A New Approach for Analysing Income Convergence across Countries.

A New Approach for Analysing Income Convergence across Countries.a Donal O’Neill* and Philippe Van Kerm** October 2003 Preliminary Draft Abstract In this paper we develop a coherent framework that integrates both traditional measures of  -convergence and  -convergence within a study of cross-country income dynamics. To do this we exploit the close links that exist between studies of income mobility and studies analysing the progressivity of the tax system. We also develop a welfare interpretation for the concept of  -convergence, which distinguishes it from the more general form of  -convergence and which also suggests that the  -process may be worthy of independent study. We illustrate our approach using data for the period 1960-2000. a We would like to thank Gerry Boyle, Olive Sweetman, Dirk van de gaer and seminar participants at the Dublin Economics Workshop (Trinity College Dublin) for helpful comments on an earlier draft of this paper. * Economics Dept., NUI Maynooth, Maynooth, Co. Kildare,Ireland, [email protected] ** CEPS/INSTEAD G.-D Luxembourg, [email protected] 1 1. Introduction The degree to which income or productivity levels have converged across countries over time has been the subject of extensive research. The initial studies tended to be descriptive in nature, highlighting the key trends in inequality over time (Abramovitz (1986), Baumol (1986)). However in recent years this research has become more closely connected with research on the theory of economic growth. Two theories have come to dominate the literature on economic growth. The traditional Solow growth model (Solow (1956)) predicts that countries that are furthest away from their steady states will tend to grow more quickly than countries closer to their steady state. For countries with the same steady state, this implies that incomes will converge along the transition path to the steady state. In contrast endogenous growth models (Romer (1986)) can generate patterns of growth that do not exhibit any tendency towards convergence.1 It was suggested that the presence or otherwise of convergence across countries could form the basis of a test of the neo-classical growth model versus more recent endogenous growth models. As a result, several papers have been written examining the nature of the convergence process across countries (Barro and Sala-I-Martin (1992), Mankiw, Weil and Romer (1992)). However, this subsequent literature has in turn generated a lot of controversy, debate and confusion regarding how to measure and interpret income convergence in general. The dominant approach in the early literature is characterised by the work of Barro and Sala-I-Martin (1992). This involves regressing income growth rates on initial income in order to test whether poor countries grow faster than richer countries.2 However, several authors (Friedman (1992) and Quah (1993)) have argued that although these regressions may detect mobility within a distribution they tell us little about convergence in the sense of a reduction in income dispersion across countries. It is possible to observe poor countries growing faster than rich countries and yet incomes diverging. For this to happen it must be the case that the initially 1 The key distinction between these two models is the presence or otherwise of diminishing returns to capital. For a more detailed discussion of alternative growth models and their implications for the evolution of the international distribution of income see de la Fuente (1997). 2 Essentially one considers a regression model of the form titi ti ti y y y,, , 1, )log(log          . Values of >0 are taken as evidence of convergence. In practice a non-linear version of this equation may be estimated but this makes little difference to the final results. It can be easily shown that  measures how rapidly an economy’s output approaches its steady state. 2 poorer country overtakes/leapfrogs the richer country so that the rankings of both countries are reversed.3,4 To distinguish between these different forms of convergence Sala-I-Martin (1996a)5 coined the term  -convergence to capture situations where “poor economies tend to grow faster than rich ones”. The term  -convergence is then defined as a situation in which “a group of countries are converging in the sense..that the dispersion of their real per capita GDP levels tend to decrease over time.”