Prescott (1997, HP)

filter, the Baxter and King (1987, BP) filter, the Beveridge and Nelson (1981)

decomposition, and the unobserved components models (Harvey 1985, Clark 1987, and

MNZ 2003). These methods, however, tend to produce very different estimates of trend and

cycle, thus we may find very different correlations depending upon the detrending approach

used. Researchers often report the correlation only for the detrended series, which ignores

the possibility of correlation across permanent shocks. Furthermore, the most commonly

used HP and BP filters are known to be problematic when applied to non-stationary series

74

such as the level of GDP for most countries (Cogley and Nason, 1995; Murray, 2003). In

addition, for this method trends and cycles are first estimated and then the correlation

between these estimated components is estimated in a second stage, which is inferior to

directly estimating the correlation at the same time as estimating the components. As an

alternative to filtering the data, first differenced data can be used, but then again information

is lost and the correlation may reflect a combination of the permanent and transitory

relationships.

The VAR approach on the other hand can be used to identify the effects of underlying

structural shocks, such as monetary and technology shocks, across economies, which can be

much more informative than simply identifying permanent and transitory correlations.

However, structural identification of shocks is sensitive to the identification assumptions of

the structural model. Furthermore, this approach depends on cointegration for finding long

run co-movements in series with unit roots (Granger 1983, Engle and Granger 1987, Vahid

and Engle 1993, Stock and Watson 1988). Highly correlated time series are not necessarily

restricted as cointegrated or having common trend and common cycle. Everaert (2007) finds

that a long run relationship without cointegration may exist between two series using

unobserved components model. As the correlation method, first differencing, which is often

used alternatively to render data stationary for VAR estimation, loses valuable information

about the data and again confounds the role of permanent and transitory shocks.

The third empirical method uses a dynamic factor model (Gregory, Head, and

Raynauld 1997; Forni, Hallin, Lippi, and Reichlin 2002; Forni and Reichlin 2001, Kose,

Otrok, and Whiteman 2003). These models typically assume the existence of a common

factor or factors to capture the cross-country correlation. This assumption may affect the

75

results. Again, these models are often applied to first-differenced data, losing information in

a similar way as for the other two methods.

The two-country correlated unobserved components model applied in this paper does

not require any prior transformation or detrending of the data and places fewer restrictions

among the series. We thus avoid the above problems in simple correlation, VAR, and

dynamic factor methods. In particular, our method combines the detrending and correlation

estimation into a single stage which improves both the estimates of the trend and cycle as

well as the estimates of the correlations. The model is an extension of the univariate

correlated unobserved components model which has been applied to the output fluctuation

analysis of the US and Canada (Basistha 2007, Morley, Nelson, and Zivot 2003). Similar

multivariate models have been applied to macroeconomic variables within single economies

such as the US and Canada (Basistha 2007, Morley 2007, Sinclair 2009), and cross countries

study for G7 countries (Mitra and Sinclair 2009). Furthermore, this model nests many of the

common detrending methods (Trimbur and Harvey, 2003) and is thus more general than

selecting a more restrictive model.

2.2 Studies on the Relationship of Macroeconomic Fluctuations of the US and China

with Other Countries

The US, as the largest economy in the world, is no doubt influential on the rest of the

world. Research on the relationship of macroeconomic fluctuations of the US with other

countries is rich and has generally focused on the correlations across industrialized countries,

mainly among G7 countries and OECD countries. The literature has documented a high

degree of correlation of the US business cycle with other industrialized countries in key

macroeconomic variables (e.g. Kose, Otrok and Whiteman, 2003). Empirical studies on the

76

relationship of the US economic fluctuations with developing countries, concentrated on

Latin American countries, show unsurprisingly strong linkages given the heavy dependence

of these countries on the US economy and the large commodity or tourism trade, as well as

capital and labor flows (e.g. Samuel and Sun 2009). On the trend of the business cycle

correlations, Heathcote and Perri (2003) examined the correlations of HP filtered, first

differenced and high-band pass filtered macroeconomic time series between the US and the

other 15 developed countries. Their study documents that the US economy has been less

synchronized with the fluctuations of the rest of the developed world since 1960 due to

change in the nature of real shocks and the increase of global financial integration.

China, as the largest developing and transitional economy, has been studied mostly

with the Asia and Pacific economies in terms of business cycle synchronization. These

studies are based on the economic integration of the region and the discussion of Optimal

Currency Area (OCA) for the region (Genberg, Liu and Jin, 2006). Trade has been

recognized as the major determinant of the output fluctuation correlation of China with other

East Asian and Pacific economies (Sato and Zhang 2006, Shin and Sohn 2006). Beyond the

region, Calderon (2007) finds increasing output co-movement of China’s output fluctuation

with Latin America countries along with the growing trade integration among the countries.

2.3 Studies on the Relationship of Macroeconomic Fluctuations of the US and China

Among the limited literature that addresses the US and China output fluctuation

correlations, Fidrmuc and Batorova (2008), using quarterly CPI deflated GDP data from

1992-2006, analyses the dynamic correlations of China’s business cycles with selected

OECD countries under different cyclical frequencies. They find that the US has a positive

correlation with China in both long run cycles (over 8 years) and short run cycles (less than

77

1.5 years). Qing (2002) and Chen (2004) 47, using classical correlation techniques, document

the business cycle correlations of China with the US, Japan and select European developed

countries and find positive weak correlation between the output fluctuations of the US and

China, while the correlations between China and Japan and the European countries are

negative. Zhang (2006) investigates the correlations over different sample periods and finds

that the US and China business cycle correlation is stronger during the recent years. Ren and

Song (2004) and Keidel (2008) find there is no correlation between the US and China after

1990 and China’s economic growth has been motivated mainly by domestic factors. In

addition to connections through aggregate output, there are increasing discussions

theoretically on the linkages of the two economies in macroeconomic variables such as

savings and consumptions, trades, finance and money supply (Ferguson and Schularick 2007;

Yang, Askari, Forrer and Teegen 2004; and Johansson 2009).

2.4 Contribution of this paper

This paper is the first study that applies the multivariate correlated unobserved

components model, a more general model with less restrictions and priors than the simple

correlation and VAR approaches, to investigate economic relationships of two economies at

different development levels and with more divergent economic structures. The relationship

between the macroeconomies of the US and China is for the first time viewed through the

lens of permanent and transitory components in the fluctuations of real output of the two

countries through our model. First, we present new properties of the permanent and transitory

US output fluctuations with information from China’s output movements which may carry

information not well studied and understood and different from the information provided by

47 Published in Chinese.

78

developed countries. Second, this paper also contributes to the limited literature on empirical

studies on properties of China’s macroeconomic fluctuations with a reasonably long sample

of quarterly data.

79

III The Model

This paper applies a two-country correlated unobserved components model similar to

Sinclair (2009) and Mitra and Sinclair (2009) to distinguish the correlation of the permanent

shocks to output of US and China, separately from the correlation of the transitory shocks.

The model simultaneously decomposes each output into a stochastic trend, or permanent

component, and a stationary transitory component. The trend, or permanent component, is

assumed to be a process of random walk with drift (Stock and Watson 1988) in order to

capture the steady-state level or long term potential output of the economy. The transitory

component, defined as real GDP deviations from the permanent trend, is assumed to be

stationary following a second order autoregressive process, or AR (2). The two-country

approach enables us to: 1) identify the correlation of the shocks to permanent and transitory

components of real output for each economy with information of dynamics of the other in

order to examine the linkages of permanent shocks and transitory shocks between the two

economies, and 2) obtain new estimates of the permanent and transitory components for each

country using the information of the other country.

Note that the transitory component captures transitory deviations (Morley and Piger

2009) from the permanent or steady state level, which may be fundamentally different from

the traditionally defined business cycle. The traditional business cycle is often isolated from

the series with a filter such as the Hodrick-Prescott (HP) or Band-Pass (BP) filter. In this

paper, we follow a more general definition of permanent and transitory components, which is

associated with the Beveridge and Nelson (1981) decomposition and the Harvey (1985) and

Clark (1987) unobserved components models. The permanent component, or the trend,

follows a stochastic process (a random walk with drift in the model) rather than a fixed or

80

pre-determined path. The transitory component is stationary and deviated from the stochastic

trend, rather than the traditional “alternating-phases” defined (Morley and Piger 2009)

cyclical component. The notion is more general than the traditional definition in that it avoids

any prior determination of appropriate business cycle frequencies. This is particularly

important for macroeconomic fluctuations of developing countries such as China, which may

not experience typical traditional business cycle fluctuations. Under the “transitory-

deviation” definition, the permanent and transitory components of the economic fluctuations

can be directly formulated in structural time series models (Harvey 1993), cast in state space

form and estimated using the Kalman filter or smoother.

The measurement equation of our model is:

ititit cy +=τ , 2,1=i , (1)

where τit is the unobserved trend component and cit is the unobserved cycle component for

country i.

The transition equations are:

ititiit u ηττ ++= −1 , (2)

ititiitiit ccc εφφ ++= −− 2211 , (3)

where itη and itε are assumed to be normally distributed (i.i.d) with mean zero. There are no

restrictions on the correlations between any of the contemporaneous shocks, i.e. no

restrictions are imposed on the variance-covariance matrix, which allows us to estimate all

potential contemporaneous correlations within and across series.

81

The variance-covariance matrix is:

==Σ

2

2

2

2

ccuscccus

cusususcusus

ccuscccus

cusususcusus

εεεεηεη

εεεεηεη

εηεηηηη

εηεηηηη

σσσσσσσσσσσσσσσσ

(4)

We cast equations (1)-(3) into state space form and estimate the unobserved

components and the parameters of the model using the Kalman filter and maximum

likelihood in GAUSS. The unobserved components are estimated with the Kalman

smoothing algorithm, which uses information from the whole sample period, i.e. the future

data as well as the past data. In the results, we will show that the smoothed components are

different from filtered estimates.

