World Developmmr, Vol. 16. No. 11, pp. 1371-1376. 1988 Printed in Great Britain.

Economic Development and Income Inequality:

Further Evidence on the U-Curve Hypothesis

0305-750x/88 $3.00 + 0.00 0 1988 Pergamon Press plc

RAT1 RAM* Illinois State University, Normal

Summary. - Internationally comparable data on inequality and income are utilized to reassess the empirical status of Kuznets’ U-curve hypothesis. The hypothesis seems well supported when both developed countries (DCs) and less developed countries (LDCs) are included in the sample. However, the position changes rather dramatically if the sample is restricted to LDCs, and very small support for the hypothesis is then observed. Also. a simple comparison indicates that some of the support reported in earlier studies may have been due to the use of conventional gross domestic product per capita. In general. results based on Gini coefficient seem less favorable to the hypothesis than those derived from household income shares.

1. INTRODUCTION

The nature of the relationship between level of economic development and income inequality has attracted much attention. One hypothesis about the relation, which was first proposed by Kuznets (1955). suggests that as economic de- velopment occurs, income inequality first in- creases and, after some “turning point,” starts declining. Kuznets formulated the hypothesis on the basis of historical data for industrialized countries and urged caution in the application of the proposition to presently developing coun- tries. However, since the expected pattern of income distribution at various stages of develop- ment is obviously of major importance, and since time-series data on income distribution for even moderate periods are not available for most de- veloping countries, the proposition has been tested by practically all researchers on the basis of cross-national observations. Despite the reser- vations some scholars had, early tests by Paukert (1973), Ahluwalia (1976) and others tended to be favorable to the hypothesis which almost gained the status of a “stylized fact.” Some recent stud- ies indicate a rather mixed picture. Scholars like Saith (1983) cast doubt on the applicability of the hypothesis to the developing countries and on its usefulness as a possible framework for studying problems of economic development. Papanek and Kyn (1986), on the other hand, report lim- ited support for the hypothesis when considered in a broader conceptual framework.

Besides the difficulty inherent in drawing infer-

ences from cross-section data about the expected temporal patterns in individual countries. almost all previous studies on the subject were charac- terized by two major data limitations. First, income distribution data lacked the kind of cross- country comparability that is important in such investigations. Lack of comparability arose from several factors, including differences in concepts of income, variations in the income-receiving units, and disparities in geographical coverage of the cross-country data utilized in the analyses. Second, the per capita dollar income measures, which have typically been employed as proxies for the level of development, were based on con- ventional exchange rates, and, as the recent work by Kravis, Heston and Summers (1982, p. 12) dramatically illustrates, introduced a major dis- tortion in the income variable. Enough attention has also not been given in some of the studies to the sensitivity of the results to sample coverage and to the choice of the inequality measure.

The main purpose of this work is to throw further light on the relationship between de- velopment and income distribution by (a) using internationally comparable income distribution data recently made available by van Ginneken and Park (1984), (b) employing measures of gross domestic product (GDP) per capita in in-

‘Two anonymous referees of this journal gave helpful comments on an earlier version. Competent research assistance was provided by Sunita Bose at initial stages of the project. The author alone is responsible for all errors and deficiencies.

1371

1372 WORLD DEVELOPMENT

ternational dollars. published by Summers and Heston (1983). (c) comparing the estimates based on Summers-Weston data with those re- suiting from conventional measures of GDP per capita, (d) comparing the results for three differ- ent inequality measures, and (e) checking on the sensitivity of the estimates to sample va;iations.

2. MODEL, DATA AND THE MAIN RESULTS

Although several other variables would belong in a fully articulated model of income inequality, for the limited purpose of investigating the valid- ity of Kuznets’ U-curve hypothesis it appears enough to include linear and quadratic income terms in the inequality equation.’ As is the almost universal practice in such cases, income terms are entered logarithmically.’ A simple re- gression model would, therefore, be of the form

YINQ = a,) + a,lnY + nz(lnY)’ + l( (1)

where YINQ stands for an index of income in- equality, Y is GDP (income) per capita and serves as a proxy for the level of economic de- velopment, In denotes the natural logarithm of the variable, and ll is the usual stochastic error term. Equation (1) is used for obtaining esti- mates of the regression parameters. In addition, some simple plots are also presented.