. While Friedman (1992) has argued that the real test of convergence should focus on the consistent diminution of variance among countries, Sala-I-Martin (1996a,b) argues that both concepts of convergence are interesting and should be analysed empirically. In this paper we establish the close links that exist between existing measures of  -convergence and measures of tax progression used in the public finance literature. We exploit this relationship in order to develop a coherent framework for studying realised cross-country income dynamics that integrates existing measures of convergence. Our approach allows us to identify the relative contributions of  - convergence and leapfrogging to overall  -convergence. It also allows for the possibility of incorporating varying degrees of inequality aversion into the measure of  -convergence. We also develop a welfare interpretation for the concept of  - convergence that illustrates why the concept may be worthy of independent study. We illustrate our approach by examining income dynamics across countries from 19602000. 2.Decomposing Inequality 2.1 Measuring the Progressivity of Income Tax In this sub-section of the paper we briefly outline the fundamental concepts and techniques used by economists studying the progressivity of the tax system. In the 3 Furthermore as noted by Friedman (1992) the presence of measurement error may bias the mobility estimates obtained from these regressions (see also O’Neill, Sweetman and Van de gaer (2002)) The approach we outline in this paper does not address the measurement error bias. However since our approach avoids the need for regression analysis it does provide a measure of  -convergence which is free of the potential biases involved in estimating dynamic data models. For a discussion of these biases in the context of Barro-Regressions see Lee, Pesaran and Smith (1997). 4 Tamura (1992), Brezis et al (1993) and Sugimoto (2003) present examples of growth models in which leapfrogging/overtaking occurs. Tamura (1992) and Sugimoto (2003) emphasise the role of inequality within countries in generating differential growth paths, while Brezis et al (1993) focus on the disadvantage of leading countries in adopting new technologies. 5 In that paper Sala-I-Martin dates the first use of this term to his Ph.D thesis in 1990. 3 next sub-section we illustrate how these techniques can be adapted to study crosscountry income dynamics. In particular we develop a coherent framework for understanding the nature of income convergence across countries. The starting point for much of the work on income redistribution is the concept of a Lorenz curve and the associated Gini-coefficient.6 The Lorenz curve plays an important role in welfare economics7 and is constructed by first ordering individuals by income, starting with the lowest. Once this is done, the cumulative proportion of total income received by the income units is plotted against the cumulative proportion of the population represented by these individuals. By definition the first ordinate on the curve corresponds to zero percent of the population which by definition must account for zero percent of total income. At the other extreme the final ordinate relates to 100% of the population which, as a group, must account for 100% of total income. The ordinates for the points in between these extremes are given by (p,Lx(p)) where : p=F(x) and  x F xssdFpL 0)( 1 )(   F is the mean of the income distribution whose cumulative distribution function is denoted by F. In situations where every member of the population receives the same income the Lorenz curve corresponds to the 45 degree line. In situations of extreme inequality, where one member of the population has all the income, the Lorenz curve will run along the horizontal axis before jumping up to the 45-degree line. In situations between these two extremes the Lorenz Curve will be a convex curve lying beneath the 45-degree line. The difference between the observed Lorenz curve and the 45-degree line is thus a plausible measure of inequality. This in turn provides the intuition behind the Gini coefficient which is equal to twice the area between the straight 45 degree line plot and the Lorenz curve Lx. Formally the Gini coefficient can be written as: 6 A more detailed discussion of what follows can be found in Lambert (1993). For an application of the use of Lorenz curves in studies of regional income convergence in the U.S see Bishop et al (1992, 1994). 