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Physica A 380 (2007) 278–286 Convergence tests on tax burden and economic growth among China, Taiwan and the OECD countries David Han-Min Wang Department of Accounting, Feng-Chia University, 100 Wen-Hwa Rd., Seatwen, Taichung, Taiwan 407, ROC Received 4 October 2006; received in revised form 7 February 2007 Available online 27 February 2007 Abstract The unfolding globalization has profound impact on a wide range of nations’ policies including tax and economy policies. This study adopts the time series and cluster analyses to examine the convergence property of tax burden and per capita gross domestic product among Taiwan, China and the OECD countries. The empirical results show that there is no significant relationship between the integration process and fiscal convergence among countries. However, the cluster analyses identify that the group of China, Taiwan, and Korea was stably moving toward one model during the 1970s, 1980s and 1990s. And, the convergence of tax burden is found in the group, but no pairwise convergence exists. r 2007 Elsevier B.V. All rights reserved. Keywords: Cluster analysis; Convergence; Per capita GDP; Tax burden I. Introduction Tax policies around the world have been shaped by economic, political, social, and other factors. The tax system evolves while each country formulates its own tax and economy policies. With the rapid trend toward globalization and internationalization, the paths and convergences of tax burden and economic growth across countries have become a significant concern to economists (such as Refs. [1–7]). The rapid growth in Asian markets including Taiwan and Korea which started off with little economic power in the 1960s and 1970s and quickly transformed their economies into major world players. Recently, China has also shown the similar growth pattern in economy. Therefore, it would be interested to examine whether these developing countries grow at a faster rate and catch-up to developed countries like the OECD countries in terms of tax burden and economic growth. The definition of convergence finds its origins in the neoclassical growth model concept. Suppose that two countries have the same production function, saving rate and population growth rate, but that their respective capital stocks in the initial year differ. Then, according to the Solow model [8], the poor country’s average economic growth rate will be higher than that of the rich country, and for this reason it will more rapidly converge to the long-run equilibrium, or to absolute b-convergence. Because countries with different economic ARTICLE IN PRESS www.elsevier.com/locate/physa 0378-4371/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2007.02.046 Tel.: +886 4 2451 7250x4226; fax: +886 4 2451 6885. E-mail address: [email protected].

Convergence tests on tax burden and economic growth among China, Taiwan and the OECD countries

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ARTICLE IN PRESS

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doi:10.1016/j.ph

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Physica A 380 (2007) 278–286

www.elsevier.com/locate/physa

Convergence tests on tax burden and economic growth amongChina, Taiwan and the OECD countries

David Han-Min Wang�

Department of Accounting, Feng-Chia University, 100 Wen-Hwa Rd., Seatwen, Taichung, Taiwan 407, ROC

Received 4 October 2006; received in revised form 7 February 2007

Available online 27 February 2007

Abstract

The unfolding globalization has profound impact on a wide range of nations’ policies including tax and economy

policies. This study adopts the time series and cluster analyses to examine the convergence property of tax burden and per

capita gross domestic product among Taiwan, China and the OECD countries. The empirical results show that there is no

significant relationship between the integration process and fiscal convergence among countries. However, the cluster

analyses identify that the group of China, Taiwan, and Korea was stably moving toward one model during the 1970s,

1980s and 1990s. And, the convergence of tax burden is found in the group, but no pairwise convergence exists.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Cluster analysis; Convergence; Per capita GDP; Tax burden

I. Introduction

Tax policies around the world have been shaped by economic, political, social, and other factors. The taxsystem evolves while each country formulates its own tax and economy policies. With the rapid trend towardglobalization and internationalization, the paths and convergences of tax burden and economic growth acrosscountries have become a significant concern to economists (such as Refs. [1–7]). The rapid growth in Asianmarkets including Taiwan and Korea which started off with little economic power in the 1960s and 1970s andquickly transformed their economies into major world players. Recently, China has also shown the similargrowth pattern in economy. Therefore, it would be interested to examine whether these developing countriesgrow at a faster rate and catch-up to developed countries like the OECD countries in terms of tax burden andeconomic growth.

