NBER WORKING PAPER SERIES RURAL INCOME VOLATILITY AND INEQUALITY IN CHINA. John Whalley Ximing Yue

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1 NBER WORKING PAPER SERIES RURAL INCOME VOLATILITY AND INEQUALITY IN CHINA John Whalley Xmng Yue Workng Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambrdge, MA December 2006 We are grateful to Jm Daves and Terry Scular for suggestons and dscusson. Xmng Yue wants to thank the Ford Foundaton Bejng Offce for supportng a year's stay at the Unversty of Western Ontaro durng whch ths research was carred out. The vews expressed heren are those of the author(s) and do not necessarly reflect the vews of the Natonal Bureau of Economc Research by John Whalley and Xmng Yue. All rghts reserved. Short sectons of text, not to exceed two paragraphs, may be quoted wthout explct permsson provded that full credt, ncludng notce, s gven to the source.

2 Rural Income Volatlty and Inequalty n Chna John Whalley and Xmng Yue NBER Workng Paper No December 2006 JEL No. O15,O20,O53 ABSTRACT Avalable data ndcates a growng urban-rural ncome gap (the rato of mean urban to rural ncomes) wth a sgnfcant ncrease from around 1.8 n the late 1980's to over 3 today. These estmates do not take nto account the hgher volatlty of rural ncomes n Chna. Current lterature based on analyses of rural ncome volatlty n Chna decomposes poverty nto chronc and transent components usng longtudnal survey data and assesses the fracton of the Foster, Greer and Thorbecke poverty gap attrbutable to mean ncome over tme beng below the poverty lne. Resultng estmates of % transent poverty pont to the polcy concluson that poverty may be a less serous socal problem than t appears n annual data due to rural ncome volatlty. Here we use a drect method nstead to adjust rural ncome for volatlty usng a certanty equvalent ncome measure and recompute summary statstcs for the dstrbuton of volatlty corrected ncomes, ncludng the urban-rural ncome gap on whch much of current poverty debate n Chna focuses. Snce an uncertan ncome stream s worth less n utlty terms than a certan ncome stream we argue that heghtened rural volatlty ncreases the effectve urban-rural ncome gap and ntensfes not weakens poverty concerns. Usng Chnese longtudnal rural survey data for whch current decompostons can be replcated, we make adjustments for certanty equvalence of rural household ncome streams whch not only wden the urban-rural ncome gap n Chna but also ncreases other dstrbutonal summary statstcs. Dependng upon values used for the coeffcent of relatve rsk averson, the measured urban-rural ncome gap ncreases by 20-30% usng a certanty equvalent measure to adjust rural ncomes for volatlty. We also conduct smlar analyses usng consumpton data, for whch slghtly larger ncreases occur. John Whalley Department of Economcs Socal Scence Centre Unversty of Western Ontaro London, Ontaro N6A 5C2 CANADA and NBER jwhalley@uwo.ca Xmng Yue School of Fnance, Renmn Unversty of Chna NO.59 Zhongguancun Street, Hadan Dstrct, Bej P. R. Chna, yuexm@sfruc.edu.cn

3 1. Introducton There has been substantal debate nsde and outsde Chna over growng relatve poverty (on nequalty) as an accompanment to Chna s hgh growth. Whle absolute poverty n terms of number of ndvduals n households below any gven poverty lne has fallen n recent years, relatve ncome measures have wdened. L and Yue (2004) usng Chnese survey data suggest that the urban-rural ncome gap (the rato of mean urban to rural ncomes) may have ncreased from around 1.8 n the late 1980 s to around 3 today. It s wdely acknowledged that a varety of factors currently unaccounted for may further wden ths gap, such as dfferental avalablty of educaton and health care. The factor we focus on here s the substantally hgher volatlty of Chnese rural as compared to urban ncomes. Recent lterature on transent and chronc poverty (Jalan and Ravallon, 1998 (JR); L, Wang and Yue, 2005) dscusses rural ncome volatlty n Chna n terms of the relatve sze of these two components rather than makng drect adjustments to welfare measures, ncome or consumpton, so as to recomputed dstrbutonal summary statstcs adjusted for volatlty. 2 JR use Chnese longtudnal data and estmate that 49% of poverty n ther sample s transent, where transent poverty s defned as the porton of the Foster, Greer and Thorbecke (FGT) squared poverty gap whch s removed by usng mean ncome over the sample perod to measure the gap. Ths fndng suggests that f poor households have access to captal markets whch allows 2 Both ncome and consumpton have been used n the lterature. Jalan and Ravallon (1998) use consumpton, whle L, Wang and Yue (2005) use both. In the conceptual dscusson that follows we use a utlty of ncome functon, but a utlty of consumpton functon can also be used. Both ncome and consumpton are used for calculatng nequalty and poverty measures only Chnese data n sectons 4 and 5. 3