IV The Data

The model is estimated with quarterly real GDP data of the US and China from

1978q1 to 2009q4. The Chinese data are from the National Bureau of Statistics of China

(NBS), the nation’s statistical authority. For quarterly real GDP before 1992, when quarterly

real GDP data were not published officially, the data are disaggregated from annual data

using the Chow-Lin (Chow-Lin ,1971) related series method based on Abeysinghe and

Rajaguru (2004)48. The output data for the United States are seasonal adjusted quarterly real

GDP from the Bureau of Economic Analysis of the US Department of Commerce.

48 The disaggregation uses money supply and international trade data, both available at the monthly frequency.

Abeysinghe and Rajaguru’s Chinese disaggregation method is the only published temporal disaggregation estimation of china’s real GDP data for the period. This essay was drafted and submitted before the first Chapter, when A&R was the only available estimation for China’s quarterly real GDP from 1978-1991. In the first Chapter, I present that, although it is less efficient than the multivariate unobserved components disaggregation estimations provided by chapter 1, the A&R estimation is valid. The year 2000 is chosen as the base year because the inflation rate (CPI inflation) was close to zero during that year, which will minimize the distortion from inflation on the quarterly data within the base year.

82

Starting Date:

Although longer history would make our study more robust, the analysis of this paper

focuses on the output fluctuations starting from 1978 due to China’s economic institutional

structure change and the limitation of Chinese data availability. We choose the first quarter

of 1978 as the starting point for the following reasons. First, in 1978, Deng Xiaoping, the

former head of China’s Communist Party after the Cultural Revolution, initiated the market-

oriented economic reform and openness in China. Although the changes did not happen

overnight, the structure of the underlying economic institutions started to change in 1978.

The economy prior to 1978 was generally an autarky and centrally planned, and the

economic growth was interrupted by the political turmoil of the Great Leap Forward

movement and the Cultural Revolution. Along with the launch and implementations of

economic reforms, the post-1978 economy is increasingly market-oriented and open to the

rest of the world. The economic institutions after the start of the reforms has much greater

influence on China’s economic growth pattern now and in the foreseeable future than

economic institutions prior to these reforms. Secondly, the methods applied in this paper

require high frequency macroeconomic data, which are not available before 1978. Due to the

institutional problem mentioned above, we also cannot apply the same disaggregation

method to the period before 1978. Thirdly, the economic growth after 1978 shows an obvious

cyclical pattern (Liu, Zhang and Zhang 2005) which allows us to investigate the dynamics of

the trend and cycle with advanced econometric techniques that have been applied to the

output fluctuations of developed countries.

83

V. Estimation Results

Table 1 presents the classical correlations of the Hodrick-Prescott (HP) and Band-

Pass (BP) cycles and the growth rates of real GDP of the US and China over the entire

sample period. As documented in most of the existing studies, the cycles and growth rates of

the two economies are significantly and positively correlated through the sample period.

Note that the relatively high correlations of HP and BP cycles may be due to spurious cycles

generated by the detrending methods.

Table 2 reports the parameters of the maximum likelihood estimation of our two-

country correlated unobserved components model for the entire sample period, as well as the

parameters estimates from the related univariate model (MNZ model) for comparison.

5.1 Parameter Estimates

Estimates of the drift terms and autoregressive parameters for both countries are all

significant based on our two-country model. With information from the other economy, the

estimated parameters values for both countries are similar to the estimates from the

comparable univariate models.

5.1.1 The Drift Terms

Since each series is in logs and multiplied by 100, the estimated drift term multiplied

by 4 can be interpreted as the average annualized growth of the permanent component, or

trend of the real output in percentage within the sample period.

According to our two-country correlated model, the average annual real growth rates

of the US GDP is estimated as 2.5%, While China’s average permanent real growth rates is

as high as 9.0% annually.

84

We tested for structural breaks in the drift terms for each country using the Quandt-

Andrews unknown date Breakpoint tests (Andrews 1993), but we did not find any significant

structural breaks in our sample period.

5.1.2 The Autoregressive Parameters

The estimated autoregressive coefficients, which reflect the dynamics of the

transitory components, are similar across the different models. The sum of the autoregressive

coefficients, which provides a measure of persistence of the transitory components, shows

that China and the US both have relatively persistent transitory components, with a sum for

each country around 0.80.

5. 2 The Estimated Permanent and Transitory Components

Figure 1 shows the estimated permanent and transitory components of the real GDP

of the US and China based on our two-country uncorrelated UC model. We will discuss each

of these estimated components in the following subsections.

5.2.1 The Permanent and Transitory Components

As MNZ (2003) pointed out, additional information introduced by the real output of

the other country does affect the estimates of permanent and transitory components of each

country in the two-country model. The influences of the information of the other country

appear clearly in the transitory components.

Figure 2-1 compares the estimated US transitory component of the two-country

model with the univariate MNZ estimate. The transitory movements of the US real GDP

better correspond to the NBER-dated recessions (shaded areas of Figure 2-1) than the MNZ

cycle. China’s economic fluctuations introduce very different information for the US output

85

transitory movements than any of the real GDP of G7 countries, with information of which

the US transitory components do not change much. (Mitra and Sinclair, 2009)49.

The official dated economic slowdowns for China, which are represented by the

shaded areas50 in Figure 1-2, appear to correspond mainly to the significant downward

movement of the permanent component. Adding information from the US economic

fluctuation does not visibly change the amplitudes and movement pattern of the transitory

component of China (Figure4). China’s transitory economic fluctuations are not influenced

or forecasted (we do not discuss causality here) by the US real output fluctuations during the

sample period.

Note that China’s transitory movements shift to the left from the MNZ filtered

transitory component, which is equivalent to the Beveridge and Nelson decomposition (MNZ

2003)51. This is due to the Kalman smoothing method we apply in estimating the permanent

and transitory components52. Beveridge and Nelson and MNZ decompositions use the

Kalman filter to estimate the components. The Kalman filter is based on historic information

available up to time t. The Kalman smoothing used here is based on all available information

in the sample. With information from the future, the turning points for China’s transitory

component are estimated to occur earlier than when only information up to time t is used to

estimate the components.53

5.2.2 The Permanent and Transitory Standard Deviations 49 In an unpublished manuscript, Mitra and Sinclair have examined the role of information from a set of Latin

American countries and a set of Emerging Asian economies, and found that the estimated transitory component for the US does not change substantially with the inclusion of information from these countries.

50 To be consistent with the data used in chapter two, the shaded area in chapter two is based on the A&R data, which are slightly different from the MUC estimates in 1984-1985.

51 MNZ (2003) show that their model is equivalent to the Beveridge and Nelson decomposition in the univariate case. Sinclair (2009) shows that this equivalence no longer holds true in the multivariate case.

52 When using basic filter, the gaps between the tuning points disappear. 53 MNZ find that the smoothed and filtered estimates are qualitatively similar for their univariate model applied to US

real GDP.

86

Presented in Table 3, based on the estimates of the two-country model, the standard

deviation of permanent shocks is larger than the standard deviation of the transitory shocks

for both countries, which is consistent with the result from the univariate MNZ models. The

result implies that the trend or permanent components for both countries are much more

variable than the traditional HP and BP smoothed trends. Permanent shocks are relatively

more important than the transitory shocks for both countries. The volatility of China’s real

output fluctuations are higher than that of the US in both permanent and transitory

components.

Figure 2-1 and Figure 2-2 compare the transitory components of the two countries

from our model with the cycles from the HP filter, with λ=1600 for quarterly data. The

transitory components from our model are larger than HP cycles in magnitude for both

countries. It is possible in our case to have both more variable permanent components and

more variable transitory components, because allowing for correlation opens up the

possibility that there may be offsetting movements between the two components (if the

correlation is negative, as we find for both countries in our study).

With information from the other country, the ratio of standard deviations of

permanent shocks over that of transitory shocks are smaller than the univariate MNZ model

results for both countries, especially for the US. This finding is consistent with Cochrane’s

(1994) argument that if we include a series which provides information that increases the

long-horizon forecastability of another series, then we will find larger transitory variation

when we include that information.

5.2.3 Correlations between the Permanent and Transitory Shocks within Economy

87

Based on our two-country correlated UC model, the correlations between the

permanent and transitory shocks with-in economies of the US and China are both

significantly negative, -0.89 for the US and -0.97 for China (Table 4). The estimates are

consistent in the sign with the univariate MNZ model results but with smaller absolute value

for both countries. Note that the correlation of permanent and transitory shock for China is

nearly perfectly negative based on both models. Negative correlated permanent and transitory

shocks have been interpreted as due to slow adjustment of the actual output of the economy

to the permanent shocks on the output. As Stock and Watson (1988) and MNZ (2003)

explained, strongly negative correlation of the permanent shocks with the transitory shocks

implies that the economic fluctuations are driven mainly by permanent shocks, while the

permanent shocks immediately shift the long term path of the output, the short run

movements may include adjustments toward the shifted trend.

5.3 The US- China Relationship—Permanent and Transitory Correlations

Table 4 shows the estimates of the correlations of the permanent-permanent shocks,

the transitory –transitory shocks cross country and the permanent-transitory cross-

correlations. The correlations are estimated simultaneously with the components. We find

that the real GDP of US and China are positively correlated in both permanent shocks (0.56)

and transitory shocks (0.60). The two giants are closely related in both long run and short run

economic fluctuations and share about half of the permanent and transitory shocks. The

values of the correlations are higher than correlations for the US with Japan, Italy, Germany

and France, and only smaller than the US with UK and Canada based on similar multivariate

models (Mitra and Sinclair 2009).

