On the rbanization of poverty Martin Ravallion 1 Development Research Grop, World Bank 1818 H Street NW, Washington DC, USA Febrary 001; revised Jly 001 Abstract: Conditions are identified nder which the rban sector s share of the total nmber of poor in a developing contry will be an increasing convex fnction of the rban share of the total poplation. This is confirmed by cross-sectional data for 39 contries and time series data for India. The empirical reslts imply that the poor rbanize faster than the poplation as a whole. The experience across developing contries sggests that a majority of the poor will still live in rral areas well after most people in the developing world live in rban areas. Key words: Urban poverty, rral poverty, rban poplation growth. JEL: I3, O15, O18 1 Address for correspondence mravallion@worldbank.org. Comments were received from Bill Easterly, Alice Mesnard and Dominiqe van de Walle. These are not necessarily the views of the World Bank or any affiliated organization.
1. Introdction As is well known, the incidence of poverty is higher in the rral areas of almost all developing contries. And (in the aggregate) most people still live in rral areas. So rban areas accont for less than half abot 30% on average of the poor. 3 Bt, as is also well known, the poplation of the developing world is rbanizing qite rapidly. In 1995, 38% of people lived in rban areas, and this is projected to rise to 5% by 00 (UN, 1996). Is the rban share of poverty also likely to grow? There is evidence that it has been doing so. 4 Will the poor rbanize faster than the nonpoor? How long will it be before most of the poor live in rban areas? The answers to sch qestions have bearing on poverty redction efforts. There are differences in the policy instrments for rban verss rral poverty. Jdgements abot whether crrent knowledge and action have the right sectoral composition for fighting poverty will then be inflenced by how the rban-rral composition of poverty is expected to evolve. There may also be implications for nderstanding the political economy of anti-poverty policy. More spatially concentrated and visible forms of rban poverty are likely to generate new pressres on governments to respond, and in ways that may or may not be coincident with good policies for overall poverty redction. To help throw light on these isses, this paper provides a simple theoretical representation of the rbanization of poverty in a developing contry, and shows that this Lipton and Ravallion (1995) srvey the evidence on this point, and related work on rralrban migration in developing contries. 3 Taking an n-weighted mean across the data set sed in this paper, one finds that 68% of the poor live in rral areas. If one weights by the total nmber of poor the figre risies to 75%. 4 Haddad et al., (1999) compile rban and rral poverty measres for eight contries; for seven of them they find that the rban share of the total nmber of poor rose over time.
is consistent with poverty data for contries over a wide range of rban poplation shares. Implications are drawn for the ftre rbanization of poverty.. A theoretical representation of the rbanization of poverty Let P S ) be a single-valed fnction from [0,1] to [0,1] giving the rban ( sector s share of the poor when its share of the poplation is S. This can be written as: P ( S ) = h( S ) S (1) where H ( S ) h( S ) () H ( S ) is the incidence of poverty in rban areas ( H ) relative to its national incidence (H). The latter is given by: H ( S r ) = S H ( S ) + (1 S ) H ( S ) (3) where H is the rral incidence of poverty. Since we are interested in the association r between rbanization (a rise in S ) and poverty, the rban and rral poverty measres are written as fnctions of S ; these fnctions are assmed to be differentiable. Writing the poverty measres as fnctions of S does not, of corse, mean that S is exogenos; here the interest is in how these variables co-move, rather than casality. What properties can we expect P ( S ) to have? At low S, one can imagine a small rban enclave, containing the government and services. The poverty rate in this initial rban enclave is far lower than in srronding rral areas. In the limiting case, we 3
