Urban sector income distribution and economic development

JOURNAL

OF URBAN

ECONOMICS

21,127-145 (1987)

Urban Sector Income Distribution Economic Development’ CHARLES

and

M. BECKER

Department of Economics,Vanderbilt University Nashville, Tennessee37235 Received May 14,1982; revised May 16,1985 This paper examines the relationship between measures of urban sector inequality and economic development for a sample of 25 developing and newly industrialized countries. A U-shaped relationship is found in which bottom urban quintiles’ income shares initially decline and then rise as per capita income increases. This relationship is strengthened when an estimate of urban per capita income replaces national per capita income as the development measure. The curves suggest that per capita incomes of the bottom quintiles will never decline as development proceeds, but may rise only very slowly. 0 1987 Academic press, IX

The hypothesis that measuresof national income inequality initially tend to worsen and then improve as an economy develops is well-known and has some empirical support. Kuznets [15] first suggestedthis U-shaped relationship and provided the first cross-country and time-series evidence on its behalf. Oshima’s [24] early study, Ahluwalia’s [l] and Chenery and Syrquin’s [7] cross-country regressions,along with Paukert’s [25] study and Cline’s [S] work in his survey based on more extensive data have also found a U-shaped relationship between bottom groups’ income shares and per capita GDP. Fields [lo] provides an extensive survey of time-series evidence and concludes that the data neither strongly confirm nor contradict the U curve found in cross-country regressions. Recent evidence, however, suggests that the British economy has indeed experienced such a long-run U-shaped inequality trend (Williamson [30]). It is also of interest whether a similar U-shaped pattern can be observed within sectors of an economy. The most common explanations of the U pattern, termed “modem sector enlargement” models by Fields [lo], are based on urban/industrial sector growth that is rapid in comparison with rural/agricultural sector growth. This long-run transformation underlies the explanation suggested by Lewis [16] and refined by Robinson [26]. Such models do not stress changing relationships within economies’ urban and ‘Valuable advice and criticism have been provided by Rudolph Blitz, Malcolm Gem, W. Arthur Lewis, Samuel Morley, Mieko Nishimizu, and in particular Edwin S. Mills, with whom I have worked closely on related topics. Lee Jarrard has provided excellent research assistance. 127 0094-1190/87 $3.00 Copyright 0 19X7 by Acadermc Press. Inc. All rights of reproduction in any form reserved

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CHARLES M. BECKER

rural sectors, and need not generate a U curve for these sectors if urban and rural income distributions also change dramatically as a country develops. However, one can also construct development models that emphasize the presence of informal sector activities within the urban economy, or that stress the presence of a heterogeneous labor market and the acquisition of skills. These models typically imply a U-shaped relationship between inequality and development level, both for the national economy and for the urban sector. In brief, one can cite standard development models that imply an urban sector U curve along with models that do not predict such a pattern. This paper examines the relationship between various indicators of urban sector income inequality and per capita income. A cross-country study finds that a U-shaped urban inequality-income relationship exists and is similar to that found for entire economies. The limited time-series data available also are consistent with the presence of an urban U curve. These results update preliminary ones reported in Mills and Becker [19]. Detailed discussion of models underpinning the relationships observed empirically is postponed to a subsequent study. 1. THE CROSS-COUNTRY STUDY Income distribution data used in the cross-country study are taken from Jain [ll]. The Appendix discussesthese data along with the bases for the different samples used. The sample contains statistics on 25 countries’ urban sector income distributions, all of which define the household as the income recipient unit. All but five surveys cover the entire urban or nonagricultural sector; the remaining surveys cover only specific cities. To obtain information regarding the U curve, characteristics of urban income distributions are regressedon measuresof the economic development level. While choosing a comparable set of dependent variables poses dit%culties, further problems arise in choosing the independent variable. The standard procedure in the national Kuznets regressions has been to take per capita incomes (GDP) converted into U.S. dollars at official exchange rates as the measure of economic development. Yet it is well-known that true per capita purchasing power is inadequately measured by GDP converted at official exchange rates.2 ‘It has been argued and found empirically (Kravis, et al. [13, 141)that exchange rates are determined by weighted averagesof the absolute prices of traded goods in different currencies, while currencies into dollars ought to be based on a basket of goods that includes nontraded goods as well. Services predominate among these nontraded goods, so that nontradeables tend to be relatively labor-intensive. Moreover, as LDCs are typically labor-rich and capital-poor, LDC wage/rental ratios are low compared to developed countries’ ratios. Consequently, the cost in U.S. dollars with conversion at official exchange rates of producing a unit of the nontraded good is less in LDCs than in developed countries. In addition, nontradeable goods