88

5.3.2 Information Carried by the Chinese Real Output to the US Transitory

Components

Figure 3 shows that the bivariate model estimation of the US transitory components

with the real GDP of China are very different from that with other economic variables. The

magnitude of the movement of the US transitory components is enlarged and the turning

points correspond much more directly to the NBER-dated recessions as compared to the

univariate result. In other studies, such as Mitra and Sinclair (2009), Morley (2007), and

Sinclair (2009), the estimated transitory component for US real GDP changes little when

other variables are included in the model. We apply the same bilateral model of US real

GDP with real GDP of Canada, the biggest trade partner of the US, and do not find larger

transitory components for US (Figure 3-2). Following Cochrane’s (1994) argument, the

Chinese real output appears to carry information relevant for forecasting US real GDP which

is not in the GDP data of developed economies such as the G7 (Mitra and Sinclair, 2009) or

in other US data series such as the unemployment rate (Sinclair, 2009) or consumption

(Morley, 2007).

Hamilton (2008) suggests that the US economic fluctuations are mainly driven by the

changes of oil price, which influenced by the increasing energy demand from rapidly

growing China. Estimating a bivariate correlated UC model with the US real GDP and the

world oil price for the same period, we get larger transitory movements for the US real GDP

but the effects are not as big as that from China.

One exception to the finding of a small transitory component for US real GDP is

Basistha and Nelson’s (2007) correlated unobserved components model of GDP, inflation,

and the unemployment rate. Their finding, when compared to the finding of Sinclair (2009)

89

which includes just GDP and the unemployment rate, suggests that inflation may provide

additional forecasting information for US real GDP. Therefore, we estimate another

bivariate model of inflation (measured as the US GDP deflator) with US real GDP. In this

case, the transitory component of US real GDP is smaller in magnitude than the estimation

with oil price, and therefore much smaller than when we use the Chinese data.

Figure 3-1 compares the different estimated transitory components of US real GDP

from four different models: 1) a bivariate model with Chinese real GDP, 2) a bivariate model

with the oil price, 3) a bivariate model with inflation, and 4) a univariate model.

5.3.3 Stability of China’s Transitory Component ---Comparing with Other Bivariate

Models

As discussed by Cochrane (1994), transitory variation, which is mean reverting, is the

forecastable component of the series. The permanent component, which is assumed to follow

a random walk with drift in our model, is the unforecastable component.

Similar to our exercise for the US, we next explore relevant alternative series and

estimate three additional bivariate models with China’s real GDP. Figure 4 compares the

estimated transitory components of China’s real GDP from bivariate models with 1) the US

real GDP; 2) China’s export to the US; 3) real GDP of Hong Kong; 4) Oil Price54. We also

include the estimated transitory component from the MNZ univariate model. None of the

additional series appears to change the magnitude of the transitory variation of China’s real

GDP from the univariate MNZ model, which uses information from China’s lagged real GDP

only. Among the series, China’s transitory component generated with real GDP of Hong

Kong is the most similar to the univariate transitory component.

54 Data resources of the series are: Direction of Trade, International Monetary Fund(China’s export to the US); Census

and Statistic Department of Hong Kong Government (Real GDP of Hong Kong); Wall street Journal (Oil Price)

90

Possible interpretations for the stability of China’s transitory components across

different bivariate models55 could be: first, most of the external shocks are permanent shocks

to China which are not forecastable and thus do not change the transitory components;

secondly, Domestic factors such as domestic demand or monetary policy may be the major

sources of China’s real GDP fluctuations, thus external information sets do not provide much

forecasting information; thirdly, China’s macroeconomic controls or adjustment policies

could have largely isolated the external shocks from greatly influencing the macroeconomic

performance of the country.

5.4 Where are the “G2” now? ----the Recession since 2007

Based on our estimates, both China and the US experienced a large (in absolute

value) negative permanent shock in 2007 which lowered their respective trends. The real

output levels of the two countries at the end of 2008 are both above the permanent trend

(positive in the transitory components) and on the way to converge down to the permanent

path. Since the transitory components are the differences between the series and the

permanent component, the slow adjustment of the actual real GDP levels to the trend after

the big negative shock leaves the transitory components peaking at the beginning of the

recession.

VI Conclusion

In this paper, we estimated a two-country correlated UC model for the real GDP of

the US and China with quarterly data from 1978 through 2008. Our model permits us to

examine both the within-country long term and short term properties of the output

55 We do not apply domestic information sets because: first, availability of quarterly data of domestic economic

indicators for our sample period are very limited , and second, the data construction of the data before 2000 has used the total international trade and money supply--the only quarterly available series.

91

fluctuations of the two countries and the cross-country relationship of the two giant

economies simultaneously. The estimation result also reveals the relative importance of

permanent versus transitory movements in the relationship.

We find that the economic fluctuations of the US and China, are significantly

positively correlated for both permanent and transitory shocks. The two countries share about

half of the shocks both in the long run trend and short run movements. The US transitory

components estimated with China data are very different from that estimated with other

information sets such as inflation, GDP of other developed countries and the oil price.

Estimates of China’s permanent and transitory components do not change too much with

information from the US and alternative external information sets as well, which suggests

that domestic factors may be the major drivers of China’s real GDP fluctuations.

92

Tables and Figures

Table2-1. Correlations of cycles of the US and China real GDP with HP, BP

decomposition and the growth rates Quarterly Data, 1978.1 – 2008.4

Growth Rates* HP Cycles

(lamda=1600)

BP Cycles

(cycle periods

6-32)

YOY

growth

rates**

0.12 0.39 0.44 0.32

*The growth rate is defined as the first difference of the log of real GDP for the US and China. **YOY growth rates: Year on Year growth rate is defined as log changes from same quarter the previous year,

which is often used by literatures published in Chinese. 100)log( ×= realGDPyt Year on year growth

rates 4−−= ttt yyg

Table 2-2. Estimation Results

Model 1 Univariate MNZ

US

(SE)

China

(SE)

US MNZ

(SE)

China MNZ

(SE)

Drift 0.6773

(0.0996)

2.2599

(0.1715)

0.7112

(0.1006)

2.2200

(0.1665)

phi1 1.2520

(0.0394)

1.2610

(0.0806)

1.3601

(0.0983)

1.3240

(0.0798)

phi2 -0.4081

(0.0331)

-0.4612

(0.0632)

-0.6160

(0.0404)

-0.5324

(0.1362)

Log

Likelihood: -288.127 -134.589 -173.023

93

Table 2-3. Standard Deviations of Shocks

Model 1 US MNZ China MNZ

US Permanent 1.0795 (0.0507)

1.1160 (0.2261)

China Permanent 1.8844 (0.0876)

1.8517 (0.4870)

US Transitory 0.9648 (0.0612)

0.7947 (0.1274)

China Transitory 0.7947 (0.1274)

1.1925 (0.6346)

US Ratio Perm/Trans

1.1189 1.4043

China Ratio Perm/Trans

1.4981 1.5529

Table 2-4. Correlations of Permanent and Transitory Shocks

Model 1 US MNZ China MNZ

Permanent shocks China – US

0.5554 (0.2156)

Transitory shocks China – US

0.5972 (0.1038)

Permanent US with Transitory China

-0.6994 (0.1673)

Permanent China with Transitory US

-0.5492 (0.1023)

Permanent US with Transitory US

-0.8859 (0.0747)

-0.9738 (0.1195)

Permanent China with Transitory China

-0.9690 (0.0040)

-0.9999 (0.0001)

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Figure 2-1: Estimated permanent and transitory components.

Figure 2-1-1 : The US

Note: Shaded areas are NBER-dated recessions.

-6

-4

-2

0

2

4

6

840

860

880

900

920

940

1980 1985 1990 1995 2000 2005 2010

US Transitory Component US Permanent ComponentUS Ln(Real GDP) *100

95

Figure2- 1-2: China

Note: Shaded areas are economic growth slowdown periods recognized by China’s Academy of Social Science

based on annual real growth rates. (Liu 2004) The periods start at the time with peak high growth rate and end

at trough. The quarterly point of peak and troughs are based on the A&R data used in the estimation.

-8

-4

0

4

8

700

750

800

850

900

950

1,000

1980 1985 1990 1995 2000 2005 2010

Transitory ComponentPermanent ComponentChina ln(RealGDP)*100

96

Figure 2-2 Transitory Components Comparison

2-2-1 US Transitory Component: Comparing with HP Cycle

2-2-2 China Transitory Components: Comparing with HP Cycle

-6

-4

-2

0

2

4

6

1980 1985 1990 1995 2000 2005 2010

US Transitory componentUS HP cycle

-8

-6

-4

-2

0

2

4

6

8

1980 1985 1990 1995 2000 2005 2010

China Hp cycleChina Transitory Component

97

Figure2- 3. US Transitory Component Comparing Different Information Sets

2-3-1 US Transitory Components Comparing: Univariate. with China, with Inflation and

with Oil price

-6

-4

-2

0

2

4

6

1980 1985 1990 1995 2000 2005 2010

US Transitory Component MNZUS Transitory Component with InflationUS Transitory Component with OilUS Transitory Component with China

98

2-3-2 US Transitory Component Comparing: with China vs. with Canada

-6

-4

-2

0

2

4

6

1980 1985 1990 1995 2000 2005 2010

US Transitory Component with ChinaUS Transitory Component with CanadaUS MNZ Transitory Component

99

Figure2- 4 China Transitory Components with Different Information Sets

-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

10.0

1980 1985 1990 1995 2000 2005 2010

China Transitory Component with USChina Transitory Component with China export to USChina Transitory Component with HKChina Transitory Component with Oil PriceChina Transitory Component MNZ

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Chapter3. Permanent and Transitory Macroeconomic Relationships between China

and the Developed World56

1. Introduction

Although research on business cycles and economic growth has traditionally focused

on developed countries, there is increasing interest in the economic fluctuations of

developing countries. In particular, policymakers and researchers have focused on the

growing importance of China, the largest developing country, within the global

macroeconomic environment. In chapter two I explored the connection between the macro-

economic fluctuations of China and the US. This paper extends that analysis to examine the

relationships between the real GDP of China and that of developed countries more generally.