can assme that P ( 0) = 0. At the other extreme, it mst of corse be the case that P ( 1) = 1. What shape might one expect the crve to have between these extremes? To otline a simple model for addressing this qestion, sppose that escaping poverty in rban areas means getting a skilled formal sector job at a real wage rate that is fixed. An rban hosehold is poor if it does not get sch a job, and everyone is poor in the rral economy. The nmber of formal sector jobs per capita of the poplation is L = ( 1 H ) S which is also the national poverty rate in this model (since getting and rban formal sector job is the only way to escape poverty). In this model, the process of rbanization generates external economies, sch that prodctivity in the rban economy rises as its share of the poplation rises. In particlar, ( the otpt of the rban formal sector is φ S ) F( L ) where φ S ) is prodctivityenhancing effect of rbanization, with φ ( S ) > 0, and F (.) > 0 is the marginal prodct of skilled labor with F (.) < 0. Firms maximize profits, sch that: where φ S ) F [(1 H ( S )) S ] = W ( S ) (4) ( W is the rban wage rate which is assmed to be a non-decreasing fnction of S. In a competitive labor market, W S ) is the (inverse) spply fnction of skilled ( ( labor. On differentiating with respect to S and solving one obtains: H ( S ) = [1 + ε ( η ω)](1 H ) / S (5.1) where H S ) = ε ( η ω)(1 H ) (5.) ( ln L lnφ lnw ε = < 0, η = > 0 and ω = > 0 lnw ln ln S S 4
Consider first the case in which and assme that: η > ω (so that rbanization redces national poverty) 1 1+ < P ( S ) ε( η ω) for all S in [0,1] (6) This is implies that the rban poverty rate rises relative to the national rate as rbanization proceeds i.e., h ( S ) > 0 for all S. I shall consider the effect of relaxing the restriction in (6). Under these conditions, the fnction P S ) mst then be strictly increasing and ( convex throghot as illstrated in Figre 1. It is plain that P S ) is strictly increasing ( given that h / ( S ) = P ( S ) S is increasing in S. It is also clear that P S ) cannot be ( linear in any interval, since this wold mean that h ( ) = 0. The only other possibility is that the fnction is strictly concave in some interval. Bt then there will be a point * * S sch that h S ) reaches a maximm within that interval, i.e., P ( S ) = h( S ). If * ( S S * < 1 * S then h(.) mst be a decreasing fnction for some S > again a contradiction. When S * = 1, ( * P ) = 1. Since P ( 1) = h (1) + h(1) S and h(1)=1, this reqires that the left derivative of h vanishes, h ( 1) = 0 also a contradiction. So the fnction mst be strictly convex throghot, as in Figre 1. If η ω then the national poverty rate will be non-decreasing in S and the rban poverty rate will be strictly increasing in S. However, it will still be tre that h ( S ) > 0 and that the fnction P S ) is strictly increasing and convex. ( 5
To illstrate a case in which the restriction in (6) does not hold, sch that h ( S ) < 0 for some S, sppose that (i) φ ( S ) = S ; (ii) the real wage rate is fixed ( ω = 0 ), and (iii) the labor demand fnction has constant elasticity, so that (4) can be written: ( ε 1 H ( S )) S = ( W / S ) (7) When ε < 1, the restriction in (6) fails for some S. Figre gives the implied P ( S ) fnctions for ε = 1,, 3, 4 (labeled (1), (),..). (The wage rate has been set sch that the poverty rate when all the poplation is in rban areas is 0.1.) The crve becomes concave at higher elasticities of labor demand, and over a wider interval as the absolte elasticity rises. 3. Calibrating the crve to cross-contry data A specification for P S ) with sfficient flexibility is a cbic polynomial, ( whereby h S ) has the qadratic form: ( h S ) = 1 β (1 S ) + γ (1 S ) + υ (8) ( ( where β and γ are parameters to be estimated and ε is a zero mean error term. P S ) passes throgh (0,0) and (1,1) when the crve is evalated at the expected vale of h. World Bank (1999, Table.7) provides a compilation of estimates of rban and rral poverty incidence for 39 contries. The estimates are drawn from contry poverty stdies by the World Bank, and all are based on hosehold srvey data. Methods of setting poverty lines vary between contries, however, and the differences can matter to 6
comparisons of rban and rral poverty incidence. 5 These data wold appear nonetheless to be the available data sorce for the present prpose. I will se the rban poplation share implicit in the rban, rral and national poverty rates, thogh I test sensitivity to sing the Censs-based rban poplation shares given in the same sorce. Using these data, I initially regressed h 1 on a constant term, 1 S and ( 1 S ) ; the constant and the coefficient on ( 1 S ) were jointly insignificant (F=0.53, which rejects the nll with probability 0.59). (White standard errors are sed throghot.) If one sets the constant to zero then the coefficient on the sqared term is not significantly different from zero (t = 0.66) and the estimate of β is 0.451 with a standard error of 0.07. (Similarly, the constant term is insignificant if one sppresses the sqared term.) Dropping both the constant and the sqared term, I obtained an estimate of 0.468 for β with a (robst) standard error of 0.060 (n=39). 6 The estimate is significantly positive, and significantly less than one. Figre 3 plots the data and fitted vales. So the data sggest that: P ( S ) = [1 β (1 S )] S (9) with β arond 0.5. The speed at which poverty rbanizes is related to the overall speed of rbanization according to: ln P t β S = 1 + P ln S. t (10) 5 See Ravallion and Bidani (1994) who compare alternative methods of setting rban and rral poverty lines in Indonesia. Also see the discssion in Haddad et al., (1999). 6 If instead one ses the Censs-based rban poplation shares the estimate is 0.473 with a standard error of 0.083. 7