URBAN INCOME DISTRIBUTION

IN LDC’S

129

In view of the problems with employing GDP as a measure of development, we employ a measure of per capita income based on a conversion into U.S. dollars at estimated purchasing power parity (PPP) exchange rates. Ideally, these PPP exchange rates are found by comparing costs in local currencies of purchasing a “world consumer’s” basket of goods in different countries. The ratio of local currency costs in one’s own country of purchasing this basket relative to the dollar costs of the same purchases in the United States, then, gives one’s PPP exchange rate. Pioneering research by Kravis et al. (KHS) [13] has led to a compilation of these PPP exchange rates for several countries. Unfortunately, true PPP exchange rates have not been compiled for all countries in our sample. However, shortcut estimates of PPP per capita income (GDPkhs) have been constructed for virtually all countries by KHS. KHS [14] compare per capita incomes converted at official and PPP exchange rates in the countries for which the latter figures are available, and devise an adjustment factor based on unadjusted per capita GDP, the economy’s degree of openness, and its inflation rate relative to that of the rest of GDPkhs estimates so derived are probably superior estimates of economic development to GDPs converted at official exchange rates.3 Several theories of income distribution change are consistent with or imply an urban sector U curve. It is shown in Becker [2], however, that a standard two-sector development model with initially surplus agricultural labor (based on either a classical or a neoclassical rural sector; see Sen [28]) and a neoclassical urban sector need not generate an urban U curve. The income distribution path it generates may or may not have a point of maximal inequality, depending on savings and fertility rates of different classes and on the urban sector’s aggregate elasticity of substitution between capital and labor. It appears virtually certain, however, that the transition from a labor surplus to a nonsurplus economy will lead to a decrease in the rate of increase of inequality measures.To the extent that this theory (based on a neoclassical two-factor, one urban good general and services as a whole tend to be characterized by low rates of technological progress, so that the nontradeables’ production functions for LDCs and developed countries are relatively similar. 3Having adjusted 1970 dollar values of per capita incomes to reflect PPP exchange rates, these estimates then must be converted into real per capita income figures for the year in which the urban sector income distribution study was conducted. This conversion is based on the assumption that real GDPkhs and real GDP growth rates are identical over the relevant period. Such a procedure is slightly inaccurate, but any loss is trivial in comparison with the uncertainty surrounding a country’s true PPP per capita income, particularly as 20 of the observations were taken within 3 years of 1970. In the event that a country had more than one urban income distribution survey that took household incomes as the recipient unit, the sample employed took that survey closest to 1970.

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M. BECKER

equilibrium model) is accepted, one would expect to find the incomeinequality relationship closely described by plotting measures of inequality on linear and squared terms of the logarithm of development. Moreover, one would expect to find a positive linear and negative (or zero) quadratic coefficient in a regression equation, so that the function would take an inverse U shape or (in non-log space) an effectively bounded one. The semilog form is also employed by Ahluwalia [l] in his national inequality-income regressions. As he offers no theoretical justification for this form, it seemsreasonable to suppose that it is the one that gave him the best U-shaped fit. This paper presents only regressions of the inequality on linear and quadratic terms of the natural log of development, as it is both the theoretically preferred and the most comparable form. Moreover, results of regressions based on other forms (available in Becker [4], Chaps. 3-4) do not substantially alter the paper’s major conclusions. Nor are the conclusions affected if GDP replaces GDPkhs as the development measure, although the explanatory power of the regressions is reduced. In addition to specifying the form of the regressions and identifying GDPkbs as our measure of development, a summary statistic representing inequality remains to be chosen. No single statistic fully captures all nuances of a multimoment income distribution. The urban sector Gini coefficient (GINI) is employed as one inequality measure; regressions are also run using the urban income share of the bottom quintile of urban households (Sl), the share of the next-to-bottom urban quintile (S2), the share of the middle urban quintile (S3), and the share of the top five percentiles of urban households (STOP) as dependent variables (Because large Gini coefficients and STOP values reflect a high degree of inequality, a pattern of rising and then falling inequality will generate an inverse U curve.) Results from the regressionsappear in Table 1. From the negative linear and positive quadratic coefficients for Sl-S3, and from the positive linear and negative quadratic terms for STOP and GINI, there appears to be a U curve for the urban sector. That is, income shares of the lower urban household quintiles initially fall as a country’s aggregate development level rises. Eventually, however, shares of the bottom urban groups increase with development level. This cross-sectional pattern is similar to that found for national income classesas development level proceeds. The explanatory power of the regressionsfollows a distinct pattern, rising as the dependent variable becomes an increasingly wealthy quintile, though the third quintile. In particular, the link between GDPkhs and Sl is tenuous. All models that generate an urban U curve assumesome degree of household homogeneity while ignoring transfer incomes. All agents are assumed to participate in a labor market or submarket within the economy. Yet in reality, many households in the bottom quintile are beyond the pale

URBAN

INCOME

DISTRIBUTION TABLE

1

Initial Urban U-Curve Regressions (Absolute Independent variable coefficients Constant In GDPkhs (In GDPkhs)’

R2 F

Mean of dependent variable SEE n

131

IN LDC’S

t Values)

Dependent variables Sl

s2

s3

STOP

GIN1

51.24* (2.13) 14.46 (1.94) 1.13 (1.97)

53.36* (2.41) 14.34* (2.09) 1.16* (2.20)

57.28* (2.95) 14.10* (2.34) 1.14* (2.46)

139.23* (2.12) 51.04* (2.51) ~ 4.01* (2.57)

-1.60 (1.76) 0.6532* (2.31) -0.0519* (2.39)

0.0815 2.0649 5.54 1.52 25

0.1982 3.9655* 9.14 1.40 25

0.2481 4.9596* 14.37 1.22 25

0.1819 3.6685* 21.17 4.13 25

14.73 13.68 14.19 16.73

17.99 23.06 22.23 14.70

Predicted value of dependent variable at GDPkhs: 10.10 186 (Bangladesh, 1966-1967) 6.54 9.04 489 (Philippines, 1971) 5.03 9.56 945 (Mexico, 1963) 5.21 12.15 2487 (Israel, 1968-1969) 7.26 Value of GDPkhs at point 483 601 of maximal inequality Predicted dependent variable value at the 9.04 4.98 turning point