4 them to ncome smooth across tme, poverty should perhaps be regarded as a less serous socal problem n Chna (and perhaps elsewhere) than currently. If the alternatve (and seemngly more realstc) assumpton s made that poor households n vllages have ether no access to captal markets, or access only at prohbtvely hgh borrowng rates, the ssue nstead s how to take rural ncome volatlty nto account when constructng measures of ncome nequalty. We use a utlty of ncome functon whch s of so-elastc form (constant relatve rsk averson CRRA), and longtudnal data for rural households to construct measures of certanty equvalent ncome (equvalent n expected utlty terms) for rural ncomes. Data only allow us to adjust rural ncomes n ths way, but t s n the rural sector n Chna that volatlty s most pronounced. We then calculate summary dstrbutonal measures for these modfed measures for Chna ncludng the urban-rural ncome gap, Gn coeffcent, and Thel measures. We compute measures for both certanty equvalent and observed ncome. Our results ndcate that both the urban-rural ncome gap and other measures of nequalty n Chna need to be revsed upwards, perhaps by percent n the case of the urban-rural ncome gap. The sze of revsons depends on the value used for the coeffcent of relatve rsk averson. Smaller but stll sgnfcant modfcatons to other measures, such as the Gn coeffcent and the Thel measure also result. The man pont s that n our analyss, volatlty of rural ncomes reduces ther certanty equvalent value relatve to observed ncomes and sgnfcantly worsens rather than amelorates relatve poverty n Chna. The ssue s whether the contrbuton of volatlty to ncome nequalty should be assessed usng a relatve ncome approach based on a poverty lne or an 4

5 approach usng dstrbutonal summary statstcs appled to modfed measures of ncome for the whole populaton. 2. Recent chronc and transent poverty measures and an alternatve certanty equvalent ncome approach to adjustng ncome for volatlty. A major theme n recent poverty research on Chna has been to dstngush between transent and chronc poverty. A central paper s by Jalan and Ravallon (1998) who measure these two components of poverty n Chna usng longtudnal rural household survey data. Ther chronc poverty measure reflects the component of poverty attrbutable to mean consumpton of households over tme. The transent measure of poverty s the dfference between the total poverty measure and ts chronc component. Sgnfcant transent relatve to chronc poverty suggests both that poverty may be less serous when vewed as a long term problem, and that dstrbutonal concerns n polcy mplementaton should perhaps receve a lower weght. In dstrbutonal lterature, both ncome and consumpton are used as n dstrbutonal measures. Conceptually, consumpton s a better measure than ncome, snce consumpton measures consumer enjoyment from consumng goods and servces, whle ncome s less accurate due to savng and dsavng. However, complng data on consumpton nvolves mputaton of servces rendered over tme from houses and other durables, whch s dffcult to perform satsfactorly. The Practcal dffcultes n treatng durables have lead some researchers to argue that consumpton has no clear advantages over ncome n studyng dstrbutonal ssues. (Atknson and Bourgugnon, 2000, p. 39) 5