The definition of convergence finds its origins in the neoclassical growth model concept. Suppose that twocountries have the same production function, saving rate and population growth rate, but that their respectivecapital stocks in the initial year differ. Then, according to the Solow model [8], the poor country’s averageeconomic growth rate will be higher than that of the rich country, and for this reason it will more rapidlyconverge to the long-run equilibrium, or to absolute b-convergence. Because countries with different economic

e front matter r 2007 Elsevier B.V. All rights reserved.

ysa.2007.02.046

4 2451 7250x4226; fax: +8864 2451 6885.

ess: [email protected].

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ARTICLE IN PRESSD.H.-M. Wang / Physica A 380 (2007) 278–286 279

structures will probably have different saving rates and birth rates, their average long-term capital stock willalso be different, and thus different countries will not necessarily converge to the same income level whichBarro [9] referred to as the conditional b-convergence. In addition to b-convergence, Quah [10], in accordancewith Galton’s fallacy,1 argues that economic growth rates across countries exhibited a reverse relationshipwith the initial year income levels of each country, which does not imply that the extent of each country’svariation in income will as a result of this decline over time. Only when variations in real income acrosscountries decrease with time among countries indicate the convergence which is referred to as varianceconvergence (s-convergence).

Many research efforts, including King and Rebelo [11], Trostel [12], Engen and Skinner [13], Milesi-Ferrettiand Roubini [14], and Alesina et al. [15], have been spent in exploring the relationship between taxation andeconomic growth. There are two theories of how economic growth is affected. The neoclassical growth modelpredicts that the changes in saving rate, population growth rate, and government-policy variables have nopermanent effect on the economy’s steady-state growth rate. The neoclassical model therefore predictsconditional convergence. However, the endogenous growth model argues that such changes will permanentlychange the growth rate of per capita output.

Instead of using neoclassical or endogenous growth model, we apply cluster analysis to classify China,Taiwan and the OECD countries into groups based on the tax burden and per capita gross domestic product(GDP). Cluster analysis is a tool of discovery without involving the setting up of an economic model.Therefore, it could discover associations and structures in data and to form ‘‘natural’’ or meaningful grouping.Cluster analysis is a classification method for partitioning a data set into clusters in which the data share somecommon traits. It may reveal associations and structures in data which, though not previously evident,nevertheless are sensible and useful once found.

Tests for convergence across nations have been extensively performed in empirical economics. By usingcross-sectional data, Baumol [16], Dowrick and Nguyen [17], and Barro and Sala-i-Martin [3,18] find that theconvergence has shown itself strongly in the economic growth of industrial nations since 1870. The findings ofBarro [9] and Mankiw et al. [19] also support the convergence hypothesis after controlling for the variables ofpopulation growth and saving rates. However, the validity of inferences drawn from cross-sectional model wasquestioned as the convergence possesses the nature of dynamic adjustment process [10,20]. This has led to anincreasing interest, for examples Refs. [21–24], of adopting time-series methods to examine the convergencehypothesis. The results of most time-series studies, contradict those for cross-sectional ones, show no favor toconvergence. This paper therefore adopts time-series method to examine the convergence property of the taxburden and per capita GDP for each country and groups of countries.

The remainder of this paper is organized as follows. Section 2 introduces the research data and empiricalmethod. Section 3 presents the empirical results, and followed by a conclusion in Section 4.

2. Research data and empirical method

The variable of tax burden used in this study is defined as total tax revenue over GDP, a standardizedmeasurement of tax burden. The tax burden is measured, like Refs. [25–30], to proxy the nation’s tax policy.And, the per capita GDP, a standardized measurement of GDP, is conventionally used as an indicator ofnation’s economy. The sample period we examine is from 1972 to 2000 to cover three recent decades ofglobalization movement. The data of tax burden are obtained from the OECD CD (2003) and the TaiwanEconomic Journal Database (TEJD). And, the data of per capita GDP are obtained from the Penn WorldDatabase.

Since there are a wide variety of tax and economy systems across nations, we use cluster analysis to explorewhether or not the countries we examine are forming different models in terms of tax and economy policies.The term cluster analysis [31] encompasses a number of different algorithms and methods for grouping objectsof a similar kind into respective categories. It is a classification method which organizes observed data intomeaningful structures without setting up a model. Cluster analysis is an exploratory data analysis tool which

1Galton’s fallacy basically means that the height of each member within a family will tend to average out, but that it does not mean that

the heights of people in general will average out.