485

13.68

581

23.22

0 1790 3.6164’ 0.4254 0.0574 25 0.3962 0.4547 0.4391 0.3344 541

0.4553

*Significance at the 5% level. All inequality measures refer to shares of household income.

of any labor market. These bottom households include large numbers whose adult members are incapacitated or abandoned, and who are constrained from receiving the market rate of return to their potential labor endowments. Their incomes will be heavily influenced as well by traditional redistributive patterns and by the social obligations faced by their more fortunate km. Such social ties need not be strongly correlated with urban per capita income. A supplementary factor working to weaken the U curve for the bottom quintile lies in changes in its demographic composition over incomes. The bottom quintile of households in industrialized societies is overwhelmingly either very young or, particularly, very old. As life spans increase, the bottom quintile becomesincreasingly populated with voluntary retirees who live on savings, especially in rich countries. Similarly, rises in secondaryschool education rates reduce young workers’ participation rates. These patterns suggest that labor-force participation rates in the bottom quintile

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CHARLES

M. BECKER

are likely to fall as a country develops, thus damping the trend toward an increasing income share on the curve’s upswing. An indicator of the U curve’s slope can be inferred from examining the predicted quintile shares at different stagesof development (Table 1). For a country near the turning point, the income share of the urban top 5% exceeds 23%; this share falls to only 15% near the upper end of the sample. The point of maximal inequality tends to come at a fairly modest stage of development, one in which national per capita income is around 500 1970 “Kravis dollars” (around 200 unadjusted dollars). 2. URBAN SECTOR AND NATIONAL

PER CAPITA INCOMES

Section 1 used national Kravis-adjusted per capita income as the measure of development. Would a similar U curve be observed in the event that urban sector Kravis-adjusted per capita income (hereafter UGDPkhs) were taken as the measure of development? Virtually all development theories predict that urban sector per capita income will be a monotonically increasing function of national per capita income. In such a case, a U curve found with GDPkhs as the development measure will also hold when UGDPkhs is the development measure. Nonetheless, it is conceivable the UGDPkhs will not grow monotonically with GDPkhs across countries. If country A has a thriving urban economy but a poor agricultural sector while country B has identical per capita incomes in both urban and rural sectors, then GDPkhs, slightly above GDPkhs, is consistent with UGDPkhs, < UGDPkhs,. Alternatively, suppose that UGDPkhs/GDPkhs is the same in both countries, but that country A is predominantly urban and country B is mainly rural. Then GDPkhs. > GDPkhs, is consistent with UGDPkhs, > UGDPkhs,. Consequently, it is not certain that the urban U curve would continue to show strongly in cross-country regressions if UGDPkhs were the development measure. Unfortunately, ratios of urban to national per capita income typically are unavailable for countries with urban income distribution data, or are available from different years. As an alternative procedure, we adjust GDPkbs terms by an estimate of UGDPkhs/GDPkhs, y. y varies with the percentage of the national population living in urban areas (PCTURB), for which data do exist, and with the ratio of urban to rural per capita income, S. However, the value of 6 is not known for most countries in the urban income distribution sample. A simple accounting identity is yi = (Si - I)P&JRB,

+ 1.

0)

For PCTURB E (0,l) and S > 1, y > 1. As ai is not generally known, it

URBAN INCOME DISTRIBUTION

I33

IN LDC’S

TABLE 2 Observed Values of Urban/Rural (6) and Urban/National (v) Per Capita Incomes for 16 Countries Grouping

6 Values

y Values

Poorest 4 (Bangladesh, India, Kenya, Pakistan) Second 4 (Philippines, Thailand, Sri Lanka, Tunisia) Third4 (Honduras, Malaysia, Peru, Colombia) Richest 4 (Brazil, Costa Rica, Cyprus, Panama)

2.87

2.16

2.16

1.70

2.33

1.45

2.26

1.39

1.86 2.56 2.02 2.45

1.56 1.76 1.43 1.43

South Asian countries All other countries All other countries, excluding Kenya South American countries Nofe. Figures are unweighted average values. Source. Becker [2], Chap. 4; also see Mohan [21].

is necessary to obtain an estimate of Si, &. From the available values of 6, there appears to be little, if any, trend in its value across development levels (Table 2). Insofar as the value of 6 does vary systematically, it appears to do so geographically rather than across income levels. In particular, one finds extremely high S values in East Africa and high values in South America. However, a systematic decline in y over both urban and national income levels does appear. Even in South American countries, higher degrees of urbanization associated with greater development compensate for large 6 terms to reduce the values of y. Regarding y as a function of UGDPkhs, because dy/dUGDPkhs < 0, the sign of the total derivative, d(inequality)/dGDPkhs, must be the same as the sign of the partial derivative ~(inequality)/LKJGDPkhs. It is thus anticipated that the urban U curve will be observed, regardless of whether GDPkhs or UGDPkhs is the development measure. Because a study of the determinants of 6 requires data superior to those available, and because no obvious trends appear, it is necessaryto treat the term as a constant. In the regression below, 2 is chosen as a plausible value for S. This value is also accepted by Mohan [21]. Substituting 6 = 2 into (1) gives an estimate of y, y *: y: = 2/(1 + PCTURB,),

(2)

