The impact of growth and inequality on rural poverty in China

Journal of Comparative Economics 34(2006)694–712
/locate/jce
The impact of growth and inequality
on rural poverty in China
Yin Zhang a ,∗,Guanghua Wan b
a Department of Economic Studies,University of Dundee,3Perth Road,Dundee,DD14HN,UK
b UNU-WIDER,Helsinki,Fin-00160,Finland
Received 8August 2006
Available online 26September 2006
Zhang,Yin,and Wan,Guanghua —The impact of growth and inequality on rural poverty in China
This paper analyzes the evolution of poverty in China from the late 1980s to the late 1990s,employing a version of Shapley decomposition tailored to unit-record household survey data.The changes in poverty trends are attributed to two proximate causes—income growth and shifts in income distribution.Different data sets,poverty lines,poverty measures,and equivalence scales are used to examine the robustness of the results.Potential biases arising from ignoring differential regional prices and inflation are also investigated.Notwithstanding some ambiguities in the results,it is consistently found that rural poverty increased in the second half of the 1990s and adverse distributional changes are the main cause.Journal of Comparative Economics 34(4)(2006)694–712.Department of Economic Studies,University of Dundee,3Perth Road,Dundee,DD14HN,UK;UNU-WIDER,Helsinki,Fin-00160,Finland.
©2006Association for Comparative Economic Studies.Published by Elsevier Inc.All rights reserved.JEL classification:O15;O53
Keywords:Rural poverty;Shapley decomposition;China
1.Introduction
East Asia is the first,and remains the only,region where the first target of the Millennium Development Goals (MDGs)—halving extreme poverty between 1990and 2015—has been met (UN Millennium Project,2005).While the dramatic poverty reductions in China are essential *Corresponding author.Fax:+441382384691.
E-mail address:y.x.zhang@ (Y .Zhang).
0147-5967/$–see front matter ©2006Association for Comparative Economic Studies.Published by Elsevier Inc.All rights reserved.
doi:10.1016/j.jce.2006.08.008
Y.Zhang,G.Wan/Journal of Comparative Economics34(2006)694–712695 to that attainment,as of2001around onefifth of the world’s poor still reside there(Chen and Ravallion,2004).Within China,rural poverty dominates the scene.The overall reduction of rural poverty since the initiation of market-oriented reform has been nothing but impressive. Notwithstanding,some recent research suggests that the process slowed down significantly in the1990s and has even shown signs of reversal(Chen and Ravallion,2004).Success in battling rural poverty clearly holds the key to further progress toward poverty alleviation in China and the achievement of the MDG poverty target on a global scale.It is thus important to understand what drives the latest poverty trend in rural China.
The agricultural sector is where China’s remarkable growth story started.By simply de-collectivizing production and allowing farmers to sell their surplus produce on the market,China propelled the annual growth rate of agriculture from an average of2.5percent in1952–1977 to7.4percent in1978–1984.As a result,rural per capita income rose by a stunning270per-cent.However,the agricultural sector moved down the government’s priority list around the mid-1980s when the focus of reform was shifted to the urban area and industrial sector.Not only were government procurement prices of farm produce set below market prices,but they also failed to keep up with price increases in other sectors during1989–1993(Fig.1).Agricul-tural growth slowed down,and the growth of grain output suffered particularly severely.In1993, a combination offloods and drought led to food shortage.Attempts to raise grain procurement prices to market levels in1994triggered a sharp increase in grain prices.Concerned about in-flation pressures and grain self-sufficiency,the government responded by increasing investment in rural infrastructure and reasserting control over the production and marketing of several ba-sic commodities.In addition,a governor’s grain bag responsibility system was implemented in 1995,which made provincial governors personally responsible for ensuring adequate supply of
Fig.1.Changes in rural CPI and procurement price index of farm produce.
696Y.Zhang,G.Wan/Journal of Comparative Economics34(2006)694–712
domestic grain within their jurisdictions.These policies succeeded in stabilizing food prices and increasing grain reserves.In the late1990s,government controls over the imports of agricultural products were gradually eased as China prepared for entry into the WTO.Increased imports along with consecutive years of good harvest boosted food supply.The demand for food,how-ever,did not rise as fast,partly due to a declining share of food in household expenditure induced by higher income.Food prices slumped and rural income stagnated.