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ARTICLE IN PRESSD.H.-M. Wang / Physica A 380 (2007) 278–286280

aims at sorting different objects into groups in a way that the degree of association between two objects ismaximal if they belong to the same group and minimal otherwise. Clustering techniques have been applied to awide variety of research problems [32]. Sanz and Velazquez [33] identified the composition of governmentexpenditure in OECD countries by means of cluster analysis and concluded that most countries convergetowards two different models.

We classify the countries in different groups based on the expectation that countries with similar fiscal policiesand economic development will be in the same group, and then test for tax burden and per capita GDPconvergence within the group. We use k-means classification method to classify the countries and to produce k

different clusters of the greatest possible distinction in terms of tax burden and per capita GDP. The k-meansalgorithm proceeds by randomly selecting objects, each of which initially represents a cluster mean. For each ofthe remaining objects, an object is assigned to the cluster to which it is the most similar, based on the distancebetween the object and the cluster mean. It then computes the new mean for each cluster. This process iteratesuntil the criterion function converges. Typically, the squared-error criterion is used, and is defined as

E ¼Xk

i¼1

X

p2Ci

p��� mij

2,

where E is the sum of squared errors for all objects in the database, p is the point in space representing a givenobject, and mi is the mean of cluster Ci. This criterion tries to make the resulting k clusters as compact and asseparate as possible. It starts by arbitrarily choosing country k as the initial cluster center, then repeatedly assignseach country to the cluster to which the country is most similar in terms of tax burden and per capita GDP in thedecades of the 1970s, 1980s and 1990s. The process does not end until the updated cluster means are stable.

We then apply time series analysis to test the tax burden and economic growth convergence within the groups.Bernard and Durlauf [21], Greasley and Oxley [22], St. Aubyn [23] and Esteve et al. [24] state that two series willconverge if the difference between them is stationary. In addition to the ADF [34,35] and PP [36] unit root tests,we also apply the KPSS [37] method to test the stationarity of the series. The null hypotheses for the ADF and PPtests are that the series is non-stationary while the null hypothesis for the KPSS test is that the series is stationary.

We also apply the cointegration method to test the group convergence in respect to the tax burden and percapita GDP. Bernard and Durlauf [21] pointed out that if the long-term forecasts of N countries in time periodt are the same, in the limn!1Eðy1tþn � ymtþnjI tÞ ¼ 08ma1, m ¼ 1,2,y,N for N countries to achieve groupincome convergence it is required that there be N�1 cointegration vectors. We use the Johansen cointegrationtest [38] and the basic model of the test is as follows:

X t ¼ P1X t�1 þP2X t�2 � � � þPkX t�k þ �t ðt ¼ 1; . . . ;TÞ,

which represents an unrestricted vector autoregression model, where Xt is an n� 1 vector, and Pi is an n� n

parametric matrix. It is rewritten as an error correction model:

DX t ¼ G1DX t�1 þ � � � þ Gk�1DX t�kþ1 þPX t�1 þ mþ �t, (1)

where Gi ¼ �ðI�P1 � � � �PiÞ ði ¼ 1; . . . ; k � 1Þ; P ¼ �ðI�P1 � � � � �PkÞ, m is a constant, Gi is a short-termdynamic adjustment coefficient matrix, and P is a long-term impact coefficient matrix. If the rank of P is apositive number, r, which is less than p, there exist matrices a and b, with dimensions p� r, such that P ¼ ab0,where b0Xt is stationary, even though z(t) is not. The hypothesis that there are at most r cointegrating vectorsis labeled H2(r); that is, P is of reduced rank rop. If there is a linear trend in the model, we label thehypothesis H2(r) in which m is unrestricted. If there is no linear trend in the model, we label the hypothesisH2(r)* in which m is restricted. Two tests are carried out using the ordered eigenvalues li or lI*, i ¼ 1,y,p. Thetrace tests with the time trend and no time trend are, respectively, as follows:

�2 lnðQ : H2jH1Þ ¼ �TXP

i¼rþ1

lnð1� liÞ,

�2 lnðQ : H�2jH1Þ ¼ �TXP

i¼rþ1

lnð1� l�i Þ.