In terms of the discussion about China’s modern role in the global economy, much of

the focus has been placed on China’s connection with the US, given that they are the largest

developing and developed economy respectively, and on China’s connection with

neighboring Asian and Pacific economies. Most research in terms of business cycle

synchronization has focused on the relationships of China with Asian and Pacific economies.

These studies are based on regional economic integration and the discussion of the possibility

of an Optimal Currency Area (OCA) for the region (Genberg, Liu and Jin, 2006). Trade has

been recognized as the major determinant of the output fluctuation correlation of China with

other East Asian and Pacific economies (Sato and Zhang, 2006, Shin and Sohn, 2006).

Beyond the region, Calderón (2007) finds increasing output co-movement of China’s output

56

The third chapter is based on the joint work with Tara Sinclair prepared for the CESifo Venice Summer Institute workshop on “The Evolving Role of China in the Global Economy” and to be published in a conference volume by MIT press.

101

fluctuation with Latin America countries along with the growing trade integration among the

countries.

Much has also been made of the “special relationship” between China and the US,

with terms such as “G-2” and “Chimerica” (Ferguson and Schularick 2007). China is,

however, also tightly connected with developed countries other than the US. For example,

although the US has been China’s largest single country trade partner since the 1990s, Japan,

South Korea, and Germany are also large trade partners with China. In total, developed

countries comprise the majority of both China’s export and import sources, but the US

comprises less than 25%. According to the IMF direction of trade database, the US averaged

only 20% of China’s export market between 2000 and 2009, but the remaining six countries

of the G7 were another 22% of China’s export market and the remaining members of the

developed OECD countries[57] were another 10% (OECD other countries account for 7%).

In terms of imports, the US on average supplies only 8% of China’s imports, whereas

the remaining countries of the G7 supply an additional 24% and the remaining developed

OECD members another 7%. There is limited literature that addresses the output fluctuation

correlations between China and developed countries. Fidrmuc and Batorova (2008), using

quarterly CPI deflated GDP data from 1992-2006, analyze the dynamic correlations of

China’s business cycles with selected OECD countries under different cyclical frequencies.

They find that despite the increasing trade and financial links between China and other 57 The developed OECD countries include the 25 OECD members in the aggregate data: Australia, Austria, Belgium,

Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, Turkey, United Kingdom and United States. The developing OECD members include: the Czech Republic, Hungary, Korea, Poland, the Slovak Republic, and Mexico. The data do not include Chile, Slovenia and Israel, new members that joined the OECD after May of 2010.

102

economies, China’s business cycle behaves differently from most other economies. Non-

European OECD countries such as the US, Korea, Australia, and Japan, which have more

intensive economic linkage with China, show relatively high positive correlation of long run

cycles (over 8 years). In general, the dynamic correlations tend to increase in more recent

years. The US has a positive correlation with China in both long run cycles (over 8 years)

and short run cycles (less than 1.5 years). Qing et al (2002) and Chen et al. (2004), using

classical correlation techniques, document the business cycle correlations of China with the

US, Japan, and select European developed countries and find positive weak correlation

between the output fluctuations of the US and China, while the correlations between China

and Japan and the European countries are negative. Zong (2007), using a VAR model on

annual data of China’s GDP, G7 countries aggregate GDP and China’s FDI, reports that G7

GDP Granger-caused the fluctuation of China’s FDI and China’s GDP, while there is no

evidence for an effect in the opposite direction. Lowe (2010) shows that the rolling

correlation of real quarterly growth of China and Australia outpaces the correlation between

growth of the US and Australia since 2000. Fidrmuc and Korhonen (2010) show that

business cycle correlations between China and developed countries are zero on average.

Given the increased emphasis on China’s role in the global economy, it is important

to further investigate the nature of the relationships between China and the developed

countries. In particular, this paper focuses on China’s relationship with two different

aggregate measures for developed economies, the G7 and the OECD. The model employed

in this paper is based on the two-series correlated unobserved components (UC) model

employed in the second chapter (Jia and Sinclair, 2009) which was applied to examine the

relationships between China and the US. The model was developed in Sinclair (2009) as a

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two-series extension of the correlated unobserved component model proposed by Morley,

Nelson and Zivot (2003, hereafter MNZ). Similar multivariate UC models have been applied

to macroeconomic variables within single economies such as the US (Morley 2007, Sinclair

2009) and Canada (Basistha 2007) and for an aggregate of the euro-zone countries (Berger,

2011). The model has also been applied for a cross-country study of the real output

fluctuations of the G7 countries (Mitra and Sinclair, forthcoming). The model specifically

allows us to distinguish cross-country correlations driven by the relationships between

permanent shocks, caused by real shocks such as changes in technology and economic and

social institutions, from those between transitory or cyclical movements, caused by changes

in aggregate demand or monetary shocks. The model also allows us to explore the role of

information from the dynamics of each series in identifying fluctuations in the other series.

The correlated unobserved components model applied in this paper does not require any prior

transformation or detrending of the data and places fewer restrictions among the series than

other models. In particular, our method combines the detrending and correlation estimation

into a single stage which improves both the estimates of the trend and cycle as well as the

estimates of the correlations. Furthermore, this model nests many of the common detrending

methods (Trimbur and Harvey, 2003) and is thus more general than most other methods.

Two different estimates are presented: one with quarterly real GDP data for China

with aggregate real GDP for the G7 countries and the other with quarterly real GDP data for

China with aggregate real GDP for the 25 OECD member countries. Both models are

estimated with quarterly data from 1978 through 2009.[58] We also compare these estimates

58 We also estimated two additional models for robustness. One was a model for a 30-country OECD aggregate. The

other was for a subsample from 1992-2009 to consider only the officially reported quarterly real GDP for China. The estimates were both quantitatively and qualitatively similar to those reported in this chapter. These estimates are available from the authors upon request.

104

with those based on a univariate unobserved components model of Chinese real GDP as well

as a trivariate model of the real output of China, the US, and Japan. To preview the results,

we find that China has little connection with the developed world aggregate. We cannot

reject that there is no cross-series correlation, and the estimates of the components for both

China and the developed world aggregates are not substantially different from the findings

based on univariate models. The results are similar whether we use the G7 or the OECD

aggregate.

The structure of the rest of the paper is as following: Section 2 presents the

econometric model and estimation method. Section 3 discusses the data used in this paper.

Section 4 presents the results of the model estimation. Section 5 concludes.

II. the Model

This paper applies a two-series correlated unobserved components model similar to

Sinclair (2009) and Jia and Sinclair (2009) to distinguish the correlation of the permanent

shocks to output of China from permanent shocks to aggregate developed country output (in

one model measured as an aggregate of OECD countries and in the other measured as an

aggregate of the G7 countries), separately from the correlation of the transitory shocks. The

model simultaneously decomposes each output series into a stochastic trend, or permanent

component, and a stationary transitory component. The trend, or permanent component, is

assumed to be a random walk with drift (Stock and Watson 1988) in order to capture the

steady-state level or long term potential output of the economy. The transitory component,

defined as real GDP deviations from the permanent trend, is assumed to be stationary

following a second order autoregressive process, or AR (2). The two-series approach enables

us to: 1) identify the correlation of the shocks to permanent and transitory components of real

105

output for each series with information from the dynamics of the other, in order to examine

the linkages of permanent shocks and transitory shocks between the two economies, and 2)

obtain new estimates of the permanent and transitory components for each series using the

information of the other series.

This model is general enough to be applied to cointegrated series, but it does not

require cointegration or common trends. The model allows any amount of correlation

between permanent shocks to the series, from zero correlation to a common trend. If the

series do share a common trend, then cointegration can be imposed in this framework to

improve the efficiency of the estimates (Morley, 2007). Johansen Cointegration tests were

applied to our series for both models and we cannot reject the null of no cointegration

allowing for either a constant or a linear deterministic trend in our data. We thus do not

impose cointegration in the model.

It is important to note that the transitory component captures transitory deviations

from the permanent or steady state level, which may be fundamentally different from the

traditionally defined business cycle (Morley and Piger, forthcoming). The traditional

business cycle is often isolated from the series with a filter such as the Hodrick-Prescott (HP)

or Band-Pass (BP) filter. In this paper, we follow a more general definition of permanent and

transitory components, which is associated with the Beveridge and Nelson (1981)

decomposition and the Harvey (1985) and Clark (1987) unobserved components models. The

permanent component, or the trend, follows a stochastic process (a random walk with drift in

the model) rather than a fixed or pre-determined path. The transitory component is stationary

and is defined as the deviation from the stochastic trend, rather than the alternative definition

of a cycle that captures alternating phases. The notion is more general than the alternating-

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phases definition in that it avoids any prior determination of appropriate business cycle

frequencies. This is particularly important for macroeconomic fluctuations of developing

countries such as China, which may not experience typical traditional business cycle

fluctuations. Under the “deviation from trend” definition, the permanent and transitory

components of the economic fluctuations can be directly formulated in structural time series

models (Harvey, 1993), cast in state space form, and estimated using the Kalman filter for

maximum likelihood estimation (MLE) of the parameters using prediction error

decomposition.

The measurement equation of our model is:

ititit cy +=τ , (1)

where τit is the unobserved trend component and cit is the unobserved cycle component for

series i (where i=DW represents the aggregate for the developed world and i = C represents

China).

The transition equations are:

ititiit u ηττ ++= −1 , (2)

ititiitiit ccc εφφ ++= −− 2211 , (3)

where itη and itε are assumed to be normally distributed with mean zero. There are no

restrictions on the correlations between any of the contemporaneous shocks, i.e. no

restrictions are imposed on the variance-covariance matrix, which allows us to estimate all

potential contemporaneous correlations within and across series.