4   1 0)(21 dppLG xx A tax-system t(x) is said to be progressive if the average tax rate x xt )( is increasing with income (x). For our purposes it will be helpful to use an equivalent formulation of progressivity based on the redistributive power of the tax system. To do this we introduce the idea of a concentration curve, which we denote as CCxz(p). The concentration curve for Z (with respect to X) plots the cumulative shares of Z against quantiles in the X-distribution. It is important to note that CCxz(p) will differ from Lz(q) in situations where the rankings of individuals based on X and Z differ and we will make use of this in our later analysis. Having defined what we mean by a concentration curve we can now state the Jakobsson-Fellman theorem which establishes the relationship between progressivity and redistribution. Jakobsson-Fellman Theorem: F(x).CCLCC dx xxtd T x X x X-T on distributi incometax -preevery for x allfor 0 )/)([  For proof see Lambert page 150. Intuitively this theorem states that the tax system is progressive if and only if the distribution of post-tax income (holding fixed rankings) is distributed more evenly than pre-tax income, which in turn is distributed more equally than tax liabilities. We will make use of this equivalence in developing our framework. In the same way as we derived the Gini-coefficient from the Lorenz curve, we can also define an area measure of the extent to which the concentration curve deviates from the 45 degree line. This is known as the Concentration coefficient Cxz. Formally the Concentration coefficient can be written as : 7 Atkinson (1970) and Shorrocks (1983) derive a series of results that show that the ability to rank distributions in terms of welfare depends on the relative positions of the respective Lorenz curves. These results are summarised in Lambert (1983). 5   1 0)(21 dppCCC X Z X Z Within this framework any change in inequality can now be viewed as a two step process. The first step measures the amount of redistribution of post-tax income from the position attainable after a distributionally neutral equal-yield taxation. It can be easily shown that this involves comparing the Lorenz Curve for pre-tax income with the concentration curve of post-tax income. Expressed in this way progressivity is viewed in terms of the relationship between pre and post tax income distributions, keeping fixed an individuals relative ranking. The second component compares the concentration curve of post-tax income with the Lorenz curve for post-tax income. As noted earlier these curves will differ (with the Lorenz curve exhibiting more inequality) in circumstances where the tax schedule results in a reranking of individuals over the two distributions. Formally we can write this decomposition as :  G=GX-GX-T=(GX-CXX-T) – (GX-T-CXX-T)=DP+R The first term measures the redistributive impact of progressivity using only the rankings from the initial distribution. This term is often referred to as the ReynoldsSmolensky index of vertical equity. The second term uses the final distribution of income and measures the increase in inequality due to reranking. In this way we can identify the relative importance of both these processes on the overall change in inequality, G. The above decomposition can be generalised to settings that utilise the generalised S-Gini coefficient (Gx(v)).8 This coefficient allows for a parameter of inequality aversion, v, when calculating the summary measure of dispersion. The formal definition is :   1 0 2)()1()1(1)( dppLpvvvG x v x where 1<v<. 8 For a more detailed discussion see Lerman and Yitzhaki (1984) 6 Intuitively the S-Gini allows for different weights to be attached to different income ranges when integrating over the Lorenz curve. The regular Gini is obtained by setting v=2. When v is set less than 2 relatively more weight is given to incomes at the top of the distribution. At the extreme value of v=1, G(v)=0, so that irrespective of the distribution inequality will be coded as zero, a form of inequality neutrality. On the other hand a value of v>2 attaches relatively greater weight to differences at the bottom of the distribution. As v  G(v) tends to 1-  min x so that reductions in inequality is disproportionally driven by the agent with the lowest income – an extreme form of inequality aversion. Our earlier decomposition carries over to this extended measure and can be written as :  G(v)=GX(v)-GX-T(v)=(GX(v)- CXX-T(v)) – (GX-T (v)- CXX-T(v))=DP(v)+R(v) 2.2: Progressivity, Reranking,  -convergence and  -convergence. In earlier research Benabou and Ok (2001) and Jenkins and Van Kerm (2002) adapt these concepts to study mobility within the distribution of individual incomes. In our paper we apply these techniques to a study of income convergence across countries. We show how the concepts developed above can be exploited so as to obtain a better understanding of income dynamics in the growth literature. To do this we simply let X from the previous section denote initial income, Y=X-T denote final income and T represents a country’s income losses or gains over this period.  