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ARTICLE IN PRESSD.H.-M. Wang / Physica A 380 (2007) 278–286 281

Critical values in both tests are given in Ref. [39, Appendix B]. The cointegration however is a necessary butnot sufficient condition for convergence. We then need to test the cointegrating vector (1, �1) for pairwisedeviations between countries [40].

3. Empirical results

Table 1 provides the results of the unit root tests for the tax burdens of China, Taiwan and the OECDcountries. We use the ADF and PP unit root tests to test the null hypothesis of the series is non-stationary, andapply the KPSS unit root test to test the null hypothesis of the series is stationary. The results indicate that, atthe 5% significance level, each of the ADF, PP and KPSS unit root tests shows that the time series forLuxembourg and Switzerland are stationary, whereas the tests for Germany lead to mixed results. Based onthe ADF and PP unit root tests, the tax burden exhibits stationarity, but according to the KPSS unit root test,the tax burden is non-stationary. As for the other countries, the tax burden series are all I(1) series at the 5%significance level. Table 2 corroborates the results of a similar test for per capita GDP with a time trend. Thereal per capita GDP series are I(1) series at the 10% and 5% significance levels for the ADF, PP, and KPSSunit root tests.

The analysis of s-convergence for all countries is performed by the box plot method [41]. Box plots are ableto visually show different types of populations without any assumptions of the statistical distribution. The boxin Fig. 1 indicates the interquartile range extending from the 25th percentile to the 75th percentile of thedistribution. Since the reduction in disparities does not show in either the tax burden or per capita GDP, weexpect that there is no s-convergence occurring in the tax burden or per capita GDP. The standard deviation

Table 1

Unit root tests for each country’s tax burden

Country ADF unit root test without trend PP unit root test without trend KPSS unit root test without trend

Level First-order difference Level First-order difference Level First-order difference

Australia �2.28(0) �3.94(0)*** �2.24(2) �3.94(0)*** 0.62(4)** 0.15(3)

Austria �1.79(0) �4.99(1)*** �1.96(5) �5.59(5)*** 0.65(4)** 0.25(5)

Belgium �2.25(3) �4.48(0)*** �3.49(2)** — 0.50(4)** 0.34(2)

Canada �1.22(0) �4.91(0)*** �1.07(5) �4.91(2)*** 0.64(4)** 0.16(5)

China �2.12(0) �5.07(0)*** �2.20(1) �5.06(2)*** 0.15(3) —

Denmark �1.09(0) �4.62(0)*** �1.11(3) �4.62(0)*** 0.61(4)** 0.11(4)

Finland �1.05(0) �5.24(0)*** �0.89(5) �5.59(5)*** 0.66(4)** 0.09(5)

France �2.54(0) �3.77(0)*** �2.54(0) �3.74(2)*** 0.61(4)** 0.37(3)

Germany �3.56(0)** — �3.78(5)*** — 0.54(3)** 0.23(5)

Greece �0.72(0) �7.83(0)*** �0.07(5) �9.72(5)*** 0.66(4)** 0.16(5)

Ireland �1.96(0) �5.26(0)*** �1.93(4) �5.26(1)*** 0.32(4) —

Italy �0.64(0) �4.43(1)*** �0.54(5) �6.59(5)*** 0.67(4)** 0.14(5)

Japan �2.19(0) �4.99(0)*** �2.16(2) �5.00(2)*** 0.48(4)** 0.45(0)*

Korea �0.49(0) �5.32(0)*** �0.42(1) �5.32(0)*** 0.66(4)** 0.12(2)

Luxembourg �3.09(0)** — �3.09(0)** — 0.29(4) —

Netherlands �2.62(0) �4.58(1)*** �2.62(5) �5.06(5)*** 0.23(4) —

New Zealand �2.25(0) �6.57(0)*** �2.23(2) �6.57(0)*** 0.54(4)** 0.23(1)

Norway �2.12(0) �4.46(0)*** �2.06(5) �4.42(5)*** 0.22(3) —

Portugal �0.48(0) �6.01(0)*** �0.16(5) �7.65(5)*** 0.69(4)** 0.12(5)

Spain �1.38(0) �5.28(0)*** �1.35(3) �5.29(2)*** 0.65(4)** 0.23(4)

Sweden �2.79(1)* — �1.77(2) �3.26(0)** 0.52(4)** 0.11(1)