6 In the emprcal part of ths paper below, we use both ncome and consumpton to calculate estmates of poverty and dstrbutonal measures, seeng how the results are senstve to the welfare measure used. In the rest of ths secton, however, we assume a utlty of ncome functon provdes the welfare measure n explanng methodology used, but the same explanaton s applcable when consumpton s used. In JR consumpton data s used. Mean consumpton used to measure chronc poverty s the tme mean of household consumpton per capta over the perod at ssue. 3 Ths mplctly assumes that households can borrow and lend durng the perod at the same nterest rate. Usng the squared poverty gap (SPG) ndex due to Foster et al. (1984), the aggregate poverty measure over tme and ts two JR components for a total populaton are: T N 1 2 A( T ) = g( y t ) (1) TN t= 1 = 1 N 1 2 C( T ) = g( y ) (2) N = 1 T( T) = A( T) C( T) (3) where A (T), C (T ) and T(T ) are aggregate poverty ndces over tme, the chronc poverty ndex and the transent poverty ndex respectvely. T and N stand for the number of years and the number of ndvduals n the sample. 4 g( y t ) s the FGT poverty gap measure for ndvdual at the tme t and s defned as g( y t yt ) = (1 ) when z 3 In earler work, Rodgers and Rodgers (1993) measure constant ncome over tme as permanent ncome ; the maxmum annual consumpton level that an agent could acheve from hs or her actual ncome stream over the same perod. (Rodgers and Rodgers, 1993, p. 31.) Permanent ncome s the tme mean of ndvdual ncome f nterest rates for borrowng and lendng are the same. Rodgers and Rodgers also dscuss the case where borrowng and lendng rates dffer. 4 We assume here that every household n the sample s present through all the observed years. Rodgers and Rodgers (1993) dscuss the case where some ndvduals may be observed only for part of the whole perod under survey due to brth, death, mgraton and other factors. 6

7 y t < z and g( ) = 0 f y t z, where z s a predetermned poverty lne. g y ) has a y t ( smlar meanng to g( y t ), but s defned over the tme mean, ndvdual observatons at tme t (denoted by y t ). y = 1 T y t T t= 1, rather than Transent poverty n JR s nterpreted by substtutng (1) and (2) nto (3) and rearrangng to yeld, T N N T ( T ) = g( yt ) g( y ) (4) T t= 1 N = 1 N = 1 The term nsde the large bracket on the rght hand sde of (4) s the dfference between the annual poverty ndex and the chronc poverty ndex n year t, and ts value can be ether postve or negatve. A postve value mples that some poverty experenced n year t s not chronc, whle a negatve value ndcates that chronc poverty s temporarly absent n year t. Transent poverty over the tme perod of observaton s smply a tme mean of the dfference n each year from the mean. 5 Ths transent poverty measure, and the relatve sze of transent to chronc poverty depends on the choce of poverty lne z. Whle ths approach to poverty measurement ams to provde an assessment of the relatve mportance of chronc and transent poverty, t can be also nterpreted as provdng a framework for nvestgatng the effects of volatlty or uncertanty on poverty. 6 Heghtened ncome varaton over tme, for nstance, wll tend to ncrease transent poverty, and hence nter-temporal aggregate poverty, unless ncome s mantaned above the poverty lne throughout the whole perod of observaton. However, drect adjustment 5 The ntuton behnd ths transent poverty measure s also clear from the term nsde the large bracket on the rght hand sde of equaton (4), y ) g( y ) g. For an ndvdual wth g( ) > 0 and g ( ) = 0 ( t the ndvdual experenced n the year s wholly temporarly, and chronc poverty s zero. 6 See also the dscusson n Ravallon (1988). y t y, the poverty that 7