The above agricultural policies have implications for rural income growth as well as for its paring the trajectories of poverty reduction and GDP growth after the late 1980s with those in the earlier years,a number of studies have emphasized the role of rising in-come inequality in slowing down poverty reduction.These include,among others,Khan(1999), Gustafsson and Wei(2000),Yao(2000),Chen and Wang(2001),and Ravallion and Chen(2004). Given a poverty line,any poverty trend can always be attributed to income growth and shifts in the distribution of income.The decision facing policy makers is often one of allocating limited resources between growth promotion and redistribution toward the poor.This paper seeks to analyze the contributions to China’s rural poverty trend attributable to income growth and distri-bution.Three features set this paper apart from previous studies on China’s poverty.Firstly,most studies rely on household survey data from the National Bureau of Statistics(NBS).The NBS data from published sources are in grouped format.Estimating poverty measures from grouped data necessarily involves interpolation in order to generate data between group boundaries.1This entails errors unless the interpolation method happens to agree with the underlying income distri-bution.2Besides,the NBS data have been criticized for their exclusion of such important income items as imputed rents of owner-occupied housing,subsidies,income in kind,and so on(Khan, 1999).Exploring alternative data sources can therefore serve the useful purpose of checking the robustness of results based on the NBS data.The two data sets employed in this paper are such examples,both of which provide household-level income data and are from sources distinct from the NBS household survey.3
The second departure of this paper lies in our method of quantifying the relative impor-tance of growth and distributional changes in forming poverty trend.Because income growth and distributional changes are interrelated,their unconditional correlation with poverty changes is uninformative of their marginal impact on poverty.Some studies regress the logarithms of a poverty index on those of the average income and an aggregate inequality measure,typically the Gini index,to obtain the marginal impacts of growth and redistribution(e.g.,Khan,1999; Yao,2000;Ravallion and Chen,2004).Implicitly,this assumes that the relationship among the three variables is approximately log-linear.The accuracy of this approximation aside,4a major problem with this approach is that the Gini index uniquely determines the Lorenz curve only 1In the rare case of the poverty line coinciding with one of the income group boundaries,grouped data lend themselves readily to the calculation of poverty measures such as thefirst three indices of the Foster–Greer–Thorbecke(FGT)family. 2Some researchers gained access to household-level NBS data,but these are typically for isolated provinces and of limited years(e.g.,Yao,2000).The exception is a recent World Bank study(Ravallion and Chen,2004),which has meticulously assembled from household-level NBS data the1981–2001series of three FGT indices both at the national level and separately for urban and rural areas.
3Another data set featuring unit-record income data is the China Household Income Project(CHIP)data set.It contains information from two household surveys conducted by the Chinese Academy of Social Sciences(CASS)in selected provinces in1988,1995,and2002.
4If the regression has a poorfit,much of the changes in poverty will be assigned to the residual term and thus go unaccounted for.
Y.Zhang,G.Wan/Journal of Comparative Economics34(2006)694–712697 under restricted conditions.5A given change in the Gini index may be caused by redistribution among the nonpoor,among the poor,or between the poor and the nonpoor.In thefirst case, poverty will not be affected at all.Poverty changes in the latter two cases will also differ.Hence, the regression coefficient on the Gini index does not identify the effects of distributional changes on poverty as it is purported to.Another,and also more appropriate in our review,approach to pinning down the relative contribution of growth and distributional changes is that proposed by Datt and Ravallion(1992)to decompose a change in a poverty measure into growth and redis-tribution components.6This paper adopts the Datt–Ravallion decomposition methodology with two extensions.First,we draw on the Shapley value decomposition framework propounded by Shorrocks(1999)to make the decomposition symmetric and exact.Second,in the Datt–Ravallion decomposition distributional changes are identified with changes in the estimates of Lorenz curve parameters.We shall show that,with microlevel data,decomposition can be conducted without resorting to parametric Lorenz functions.
Finally,measurement issues loom large in poverty research,especially for studies about tran-sition and developing economies.Apart from the problems with the availability and quality of household survey data,there are often ambiguities about the appropriate poverty line,equiv-alence scale,poverty measure,and price index to use.As some arbitrariness is inevitable in making the choice,we examine the sensitivity of poverty trend and decomposition to alternative measurement assumptions rather than focusing exclusively on a particular one of them.