Switzerland �3.03(0)** — �3.02(1)** — 0.20(3) —

Taiwan �0.91(0) �4.43(0)*** �1.31(2) �4.42(1)*** 0.26(3) —

United Kingdom �1.85(5) �5.18(0)*** �1.94(4) �5.17(1)*** 0.20(3) —

United States �0.19(0) �5.76(0)*** �0.19(0) �5.97(4)*** 0.58(4)** 0.19(1)

***Denotes significance at the 1% level; **denotes significance at the 5% level; *denotes significance at the 10% level.

Figures in parentheses refer to optimum lag periods, in which the ADF test is based on the selection of the Schwartz information criterion,

and the PP and KPSS tests are based on the selection of the Newey–West Bandwidth criterion.

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Table 2

Unit root tests for each country’s per capita GDP

Country ADF unit root test with trend PP unit root test with trend KPSS unit root test with trend

Level First-order difference Level First-order difference Level First-order difference

Australia �1.31(0) �4.69(0)*** �1.27(5) �4.66(3)*** 0.18(4)** 0.10(5)

Austria �1.29(0) �3.77(3)** �1.27(1) �4.00(2)** 0.18(4)** 0.06(1)

Belgium �1.34(1) �4.05(0)** �1.53(2) �4.08(2)** 0.18(4)** 0.05(2)

Canada �2.58(0) �3.23(0)* �2.62(5) �3.24(1)* 0.18(4)** 0.13(2)*

China �2.13(2) �4.20(0)** �1.12(1) �4.24(2)** 0.14(4)* 0.09(0)

Denmark �0.65(0) �5.80(0)*** �0.51(2) �5.89(5)*** 0.18(4)** 0.10(2)

Finland �1.93(1) �3.24(1)* �1.68(2) �2.61(0) 0.17(4)** 0.07(2)

France �1.20(1) �3.11(0) �1.12(0) �3.11(0) 0.18(4)** 0.10(0)

Germany �0.07(0) �3.76(0)** �0.07(0) �3.56(5)* 0.18(4)** 0.07(0)

Greece �2.45(0) �5.43(0)*** �2.52(2) �5.41(1)*** 0.16(4)** 0.12(3)*

Ireland �1.85(1) �5.16(0)*** �1.99(0) �5.16(1)*** 0.13(4)* 0.09(0)

Italy �0.41(5) �5.35(4)*** 0.01(2) �3.56(2)* 0.19(4)** 0.05(2)

Japan 0.31(1) �4.03(3)** 1.11(0) �3.64(1)** 0.18(4)** 0.11(2)

Korea 0.75(0) �4.53(0)*** 1.53(5) �4.51(2)*** 0.18(4)** 0.13(5)*

Luxembourg �3.15(0) �6.65(0)*** �3.16(3) �6.89(1)*** 0.12(1)* 0.10(5)

Netherlands �1.96(2) �3.93(1)** �2.66(5) �2.79(2) 0.19(4)** 0.13(5)*

New Zealand �1.13(1) �3.23(1) �1.10(0) �3.80(0)** 0.17(4)** 0.06(1)

Norway �2.29(1) �2.42(0) �2.10(1) �2.14(4) 0.17(4)** 0.19(0)**

Portugal �0.41(4) �4.46(3)*** �1.06(0) �3.78(0)** 0.15(4)** 0.05(1)

Spain �2.02(0) �5.54(0)*** �2.02(0) �5.70(4)*** 0.17(4)** 0.07(4)

Sweden �1.74(1) �4.42(1)** �1.42(5) �3.09(5) 0.18(4)** 0.10(5)

Switzerland �0.34(2) �3.44(1)* �0.46(1) �2.85(3) 0.18(4)** 0.08(1)

Taiwan �2.01(1) �3.44(0)* �1.44(2) �3.44(0)* 0.09(3) —

United Kingdom �0.74(0) �4.98(0)*** �0.74(0) �4.98(0)*** 0.18(4)** 0.08(0)

United States �1.54(0) �4.36(0)*** �1.52(1) �4.38(1)*** 0.18(4)** 0.11(1)

***Denotes significance at the 1% level; **denotes significance at the 5% level; *denotes significance at the 10% level.

Figures in parentheses refer to optimum lag periods, in which the ADF test is based on the selection of the Schwartz information criterion,

and the PP and KPSS tests are based on the selection of the Newey–West Bandwidth criterion.