G denotes the change in income dispersion over time and is therefore a direct measure of  -convergence. The extension to the S-Gini allows us to examine the sensitivity of trends in  -convergence to different specifications of inequality aversion. The Progressivity term, DP(v), captures the extent to which income inequality is reduced over time as a result of higher growth rates among lower income countries. Measuring the progressivity of the tax system in terms of the redistributive impact of the tax system is completely analogous to examining the impact of variations in growth rates across countries on income inequality in the convergence setting. In particular,  - convergence, defined as situation where “poor economies tend to grow faster than 7 rich ones” is nothing more than progressive income growth. Thus the first term in our decomposition measures the contribution of  -convergence towards the overall reduction in income dispersion. The second term in the decomposition measures the negative impact of positional mobility on income inequality. In the growth context this captures the notion of leapfrogging. We can use Figures 1, 2 and 3 to illustrate our decomposition. Figure 1 illustrates a situation where both  -convergence and  -convergence coexist without any leapfrogging/reranking. In our approach the  -convergence would be captured by a fall in the Gini-coefficient. For this example all of this reduction would be attributed to the progressivity of income growth, so that  G=DP. The absence of reranking would be reflected in a measure of R=0. Figure 2, illustrates a situation where there is  -convergence but no  - convergence. In this example inequality has not changed over time – so there has been no  -convergence (  G=0). On the other hand there has been substantial  - convergence – the poor country has grown faster than the richer country. However this is masked in the overall inequality figure by the complete reranking of the two countries. Our approach will identify the redistributive contribution of  -convergence to inequality in these data but this will be entirely offset by the contribution of the leapfrogging component, so that –DP=R>0. Not only will our framework identify the tendency of poor countries to grow faster but it simultaneously quantifies the extent to which this is offset by reranking in the data. Finally, Figure 3 illustrates another process for which there is no  - convergence. However this case differs from that in Figure 2 in that this new process is static. Again  G=0 but for this process our decomposition would result in DP=R=0. Our decomposition would identify this as a growth process without either  -convergence or leapfrogging. These examples help clarify an important point. Sala-I-Martin (1996b) begins his paper by defining  -convergence in the traditional way by noting that “there is  - convergence if poor economies tend to grow faster than rich ones”. However later in the paper he suggests that  -convergence studies the mobility of income within the same distribution. As a result, some researchers (Boyle and McCarthy (1997)) have drawn parallels between  -convergence and measures of rank mobility, defining indices of rank concordance as direct measures of  -convergence. Clearly for a 8 distribution to exhibit  -convergence without  -convergence it must be the case that countries are changing ranks (Figure 2). However as Figure 1 shows it is possible to have  -convergence without any positional mobility. It is also possible to have rank mobility without  -convergence. The definition of  -convergence simply requires poor countries to grow faster than rich countries, irrespective of whether or not there is leapfrogging. Both a Barro-regression approach and our redistributive approach would indicate a strong role for  -convergence for the process illustrated in the example in Figure 1, measures based on rank correlations would not. While the issue of positional mobility is interesting, it is captured by our measure R, which in turn measures reranking/leapfrogging and not progressivity/  -convergence. In this example R would contribute nothing to the change in income inequality. We believe that these examples illustrate the potential that our framework offers to provide a coherent approach that integrates the three important features of the growth process:  -convergence,  -convergence and leapfrogging. The next section provides an empirical illustration of this approach. We apply our decomposition to data on cross-country income dynamics taken from the latest release of the Penn-World tables. We briefly discuss the data before applying our approach to data on a full sample of 98 countries and also a restricted sample of 25 OECD countries. We conclude with a discussion of the welfare implications of our analysis. 