134

CHARLES

M. BECKER

TABLE

3

Urban U-Curve Regressions Using UGDPkhs* as a Measure of Economic Development (Absolute f Values) Dependent variables Independent variable coefficients Constant

In UGDPkhs* (In UGDPkhs*)* 3 F

Mean of dependent variable SEE n

Sl 96.28*' (3.02) -26.92" (2.90)

s2 87.61** (2.92) - 23.75' (2.72)

s3

STOP

GINI

239.64* (2.64) 77.85** (2.95) -5.76+' (3.02)

-3.22* (2.65) 1.0954** (3.10) -00x17** (3.19)

(2.95)

(2.84)

84.69** (3 16) 21.51* (2.76) 1.63** (2.89)

02356 4.6982* 5.54 1.38 25

0.3064 6.3001** 9.74 1.30 25

0.3259 6.8027** 14.37 1.16 25

02612 5.2419* 21.17 3.92 2s

14.63 13.73 14.17 16.52

18.68 23.28 22.66 15.79

1.9s**

1.79**

Predicted value of dependent variable at UGDPkhs’ : 348 (Bangladesh, 1966-1967) 9.92 6.55 741 (Philippines, 1971) 4.85 8.83 4.98 9.25 1235 (Mexico, 1963) 2718 (Israel, 1968-1969) 7.22 11.73 Value of UGDPkhs* at point of maximal inequality 761 X96 Predicted dependent variable value at the 4.78 8.83 turning point

134

13.73

X61

23.41

0.3126 6.4558** 0.4254 0.0525 25 03924 0.4509 0.4376 0.3333 815

0.4517

Nore. All inequality measuresrefer to shares of household income *Significance at the 5% level. **Significance at the 1% level.

which gives an estimate of urban sector PPPper capita income, UGDPkhs*: UGDPkhs: = y: - GDPkhs; = 2*GDPkhs,/(l

+ PCTURB,).

(3)

The next step is to regressinequality measureson UGDPkhs*, using the log quadratic specification. Results from these regressions are presented in Table 3.4

4Sensitivity analysis was performed with regard to the choice of 6. It turns out that increasing 6 to 2.5 or 3 has little impact on the results. It is also worth noting that only 9 of the 16 countries whose urban per capita income values were used to derive the 6 term had income distribution surveys used in the sample set of income distribution surveys (the addition of Hong Kong, whose national survey was used, makes 10 cases in which the proper independent variable would be known).

URBAN

INCOME

DISTRIBUTION

IN LDC’S

135

The most important result of the new regressions is that the U curve’s presence is unchanged by the addition of y* to form UGDPkhs*. In fact, the picture given (including results reported in Becker [2], Chap. 4) is generally one of improvement, regardless of the sample set of income distribution surveys or equation form (semilog or nonlog). It is difficult to escape the impression that the urban U curve is neither sample-peculiar nor due to the presence of an inappropriate independent variable. It is apparent from Table 3 that the explanatory power of the urban U-curve regressions improves greatly when an estimate of real urban per capita income replaces national per capita income as the development level term. Increases in x2 are particularly striking in the bottom quintile share (Sl) and Gini coefficient cases. t values also increase for all coefficients, while the F statistics are all significant at or below the 2% level. Comparison of the UGDPkhs* and GDPkhs regressions also show much larger coefficient values in the former case. This pattern holds regardless of data set, and despite the fact that all independent variable values have increased. For the bottom quintile, a greater dispersion of predicted income-share values is associated with the increased curvature of the UGDPkhs* regressions. It can be seen from Tables 1 and 3 that predicted bottom quintile shares for countries at the tails of the development distribution are virtually unaffected by choice of the income term, while predicted share values for countries near the trough decline substantially when UGDPkhs* is used. While predicted S3 values are nearly identical in both cases, use of UGDPkhs* tends to reduce considerably the predicted second quintile’s share at most development levels. The decreasedGini coefficient estimates at all but the highest development level accompanying use of UGDPkhs* therefore must reflect decreasedestimates of the shares of some top groups as well as of the bottom quintiles, and serves as a reminder of the Gini’s limited value as an indicator of overall inequality. The problem of data comparability never disappears from discussions of cross-country income distribution studies. Despite our efforts to obtain a comparable sample from Jam’s data set, imperfect comparability limits the confidence one can place in the regression results. One indication as to whether the urban U curve merely reflects systematic patterns in income distribution sampling procedures or whether it captures a true pattern can be obtained by improving the comparability of the data set. We do this by including six regional urban inequality estimates for Brazil (1970 data taken from Benevides [3]) and substituting 14 state urban inequality estimates for the national Indian urban inequality terms (1963-1964 data taken from Mills and Becker [20], Chap. 9). These 19 additional observations greatly enhance the data sets’ overall comparability. Moreover, the income terms are not closely clustered: the ratio of highest to lowest regional urban per capita income in the Brazilian

136

CHARLES M. BECKER

set is 1.93; for Indian states this ratio is 1.82. The results from regressing urban Gini coefficients on UGDPkhs* are Gini =

-4.33

+ 1.3888(lnUGDPkhs*)

Gini =

-2.28 (t = 2.28

(4)

F= 20.295;SEE = 0.0604;n = 44); +0.8238(In UGDPkhs*) - 0.0621(In UGDPkhs* )2 (-2.96)

(2.84) +0.109 (4.90)

(ji*

- 0.1005(In UGDP~~S*)~ (-4.81)

(t = 4.73) (5.00) (x2 = 0.4730;

= 0.6750;

(D-BRAZIL) - 0.071(D-INDIA) (-2.18)

(5)

F= 23.326; SEE= 0.0474; n = 44).