D.H.-M. Wang / Physica A 380 (2007) 278–286282

for each decade exhibits no significant decrease confirming that there is no tax burden or economic growthconvergence process. The results imply that there is no indication of a harmonization process in fiscal policyand economic development among Taiwan, China and the OECD countries.

We then apply a k-mean algorithm to assign each country to the cluster to which the country has the mostsimilar pattern in tax burden and per capita GDP for the decades of the 1970s, 1980s and 1990s. We use theWard’s method, the agglomerative procedure to find the accurate number of groups. Each country treat as itsown cluster then we combine two clusters that minimize the sum of the within deviations of the resultingclusters till stop the combining clusters by using the stopping rule [42]. Therefore we differentiate four groupsfor each of the decades. Table 3 contains the average values for each group and for each decade and theirEuclidean distances. Fig. 2 shows that the countries move toward different clusters in the 1970s, 1980s and1990s. The first group, labeled Asia, includes Taiwan, China and Korea with the lowest tax burden and percapita GDP. They were moving stably toward one model in the 1970s, 1980s and 1990s. The second group,labeled European which includes most major European Countries, is the closest to the overall average of thetax burden and per capita GDP. The third group, labeled Nordic, includes most Nordic countries with thehighest tax burden and per capita GDP. The last group, labeled Mixed, includes Japan, the US, etc. To furtherexamine whether or not the regional characteristics affect the results of the convergence tests above,we apply Johansen’s cointegration test to analyze the tax burden and per capita GDP convergence for themost stable Asian cluster. Tables 4 and 5 present a number of cointegrated vectors in the Asian cluster.The results indicate that there exists the tax burden convergence for the group, but the per capita GDPconvergence is not found.

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90's80's70's

11

10

9

8

7

6

5

5

5

14

5

Per Capita GDP

14

90's80's70's

60

50

40

30

20

10

0

Tax Burden

Fig. 1. Box plots of per capita GDP and tax burden by decades.

D.H.-M. Wang / Physica A 380 (2007) 278–286 283

Furthermore, we also test for the pairwise tax burdens and per capita GDP convergence between China,Korea, and Taiwan. Tables 6 and 7 show no evidence to support pairwise convergence between thesecountries, and there is no catching up for these countries to Japan. Thus, the results suggest that there is nosignificant relationship between China, Taiwan and Korea in terms of their long-term fiscal policy andeconomic development.

4. Conclusion

This study adopts the time series and cluster analyses to examine the convergence property of the tax burdenand per capita GDP among Taiwan, China and the OECD countries in the 1970s, 1980s and 1990s. We also

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Table 3

Cluster analyses for tax burden and per capita GDP

1970s

Variable Asia European Nordic Mixed Overall mean F-statistic P-value

Tax burden 15.49 35.65 41.73 25.09 30.21 1077.04 0.00

Real capita GDP 7.07 8.72 8.79 8.58 8.48 4085.85 0.00

No. of cases 3 7 5 10

1980s

Variable Far Eastern European Nordic Mixed Overall mean F-statistic P-value

Tax burden 16.56 37.76 45.08 29.11 34.20 1775.17 0.00

Real capita GDP 7.99 9.31 9.49 9.54 9.23 5537.53 0.00

No. of cases 3 6 7 9

1990s

Variable Far Eastern European Nordic Mixed Overall mean F-statistic P-value

Tax burden 16.47 41.99 46.94 32.59 35.41 1207.19 0.00

Real capita GDP 8.90 10.05 9.93 9.85 9.70 6716.82 0.00

No. of cases 3 5 5 12

China KoreaTaiwan

Belgium DenmarkNetherlands NorwaySweden

Austria Canada Finland France Germany Luxembourg UK

Australia GreeceIrelandItaly Japan New Zealand Portugal Spain Switzerland USA

Asia Nordic

EuropeanMixed

Fig. 2. Cluster analyses based on tax burden and per capita GDP by decades.

D.H.-M. Wang / Physica A 380 (2007) 278–286284

investigate whether the regional characteristics would affect the convergence relationships between these twovariables.