3: Data and Results 3.1 Data In this section of the paper we analyse income convergence between 1960 and 2000, taken from the latest version of the Penn-World Tables.9 The Penn World Table provides purchasing power parity and national income accounts converted to international prices for 168 countries for some or all of the years 1950-2000. In this paper we use data for a sample of 98 countries that provided complete data over the period 1960-2000. We also look at income dynamics for a restricted set of 25 OECD countries. Income is measured as real per-capita gross domestic product in 1996 international prices. These data have been used extensively in previous studies of 9 Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 6.1, Center for International Comparisons at the University of Pennsylvania (CICUP), October 2002. 15 (relative to the initial distribution) according to any individualistic, symmetric, additively separable and inequality averse social welfare function (by definition GLC(x+t(x)) > GLC(x) (see Lambert (1993) page 152 for a discussion in the context of taxes)).16 However we can show further that having -convergence (progressive income growth) is welfare improving, not only in relation to the initial income distribution, but also relative to an equal-yield proportional income growth counterfactual. The following theorem establishes this result. Theorem: For every individualistic, symmetric, additive separable and inequality averse social welfare function, progressive income growth (  -convergence) over the full range of incomes, without leapfrogging, increases social welfare more than an equal yield proportional growth rate applied to the same pre-growth income distribution. Proof: If the growth rate is proportional then the Lorenz curve for final income (y) coincides with the Lorenz curve for initial income (x): Lprop(p)=Lx(p) for all p [0,1] By definition average final income is given by  y=  x(1+t), where t is the overall average growth rate. Hence the Generalised Lorenz Curve for final income after progressive growth at rate t can be defined as : GLCy(p)=  x(1+t)Ly(p). From the Jakobbson-Fellman theorem (See Lambert page 150) and our assumption of no reranking we can conclude that : GLCy(p)=  x(1+t)Ly(p)   x(1+t)Lx(p)=  x(1+t)Lprop(p) all p [0,1]. The last equality follows from step 1 of the proof. By definition this implies that : GLCy(p)  GLCprop(p) all p [0,1]. Referring to Shorrocks’ theorem (Lambert page 59) completes the result. It is worth emphasising that the concept of  -convergence is the key convergence force underlying this theorem. A reduction in  -convergence is not sufficient to generate this result. It is possible for inequality as measured by say the Gini coefficient or the coefficient of variation to fall and for there to be no reranking rescaling constants will led to different values for the residualised Gini and also to different values for the estimated components of inequality. 16 GLC(x) denotes the generalised Lorenz curve and is derived by multiplying the original Lorenz Curve by mean income. 16 and yet for the Generalised Lorenz curves to cross so that unambiguous welfare comparisons may not be possible. This reflects the fact that the Gini-coefficient can fall even when income growth is not progressive over the entire range of incomes. Although our earlier results clearly highlight the redistributive effect of observed growth patterns for the OECD countries being studied, the analysis up to now has used an overall index of effective progressivity. In order to apply the above theorem we need to be able to measure income progression along the entire income scale. That is we need to switch from an index of effective progression to a measure of local progression. The progressivity index we have discussed so far is based on the difference between the initial Lorenz curve and the concentration curve for final income. As such it measures the redistributive effect of the income growth and is associated with Residual Progression measure