The variance-covariance matrix is:

107

=Σ

2

2

2

2

ccDWcccDW

cDWDWDWcDWDW

ccDWcccDW

cDWDWDWcDWDW

εεεεηεη

εεεεηεη

εηεηηηη

εηεηηηη

σσσσσσσσσσσσσσσσ

(4)

We cast equations (1)-(3) into state space form and estimate the unobserved components and

the parameters of the model using the Kalman filter and maximum likelihood in GAUSS.

The unobserved components are estimated with the Kalman smoothing algorithm, which uses

information from the whole sample period, i.e. the future data as well as the past data.[59]

III. the Data

The model is estimated with quarterly real GDP data for China and a developed

country aggregate from 1978 through 2009. The Chinese data are from the National Bureau

of Statistics of China (NBS), the nation’s statistical authority.[60] Our study focuses on the

real output fluctuations since 1978, when China embarked on the market-oriented and

openness economic reform. Our data include the most recent official revisions for 2005

through 2009 based on the information collected through the second economic census

completed at the end of 2009. For quarterly real GDP before 1992, when quarterly real GDP

data were not published officially, the data are disaggregated from annual data using the

Chow-Lin (1971) related series method based on Abeysinghe and Rajaguru (2004).[61] Their

disaggregation uses money supply and international trade data, both available at the quarterly

59 The smoother does produce different estimates of the components as compared to the filter, particularly for Chinese real

GDP. The cycle based on the smoothed estimates is substantially larger. Results for the filtered estimates are available from the authors upon request. 60

The official data are published as cumulated year on year growth rate at comparable price. Data from 1992-2005 are from

the publication of National Bureau of Statistics of China: Historical Data on China Quarterly GDP Estimator 1992-2005, 2/2008 China Statistics Press ISBN/ISSN 9787503753565 61

The year 2000 is chosen as the base year because the inflation rate (CPI inflation) was close to zero during that year,

which will minimize the distortion from inflation on the quarterly data within the base year.

108

frequency, as related series. Abeysinghe and Rajaguru estimate the quarterly growth rates of

real GDP for 1978 through 1994 based on the estimated relationship of annual real GDP

growth rates and the related series from 1978 through 1996.[ 62 ] The results of the

disaggregation are tested by the authors through model fitting and out-of-sample forecast

evaluation. The Abeysinghe and Rajaguru estimates are the only published estimates of

quarterly real GDP data for China for this period. The data allow us to investigate the

relationship of the Chinese economy with the developed world since it started to integrate

with the world economy. This longer time series provides more information on China’s

macro-economic fluctuations and improves the efficiency of the estimation. To investigate

the possible irregularity caused by the difference of data sources and the robustness of the

result, the model was also estimated with official Chinese real output data from 1992 through

2009. We find that the results are remarkably similar to the full sample results.

The Chinese real output data are seasonally adjusted using the X-12 ARIMA method.

The X-12 ARIMA (2, 1, 2) and Tramo/seat (Time series Regression with ARIMA noise,

Missing Values and Outliers/Signal Extraction in ARIMA Time series) methods give similar

results. The finding is consistent with Blades (2007), who performed similar tests on current

price quarterly GDP of China. The seasonal pattern of China’s quarterly real GDP is regular

and predictable. The method is consistent with the one applied by the OECD for the

developed world data.

For the developed countries data, we focus on two measures: real GDP for the G7

countries and real GDP for 25 OECD countries (although a model of 30 OECD countries

yielded equivalent results). The data come from the OECD and are measured as millions of

62 We only use Abeysinghe and Rajaguru’s data through 1991 and then use the NBS data.

109

US dollars, volume estimates, fixed PPPs, OECD reference year, annual levels, seasonally

adjusted.[63] The 25 OECD countries included in the OECD aggregate are: Australia, Austria,

Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy,

Japan, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden,

Switzerland, Turkey, United Kingdom, and United States (the 30-country aggregate adds the

Czech Republic, Hungary, Korea, Poland, and the Slovak Republic).[64] The G7 countries are

Canada, France, Germany, Italy, Japan, United Kingdom, and United States. It is important

to note that all of the G7 countries are also included in the OECD aggregate.

3.1 Chinese Data Quality

Along with the increasing interest in China’s economic performance, the quality of

Chinese official macroeconomic statistics, including the GDP data,[65] has been repeatedly

questioned by a number of researchers and media reports. Despite the efforts made by NBS

to explain and improve the GDP estimates over years, confidence in the accuracy of official

data is still low. The data quality still remains a problem that must be addressed for empirical

research on Chinese macroeconomic issues.

In the early 2000s, heated discussions on the quality of Chinese macro data generated

a large number of publications on this issue. The criticisms of China’s official data are based

on evidence from alternative GDP calculations (Maddison, 1998; Wu, 2000; Young, 2003),

63 The data were extracted on September 29, 2010 from OECD.Stat. 64 The 30-country aggregate was the largest available OECD aggregate at the time of the writing of this chapter. According to OECD.stat, “Chile became a member of the OECD on 7 May 2010, Slovenia on 21 July 2010 and Israel on 7 September 2010 and data for them now appears in the list of OECD member countries. Nevertheless, Chile, Israel and Slovenia have not yet been included in OECD area aggregation in the quarterly national accounts database for technical and timing reasons.” The estimates using the 30-country aggregate are available from the authors upon request. 65 The Economist (2008) cited Goldman Sachs’ ranking of the reliability of Chinese statistics from high to low as: Foreign trade, Money supply, Industrial production, consumer prices, GDP, retail sales, fixed investment, Employment, Average earnings, Unemployment, where GDP is in the middle.

110

comparison with energy and transportation consumption data (Rawski, 2001), and suspects

of data falsifications, especially on the local level, under the non-democratic political

system.[66] In the media, people are also concerned about the quick publication, only two

weeks after the end of reporting periods, of the preliminary national account data for such a

big economy.[67] This criticism persists even though before 1988 the Bureau of Economic

Analysis released real GDP estimates for the US just 15 days after the end of the quarter

(Young, 1993).

Refutations to the criticisms show the alternative data series constructed or corrected

by researchers have not been proved to be more precise or reliable (Holz, 2006). Many

researchers find that GDP data problems are unlikely to be unique to China and the evidence

is not robust for a conclusion of data manipulation or systematic data falsification (Holz,

2005 and 2006; Chow, 2006; Klein and Ozmucur, 2003). Chinese statistical authorities

explain most of the questions as lack of understanding of China’s transitional statistical

system and the nature of a transitional economy. Some problems have gained

acknowledgement from the authorities (Xu, 2002 and Xu, 2004) and efforts have been made

to improve the data quality. The data are compiled and revised based on the information

gained from recently established regular surveys and economic censuses, revised financial

statement reports for enterprises and the more sophisticated data sources system.

Manipulating statistics to meet political objectives, as the most usual concerns, are much

66 See Holz (2006) for a detailed survey of the literature. 67 The most recent official announcement on the timing of revisions of the quarterly data has become more cautious and leaves more time for the first and final revisions of the number.

111

harder at the national level. Xu Gao of the World Bank provides evidence of the consistency

of data from different government institutes for recent years in his official blog.[68]

After carefully reviewing the literature on Chinese data quality and their national

accounting system, and comparing different data resources and data construction methods,

we agree with many researchers and most international organizations (OECD, IMF[69]) that

although there are weaknesses or short-comings in the statistical system that provides

Chinese national accounts estimation, the Chinese official macroeconomic data after 1978

are not proved to be politically manipulated or systematically biased. The official data can

serve as “a reliable guide” to the level and growth pattern of GDP, even though the margins

of error are “certainly larger than that of the most developed countries” (Lequiller and

Blades, 2006).

IV. Results

Table 1 presents the classical correlations of the Hodrick-Prescott (1997) and Baxter-

King (1999) cycles and the growth rates of real GDP of China with the G7 and the OECD

aggregates over the entire sample period.[70] Note that the correlations of Hodrick-Prescott

and the Baxter-King cycles may be due to spurious cycles generated by the detrending

methods (Cogley and Nason, 1995, and Murray, 2003). Compared with the correlations

68

http://blogs.worldbank.org/eastasiapacific/are-chinese-statistics-manipulated 69

The World Bank criticized the Chinese national account statistics and revised their GDP estimation for China upward for

34% from the officially reported number in 1993. In 1996, the World Bank accepted China’s reformed statistical system and the official GDP number again. But the World Bank revision and method of estimation are also questioned by many researchers.

70 The quarterly growth rate is defined as the first difference of the log of real GDP. The year-on-year growth rate is defined

as log changes from the same quarter of the previous year, which is often used by articles published in Chinese, i.e.

100)log( ×= realGDPyt Year on year growth rates .4−−= ttt yyg

112

between the US and China as reported in the second chapter, the pattern is similar but in all

cases the correlations are lower between the G7 and the OECD with China than between the

US and China. Depending on the choice of method to address the nonstationarity that is

present in the real GDP series the conclusion about the tightness of the relationship between

China and the developed world differs substantially. In general it appears that China and the

developed world share somewhere between less than 10% and 25% of their fluctuations. This

lack of clear conclusion suggests that further investigation is warranted.

4.1 Correlated Unobserved Components Model Parameter Estimates

Tables 2 – 5 report the parameters of the maximum likelihood estimation of our two

correlated unobserved components models for the entire sample period. The results are

strikingly similar for China when we use either aggregate, although the standard errors

suggest that the results based on the larger OECD aggregate are more precisely estimated

than for the model using the G7 aggregate. The estimates for both aggregates are similar as

well, and are consistent with estimates for developed countries individually, such as those

reported in MNZ for the US and in Mitra and Sinclair (forthcoming) for the G-7 countries.

4.1.1 Drift Terms

Since each series is in logs and multiplied by 100, the estimated drift term multiplied

by 4 can be interpreted as the average annual growth of the permanent component.

According to our estimates, China’s average permanent real growth rate is 9.6% annually

whereas for the G7 it is 2.2% and for the OECD it is 2.3%. These estimates are similar to

other estimates reported in the literature.