The remainder of the paper is organized as follows.The next section explains the decom-position methodology and discusses various uncertainties involved in assessing poverty trend and decomposition.Section3introduces the data and presents the time profiles of three poverty measures of the Foster–Greer–Thorbecke(FGT)family.In Section4,we discuss the decompo-sition results.Particular attention is given to results that are consistent across different data sets and poverty measures and under alternative assumptions about the poverty line and equivalence scale.Some concluding comments are offered in Section5.
2.Growth–redistribution decomposition and the robustness of poverty measurement
A poverty measure P is a function of the income distribution Y and poverty line z,i.e.,P t= P(Y t,z t).If the poverty line is held constant over time,a change in poverty between period0 and period T can be written as
P=P(Y t)−P(Y0),
(1) where the letter z representing the poverty line is dropped for simplicity.7The basic idea behind the growth–redistribution decomposition is that,at any point of time t,the income distribution Y t can always be fully described by its mean incomeμt and Lorenz curve L t,the latter of which is uniquely determined by the probability density function(PDF)of relative income.8Thus,
5If the size distribution of income is log-normal,for example,then there is a one-to-one relationship between the Gini index and the Lorenz curve.However,empirical evidence shows that the log-normal distribution does not describe real income data well(McDonald,1984).
6For applications of the Datt–Ravallion decomposition to the Chinese context,see Fang et al.(2002)and Chen and Wang(2001).
7Changes in the poverty line can be easily accommodated in the framework described below.
8We use the term‘relative income’to refer to income values normalized by the mean income.
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P stems from changes in either of the two determinants of Y .If income growth is distribu-tion neutral,or the income of every individual grows by the same proportion,then the Lorenz curve (or,equivalently,the PDF of relative income)will stay unchanged and P is due en-tirely to changes in the mean income.Conversely,when the mean income neither grows nor contracts,a change in poverty will occur if and only if the Lorenz curve shifts,i.e.,there is income redistribution among some individuals.Applied to the general case with both income growth and distributional changes,the preceding reasoning implies that P can be separated into two components measuring respectively the growth and distributional effects.To express the two components mathematically,let Y (μi ,L j )be a hypothetical income distribution with mean income μi and Lorenz curve L j taken from different distributions,i.e.,i =0or T ,j =0or T ,and i =j .And let P (μi ,L j )represent the poverty level corresponding to Y (μi ,L j ).The growth component of P can be defined as
(2)growth component ≡P (μT ,L 0)−P (Y 0),
or,alternatively,as
(2A)growth component ≡P (Y T )−P (μ0,L T ).
Similarly,the redistribution component can either be defined as
(3)redistribution component ≡P (μ0,L T )−P (Y 0),
or as
(3A)redistribution component ≡P (Y T )−P (μT ,L 0).Four decompositions of P can be formed by combining the alternative definitions of the growth and redistribution components differently.If definitions (2)and (3)are used,period 0is the ref-erence period;if,instead,definitions (2A)and (3A)are chosen,the reference period is period T .The results from the two decompositions need not agree,and both are inexact in that the growth and redistribution components do not add up to P .If the combination (2)and (3A)or (2A)and
(3)is used,the decomposition will be exact since
P (Y T )−P (Y 0)=growth component +redistribution component (4)= P (μT ,L 0)−P (Y 0) + P (Y T )−P (μT ,L 0) (5)= P (Y T )−P (μ0,L T ) + P (μ0,L T )−P (Y 0) .However,the growth and redistribution components in expressions (4)and (5)are measured against different reference periods.Again,the two decompositions produce different results in general,and thus are equally arbitrary or equally justified.
The decomposition methods used in previous studies,such as those of Datt and Ravallion (1992),Kakwani and Subbarao (1990),and Jain and Tendulkar (1990),essentially comprise one or two of the above decompositions.Hence,they are sensitive to the choice of the reference period,and are inexact or have a nonvanishing residual term whenever growth and distributional changes are both present.A solution to these problems created by the reference point is to take the average of expressions (4)and (5)to arrive at
P =0.5 P (μT ,L 0)−P (Y 0) + P (Y T )−P (μ0,L T ) (6)
+0.5 P (Y T )−P (μT ,L 0) + P (μ0,L T )−P (Y 0) .