of local progression (Lambert page 161). In a study of income convergence this seems an obvious approach to take. An alternative way of measuring local progression which is easy to implement and which turns out to be important in linking the growth and tax literature is to focus directly on the behaviour of the average growth rate : X Xt X XY )(  , where t(X) is the change in income over the two periods and X is initial income. An equivalent way to measure progression is to examine whether 0 ) )( ( dx x xt d. This forms the basis for Average Rate Progression.17 It is clear that a declining growth schedule, deviations from proportional growth and the redistributive effect of observed growth patterns are very closely connected. Proportional income growth implies a flat growth schedule and no change in inequality. With progressive growth on the other hand a disproportionate share of the benefits is received by low-income countries, the growth schedule is downward sloping and the redistributive effect of the change is positive. To check whether or not 0 ) )( ( dx x xt d for all values of X we first sorted the data by income level and then plotted X Xt )( against X for the period 1960-2000. The results are given in Figure 6. From this we can see that there are a number of observations 17 In the same way as the tax yield from equiproportionate increases in initial income is larger the more progressive is the tax schedule (Lambert 1993 page 206) we can also show that the total income yield from am equiproportionate increase in initial income is larger the greater the degree of Average Rate Progression observed in the growth process. 17 that violate our progressivity condition (that is countries for which the growth rate in income was larger than the next lowest ranked country). These countries are represented by a hollow circle. This makes the application of theorem 1 difficult when applied to realised outcomes. However, those familiar with the recent literature on growth will quickly recognise this way of presenting the results. It is nothing more than a plot of the data underlying the standard Barro-regression approach to measuring  -convergence.18 The solid line on the graph denotes the OLS fit from a Barro-regression. In order to look at the contribution of  -convergence and leapfrogging to observed changes in income inequality we have defined progressivity in terms of realised outcomes. It would also be possible to use the framework developed above to examine the progressivity of the underlying growth process. This would simply involve comparing the distribution of initial incomes with the distribution of conditional expected incomes rather than actual incomes.19 The same decompositions and theorems as outlined earlier would apply. The only difference being that the results would now be interpreted in terms of the opportunities afforded by the process rather than in terms of realised outcomes. Since we can view the estimated Barro-regression as providing the best fit of (X, X Xt )( ) we can implement this approach using the average growth schedule as predicted by a Barro-regression. For the OECD countries that we have analysed the expected average tax schedule is downward sloping. This implies a globally progressive growth process which welfare dominates a equal yield proportional growth process. In this context the violations of “local” progression that we outlined in the outcomes-based approach may be interpreted as simply reflecting stochastic deviations from the systematic component of the growth process.20 When viewed in this light the Barro-regression measure of convergence and the redistributive measure that we adopt in this paper differ only in the principles used to 18 To see this formally we note that an equivalent unit free measure of average rate progression can be derived as )ln( ln )ln( ) )( ( . ) )( ( * xd X Y d xd x xt d x dx x xt d ARP        . This latter term corresponds to the -parameter from a standard Barro-regression. 19 This is the approach adopted by Benabou and Ok (2001) in their study of individual income dynamics behaviour. 20 Aronson, Johnson and Lambert (1994) extend the decomposition that we use in this study to formally allow for randomness in the tax/growth schedule. This enables them to identify the effect of horizontal 18 measure progressivity. The first focuses on the rate at which the average growth rate changes with initial income (Average Rate Progression), while the latter focuses on the elasticity of terminal income to initial income (Residual Progression). Irrespective of whether one is interested in interpreting realised growth patterns and the subsequent changes in inequality or in analysing the underlying growth process, our analysis lends support to the view that both  -convergence and  - convergence are important features of the growth process that should be studied together. Our paper provides an integrated framework for this analysis. 