8 of ncome for volatlty has been overlooked thus far n the poverty debate n Chna. If rural ncomes are consderably more volatle than urban ncomes, as s true today n Chna volatlty should worsen the relatve poverty pcture, not amelorate t as results from exstng chronc-transent decomposton mplctly suggest. Hgher rural volatlty reflects weather and other features whch urban resdents do not face. Ths dfference n ncome volatlty between urban and rural resdents thus has mplcatons for both the sze of urban-rural ncome gap and for other dstrbutonal summary statstcs, such as the Gn coeffcent and the Thel measure f volatlty corrected measures of ncome are used. We can adjust observed rural ncomes to account for volatlty usng the certanty equvalence of an ncome stream, snce uncertanty of ncome reduces ndvdual welfare when expressed n terms of expected utlty relatve to a constant and certan ncome. We ' '' take as gven an ndvdual utlty of ncome functon, U ( y) ( U ( y) > 0, U ( y) < 0), and an ncome stream for a household over a perod of observaton, y y..., y,, 1 2 T. Gven the concavty of U(y), T U ( y ) > w U ( y ) (5) t= 1 t t 1 T where y, mean ncome of household, s defned as y = t = y 1 T t w t., where T t = 1 ( w = 1) and the rght hand sde of (5) ncludes perod weghts, representng the t probablty that ncome y t occurs n year t. Thus, f there are two households, one recevng a varable ncome stream y, y2 1,..., y T, and the other recevng an dentcal amount of ncome equal to y n each perod, the expected utlty over the observed 8

9 perod s lower for the household wth tme-varyng ncome than for the household who receves constant or certan ncome. Equaton (5) thus allows us to construct a measure of certanty equvalent ncome, c denoted as y, for any tme varyng ncome stream y, y, , yt. Ths can be obtaned by solvng the equaton: U ( y ) = c T t= 1 w U ( y ) t t The concavty of (5) mples that the certanty equvalent ncome, c y (6), s smaller than the average of the tme-varyng ncome stream y. Adjustng rural ncome for volatlty n ths way wll ntensfy rather than amelorate relatve urban-rural poverty n Chna n contrast to the drecton that currently avalable decompostons of poverty nto chronc and transent components pont. Per capta ncomes of urban resdents n Chna have been rsng for the past two decades and wth no adjustment for volatlty the urban-rural ncome gap was 3.2 n 2002, one of the hghest n the world. 7 8 Estmates of nequalty usng certanty equvalent ncome to adjust for volatlty of ncomes allow us to re-assess relatve nequalty for a populaton where ncomes are certan for one part of the populaton but uncertan for another. 7 See Knght and Song (1999). 8 The ncome defnton underlyng these estmates (and used by the Natonal Bureau of Statstcs of Chna (NBS)) does not capture subsdes to educaton and health care from varous levels of government, securty nsurance, pensons and other features. These subsdes mostly accrue to urban resdents and an urban-rural ncome gap capturng these s also lkely to be hgher. Besdes dsparty n the publc servces as well as ncome volatlty between urban and rural, urbanrural dfferences n the cost of lvng are a further factor that potentally affects the urban-rural ncome gap and overall nequalty n Chna. Unlke publc servces and ncome volatlty, the gap n the cost of lvng between urban and rural sector wll bas the urban-rural gap downwards f t fals to taken nto accounts, as the cost of lvng tends to be hgher n urban than n rural. Scular et al. (2006) attempts to measure urban-rural ncome gap and overall nequalty by controllng for gap n the cost of lvng between urban and rural and fnds a substantal declne n the estmated urbanrural ncome rato, from 3.39 to 2.38 n

10 Certanty equvalent ncome measures also defne an equvalence scale, denoted as s, as the rato of certanty equvalent ncome to the tme mean of the uncertan ncome stream. s = y / y has values whch le between 0 and 1,.e. 0 s 1. = 1 c < s mples that household receves constant ncome throughout the whole perod of c observaton; the more volatle ncome s the smaller s s. s also depends on, whch n turn depends on the degree of curvature of the utlty functon; the more concave the c utlty functon, the smaller y, as well as s. In the calculatons of certanty equvalent rural ncome for Chna we report below, we use a utlty functon wth constant relatve rsk averson (CRRA) whch allows the proportonal adjustment to ncome for certanty equvalence to be unt ndependent. 9 Usng a constant absolute rsk averson utlty functon does not acheve ths result. 10 We specfy preferences as: 1 γ y u ( y) = (7) 1 γ y where y represents ncome. The Arrow-Pratt measure of constant relatve rsk averson for these preferences s gven by: '' u ( y) y γ = (8) ' u ( y) 9 Pror lterature alludes to but t does not explctly set out the approach we detal here usng a CRRA utlty functon. Morduch (1995) brefly dscusses but does not explctly calculate certanly equvalence ncome measures for use n dstrbutonal statstcs, and suggests usng a Taylor seres expanson of u(y). Newbery and Stgltz (1981), n dscussng commodty prce stablzaton schemes, suggest calculatng the amount the ndvdual wll pay to forgo uncertanty, but they do not dscuss the applcaton of certanty equvalence calculatons to dstrbutonal measures. 10 Constant absolute rsk averson preferences, u( y) = 1/ σ *exp( σy), or related varants are also less commonly used utlty functons. 10