Y.Zhang,G.Wan /Journal of Comparative Economics 34(2006)694–712699
As argued in Shorrocks (1999)and Kolenikov and Shorrocks (2005),the decomposition in ex-pression (6)is not an arithmetic gimmick,but has its theoretical roots in the cooperative game theory.Apart from notational difference,expression (6)is identical to what Shorrocks (1999)derived using the Shapley value.The growth component G and the redistribution component R of the Shapley value decomposition of P are thus (7)G ≡0.5 P (μT ,L 0)−P (Y 0) + P (Y T )−P (μ0,L T ) ,(8)R ≡0.5 P (Y T )−P (μT ,L 0) + P (μ0,L T )−P (Y 0) .It can be easily seen that the Shapley decomposition is symmetric and exact.
There remains the question of how to obtain the poverty indices P (μT ,L 0)and P (μ0,L T )of the hypothetical distributions.The method used in previous studies is to assume a parametric Lorenz curve or PDF.Then,the formula for the poverty measure as a function of the mean income and parameters of the Lorenz curve or PDF is derived.The parameters are estimated economet-rically for both periods 0and T .Plugging into the derived formula the parameter estimates for period 0and mean income of period T give P (μT ,L 0).P (μ0,L T )is obtained similarly.The weakness of this parametric procedure is that the specification and estimation of the Lorenz curve or PDF can give rise to errors that bias subsequent estimates of the poverty measure.When grouped data are all that is available,the Lorenz curve (and the PDF)will have to be estimated and the parametric procedure is at least a good place to start with.However,if unit-record data are available,which is the case of this study,a simpler solution exists.To keep the Lorenz curve of an income distribution intact but give it a new mean,one can simply scale every observation by the new mean divided by the old mean.In other words,the two hypothetical distributions can be constructed as Y (μ0,L T )=Y T ×(μ0/μT )and Y (μT ,L 0)=Y 0×(μT /μ0).The poverty indices P (μ0,L T )and P (μT ,L 0)can then be calculated directly from the constructed distributions.Even with unit-record data,assessing poverty trend is still subject to a host of uncertainties,which in turn affect poverty decomposition.We consider three such uncertainties here:poverty measures,poverty lines,and equivalence scales.The most widely used poverty measures are the first three FGT (Foster et al.,1984)poverty indices that can be generically expressed as (9)P α=1N Y i z
z −Y i z α
,α 0.P 0,the head-count ratio,gives the proportion of the population whose incomes fall below the poverty line z .The poverty gap index P 1measures the average income shortfall in meeting the poverty line,where the shortfall is expressed as a proportion of the poverty line and the poverty gap of the nonpoor is assigned zero.The squared poverty gap index P 2is the sum of the proportionate poverty gaps weighted by themselves,and is thus more sensitive to the income changes of poorer individuals.The three indices reflect different aspects of the same poverty experience,measuring respectively the incidence,depth,and severity of poverty.Therefore,the magnitude and direction of their changes need not always concur.This will then lead to different assessments of the relative role played by income growth and redistribution in affecting poverty.99To take a simple example,suppose that an income distribution has changed from (1,2,3,4)to (2,2,2,4)and the poverty line is set at 2.5.The head-count ratio would indicate an increase in poverty (from 0.5to 0.75)whereas the poverty gap index would show a decrease (from 0.2to 0.15).Decomposing the change in the head-count ratio according to definitions (7)and (8)would put the contribution of growth at zero and the contribution of redistribution as poverty worsening (R >0).The same decomposition applied to the change in the poverty gap index would give a negative redistribution component.