4.1.2 Autoregressive Parameters

113

The estimated autoregressive coefficients, which reflect the dynamics of the

transitory components, are similar across the different models. The sum of the autoregressive

coefficients, which provides a measure of persistence of the transitory components, suggests

that China has a more persistent transitory component than either the G7 or the OECD

aggregate. Both the G7 and the OECD have persistence measures less than 0.5, whereas for

China it is 0.83.

4.1.3 Permanent and Transitory Standard Deviations

Presented in Table 3, the estimated standard deviations of the permanent and

transitory shocks are similar across models. The standard deviation of the permanent shocks

is larger than the standard deviation of the transitory shocks for both China and the

developed country aggregate for both models. The result implies that the trend or permanent

component for each series is much more variable than the traditional HP and BP smoothed

trends. Furthermore, permanent shocks are relatively more important than the transitory

shocks for each series. Permanent shocks to Chinese real GDP are substantially more

variable than permanent shocks to the developed aggregates. Chinese permanent shocks have

almost twice the standard deviation of the developed world permanent shocks. For the

transitory components, the difference is even more dramatic, with transitory shocks for China

having almost three times the standard deviation as transitory shocks to the developed world.

Thus, although the absolute magnitudes of both the transitory and the permanent standard

deviations are higher for China than for the developed world aggregates, as might be

expected given China’s higher average growth rate, the ratio of permanent to transitory

variability is less for China than the developed world aggregates. In both cases they are

greater than one, however, suggesting an important role for permanent shocks for all series. It

114

is possible in our case to have both more variable permanent components and more variable

transitory components, because allowing for correlation opens up the possibility that there

may be offsetting movements between the two components.

4.1.4 Within Series Correlations

Based on our two-series correlated UC model, the correlations between the permanent

and transitory shocks within the economies of China and the developed world are all

significantly negative (Table 4). In fact the correlation of permanent and transitory shocks for

all series is nearly perfectly negative based on both models. Negatively correlated permanent

and transitory shocks are a common finding for real GDP. These results are consistent with

prior research that has examined the correlation between permanent and transitory shocks for

the real GDP of the U.S. (MNZ; Sinclair, 2009), Canada (Basistha, 2007), the U.S. and the

U.K. (Nagakura, 2008), and the G-7 countries (Nagakura, 2007; Mitra and Sinclair,

forthcoming). The negative correlation has been interpreted as due to slow adjustment of the

actual output of the economy to the permanent shocks to output. As Stock and Watson (1988)

and MNZ (2003) explained, strong negative correlation of the permanent shocks with the

transitory shocks may be interpreted as implying that the economic fluctuations are driven

mainly by permanent shocks, while the permanent shocks immediately shift the long term

path of the output, the short run movements may include adjustments toward the shifted trend.

4.1.5 Cross Series Correlations

Table 5 shows the estimates of the correlations of the permanent-permanent shocks,

the transitory –transitory shocks cross country and the permanent-transitory cross-

correlations. The correlations are estimated simultaneously with the components. We find

that for the G7 aggregate we cannot reject the null that there is no cross-series correlation. A

115

likelihood ratio test with four restrictions results in a chi-squared statistic of 3.45 which has

p-value of 0.49. Similarly, for the OECD aggregate, the likelihood ratio test statistic is 4.51

with a p-value of 0.34. This finding is consistent with the finding of Fidrmuc and Korhonen

(2010) that business cycle correlations between China and developed countries are zero on

average.

4.2 Estimated Permanent and Transitory Components

Figure 1 shows the estimated permanent and transitory components of the real GDP

of China based on our two different bivariate models as well as the estimated components for

the G7 and the OECD aggregates. These estimates suggest that the transitory components for

the developed-world aggregates are small and noisy, similar to previous findings for

estimates of the developed countries individually (for example see Mitra and Sinclair,

forthcoming, for the G7 countries). The permanent components appear very similar to the

series themselves. For China, however, there appears to be more substantial transitory

movement. Some of this more substantial transitory movement is simply due to the larger

size of fluctuations more generally as compared to the developed countries. Recall from

Section 4.1.3 that the transitory fluctuations for China are almost three times as variable as

those of the developed world. The permanent component for Chinese real GDP still appears

quite similar to the series itself.

The role of the information of the other countries is presented in the estimated

transitory components in Figures 2 and 3. In Figure 2 we compare the estimated transitory

component from two different models – the bivariate model with China and a developed

country aggregate (the G7 and the OECD aggregate provide cycle estimates for China that

are indistinguishable from each other) and the univariate correlated UC model applied to

116

China alone. We see that the estimated components are broadly similar. Figure 3 shows that

separating out two of the key members of the G7, i.e. the US and Japan, to create a trivariate

model does not substantially change the estimated transitory component for China either. We

also estimated a model with a larger OECD aggregate which included the real GDP of 30

OECD Member countries: Australia, Austria, Belgium, Canada, Czech Republic, Denmark,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea,

Luxembourg, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak

Republic, Spain, Sweden, Switzerland, Turkey, United Kingdom, and United States. The

results were unchanged.

Result of chapter two showed that adding information from US economic fluctuations

does not visibly change the amplitudes and movement pattern of the transitory component of

China as compared to the univariate results. They further show that adding other alternative

external information sets such as the real GDP of Hong Kong or the oil price does not change

this result. A further investigation of the China’s real GDP fluctuation with China’s

international trade variables, using the bivariate model shows similar result (Figure 4). Here

we show that even a large aggregate of developed world GDP provides little new information

for China’s real output fluctuations. Possible interpretations for the stability of China’s

transitory components across different bivariate models could be: first, most of the external

shocks are permanent shocks to China which are not forecastable and thus do not change the

transitory components; secondly, domestic factors such as domestic demand or monetary

policy may be the major sources of China’s real GDP fluctuations,[ 71 ] thus external

information sets do not provide much forecasting information; thirdly, China’s

71 We do not consider domestic information sets because: first, availability of quarterly data of domestic economic

indicators for our sample period are very limited, and second, the data construction of the data before 2000 has used the total international trade and money supply--the only quarterly series available.

117

macroeconomic controls or adjustment policies could have largely isolated the external

shocks from greatly influencing the macroeconomic performance of the country.

The result is in agreement with the finding of chapter one. Using a global vector

autoregression model (GVAR), chapter one shows that supply side shocks and domestic

factors play an important role in China’s real output movements, while none of the foreign

variables, such as the trade weighted aggregate real output, interest rates and equity price of

the rest of the world and the world oil price, appears to be significant for China’s real output

fluctuations.

4.3 The “Great Recession”

From 2007 through 2009 most of the world experienced the “Great Recession.”

Although China did not experience an absolute decline in real GDP, according to most

sources, including the Economic Cycle Research Institute (ECRI),[72] China experienced a

growth cycle peak in May of 2007 and a trough in December of 2009. Similarly, the G7 and

OECD countries all experienced business cycle peaks and troughs during this period.

Therefore, we next investigate what the model suggests about this important episode in our

sample. Figure 5 presents a “zoom-in” on Chinese real GDP and our estimates for the

permanent component based on three different models for the period 2007-2009. The

estimates show that, although the estimates are broadly similar, if we relied on a univariate

model to estimate the permanent component for China that we would assume that the

permanent component moved substantially below the series between the second quarter of

2007 and the third quarter of 2008. According to the bivariate model, however, the

permanent component remained much closer to the series. By contrast, the estimates for both

72 www.businesscycle.com

118

the G7 and the OECD aggregates suggest that there was substantial downward movement in

their permanent components during this recession (Figure 6).[73]

V. Conclusion

In this paper, we presented the estimates of two different bivariate correlated UC

models for the real GDP of China with aggregate measures of developed country real GDP

with quarterly data from 1978 through 2009: one with a G7 country aggregate and one with

an OECD country aggregate. Our model permits us to examine both the within-country long

term and short term properties of the output fluctuations of the two series and the cross-series

relationships of the two series simultaneously. The estimation results also reveal the relative

importance of permanent versus transitory movements in the relationship. We find that

although China and the developed world share substantial trade connections, we cannot reject

that there are no cross-series correlations between Chinese real GDP and an aggregate of

developed world GDP measured by either the G7 countries or the OECD countries.

Although there seems to be little correlation between the real output fluctuations of

China and the developed world in terms of the permanent and transitory shocks and also little

evidence of additional information for each other’s fluctuations, there remain interesting

similarities between China and the developed world. Like the findings for both individual

developed countries reported in the literature as well as for the developed country aggregates

reported here, we find that China has significant negative correlation between permanent and

transitory shocks to its real GDP. We also find that China has an important role for

73 Comparing the smoothed estimates reported here with the filtered estimates (available from the authors upon request)

does suggest that hindsight improves our understanding of the role of permanent versus transitory shocks particularly for China in this episode. The filtered estimates suggest a much larger drop in the permanent component for China (more similar to the estimates reported for the developed country aggregates) as compared to the smoothed estimates.

119

permanent shocks in its real GDP fluctuations, which is similar to the finding for the

developed countries. China does, however, have a much larger drift term, such that

permanent shocks are substantially larger on average. These larger permanent shocks drive

China’s faster growth rate. Consistent with this faster growth rate, both the permanent and

transitory shocks are substantially more variable for Chinese real GDP than those of

developed countries. The similarities suggest that similar macroeconomic policies may be

appropriate for China as for developed countries, although the lack of correlation and the

greater size and variability of shocks may mean that different timing and size of policy may

be necessary. The small correlation of China’s output fluctuations with the developed world

indicates that domestic factors such as economic reforms, domestic demand, and economic

policies may be the major drivers of China’s macro economic fluctuations.