Even when country dummy variables (D-INDIA and D-BRAZIL) are included, the t statistics on the income terms remain nearly as high as those in Table 3; they rise considerably when dummy variables are not included.5 The point of maximal inequality declines modestly from UGKPkhs* = 815 in Table 3 to $760 in (4) (but rises to $1002 in (3) due to the “Brazil effect” discussed in note 4), a remarkably minor change. Overall, the urban U appears to be a highly robust pattern. 3. TURNING

POINTS AND POINTS OF INFLECTION

It is straightforward to determine the levels of GDPkhs and U* at which income distribution measures cease to become less egalitarian. Minimizing the inequality variable with respect to the development level term (INC) gives a turning point at which the inequality measure is greatest or where the share of a lower quintile is least. An interior solution occurs at INC* = e-‘+1/(242), (6) where &I and B, are the estimated coefficients on the linear and quadratic development terms, respectively, given in Tables 1 and 3. It can be seen from the coefficient estimates in Tables 1 and 3 that INC* is a minimum point for the Sl, S2, and S3 regressions, and a maximum point for the STOP and GIN1 regressions. d,/bi, must be negative to ensure INC* > 1, and bi, must be positive (negative) in the Sl, S2, and S3 (STOP and GINI) cases. ‘Adding state data for India and regional data for Brazil without incorporating dummy variables leads to an excessively strong urban U. Brazil’s regions tend to be just beyond the trough and have above-average inequality, while India’s states have relatively low urban per capita incomes but are slightly more egalitarian than average. Thus, excluding dummies but adding observations effectively increases the weights on components of the sample that give rise to the U shape. In addition, Brazil’s sample covers income recipients, while India’s distribution is over household per capita expenditures. For these reasons, (4) seems to be a more appropriate indicator of the urban U. Only Gini coefficients were available for India. It also should be noted that actual (rather than predicted y* ) regional urban income terms for Brazil and India were employed, after being converted to U.S. dollars by a PPP adjustment factor.

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137

These turning points and associated inequality levels are given in Tables 1 and 3. They are not terribly sensitive to the income distribution sample set chosen (Becker [2], p. 115). The turning points of different quintile shares and of overall inequality statistics cannot be expected to occur at the same income level; in fact, the shares’ turning points may well differ systematically. INC* values are higher in Table 3 than in Table 1 since a given country’s UGDPkhs* will exceed its GDPkhs value. Turning points tend to occur at slightly lower levels of development when UGDPkhs* is used in place of GDPkhs. Nations in the turning-point regions generated by both the initial and the revised regressions include the Philippines, El Salvador, and Ecuador. Sri Lanka and Thailand appear in the revised turning-point region, while relatively more developed Honduras appears only in the turning-point region determined by the initial regressions. The revised caseturning-point region occurs near an urban sector per capita income level of 800 (1970) $U.S. based on Kravis-adjusted exchange rates. This level is quite low in an absolute sense, and corresponds to unadjusted national per capita income values of $180-300. Nonetheless, the majority of the world lives in countries at or below this level of development. These urban turning-point region countries may be compared to those found by Chenery and Syrquin [7] for national Kuznets curves. Honduras, El Salvador, Ecuador, and the Philippines are near the national turning points, while Sri Lanka is slightly poorer than countries at the national turning-point region. Thus urban turning points come at the same time or slightly before national turning points. The absolute decline in a lower quintile’s income share as GDPkhs or UGDPkhs* moves from very low to turning-point values tends to be smaller for higher quintiles. Taken as a percentage of the base income share for a very underdeveloped country, the relative declines are greater still for the poorest quintiles. The bottom quintile’s predicted share (Table 3) at the turning point is only 73% of its value for the poorest country in the sample (Bangladesh), while the maximum declines for the second and third quintiles are 11 and 9% of their Bangladesh share values, respectively. Other than the bottom quintile’s share decline, the gain of the very top groups is most striking: the top 5% of the distribution gains nearly five percentage points of total income at its peak, a 25% rise in its share. An important pattern emerges as one moves from lower to higher quintiles (through S3) in the urban income distribution: the higher the quintile, the lower the development level at its turning point. This decrease in the dependent variable at the turning point is observed nearly regardless of income distribution sample set and choice of income variable. This pattern is consistent with several models, particularly those based on sectoral transformations. The standard transformation model is one in

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CHARLES M. BECKER

which a high-productivity, high-wage sector grows at a more rapid rate than a “traditional,” low-wage sector. Such a model is quite common in the development literature for both whole economies and urban sectors with modem and traditional subsectors. Transformation models also have been shown to generate U curves (Robinson [26]; Fields [lo]). A variation of this model assumes that human capital and hence high wages are linked to the provision of essential public services (education, water, transportation). As long as these services are “lumpy” so that their provision is extended to the population only gradually, a similar transformation may occur (Becker [2], Chap. 5). Yet another more sophisticated transformation story, based ultimately on shifts in demand patterns, are the “job competition” models of Morley and Williamson [23] and Williamson [29]. In these models, a large portion of the population (say the bottom four quintiles) begins by earning the samewage. When a person receives either a high-paying job or public services,he moves to the top of this group. Initial expansion of high-paying jobs (or lumpy services) thus increases the relative earnings of those by definition in the wealthier part of the relevant population, while it decreasesthe shares of those yet to receive good jobs or services. As the economy grows, increasingly lower groups become serviced or well-paid, thus raising their shares in turn. Thus, the beginning of an improvement in any given quintile’s share will take place at a higher level of development, the lower the quintile.6 It is important to determine whether the urban U curves estimated slope so steeply at any point as to suggestthat a given class could be made worse off as development proceeds. This issue can be analyzed by writing per capita income in the jth urban household quintile, INCj, as a function of urban sector per capita income, INC. If every household 111percentile j had Hi members, then defining 5 to be per household income in the jth percentile:

By definition, where 5 is the jth quintile’s share of household income (expressed fractionally), 5 = 5 . Sj . INC . H,

(8)

%imple versions of these models also imply that incomes shares will subsequently fall after rising for the second and third quintiles. However, a modified scenario in which job quality (or services) continues to improve for workers in these groups could avoid this decline. These theories also are strictly limited to labor income shares; further restrictions are required to ensure that capital income growth does not swamp these effects.

URBAN INCOME DISTRIBUTION

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IN LDC’S

TABLE 4 Inflection Points and Corresponding Values of d INC,/d INC for the Lower Quintiles INC evaluated at assuming H = H, Quintiles (3) (2) ..___ Calculations based on UGDPkhs* as the development-level term (INC) 2.80 0.14 Bottom: Sl 330 7.04 0.35 Second: S2 280 12.10 0.60 Middle: S3 270 d INC,/d INC + (/?/lOO)

INC (1)

d INC,/d

m,

evaluated at INC

Calculations based on GDPkhs as the development-level term (INC) 3.85 0.19 Bottom: Sl 221 7.88 0.39 Second: S2 178 Middle: S3 12.54 0.63 178 Note. dINC,/dINC = /3((S, + a,) + (at + 2ba)lnINC + &,(lnINC)*). are in 1970 U.S. dollars converted by the Kravis adjustment procedure.

All values

where H is the number of persons per household in the urban sector.7Then assuming fi = 5H/Hj to be constant and substituting in for Sj from the estimated form lOOA’,= &a + &,ln INC + &,(ln INC)2, INC, = &, (8, * INC + hi, . INC . In INC + &2 . INC . (In INC)‘).

(9)

Thus, the & coefficient estimates can be used to determine whether d INCj/d INC is ever negative. To check, it is necessaryto find the value INC for which d21NCj/d(INC)2 = 0 and calculate dINC,/dINC at that point. It is straightforward to see that A

lnINC=

-1 - F,a1

(10)

with second-order conditions obtaining for INC to be a minimum in the Sl-S3 regressions if h2 > 0. The values of INC and dINCj/dINC at these inflection points appear in Table 4. These inflection points occur at very low levels of development. Regardless of whether the region is determined by the UGDPkhs* or the GDPkhs regressions, only 1958 Burma and ‘Define NH as the number of urban households, NH, as the number in the j th quintile, Q as urban sector income, P, as the j th quintile’s income, and POP as the urban sector population. Then NH = POP/H; NH, = 0.20 NH = POP/5 . H; Q, = S, Q = S, INC POP: Y, = Q/NH,, whence (8).

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1966-1967 Bangladesh have development levels in the inflection point region. If household size patterns are ignored, then the third column in Table 4 gives the minimum values of dINCj/dINC at any development level predicted by the U-curve regressions. Since the shares of the bottom urban groups initially fall as development takes place, this derivative should be less than unity. If it is negative, then decreases in real incomes of a particular quintile will be associated over some range with rising total urban income per capita, termed an irnmiseration effect. As it turns out, no quintile’s per capita income is predicted to decline at any point. Less optimistically, the regressions do suggest that initial increments to the income levels of bottom urban groups may be very small as development occurs: a $1 increase in real urban per capita income may be accompanied by only a 14-19t use in per capita incomes of the bottom quintile at early stages of development. Such a pattern is consistent, of course, with the predictions of Lewis-type transformation models. Even negative signs of dINC,./dINC are hardly a sufficient condition for immiseration of a given group to take place as urban development proceeds. Both cross-sectional studies and rare studies with longitudinal components do indicate a degree of household mobility between income levels, much of it related to acquisition of job experience and education by family members (see Berry [4], Berry and Sabot [5], and Mazumdar [17]). In particular, if an economy experiences high rural-urban migration rates, and if migrants tend to enter the bottom rungs of urban society, then it would be possible for all households to be richer while, simultaneously, households in the bottom quintile(s) at any instant are poorer than the occupants of that quintile in the preceding instant. This is clearly a false form of immiseration. However, studies that include information on the educational characteristics of migrants (e.g., Joshi et al. [12]; Mazumdar [18]; Sabot [27]; Collier and La1 [9]) suggeststhat migrants are unlikely to enter en masse at the bottom of urban society. Migrants frequently have at least a primary education, and are also more likely than permanent residents to be of prime working age. Consequently, migrants are likely to enter the labor force at different points in all but the highest part of the urban income distribution. Growth in the labor force due to the entry of young workers at the bottom can generate a similar appearance of immiseration. Morley [22] finds this to be an important factor in the findings of low per capita income growth for Brazil’s poor. He finds that the base-period bottom (national) decile enjoyed a 75% real income gain during the 196Os,while a comparison of the per capita incomes of the bottom deciles in the initial and terminal dates of his study yielded only a 28% gain.