700Y.Zhang,G.Wan/Journal of Comparative Economics34(2006)694–712 The evaluation of poverty trend may also be sensitive to where the poverty line is drawn.For example,if the poverty line happens to be near a local mode of the income distribution,an im-material shift of the poverty line might cause a large swing of measured poverty,especially for poverty measures such as P0and P1,which are not continuous at the poverty line.Given the inevitable arbitrariness in defining the poverty line,an assessment of the poverty trend that can be easily reversed by a slight change to the poverty line will hardly inspire much confidence.In this paper,we consider six national and international poverty lines.10These include the US$1.08 and US$2.15per capita per day poverty lines in1993PPP,the US$1and US$2per capita per day poverty lines in1985PPP,the rural poverty line proposed in Ravallion and Chen(2004) (850yuan in2002prices),and the official rural poverty line of530yuan in1995prices.An-other concern about the poverty line is whether a poverty line should be applied uniformly to all regions under examination.The costs of living vary across Chinese provinces sometimes by wide margins.Official CPIs published by the NBS,available at the provincial level,allow one to trace changes in the costs of living within a province,but not the differences across provinces. Using official CPIs and price data for1990,Brandt and Holz(2004)constructed several panels of provincial price levels.One of these is adopted in this paper to convert national poverty lines to their provincial counterparts or,equivalently,to convert nominal incomefigures to real incomes measured in national prices of the base year.11
In most poverty studies on China,the indicator of individual welfare is on a per capita basis—total household income(or consumption)divided by the number of people in the household. This practice assumes away the possibility that the per capita cost of semipublic goods such as housing,utilities,transportation,and so on is negatively related to household size.Even for ri-val goods such as food,the unit price paid by large households may be lower than that paid by small households because the former are more likely to make bulk purchases.It is also possi-ble that the costs for reaching a given welfare level are different for demographically different but otherwise identical households.Studies on other developing countries show that the scope for economies of scale in household consumption can be considerably large by some measures but negligible by others,and that the effects of demographic compositions on household con-sumption are insignificant(Lanjouw and Ravallion,1995).In a study of urban residents in12 Chinese cities,Gustafsson et al.(2004)find that the size and age composition of households have a modest impact on households’perception of minimum living expenditure.Whether their finding also applies in rural areas is an open question,since rural households tend to be larger and have different consumption pattern than urban households.
The average household sizes of both our data sets exhibit a decline trend over the period of1988to1999,one from4.71to4.13persons,and the other from4.33to3.74.If there ex-ist significant economies of scale and poor households are getting smaller on average,then a poverty trend based on per capita income will understate the increase(or overstate the reduction) in poverty.12To examine how allowing for economies of scale would affect the assessment of 10Poverty lines are sometimes defined relative to the mean income.We will confine ourselves to absolute poverty lines. 11The rural price levels by provinces were obtained by applying to a1990rural consumption basket the official rural CPIs adjusted for consumption of self-produced products.Note that Brandt and Holz(2004)used the same composition of the consumption basket for all provinces throughout1984–2000.As a result,regional differences in and changes over time of consumption patterns are ignored.In addition,the consumption basket used for deriving CPIs is meant to be representative of the consumption pattern of all rural residents,and hence may well differ from the consumption pattern of the rural poor.
12We do not have sufficient information to investigate the existence of economies of scale in the data sets.
Y.Zhang,G.Wan/Journal of Comparative Economics34(2006)694–712701 poverty trend and its decomposition,we employ three constant-elasticity equivalence scales to normalize household sizes.More specifically,if n i represents the number of people in house-hold i,the normalized household size is given by k i=nθi,whereθis alternatively set to1,0.8, and0.5.
3.Data and poverty trend
In this section,we will examine poverty trend in rural China from the late1980s to the end of1990s,using household-level income data from two different surveys.13Thefirst survey was administered annually by the Research Centre for Rural Economy(RCRE)of the Ministry of Agriculture of China in eight provinces between1987and1999except1992and1994.The number of households covered by the survey was exceptionally small in1990and1991.For the other years,it varied between6200and6900households.14Our second data source is the China Health and Nutrition Survey(CHNS).15Five rounds of CHNS were conducted in1989, 1991,1993,1997,and2000.Each round covered around15,000individuals from about4000 households spread over nine provinces.Of these,about two thirds of the households and70 percent of the individuals are classified as rural.The incomefigures reported in each round appertain to the year immediately prior to the survey year.
Observations in both data sets are checked for completeness and internal consistency.To retain as many data points as possible,only those with missing or dubious entries for household size or total income are dropped.We select from each survey4years of data to make the sample periods of the two data sets comparable.For CHNS,the four rounds chosen contain data for1988,1992, 1996,and1999;for RCRE survey,the sample years are1988,1993,1996,and1999.