11 s and γ are negatvely related,.e. a larger γ yelds a more concave utlty functon, leadng to a lower value of s. Both the equvalence scale and the sze of certanty equvalent ncome depend on the values used for the coeffcent of rsk averson, γ. There s a large body of lterature on estmates of rsk averson wth wdely dspersed results. Usng U.S. labor supply data recent work of Chetty (2006) gves estmates of γ around 1, whle earler studes usng data on nsurance produce estmate of γ rangng from 2 to Lterature on rsk averson n developng economcs suggests moderate rsk averson, wth a coeffcent of rsk averson rangng from 1 to 2. Alderman and Paxson (1994) provdes a detaled survey of lterature estmates of coeffcents of rsk averson n developng countres. We use a number of hypotheszed values of γ between 0.9 and 10.0 appealng to lterature estmates of γ n Chetty (2003), and assess how senstve averson. s s to the degree of rsk We examne the mpact of more volatle ncomes n rural Chna on both the urbanrural ncome gap and other nequalty measures for Chna reportng ratos of urban to rural ncomes based on certanty equvalent ncomes, as well as a number of nequalty ndces. Of the nequalty ndces we report, the Atknson ndex s of partcular relevance to our certanty equvalent ncome approach snce t deals wth the related ssue of socal nequalty averson and uses a smlar functonal form. Ths ndex can be expressed as: I yede = 1 (9) y 11 See Chetty (2003) for bref survey of studes of rsk averson usng nsurance data and expermental methodology. 11

12 where y ede, s the equally dstrbuted equvalent ncome, and defned as that ncome level whch, f equally dstrbuted, would gve the same level of socal welfare as the exstng dstrbuton. The nterpretaton of Atknson ndex s the proporton of total ncome that would be requred to acheve the same level of socal welfare f ncomes were equally dstrbuted. A value of 0.12, for nstance, means that we could reach the same level of socal welfare wth only 88 ( ) percent of the present ncome. 12 Assumng that each ndvdual has a constant absolute rsk averson utlty functon (as n equaton (7)) and that total socal welfare s sum of ndvdual utltes, the equally dstrbuted equvalent ncome can be derved as: 1 n ε ε 1 1 ede = Y = 1 y (10) It should be noted that ε here has dfferent meanng from γ n our defnton of certanty equvalent ncome above. In defnng certanty equvalent ncome, γ captures ndvdual evaluaton of ncome rsk whle n the Atknson ndex ε represents the socal averson to nequalty. More mportantly, ε represents the weght that socety, or an nvestgator, attaches to nequalty n the ncome dstrbuton. ε takes values of above 0 and a larger value of ε attaches more weght to lower ncomes n the dstrbuton and ndcates that socety s more concerned over the stuaton of lower ncome ndvduals. The choce of ε s a matter of subjectve judgment and nevtably arbtrary, but 2 s wdely used and thought by others to be both reasonable and broadly acceptable. 13 In calculatons later usng the Atknson ndex as a summary measure of the overall dstrbutons after adjustment for certanty equvalence, we use the same values of ε as 12 See Atknson (1975) pp See Anand (1983) p. 84 for further dscusson of values for γ. 12