The empirical results show that there is no tax burden or economic growth convergence process amongTaiwan, China and the OECD countries for each decade. The results imply that there is no indication of aharmonization process in fiscal policy and economic development among countries. Nevertheless, the clusteranalyses identify that China, Taiwan and Korea were stably moving toward one model in the 1970s, 1980s and

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Table 4

Group tax burden convergence tests for Asian region

Eigenvalue H0 Trace test 5% Critical value Maximum eigenvalue test 5% Critical value

0.815793 r ¼ 0 64.63324* 35.19275 42.29237* 22.29962

0.512349 rp1 22.33987* 20.26184 17.95390* 15.89210

0.160911 rp2 4.385974 9.164546 4.385974 9.164546

*Denotes significance at the 5% level.

Based on the Akaike information criterion, the optimal number of lagged periods is three periods.

Table 5

Group per capita GDP convergence tests for Asian region

Eigenvalue H0 Trace test 5% Critical value Maximum eigenvalue test 5% Critical value

0.535488 r ¼ 0 35.92859* 29.79707 19.93598* 21.13162

0.323074 rp1 15.99261* 15.49471 10.14504* 14.26460

0.201409 rp2 5.847569* 3.841466 5.847569* 3.841466

*Denotes significance at the 5% level.

Based on the Akaike information criterion, the optimum number of lagged periods is two periods.

Table 6

Tax burden convergence tests for Asian region

Countries ADF unit root test no trend PP unit root test no trend KPSS unit root test no trend

Level First-order difference Level First-order difference Level First-order difference

China–Japan �2.00(0) �4.97(0)*** �1.99(3) �4.99(3)*** 0.51(4)** 0.12(4)

Korea–Japan �0.41(0) �4.32(0)*** �0.68(2) �4.34(1)*** 0.16(4) —

Taiwan–Japan �1.17(0) �5.33(0)*** �1.16(1) �5.33(1)*** 0.52(4)*** 0.10(1)

China-Korea �1.22(0) �4.69(0)*** �1.22(0) �4.67(3)*** 0.42(4)* 0.09(3)–

China–Taiwan �1.84(0) �4.32(0)*** �1.85(0) �4.30(2)*** 0.09(3)

Taiwan–Korea �0.40(0) �6.40(0)*** �1.32(8) �6.40(0)*** 0.65(4)** 0.27(5)

***Denotes significance at the 1% level; **denotes significance at the 5% level; *denotes significance at the 10% level.

Figures in parentheses refer to optimum lag periods, in which the ADF test is based on the selection of the Schwartz information criterion,

and the PP and KPSS tests are based on the selection of the Newey–West Bandwidth criterion.

Table 7

Per capita GDP convergence tests for Asian region

Countries ADF unit root test with trend PP unit root test with trend KPSS unit root test with trend

Level First-order difference Level First-order difference Level First-order difference

China–Japan 1.86(1) �3.63(0)** 1.36(0) �3.64(1)** 0.05(1) —

Korea–Japan �1.61(0) �4.10(0)** �1.99(2) �4.11(1)** 0.11(1) —

Taiwan–Japan �2.34(1) �3.79(0)** �1.75(2) �3.79(0)** 0.13(4)* 0.09(1)

China–Korea �1.02(0) �3.99(0)** �1.22(1) �3.99(0)** 0.14(3)* 0.07(2)–

China–Taiwan �2.88(2) �3.61(0)** �1.94(3) �3.68(2)** 0.08(4)

Taiwan–Korea �2.38(1) �3.79(0)** �1.69(1) �3.82(1)** 0.15(4)** 0.07(1)

***Denotes significance at the 1% level; **denotes significance at the 5% level; *denotes significance at the 10% level.

Figures in parentheses refer to optimum lag periods, in which the ADF test is based on the selection of the Schwartz information criterion,

and the PP and KPSS tests are based on the selection of the Newey–West Bandwidth criterion.

D.H.-M. Wang / Physica A 380 (2007) 278–286 285

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ARTICLE IN PRESSD.H.-M. Wang / Physica A 380 (2007) 278–286286

1990s. And, the tax burden convergence is found in this group. However, no pairwise convergence is found.The findings imply that, in terms of long-run fiscal policy and economic development, none of the Asiancountries converges with any of the others.

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