That the RCRE survey and the CHNS each cover only eight or nine provinces might raise con-cerns about how representative they are of the30odd Chinese provinces in total.The provinces included in the two data sets are given in Table1.These provinces are diverse in economic struc-ture,level of development,and growth performance during the sample period.A good few of them are among the most populous provinces.According to the end-of-year population statistics for2003(National Bureau of Statistics,2004),the combined population of the eight provinces in the RCRE survey is about40percent of the national total,while the population share of the nine provinces in the CHNS exceeds43percent.The share of total rural population of the sampled provinces may be even higher.In our view,the surveyed provinces in each data set constitute a fairly balanced representation of China’s economic geography.The poverty trend in
Table1
Provinces included in the data sets
RCRE Anhui,Gansu,Guangdong,Henan,Jiangsu,Jilin,Shanxi,Sichuan
CHNS1988,1992:Guangxi,Guizhou,Henan,Hubei,Hunan,Jiangsu,Liaoning,Shandong
1996:Guangxi,Guizhou,Heilongjiang,Henan,Hubei,Hunan,Jiangsu,Shandong
1999:Guangxi,Guizhou,Heilongjiang,Henan,Hubei,Hunan,Jiangsu,Liaoning,Shandong
13Since we are interested in poverty among individuals,individual-level income data would be ideal.The data sets do contain some information on individual earnings.However,household members usually pool their earnings,and little is known about intrahousehold redistribution.Following standard practice,we assume perfect income equality among individuals of the same household.
14A brief description of the history of the RCRE survey can be found in Wan and Zhou(2005).
15The data can be downloaded from /projects/china.
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these provinces should also be able to convey the varied poverty reduction experience across the country.That said,it is necessary to stress that this section is not about establishing the exact val-ues of certain poverty measures in the rural areas of China,though we do present estimates of the three FGT indices based on the two data sets.To undertake that task requires surveys with a much more expansive sampling frame both in geographical coverage and preferably in the number of participating households.At present,the NBS urban and rural household surveys are probably the only ones that are sufficiently comprehensive for such a ing the NBS survey data, Ravallion and Chen(2004)have done a meticulous job assembling long series of the FGT indices both at the national level and separately for the rural and urban areas.Rather than trying to better their estimates,the objective here is to assess the trend of income poverty in a broad spectrum of provinces.The results derived herein are indicative of whether the poverty trend observed in the NBS data is sensitive to geographical coverage and,since our data are not culled from the NBS surveys,whether the trend is survey specific.That the two data sets themselves come from different sources serves an analogous purpose—a sensitivity check on the poverty trend present in each data set.
Table2provides the estimates of the head-count ratio,poverty gap,and squared poverty gap indices for the two data sets under different combinations of alternative assumptions about poverty measurement.The left half of the table shows the results for the RCRE data,and the right half for the CHNS data.Horizontally,the table is divided into two panels,each containing results based on a different equivalence scale.16Hence,in the upper-left block wefind the values of P0,P1,and P2for the RCRE data when per capita income(θ=1)is the welfare indicator. Every poverty index is measured against the six poverty lines stated earlier.To explore the sen-sitivity of the results to interprovincial differences in the costs of living,nominal income values are alternately adjusted for provincial deflators constructed by Brandt and Holz(2004)and the rural CPI.
It can be seen from the estimated head-count ratios(P0)that the six poverty lines represent roughly three different classes of poverty.The lowest poverty line z1(530yuan in1995prices) cuts the income distribution at the bottom5to15percent of the population,thus can be viewed as the threshold for extreme poverty in this ing the second,third,or fourth poverty line,around20to30percent of the sampled rural residents would be classified as poor,an assessment in agreement with the general perception of rural poverty in China.The other two lines,US$2.15in1993PPP and US$2in1985PPP per person per day,designate60to70 percent of the population as poor.They seem rather too high at the present stage to serve as poverty thresholds for policy purpose.17
Poverty trends appear to differ when measured against the three classes of thresholds.For example,in thefirst four columns of the upper-left block where interprovincial price differences are factored in,the prevalence(P0)of extreme poverty(measured against z1)started rising as early as1993.The downward trend in the second poverty class(measured against z2–z4)did not reverse until1996,whereas the decline in the third poverty class(measured against z5–z6)was sustained throughout this period.The choice of a poverty index can also affect the assessment of poverty trend.Judging by the head-count ratio,for instance,a sizable reduction in poverty can 16Settingθto0.5does not change our major conclusion about the evolution of poverty trend in this period.However, given the current income level and expenditure pattern in rural China,the scope for scale economies is probably not large enough to justifyθ=0.5.A value of0.8is arguably more appropriate.The results withθ=0.5are available upon request.
17We thank an anonymous referee for highlighting this point.。