At sample means ( S =0.43; P =0.31, with β =0.468), the poor rbanize at a speed 6% higher than the poplation as a whole. How mch does H / H rise with rbanization? It is readily verified that: r H H r 1 β (1 S = 1+ β S ) (11) H / H r increases monotonically with S (with a slope of [ β /(1 + β S )] ). (Eqation 11 is derived by first noting that H H = h(1 S ) /(1 hs ) and then sbstitting / r h = β (1 S ).) At its lower bond, H 0) / H (0) = P (0) = 1 β while 1 ( r H 1) / H (1) = 1/(1 + β ). So, with rbanization, the rban poverty rate rises relative to ( r the rral rate, bt it does so rather slowly; between S = 0 and S = 1, the rban poverty rate rises from abot one half to two-thirds of the rral rate. 4. Time series evidence for India There are very few contries with the time series data needed to estimate (8). An exception is India, for which a reasonably long time series of comparable, nationally representative, hosehold srveys allow s to stdy how the rban-rral poverty profile has evolved with rbanization. I repeated the above analysis sing 14 srvey ronds spanning 1974-1997/98. 7 Again I fond that a linear h fnction performed well giving an estimate of 0.151 for β with a robst standard error of 0.019. Again this is significantly positive (and less than one). However, the estimate is mch lower than for the cross- 7 The data are from Datt (1999) and are a slightly pdated version of the data set described in Özler, Datt and Ravallion (1996) and http://www.worldbank.org/poverty/data/indiap aper.htm. 8
contry data. The India crve implies a lower rban-rral disparity in poverty rates, and this varies little with rbanization. It may, however, be hazardos to try to infer what happens with rbanization from these data for India. Over this 5-year period, the rban share of the poplation in India spans a relatively narrow range, from 1% to 7%. By contrast, the cross-contry comparisons above span a range from 10% to 85%. The India crve may be close to the 45-degree line at low levels, bt fan ot later. 5. Conclsions Under certain conditions, the rban share of the poor in a developing economy will be an increasing convex fnction of the rban share of the poplation; the higher the initial level of rbanization, the larger the effect on the proportion of the poor living in rban areas of any given increment to the rban poplation share. Spportive evidence for this relationship is fond in data for a cross-section of developing contries and in time series data for India. If poverty rbanizes consistently with the cross-contry relationship modeled above, then the rban share of poverty will reach 40% in 00, when the rban share of the poplation is projected to reach 5% (UN, 1996). At the projected growth rate in the rban poplation share between 015 and 00 in UN (1996), the rban share of the total nmber of poor will reach 50% by 035, when the rban poplation share reaches 61%. 9
References Datt, Garav (1999). Has poverty in India declined since the economic reforms?, Economic and Political Weekly 34 (December 11-17). Haddad, L., Rel, M. T., Garrett, J. L. (1999). Are rban poverty and nderntrition growing? Some newly assembled evidence. World Development 7(11), 1891-1904. Lipton, Michael and Martin Ravallion, (1995). Poverty and policy, in J. Behrman and T.N. Srinivasan (eds) Handbook of Development Economics Volme 3, Amsterdam: North-Holland. Özler, Berk, Datt, Garav, and Martin Ravallion (1996). A database on poverty and growth in India, http://www.worldbank.org/poverty/data/indiap aper.htm. Ravallion, Martin and Ben Bidani (1994). How robst is a poverty profile? World Bank Economic Review 8(1), 75-10. United Nations Secretariat (1996). World Urbanization Prospects: The 1996 Revision, Poplation Division, Department of Economic and Social Affairs. World Bank (1999). World Development Indicators, Washington DC: World Bank. 10
Figre 1: The rbanization of poverty 1.0 Urban share of the poor 0.8 0.6 0.4 0. 0.0 0. 0.4 0.6 0.8 1 Urban share of poplation Figre : Urban share of poverty for varios labor demand elasticities 1.0 Urban share of poor 0.8 0.6 0.4 (4) (3) () 0. (1) 0.0 0.0 0. 0.4 0.6 0.8 1.0 Urban share of poplation 11
Figre 3: Data for 39 developing contries 1.0 Urban share of the poor 0.8 0.6 0.4 0. 0.0 0. 0.4 0.6 0.8 1 Urban share of poplation 1