Data on income distribution are taken from van Ginneken and Park (1984) and are based on household income shares. These data possess a degree of cross-country comparability that is probably better than that obtainable from any other source.3 The three inequality measures in- cluded are Gini coefficient (GINI), income share (in percentage points) of the poorest 20% of households (BOT20), and (percentage) income share of the poorest 40% of households (BOT40). Note that information on income dis- tribution is based on income “available” to each household which is treated as the income- receiving unit. As van Ginneken and Park (1984, pp. 2-9) discuss, distribution of persons by household income “per equivalent unit” is prob- ably the best measure of income distribution. However, such distributions are available only for a few countries. Even distribution of persons by household income per head is given by them for only 14 countries. Moreover, apart from the consideration of data availablity, van Ginneken and Park (1984, p. 9) summarize the difference between the distributions based on household in- come and income per head by saying that the per head distribution is “somewhat more equal”

than the per household distribution in most cases. Their observation suggests that use of household income distributions may not have a significant effect on the results reported in this work.’

Data on income are taken from Summers and Heston (19&l). These are in terms of GDP per capita in international dollars. Conventional dol- lar measures of GDP per capita, derived from the same source. have also been used for comparing results obtained from the two income measures.’

The Appendix lists the 32 countries for which income distribution data are available. The basic data are included in the Appendix. Yugoslavia has been excluded partly because it is a socialist country and probably belongs to a different struc- ture, and partly because it is difficult to get con- ventional GDP data for it from Summers and Heston (19S-l). Eight of the 32 countries are de- veloped countries (DCs) in terms of the World Bank (198-l) classification; the remaining 2-l are less developed countries (LDCs).

For a broad visual depiction of the relationship between development and distribution. Figure 1 presents simple plots of the share of the poorest 40% of households against GDP per capita.‘The plots have been drawn for the internationally comparable income measure as well as for con- ventional GDP per capita. Plots for the LDC subsample as well as the full sample are given. Although it is difficult to draw clear conclusions from such plots. it can be observed that while the full-sample plots give some indication of a U- shaped relationship, hardly any pattern is dis- cernible in plots for the LDC subsample.

In view of the difficulty of assessing the pattern from the plots alone, it is useful to consider esti- mated parameters of equation (1). Table 1 con- tains the main estimates for three cross-section samples in respect of each of the three inequality measures, and for GDP per capita in both inter- national and conventional dollars. The following points may be observed from Table 1.

1. If the entire sample of 32 countries is con- sidered. estimated coefficients of income terms as well as the regression F-statistics show high statistical significance, and the coefficients of linear and quadratic income terms have the ex- pected opposite signs. That is true for all three in- equality indices and for both income measures. The results could thus be deemed to be quite sup- portive of the inverted U-curve hypothesis.’

2. When the sample is limited to the 24 de- veloping countries, the statistical significance of the estimates suffers a major drop. Focusing on the estimates based on GDP per capita in inter- national dollars, it is obvious that only one of the three regressions shows statistical significance at

FURTHER EVIDENCE ON THE U-CURVE HYPOTHESIS 1373

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I I I I I I I 1 I I I I I I I 400 800 1400 2400 3mO 3600 2004CO 800 12cO 1600 2ccQ 24cO

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Figure 1. Plots of the income share (in percentage points) of the poorest 40% of households (BOT40) and real GDP per capita CRY) and conventional GDP per capita (EY). Based on data in the Appendix. Scales differ in the four

sections.

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the 10% level, and even in that case the indi- vidual coefficients lack significance at almost any reasonable level. Therefore, it seems that the full-sample results that are favorable to the hypothesis reflect mainly the intergroup dif- ference between developed and developing countries, and do not suggest the existence of a statistically significant U-shaped relation be- tween development and distribution in develop- ing countries.s This view is also consistent with the visual impression one gets from Figure 1.

3. In general, results based on conventional measures of GDP per capita support the U-curve hypothesis more than those derived from GDP per capita in international dollars. In fact, if one considers the estimates based on conventional GDP per capita, at least a limited degree of sup- port for the hypothesis can be inferred even in samples of developing countries. In four of the six cases, the regression F-statistics are statisti- cally significant at the 5% level. It is, therefore,

possible that some of the support for the U-curve hypothesis reported in several earlier studies arose simply from the use of conventional GDP per capita which, as has become well known now, is not a good proxy for the level of income or eco- nomic development.

4. There is some variation in the results for the three indices of inequality. Estimates based on income share of the poorest 20% of households provide more support for the U-curve hypothesis than the other two measures. and estimates de- rived from the Gini coefficient equations seem to provide least support for the hypothesis. These results indicate need for caution in drawing strong inferences from a single inequality index.