120

Tables and Figures

Table 3-1:Correlations of Cycles for China and the Developed Country Aggregates

Developed

Country

Aggregate

Quarterly

Growth Rates

Year-on-

Year Growth

Rates

Hodrick

Prescott

Cycles

(lamda=1600)

Baxter-King

Cycles (cycle

periods 6-32)

G7 0.09 0.18 0.28 0.21

OECD 0.11 0.16 0.24 0.14

Table 3-2: Estimation Results

China and G7 China and OECD

Log

Likelihood: -251.16 -247.13

China

(SE)

G7

(SE)

China

(SE)

OECD

(SE)

Drift 2.40

(0.18)

0.56

(0.09)

2.39

(0.18)

0.58

(0.09)

phi1 1.31

(0.04)

0.56

(0.25)

1.31

(0.05)

0.56

(0.15)

phi2 -0.48

(0.04)

-0.07

(0.20)

-0.48

(0.05)

-0.10

(0.17)

121

Table 3-3: Standard Deviations of Shocks

China and G7 China and OECD

Developed

Permanent

1.04

(0.68)

0.99

(0.05)

China

Permanent

1.97

(0.96)

1.97

(0.08)

Developed

Transitory

0.59

(0.61)

0.62

(0.08)

China

Transitory

1.43

(0.09)

1.43

(0.03)

Developed Ratio

Perm/Trans 1.76 1.60

China Ratio

Perm/Trans 1.38 1.38

122

Table 3-4: Within Series Correlations of Shocks

Table 3-5: Cross Series Correlations of Shocks

China and G7 China and

OECD

Permanent Developed with

Transitory Developed

-0.99

(0.03)

-0.97

(0.02)

Permanent China with

Transitory China

-0.99

(<0.01)

-0.99

(0.01)

G7 OECD

Permanent China with

Permanent Developed

0.07

(0.17)

0.07

(0.04)

Transitory China with

Transitory Developed

0.03

(<0.01)

-0.02

(0.01)

Permanent Developed with

Transitory China

0.07

(0.19)

0.07

(<0.01)

Permanent China with

Transitory Developed

-0.16

(0.02)

-0.11

(0.06)

123

Figure3- 1: Estimated permanent and transitory components.

1.a. China Based on Bivariate Model with G7

1.b. China Based on Bivariate Model with OECD

124

1.c. G7 Based on Bivariate Model with China

1.d. OECD Based on Bivariate Model with China

125

Figure 3-2: Comparing the Different Filtered Cycle Estimates: Univariate and Bivariate

Models

Figure 3-3: Comparing the Different Cycle Estimates: Univariate, Bivariate, and

Trivariate Models

126

Figure 3-4: Comparing the Cycle Estimates: DW aggregate, Exports and Trade Balance

Figure 3-5: 2007 – 2009 Chinese Real GDP and Permanent Component Estimates

127

Figure 3-6: 2007 – 2009 G7 and OECD Real GDP and Permanent Component

Estimates

128

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143

Appendix 1-1: Literature review on studies of China’s macro data

quality

The quality of Chinese data did not draw much attention from researchers outside

China until the late 1990s, when China kept growing at exceptionally rapid rates of growth,

averaging over 8% annually. In the early 2000s, heated discussions 74on the quality of

Chinese macro data generated a large number of publications on this issue.

The criticisms75 of China’s official data are based on evidence from alternative GDP

calculations (Maddison 1998, Wu 2000, Young 2003,), and comparison with energy and

transportation consumption data (Rawski 2001). One source of falsifications in the data is

from the local level. For example, local government officials have incentives to report

inflated numbers to meet the targets of five year plans. In the media, people are also

concerned about the quick publication of GDP data, usually only two weeks after the end of

reporting periods. The release of the preliminary national account data for such a big

economy is considered remarkable (Economist 2008)76.

Studies by Rawski (2001) and Maddison (1998) are two of the most influential

publications. Rawski has followed the Chinese data issue since 1976 (Rawski 1976) and is

one of the most cited authors on Chinese economic data problems. Rawski (2001) challenges

the official statistics by checking the quantitative consistency over output, energy use,

employment and price index. Rawski and Xiao (2001) and Wang and Meng (2001) point out

74 Example of the discussion is the collection of papers on Chinese economic statistics in China Economic Review

12(2001), reviewed and summarized by Rawski and Xiao (2001) 75 See Holz (2006) for a detailed survey of recent literature. 76 The most recent official announcement on the timing of revisions of the quarterly data has become more cautious and

leaves more time for the first and final revisions of the number.

144

the possible falsifications at the local level77. Holz (2004) and Keidel (2001) question the

official GDP estimation from the components, especially the household consumption data of

the expenditure accounting approach. Maddison (1998) offers an alternative real GDP for

China from 1952 to 1995, through checking the real growth rates sector by sector. Maddison

gets a 2.5% lower average annual real GDP growth rate than the official growth rate for years

1978-1995. Maddison’s estimates are used in the Penn World Tables (PWT) Version 6 which

was used widely by researchers on cross-country studies. The major differences of

Maddison’s sector growth rates and the official ones are in “other services” and industry.

Maddison uses employment, which has been criticized by Holz (2004) as invalid, as an

alternative indicator for output growth. Holz argues that the assumption of zero labor

productivity growth in Maddison’s estimation is not valid.

Although the Chinese statistical authorities explain most of the questions as lack of

understanding of China’s transitional statistical system and nature of the transitional

economy, they do acknowledge several problems with its GDP statistics (Xu 2002 and Xu

2004). These include lack of tracking and accurate measurements on housing services, fiscal

subsidies and non marketable welfare services provided within economic entities, weakness

in rural small enterprises statistics and livestock products, as well as the possible falsification

at the local level. For example services that used to be provided within state-owned

enterprises or commodities highly subsidized (such as housing and food) during the late

1970s and early 1980s are now mostly evaluated at market values. This can cause

measurement inconsistency problems for the GDP data (Xu 2002).

77 The possibility of a number emanating from the central government mentioned by media reports (Economist 2008) is

considered low in the academic literature. The Chinese commentaries from central government has explicitly recognized local statistics problems (Rawski and Xiao 2001). The NBS has stopped using local data to generate national economic growth data from 1998. (Xu, 1999)

145

The criticism and discussions urged the Chinese statistical authorities to launch a

comprehensive economic census in 2004, after about 10 years since the 1995 tertiary sector

census. The results of the census led to later revisions in the data, sources and methods.

Contrary to most of the studies stating the official growth rates are overstated, the official

real growth rate estimation of year 1995-2004 were revised significantly upward in 2006.

This was based on the information collected from 2004 economic census. The census results

indicate that untracked economic activity, mainly in the services sector, is growing fast and

accounts for a larger share than previously estimated of the economic activity.

Xu (2009), an NBS official, acknowledges several problems still exist in the service

sector, price indices, quarterly GDP estimation and regional GDP estimation. In his other

publication, Xu (2008) lists the current differences between China’s GDP measurements and

the 1993 UNSNA standards. The above problems are considered common in developing and

transitional economies and should not imply that the errors of China’s GDP estimation are

larger than other developing economies.

Although the media still frequently questions Chinese official data, many researchers

in the academic studies in recent years find that Chinese GDP data problems are not unique

to China and there is no robust evidence for concluding there is systematic data manipulation

or data falsification (Holz 2005 and 2006, Chow 2006). The most recent evidence on the

reliability of Chinese data is from Curtis and Mark (2010), who find that China’s economic

fluctuations have not deviated much from the standard business cycle models using official

aggregate and provincial level data, which means the data are not inconsistent with economic

theory.

146

With the establishment of a more scientific statistical system including regular

surveys and better financial statement reports for enterprises, the quality of Chinese macro

statistics continue to improve. Manipulating statistics to meet political objectives, the most

common concern, is more difficult at least at the national level. Xu Gao from the World Bank

in the official blog 78provides evidence of the consistency of data from different government

institutes in recent years. After working with China’s national account statisticians for about

two decades, OECD (2006) was convinced that although there are weaknesses in the system,

data manipulation does not happen at national level.

One of the big concerns for China’s GDP growth is why the Chinese economy grows

mostly near the government target? One specific feature of Chinese economy should be

noted: although pursuing market-oriented reforms for more than 30 years, the level of

government control of the economy is still relatively high. The political system and the

government institutional structure also largely ensure that government investment and

expenses, economic activities of state owned or controlled enterprises follow the goal of

economic growth set by the government. The close to the target economic growth can be

result of these government influenced economic activities.

Caution about the data

Although I agree that the official data are the best available and not systematically

biased, Cautions must be taken when using the official output data based on the following

considerations, in addition to the problems acknowledged by the authorities mentioned

above:

78 http://blogs.worldbank.org/eastasiapacific/are-chinese-statistics-manipulated

147

First, China’s statistical system and national account data compilation system are still

in a transition from a pure reporting system for a centrally planned economy to a system that

follows international standards79. Transition and reforms in the economy and the statistical

system may result in problems of consistency and comparability of data overtime. Note that

the issue has been partly mitigated by more frequent survey and economic census.

Second, the service sector was very limited in breadth and depth before 1978,

whereas it accounts for more than 40% of total output in 2010. This problem of accurate

service sector data sources is highly focused in the national economic surveys. Still, there are

a lot of weaknesses and emerging problems in this sector. For example informal economic

activities may still cause more potential data problems for this sector.

Third, for real GDP data, the reporting system for state owned sectors still has MPS

features and relies largely on enterprise reporting. For example, output in constant prices is

reported by many enterprises at equal rates of nominal and real change over years due to the

difficulty of calculation with correct deflators80(Woo 1998, Xu 2004). Although modern

statistical methods such as regular surveys are being established, inconsistency in valuation

of real output may still exist.

Fourth, although there is no evidence of systematic manipulation of national level

data, the political events and the communist party administrations may cause some

irregularities in the data. It is always necessary to check irregularities of the data in the

model. Significant irregularities in the real GDP series have not been found in the temporal

79 For detailed prescription and comments on the transformation of institutional organizations and data completion

methods in China, see Holz (2006). See Xu 2002 and Xu 2004 for the NBS explanation about data compilation methodology and officially recognized problems. The system for the planned economy was Soviet Material Product System and the standard China’s statistics following now is Standard National Accounts (SNA)

80 Bosworth and Collins (2007) test this reporting problem by using alternative price index constructed by Young (2003) and find the problem may affect only on secondary (industry) sector.