4. Conclusion The results presented in this paper are consistent with earlier studies that found that the growth process among OECD countries in the last 40 years has resulted in a reduction in income inequality over this time period. While these results are in line with those presented in earlier research we believe that the approach adopted in this paper represents a significant development in the analysis of cross-country income dynamics. The techniques we use allow us to “marry” the approaches advocated by Friedman and Quah to study income dynamics, on the one hand, and those suggested by Barro and Sala-I-Martin on the other hand. In doing so we develop a coherent integrated framework involving concepts which up to now have often been viewed as competitors in the analysis of income dynamics. We do this by adapting earlier work analysing progressivity in the tax system and applying it to cross-country income dynamics. This allows us to separately examine the contribution of nonproportional income growth and reranking to changes in income inequality. We also develop a welfare interpretation for the concept of -convergence. We show that the typical Barro-Regression approach to identifying  -convergence, is equivalent to Average Rate Progression measures in the taxation literature, whereas our redistributive approach is based on Residual Progression measures. In developing the link between the tax and growth literature we feel we have provided an integrated framework for studying income dynamics, through which the connections between the various sources of convergence can be better understood and evaluated. inequity (unequal treatment of equals) on redistribution. Unfortunately the relatively small sample sizes available across countries prohibits the use of their decomposition in our setting. 19 References Abramovitz, M (1986), “Catching Up, Forging Ahead and Falling Behind,” Journal of Economic History, 46, June, pp. 385-406. Aronson, J, P.Johnson and P. Lambert (1994), “Redistributive Effect and Unequal Income Tax Treatment,” Economic Journal, Vol. 104 (March) pp. 262-270. Atkinson, A (1970), “On the Measurement of Inequality,” Journal of Economic Theory, Vol. 2, pp. 244-263. Barro, R and X. Sala-Martin (1992), “Convergence,” Journal of Political Economy, 100, 2 (April), 223-251. Barro, R and X. Sala-Martin (1995), Economic Growth, McGraw-Hill, New York. Baumol, W (1986), “Productivity Growth, Convergence and Welfare: What the LongRun Data Show,” American Economic Review, 76, December, pp. 1072-85. Benabou, R and E. Ok (2001), “Mobility as Progressivity: Ranking Income Processes According to Equality of Opportunity,” NBER Working paper 8431. Bishop, J, J. Formby and P. Thistle (1992), “Convergence of the South and NonSouth Income Distributions, 1969-1979,” American Economic Review, March, pp. 262-272. Bishop, J, J. Formby and P. Thistle (1994), “Convergence and Divergence of Regional Income Distributions and Welfare,” Review of Economics and Statistics, pp. 228-235. Boyle, G and T.McCarthy (1997), “A Simple Measure of -Convergence,” Oxford Bulletin of Economics and Statistics, Vol. 59, No. 2, pp. 257-264. Brezis, E, P. Krugman and D. Tsiddon (1993), “Leapfrogging in International Competition: A theory of Cycles in National Technological Leadership,” American Economic Review, Vol 83 (5) pp. 1211-1299. de la Fuente, A (1997), “The Empirics of Growth and Convergence: A Selective Review,” Journal of Economic Dynamics and Control, Vol. 21, pp. 23-73. Friedman, M (1992), “Do Old Fallacies Ever Die?,” Journal of Economic Literature, Vol. XXX, no. 4, pp. 2129-2132. Hart, P (1995), “Galtonian Regression Across Countries and the Convergence of Productivity,” Oxford Bulletin of Economics and Statistics, Vol. 57, no. 3 August. Jenkins, S and P. Van Kerm (2002), “From Rags to Riches: Are Income Changes Redistributive,” Ph.D Thesis, University of Namur. 