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Moreover, even if an immiseration effect were found for a fixed group of households, it would be possible for a household’s discounted value income stream to rise with the development level. True income declines would require observed immiseration effects for a wide range of percentiles, as a given household is likely to be in many percentiles during its lifetime. Finally, even if it were found that the growth process led to reduced permanent incomes for large classesof the urban poor, then welfare levels for these groups could be increasing. To some extent, the urban poor will benefit from consumption of publicly provided goods, even though such goods will be unevenly distributed. The urban poor will also have the knowledge that even if their incomes remain unchanged, the incomes of their children are likely to be much larger than their own. Since children are a source of support for retired people, the development process may increase expected transfers if not lifetime earned income.8 Despite these caveats, the reasonably large slopes of the urban U curve found when Sl and S2 are dependent variables are not encouraging. The cross-country regressions do suggest that poor urban groups are unlikely to participate fully in the development process during initial growth stages, and that there may be a long stretch when real per capita income of the bottom groups increases at a very low rate. It is quite possible that certain types of poor urban households may find that returns to experience and skills are altered systematically by demographic or economic forces as an economy grows, or that opportunities for human capital acquisition are constrained in the early development phases. Such setbacks are a serious matter, whether due to institutional constraints or to shifting demographic and economic patterns. 4. FURTHER EVIDENCE ON THE URBAN U CURVE Cross-country regressions alone are not an extremely strong basis for making predictions regarding time-series patterns that nations are expected to undergo, particularly given that there are differences in sampling procedures. One would like to have information on urban sector income distribution trends over time in individual countries before accepting the urban U curve as a stylized fact. No less developed nations provide income distribution figures for a sufficient period and with sufficient frequency to establish an adequate time-series data base. Israel and India have the best urban income distribution data series, but in neither case are clear time-series patterns evident. Pakistan did appear to experience a marked decline in inequality between 1963 and 1970, but an g-year span for a nation nearly at the turning point *I an indebted to W. Arthur Lewis for this point.

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(1970-1971 UGDPkhs* = 694) offers little information. Interpretation of an apparent increase in the Philippines’ urban inequality between 1956 and 1971 suffers from similar problems. Fragmentary long-term time-series evidence exists but is limited to information on the United Statesand Great Britain. Recent analysesof long-term urban income distribution trends by Williamson strongly suggest an urban sector inequality-income U curve. In his study of U.S. urban inequality, Williamson [29] finds that over long periods, inequality measures first rise and then fall, suggesting a reasonably well-behaved relationship between inequality and the natural logarithm of per capita urban income. He finds that inequality increases-dramatically during much of the 19th century-until the early 20th century. Since 1929, however, there has been an “equality revolution.” Williamson’s work [30] with British nonfarm male earnings finds a similar (inverse) U curve of the Gini coefficient over time, and thus over income per capita. Given the virtually constant share of wages in British national income since at least the 1860s it appears likely that the U curve uncovered will hold for the total urban income inequality as well. Williamson finds that the Gini coefficient of nonfarm male earnings rises considerably between 1827 and 1851 (from 0.29 to 0.36) but begins a slow decline thereafter. A final piece of evidence on the urban U curve is provided by Carvajal [6], who regresses 1973 urban sector Gini coefficients for family incomes from each of 79 Costa Rican counties on county per capita income in a linear quadratic specification. A highly significant U curve emerges(R* = 0.805). His curve peaks at a per capita income value of 3596 colones. This value translates into 500-600 U.S. dollars, an amount slightly below Costa Rica’s national per capita income, and suggestsa UGDPkhs* at the turning point of approximately $1500-$1600. It is difficult to escape the impression that there exist socioeconomic forces which generate increasing urban inequality at low development levels. Moreover, it appears that these tendencies are eventually overshadowed by countervailing forces promoting egalitarian income distributions. The urban U curve found in cross-country analysis is largely inpervious to alterations in the inequality statistic, the development term, the form of equation fitted, and the income distribution sample set. Longterm trends for the United States and the United Kingdom both provide U curves as well. A wide variety of models have appeared in the development literature over the past 25 years that have implications for the parameters of the urban sector income distribution. These implications to date have received little attention, as there has been no empirical basis on which to judge the theory. The patterns tentatively identified here provide some basic general-

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izations. While the evidence appears reasonably strong, the U-shaped link between equality and development measures is far from perfect. The pattern is suggestive, and has been the long-term experience of at least two countries, yet it is far from inevitable. Models which generate an urban U curve all have control variables that can be affected by government policy. Consequently, in the absence of particular accepted theories of urban income distribution and government behavior, there can be no suggestion that a given country will necessarily follow the suggesteddistribution trend path. APPENDIX:

INCOME DISTRIBUTION

SAMPLES

Data used in the cross-country regressions are taken from Jain [ll]. Jain provides income distributions for 32 countries’ urban or nonagricultural sectors, or in a few cases distributions for specific cities. The national income distribution for Hong Kong is also taken as an approximation to its urban sector’s income distribution. Several problems associated with the comparability of different income distributions must be treated. First, while in principle the terms “urban” and “nonagricultural” are distinct, the practical difference between them in many casesis limited. A second problem is that the distribution for one city may be a poor approximation to a national urban sector income distribution, especially if levels of per capita income vary considerably among cities. These comparability and coverage problems were treated by running regressions based on income distribution samples both restricted to coverage of urban sectors alone and including nonagricultural and specific cities’ income distributions as well. Sample changes do not crucially affect the results; indeed, the most striking outliers tend to come from distributions excluded from the relatively “pure” sample set. A pure sample of income distributions was defined to include only the distributions defined exactly over the whole urban sector and only those studies that generate the distribution of household incomes. While there is no intrinsic merit to using surveys of household incomes as opposed to samples covering income recipients, household survey samples are by far the most common. It is possible to obtain 20 income distributions based on samples of urban sector households. A “full sample” (for which results are qualitatively unchanged, and reported in Becker [2], Chap. 3) includes the pure sample plus nine distributions based either on surveys of household incomes in specific cities or on studies of the distribution of income recipients in the urban sector, along with one from Brazil covering the economically active population. The “final” sample of 25 observations used in this paper includes the pure set of distributions plus five observations on household income distribution, but for specific cities rather than for complete urban sectors.

CHARLES M. BECKER

REFERENCES 1. M. S. Ahluwalia, Income, poverty, and development, J. Dev. Econom., 3, 307-342 (1976). 2. C. M. Becker, “The Urban Income Distribution in LDCs and a Model of Optimal Investment for an Underdeveloped Economy,” unpublished Ph.D. dissertation, Princeton University (1981). 3. C. M. Benevides, “Income Distribution in Brazil: 1970-1980 Compared,” unpublished Ph.D. dissertation, Vanderbilt University (1985). 4. R. A. Berry, Education, income, productivity and urban poverty, in “Education and Income” (T. King, Ed.). World Bank StatI Working Paper no. 402, Washington, D.C., (1980). 5. R. A. Berry and R. H. Sabot, Labour market performance in developing countries: A survey, World Dev., 6, 1199-1242 (1978). 6. M. J. Carvajal, Report on income distribution and poverty in Costa Rica, USAID General Working Document no. 2 (Rural Development Div., Bur. For Latin Amer. and the Caribbean) (1979). 7. H. B. Chenery and M. Syrquin, “Patterns of Development, 1950-1970,” Oxford Univ. Press, New York (1975). 8. W. Cline, Distribution and development: A survey of literature, J. Dev. Econom., 1, 359-400 (1975). 9. P. Collier and D. Lal, Poverty and growth in Kenya, World Bank Staff Working Paper no. 389, Washington, D.C. (1980). 10. G. Fields, “Poverty, Inequality and Development,” Cambridge Univ. Press, Cambridge, U.K. (1980). 11. S. Jam, “Size Distribution of Income,” World Bank, Washington, D.C. (1975). 12. H. Joshi, H. Lubell, and J. Mouly, “Abidjan: Urban Development and Employment in the Ivory Coast,” ILO, Geneva (1976). 13. I. B. Kravis, A. Heston, and R. Summers, “United Nations International Comparison Project: Phase II; International Comparisons of Real Product and Purchasing Power,” Johns Hopkins Press,Baltimore (1978). 14. I. B. Kravis, Real GNP per capita for more than one hundred countries, Econom. .I., 68, 215-242 (1978). 15. S. Kuznets, Economic growth and income inequality, Amer. Econom. Rev., 45, l-28 (1955). 16. W. A. Lewis, Economic development with unlimited supplies of labour, Manchester School Econom. Sot. Stud., 22, 139-192 (1954). 17. D. Mazumder, The urban informal sector, World Dev., 4, 655-679 (1976). 18. D. Mazumder, Paradigms in the study of urban labor markets in LDCs: A reassessmentin light of an empirical study of Bombay City, World Bank Statf Working Paper no. 366, Washington D.C. (1979). 19. E. S. Mills and C. M. Becker, Urbanization, public services and income distribution in developing countries, in “National Development and Regional Policy” (B. Prantilla, Ed.), Maruzen Asia, Nagoya (1981). 20. E. S. Mills and C. M. Becker, “Studies in Indian Urban Development,” Oxford Univ. Press, New York (1986). 21. R. Mohan, Urban land policy, income distribution and the urban poor, in “Income Distribution and Growth in Less Developed Countries” (C. R. Frank, Jr., and R. C. Webb, Eds.), Brookings Institute, Washington, D.C. (1977). 22. S. A. Morley, The effect of changes in the population on several measures of income distribution, Amer. Econom. Rev., 71, 285-294 (1981). 23. S. A. Morley and J. G. Williamson, Demand, distribution and employment: The case of Brazil, Econom. Dev. Cult. Change, 23, 33-60 (1974).

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24. H. Oshima, The international comparison of size distribution of family incomes with special reference to Asia,” Rev. Econom. Statist., 44, 439-445 (1962). 25. F. Paukert, Income distribution at different levels of development: A survey of evidence, ht. Lab. Rev., 108, 97-125 (1973). 26. S. Robinson, A note on the U hypothesis relating income inequality and economic development, Amer. Econom. Rev., 66, 437-440 (1976). 27. R. H. Sabot, “Economic Development and Urban Migration: Tanzania 1900-1971,” Clarendon Press, Oxford (1979). 28. A. K. Sen, Peasants and dualism with or without surplus labor, J. Polit. Econom., 74, 425-450 (1966). 29. J. G. Williamson, American prices and urban inequality since 1820, J. Econom. H&t., 36, 303-333 (1976). 30. J. G. Williamson, Earnings inequality in nineteenth-century Britain, J. Econom. Hist., 40, 457-475 (1980).