148

disaggregation models, partially due to the stochastic specifications of the components of the

models, and also might due to the “Gradualism” of China’s economic transition.

149

Appendix1-2. the unobserved components decomposion model

As discussed in the data disaggregation part, the measurement equation of the UC models

is:

ttt cy += τ

Where tτ is the unobserved trend component and tc is the unobserved cycle

component.

The data disaggregation estimation shows that the variation of drift term is

insignificant and close to zero, thus here I follow Harvey (1989) and Watson (1986) and

assume a constant drift term for the trend, the model’s transition equations are specified as81:

ttt ηµττ ++= −1

),0( ~ , ct2211 cctttt QNiidccc ηηϕϕ ++= −−

For both models, � ~iid N�0, σ��); and � ~iid N�0, σ�

�);

The correlations between trend and cycle residuals, interpreted as shocks or

innovations to trend and cycle respectively, are assumed as zero82.

81 While the Clark (1987) model specification is:

tttt ηµττ ++= −− 11 and ttt υµµ += −1 c � ��c �� � ��c �� � η

� , η

� ~iid N�0, Qητ)

i.e. the drift of the trend is a random walk. 82 Morley et al. 2003 introduce correlation between permanent and transitory shocks in to the model, which is an

important release on the restrictions of the model. In the authors’ papers on the relationship of China’s economic fluctuations with the US and the aggregate output of developed countries (coauthored with Tara Sinclair), external series, such as the US real output, developed countries real output, oil price and global volume of trade, are added in a bivariate UC model with correlated cross components shocks to help the identification of the correlation of the permanent and transitory shocks for China’s real output. In this paper, to evaluate the contribution of MUC temporal disaggregated data I focus on apply the MUC data to the most commonly used univariate analytic method and compare the results of MUC data with the literature.

150

Appendix1-3. Standard bivariate Blanchard-Quah model and

decomposition

First, an unrestricted VAR model is formed as:

t

p

iitit eYY ++= ∑

=−

10 φφ , VeEe tt ='

∆

∆=

t

tt

yY

π,

=

t

ytt e

ee

π

Where ty∆ is the first difference of log seasonal adjusted real GDP and tπ∆ is the first

difference of the log inflation rate.

The parameters Π , residuals te and the variance-covariance matrix V can be obtained

by the OLS estimation of the unrestricted VAR. The structural VAR then can be set up as:

tt BuAe =

=

2221

1211

BB

BBB

,

=

d

s

tu

uu

,

Where su and

du are the assumed orthogonal or uncorrelated shocks, in this exercise

the supply shocks and demand shocks (they also can be monetary shocks or external shocks,

based on the endogenous variables in the VAR). Thus, IuEu tt ='

and VBB =' . The

variances of the demand and supply shocks are normalized to one.

151

To recover the two different shocks, we need to indentify B. There are four unknowns

in B, While only three restrictions (by assuming the structural shocks are uncorrelated and

the normalization of the variances). Blanchard and Quah (1989) proposed the identification

method on long -run impact of the orthonormal shocks to help identify B. The accumulated

long-run response C to the structural innovations takes the form:

BAC 1−∞

∧

Π= , where ∞

∧

Π is the estimated accumulated responses to the reduced form

shock te .

Imposing a restriction of 012 =C can be explained as the long-run response of the jth

variable to the ith shock is zero83.

The growth in the output gap is given by:

d

i

gapt uBy ∑

∞

=

=∆1

12

In the exercise, I sum over only 40 periods responds (responds over 40 periods are

near zero, thus extending the sum periods won’t make significant difference to the result). To

obtain the levels of output gap, the gap

ty∆ ,are summed up to t and the zero line is closed at

the mean of the gap

ty∆ 84.

83 Note if using Eviews to estimate the SVAR, A is set to be identity matrix. 84

In the literature, the decomposition is called “historical decomposition”

152

Appendix1-4: More results from the GVAR model estimation with

MUC and DdPS data.

Tests of equality of cointegrating coefficients (Table A4-1) shows that the MUC data

estimation results in much stronger effects from all variables than the original DdPS data,

however there are no discrepancies in the direction and significance of the effect.

Table A4-2 presents the short run or error correction model coefficient estimations for

the four endogenous variables in DdPS model for China, based on the two datasets.

Estimations of coefficients of the real GDP based on MUC data are very different from that

based on the DdPS data. The estimated coefficients for equations of other variables do not

change substantially. Real GDP appears to be exogenous based on the MUC data estimation.

Impulse response functions on China’s real GDP (the first column of Figure 4A-1) also

shows difference of the response of China’s real output to shocks from other variables based

on the two datasets. Not only the economy recovers much quicker, but the direction of the

response to shocks from short term interest rates is different85.

85 Further investigation on the data of China’s inflation and interest rates should be done before making any conclusion

on the economic meaning.

153

Table 4A-1. Likelihood ration tests on the equality of cointegrating coefficients

estimated by GVAR modeling for China with MUC data and DdPS original data

Hypothesis

MUC coefficients=

DdPS estimated

coefficients

DdPS coefficients= MUC

estimated coefficients

Variables Chi^2(1) Prob Chi^2(1) Prob

Endogeous variables

China GDP

China inflation 0.538 [0.4633] 0.582 [0.4454]

real exchange rates 0.916 [0.3386] 0.760 [0.3833]

ST interest rate of China 0.583 [0.4453] 0.625 [0.4293]

Exogenous variables

foreign aggregate GDP 2.078 [0.7795] 0.209 [0.6475]

foreign inflation 0.115 [0.7340] 0.329 [0.5662]

foreign real equity price 0.003 [0.9538] 0.014 [0.9074]

foreign ST interest rates 0.519 [0.4715] 0.871 [0.3506]

foreign LT interest rates 0.363 [0.5470] 0.586 [0.4440]

oil price 0.534 [0.4649] 0.796 [0.3724]

TREND 0.087 [0.769] 0.238 [0.6258]

154

Table 4A-2: Short run error correction equation coefficients of GVAR estimated

based on MUC data and DdPS data

MUC data estimates DdPS data estimates

Short run equation for: China Real GDP

Coefficient Std.Error t-value t-prob Coefficient Std.Error t-value t-prob

China real GDP t-1 0.209 0.113 1.850 0.067 0.815 0.064 12.800 0.000

China inflation t-1 0.182 0.150 1.210 0.229 0.152 0.068 2.230 0.029

real exchange rates t-1 0.006 0.026 0.232 0.817 -0.007 0.012 -0.618 0.538

China ST interest rate t-1 -0.025 0.978 -0.025 0.980 0.682 0.449 1.520 0.133

foreign aggregate GDP 0.078 0.281 0.279 0.781 -0.095 0.130 -0.729 0.468

foreign inflation 0.204 0.346 0.588 0.558 -0.074 0.159 -0.465 0.643

foreign real equity price -0.010 0.021 -0.475 0.636 0.004 0.010 0.456 0.650

foreign ST interest rates -0.093 0.660 -0.142 0.888 -0.157 0.294 -0.533 0.595

foreign LT interest rates -0.581 1.517 -0.383 0.702 -0.181 0.698 -0.260 0.796

World oil price 0.001 0.010 0.108 0.914 0.007 0.005 1.440 0.153

ECM term t-1 -0.020 0.014 -1.470 0.145 -0.020 0.006 -3.100 0.003

constant 0.208 0.130 1.610 0.111 0.190 0.060 3.180 0.002

Short run equation for: China inflation

China real GDP t-1 0.136 0.094 1.460 0.149 0.258 0.113 2.280 0.025

China inflation t-1 -0.177 0.125 -1.420 0.160 -0.162 0.121 -1.330 0.186

real exchange rates t-1 -0.031 0.022 -1.430 0.156 -0.032 0.022 -1.500 0.136

China ST interest rate t-1 -1.484 0.813 -1.830 0.071 -1.456 0.799 -1.820 0.072

foreign aggregate GDP 0.274 0.233 1.180 0.243 0.216 0.232 0.933 0.353

foreign inflation 0.634 0.288 2.200 0.030 0.606 0.283 2.140 0.035

foreign real equity price -0.016 0.018 -0.910 0.366 -0.017 0.017 -0.973 0.334

foreign ST interest rates -0.677 0.548 -1.230 0.221 -0.803 0.523 -1.540 0.128

foreign LT interest rates 1.574 1.261 1.250 0.215 1.711 1.240 1.380 0.171

World oil price -0.017 0.008 -2.080 0.041 -0.016 0.008 -1.950 0.054

ECM term t-1 -0.004 0.011 -0.350 0.728 -0.006 0.011 -0.530 0.597

constant 0.033 0.108 0.302 0.763 0.049 0.106 0.462 0.645

Short run equation for: China real exchange rate

China real GDP t-1 -0.352 0.456 -0.772 0.442 -0.248 0.562 -0.441 0.660

China inflation t-1 0.083 0.608 0.136 0.892 0.017 0.602 0.029 0.977

real exchange rates t-1 0.163 0.107 1.530 0.129 0.162 0.107 1.520 0.133

China ST interest rate t-1 -1.968 3.953 -0.498 0.620 -1.932 3.963 -0.488 0.627

foreign aggregate GDP 0.655 1.135 0.578 0.565 0.631 1.149 0.549 0.584

foreign inflation 1.798 1.400 1.280 0.202 1.776 1.405 1.260 0.210

foreign real equity price 0.002 0.086 0.021 0.984 0.006 0.086 0.072 0.943

foreign ST interest rates 2.454 2.668 0.920 0.360 2.896 2.595 1.120 0.268

155

Figure 4A-1 Impulse response function: MUC data and DdPS data

a. Impulse response function, MUC data

b. Impulse response function: DdPS data