20 Johnson, P (2000), “A Nonparametric analysis of Income Convergence across the U.S States,” Economic Letters, 69, pp. 219-23. Lambert, P (1993) The Distribution and Redistribution of Income, Manchester University Press, Manchester, U.K.. Lee, K, M. Pesaran and R. Smith (1997), “Growth and Convergence in a MultiCountry Empirical Stochastic Solow Growth Model,” Journal of Applied Econometrics, Vol. 12, Issue 4, pp. 357-392. Lerman, R and S. Yitzhaki (1984), “A Note on the Calculation and Interpretation of the Gini Index,” Economic Letters, Vol. 15, pp. 363-368. Mankiw, G, D. Weil and P. Romer (1992), “A Contribution to the Empirics of Growth,” Quarterly Journal of Economics, Vol. 107, pp. 407-37. O’Neill, D, O.Sweetman and D. Van de gaer (2002) “The Consequences of Specification Error for Distributional Analysis with an Application to Intergenerational Mobility,” NUI Maynooth Working paper N11/01/02. O’Neill, D (1996), “Education and Income Growth: Implications for Cross-Country Inequality,” Journal of Political Economy, Vol. 103, no. 6, pp. 1289-1301. Quah, D (1993), “Galton’s Fallacy and tests of the Convergence Hypothesis,” The Scandanavian Journal of Economics, 95, pp. 427-443. Romer, P. (1986) “Increasing Returns and Long-Run Growth,” Journal of Political Economy, 99, June pp. 500-21. Sala-I-Martin, X (1996a) “The Classical Approach to Convergence Analysis,” Economic Journal, Vol. 106, pp. 1019-1036. Sala-I-Martin, X (1996b) “Regional cohesion: Evidence and theories of Regional Growth and Convergence,” European Economic Review, Vol. 40, pp. 1325-1352. Shorrocks, A (1983) “Ranking Income Distributions,” Economica, Vol. 50, pp. 1-17. Solow, R. (1956) “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, 70, February, pp. 65-94. Sugimoto, Y. (2003), “ Inequality, Growth and Overtaking,” Dept. of Economics, Brown University. Summers, R and A. Heston (1991) “The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988,” Quarterly Journal of Economics, 106, pp. 327-368. Tamura, R (1992), “Efficient Equilibrium Convergence: Heterogeneity and Growth,” Journal of Economic Theory, Vol. 58, no. 2, pp. 355-376. 21 Table 1: Full Sample of 98 countries included in the analysis Argentina Costa Rica India Malawi Sweden Australia Denmark Ireland Malaysia Switzerland Austria Dominican Republic Iran Niger Seychelles Burundi Algeria Iceland Nigeria Syria Belgium Ecuador Israel Nicaragua Chad Benin Egypt Italy Netherlands Togo Burkina Faso Ethiopia Jamaica Norway Thailand Bangladesh Finland Jordan Nepal Trinidad and Tobago Bolivia France Japan New Zealand Turkey Brazil Gabon Kenya Pakistan Tanzania Barbados Ghana Korea Panama United Kingdom Canada Guinea Sri Lanka Peru Uganda Chile Gambia Lesotho Philippines Uruguay China Guinea-Bissau Luxembourg Portugal United States of America Cote d’Ivoire Equatorial Guinea Morocco Paraguay Venezuela Cameroon Greece Madagascar Romania South Africa Congo, Republic of Guatemala Mexico Rwanda Zambia Colombia Hong Kong Mali Senegal Zimbabwe Comoros Honduras Mozambique Spain Cape Verde Indonesia Mauritius El Salvador 22 Table 2: OECD Countries included in the analysis* Australia Finland Italy Netherlands Sweden Austria France Japan Norway Switzerland Belgium Greece Korea New Zealand Turkey Canada Ireland Luxembourg Portugal United Kingdom Denmark Iceland Mexico Spain United States * Of the 30 countries currently listed as members of the OECD, the Czech Republic, Slovakia, Poland, Hungary and Germany did not have consistent data for the period 1960-2000. 23 Table 3: Relative Trends in Income Inequality for the OECD countries with alternative degrees of Inequality Aversion Time Period G(1.5) G(2) G(2.5) 1960 .163 .253 .318 1970 .132 .205 .260 1980 .108 .174 .226 1990 .105 .169 .218 2000 .114 .171 .214 Table 4: Relative Trends in Income Inequality for the Full-Sample (N=98) with alternative degrees of Inequality Aversion Time Period G(1.5) G(2) G(2.5) 1960 .327 .483 .572 1970 .337 .503 .600 1980 .336 .510 .612 1990 .358 .538 .641 2000 .370 .553 .659 24 Table 5: Income Convergence Dynamics for 25 OECD Countries: 1960-2000 Time period -Convergence G(2) -convergence DP(2) Reranking R(2)  Barro-Regression (s-errors in brackets) 19602000 .171-.253 = -.083 -.116 .033 .012** (.0025) 19601970 .205-.253 = -.048 -.056 .008 .016** (.005) 19701980 .174-.205 = -.031 -.045 .014 .013** (.004) 19801990 .169-.174 = -.005 -.013 .008 .012** (.006) 19902000 .171-.169= .002 -.009 .011 .005 (.006) Table 6: Income Convergence Dynamics for the full-sample of 98 countries: 1960-2000 Time period -Convergence G(2) -convergence DP(2) Reranking R(2)  Barro-Regression (s-errors in brackets) 19602000 .553-.483 = .07 .017 .053 -.004** (.0015) 19601970 .503-.483 = .02 .012 .008 -.006** (.002) 19701980 .510-.503 = .007 -.003 .01 -.003 (.002) 19801990 .538-.510 = .028 .02 .008 -.003 (.002) 19902000 .553-.538= .015 .01 .005 -.007** (.002)