5. Although statistical significance of the esti- mates changes in a major way when one moves from full sample to the subsample of developing countries, the results do not seem to show much sensitivity to sample coverage within the de- veloping group. For example, structure of the

1371 WORLD DEVELOPMENT

Table 1. Eslimares of income distriburion equakms for three inrercounrry samples. rhree inequal+ indices and Iwo measures of GDP pur capita’

Real GDP per capita in Conventional GDP per capita international dollars (RY)

LRY (LRY)’ R’(R

based on exchange rates (ET) LEY (LEY)- R’(F)

Full sample of both developed and developing countries (N = GlNI 0.711~ -0.053: 0.36; 0.348:

(2.95) (-3.11) (8.31) (3.31) BOT20 - 17.573s 1.216f 0.34 -8.61 I$

(-3.58) (3.66) (7.40) (-4.40) BOT40 -37.838$ 2.649$ 0.34; - 17.8621

(-3.31) (3.42) (7.45) (-3.81)

Developing countries only (N = 24) GINI 0.463 -0.032 0.06 0.388

32) -0.027:

(-3.59) 0.64li

(4.56) 1.353$

(4.02)

-0.030 (0.86) (-0.83) (0.70) (1.37) (-1.28)

BOT20 -7.839 0.489 0.24t -7.303 0.516 (-0.81) (0.70) (3.36) (-1.49) (1.29)

BOTJO -20.111 1.316 0.15 - 16.971 1.23s (-0.86) (0.78) (1.91) (- I .40) (1.25)

Developing countries excluding Argentina and Venezuela (N = 22) GIN1 0.427 -0.029 0.07 0.3h8 -0.028

(0.60) (-0.56) (0.70) (0.94) (-0.85) BOT30 -7.503 0.461 0.2-l+ -7.466 0.527

(-0.58) (0.49) (3.06) (-1.11) (0.94) BOTJO -21.645 1.122 0.16 -18.181 1.335

(-0.70) (0.63) (1.86) (-1.10) (0.97)

0.42; (10.39)

0.4-r;

(11.59) 0.41;

(10.20)

0.1s (1.80) 0.36i

(6.03j 0.26:

(3.60)

0.16 (1.75) 0.37:

(5.63) 0.27;

(3.53)

*The corresponding r-statistics are given in parentheses below the estimated coefficients of the linear and quadratic income terms. F-statistics are below R’s. A constant term is included in all resressions; but, to save space. its estimates are not reported. tStatistically significant at the 10% level. SStatistically significant at least af rhe 5% level.

estimates for developing countries remains prac- tically unchanged whether two of the highest income countries (Argentina and Venezuela) are included or excluded.

3. CONCLUDING REMARKS

Several well known caveats are appropriate in interpreting such results even when one utilizes internationally comparable measures of inequal- ity and income. The most important limitation arises from the use of cross-section data for draw- ing inferences about the expected intertemporal distributional patterns in individual countries.’ Also, variations in functional forms and sample coverage’ could significantly affect the results. Subject to these caveats, however, it seems

reasonable to say that use of internationally com- parable data on Income and distribution indicates very limited support for the U-curve hypothesis in the developing world.“’ The results that are favorable to the hypothesis appear to arise from either structural differences between developed and developing countries, or from the use of un- satisfactory dollar income variables that are based on conventional exchange rates. Employ- ment of narrowly-based inequality measures (like income share of the poorest 20%) also probably contributes to inferences favorable to the hypoth- esis. While it is certainly possible for different re- sults to emerge if better data sets, especially intracountry observations, are used and/or richer functional forms are employed, the reported evi- dence indicates need for caution in the use of U- curve hypothesis as a fair representation of what may be expected to happen to income distribu- tion as economic development occurs in the less developed world.

FURTHER EVIDENCE ON THE U-CURVE HYPOTHESIS 1375

NOTES

1. See Ahluwalia (1976). Lecaillon er al. (1984). and Papanek and Kyn (1986). besides many others. for a list of the other variables that could be included.

2. For example, Saith (1983) explores the validity of the U-curve hypothesis primarily through an equation that includes (logarithmic) linear and quadratic income terms.

3. Although the exact reference period varies some- what, most income distribution data are for the early 1970s. GDP per capita has been taken for the same year to which the distribution data pertain.

4. See van Ginneken (1984. pp. 2-15) for a discus- sion of several details concerning their data on income distribution.

5. Being based on short-cut methods, the estimates in international dollars are indeed subject to some error; but, as proxies for levels of development of diffe- rent countries, these still seem far superior to conven- tional data on GDP per capita.

6. Note that the share of the poorest 40% of house- holds (BOT40) is plotted against level of GDP per capita and not its logarithmic transformation. The reason is that the basic relation is postulated in terms of income (as a proxy for the level of development) and distribution of income, and that is what the plots show. The plots, however, have a similar pattern if logarithm

of income is used. Out of the three inequality mea- sures. BOT-10 is chosen for the plots because this seems to be the measure most commonly used. Of course. the plots would show a similar structure if another inequal- ity measure is used.

7. It is obvious that the sign of each income term in the Gini equation will be the opposite of the sign of the corresponding term in BOTZO and BOT-lO equations.

8. Signs of individual coefficients do suggest some support for the U-curve hypothesis; but in the absence of statistical significance of these coefficients or the regression F-statistics. it is difficult to interpret the esti- mates as being favorable to the hypothesis in a statisti- cally significant sense.

9. As a perceptive referee noted, some evidence based on time-series observations for individual coun- tries like Mexico and South Korea could be interpreted as supportive of the U-curve hypothesis. As multiple observations on income distribution become available for more countries. it should be interesting to compare results from cross-section and individual-country data sets.

10. Saith (1983) proposes a similar conclusion; but his distribution data lacked adequate cross-country compa- rability, his income measure was based on conventional exchange rates, and the results focused on one in- equality index.

REFERENCES

Ahluwalia, M. S.. “Income distribution and develop-

Kravis. I. B., A. Heston, and R. Summers, World Pro- duct and Income (Baltimore, MD: Johns Hopkins

ment: Some stylized facts,” American Economic Re-

University Press, 1982). Kuznets, S..

view, Vol. 66 (1976). pp. 128-135.

‘*Economic growth and income in- equality,” American Economic Review, Vol. 45 (1955). pp. l-28.

Saith, A., “Development and distribution: A critique

Paukert, F., “Income distribution at different levels of

of the cross-country U-hypothesis,” Journal of Development Economics, Vol. 13 (1953). pp.

development: A survey of evidence,” lnrernational

367-382.

Labour Review, Vol. 108 (1973). pp. 97-125.

Summers, R., and A. Heston, “Improved international comparisons of real product and its composition, 1950-80,” Review of Income and Wealth. Vol. 30 (1984). pp. 207-262.

Lecaillon, J., F. Paukert, C. Morrisson, and D. Germi- dis, Income Distribution and Economic Develop- menI: An Analytical Survey (Geneva: International Labour Office, 1984).

Papanek, G. F., and Oldrich Kyn, “The effect on in- come distribution of development, the growth rate and economic strategy,” Journal of Development Economics, Vol. 23 (1986). pp. 55-65.

van Ginneken, W., and J. Park (Eds.), Generaring In- ternationally Comparable Income Diwibution Estimates (Geneva: International Labour Office, 1984).

World Bank, World Tables, The Third Edition (Balti- more, MD: Johns Hopkins University Press, 1984).

1376 WORLD DEVELOPMENT

APPENDIX: Table Al. Basic country data

country BORO’ BOT40’ GINI’ BY’ EY’

Argentina Banpladesh B&l Chile Costa Rica Denmarkt Egypt Fiji Francet Germany (FRG)t Honduras India Iran Ireland? Kenya Korea (South) Mexico Nepal Panama Peru Philippines Sierra Leone Spaint Sri Lanka Sudan Sweden? Tanzania Trinidad & Tobago Venezuela United Kingdomt USAt Zambia

4.4 6.8 2.0 4.4 3.3 7.4 5.8

::: 6.9 2.3

:.: 712

::: 2.7 4.6 2.0

::;

::; 7.5 4.0 7.2 5.8 3.8 3.0

s’:; 3.4

14.1 0.44 2.750 1,622 18.2 0.35 365 153 7.0 0.61 1.466 777

13.4 0.45 2,015 1.128 12.0 0.49 1,658 779 20.0 0.30 6.444 7.926 16.5 0.40 841 336 12.5 0.47 1,962 1.079 16.4 0.39 5,864 6,450 17.9 0.37 5,919 6.866 7.3 0.61 841 395

16.2 0.42 472 146 11.3 0.52 2,381 1,286 20.3 0.32 3,038 2,430

9.0 0.59 448 260 16.9 0.38 1.648 742 9.1 0.56 1,875 900

12.6 0.53 365 102 7.2 0.57 1.804 956 7.0 0.57 1.662 764

14.1 0.46 781 258 15.2 0.44 504 227 17.3 0.37 3,841 2.458 19.2 0.35 795 191 13.0 0.44 731 219 20.0 0.30 6,950 10,286 16.0 0.42 374 131 13.3 0.45 2,878 1,468 10.3 0.49 3,667 2,273 19.7 0.32 5,067 5.320 15.8 0.39 6.774 6,774 10.8 0.56 732 483

l BOT20 and BOT40 denote percentage income shares of poorest 20% and 40% households respectively; GINI stands’ for the Gini coefficient: RY is GDP per capita in real (international) dollars; EY is conventional GDP per capita in dollars. BOT20, BOT40, and GIN1 are based on van Ginniken and Park (1984). and RY are EY are based on Summers and Heston (1984). Data Table. Note that EY is obtained by multiplying RY with the “price level” and dividing by 100. tThese are developed countries (DCs) in terms of the classification used by World Bank (1984). All others are taken as LDCs.