13 we use for γ n calculatng certanty equvalent ncome. Ths allows us to compute total measures of ncome nequalty capturng both socal averson to nequalty and volatlty of ncome, and assess each component. 3. Data used, potental bases, and correctons The data we use for the certanty equvalent ncome adjustments to rural ncomes that we make come from the thrd round of the Chnese household ncome surveys (CHIP for short below). Ths was conducted n 2003 for the reference year 2002, and contans both urban and rural sub-samples, as well as a mgrant sample. 14 Each of the urban and rural samples s natonally representatve, and ncome per capta and Gn coeffcents for both urban and rural samples are close to estmates publshed by Chnese offcal sources and are based on the same defnton of ncome used by the Natonal Bureau of Statstcs (NBS). Combnng both urban and rural samples from ths data yelds estmates of overall nequalty that are also natonally representatve. 15 The NBS sample survey data s unfortunately not publcly avalable. Data provded by ths survey s cross-secton and at a household level. Complete nformaton was only collected for households for the sngle year of 2002: However, for the questons on ncome, consumpton and the number of household, households were also asked n the rural questonnare to record ther ncome and consumpton back to Ths yelds longtudnal data for these varables from 1998 to 2002 for each household n the rural sample whch can be used to adjust rural ncome or consumpton 14 For detals of survey desgn and other ssues n the use of ths survey data see L, et. al (2005). 15 Ths s acheved by weghtng the urban and rural sample so that the dstrbuton of sample ndvduals between urban and rural segments equals the urban-rural dstrbuton n the Chnese populaton. 13

14 for 2002 for certanty equvalence. Ths s the longtudnal panel data that we use to adjust rural ncomes to assess the extent to whch ncome volatlty n the rural sector affects the measured urban-rural ncome gap. Income and consumpton n all household surveys s measured wth error. Here a central ssue wth ts relablty s that the measurement of household ncome and consumpton by respondents s based on recall. The accuracy of reported ncome may thus be a more serous problem as the date for whch the respondents are asked to remember ther ncome recedes from the date at whch the survey takes place. Underestmaton of ncome s most lkely when collected by recall f there s loss of memory as tme passes. Such msestmaton wll also bas estmates of chronc and transent poverty, because msestmaton can lead to a lower tme mean of household ncome. Msestmaton of ncome can also lead to msmeasurement of the varaton of household ncome over tme, potentally leadng to an upper bas n the estmated certanty ncome equvalent scale s. Gven a predetermned poverty standard, chronc poverty may also be underestmated. Checkng ncome levels and ther dsperson for each year n our data relatve to estmates that are publshed by Chnese offcal sources for each of the correspondng years serves as a partal source of verfcaton of our data. NBS estmates of ncome and ts dstrbuton are based on annual surveys and are free of memory error whch attaches to data generated by recall. The NBS sample, from whch the CHIP sample s selected, s large (around 60,000 households every year) and households are sampled usng a two stage stratfed systematc random samplng scheme. The samplng bas of offcal estmates of ncome and ts dsperson s thus small. 14

15 Table 1 compares ncome per capta estmates and Gn coeffcents between the NBS large sample and the CHIP small sample for the years 1998 through The average ncome from the CHIP sample, whch s based on recall by respondents, s underestmated by 8.29 percent for 1998 and 4.71 percent for 1999 compared to estmates of ncome per capta based on the NBS sample. For the other three years, per capta ncomes based on the CHIP sample are all hgher than those from the NBS sample but are close. The underestmaton s larger for consumpton per capta. All consumpton per capta estmates based on recall from the CHIP sample (for 1998 through 2001) are below those of the NBS sample. Consumpton per capta based on the CHIP sample s lower than n the NBS sample by percent n 1998 and percent n Unlke ncome per capta, the dsperson of ncome measured by Gn coeffcents s smlar between the two samples. 16 Underestmaton of ncome n 1998 and 1999 thus appears to be roughly unform across households surveyed. If the use of recall underestmates ncome per capta smlarly for all households, the Gn coeffcent wll be unchanged snce the Gn coeffcent s ndependent of the unt measure of ncome used. Estmates of both transent poverty and certanty equvalent ncome and consumpton are thus based unless underestmaton of average ncome and consumpton per capta over tme for recall bas s corrected for. We have made a correcton for each of the years from 1998 to 2002 n our data by scalng up (f estmates of per capta ncome based on the CHIP sample are below those from the NBS sample) or down (f estmates of per capta ncome based on a CHIP sample are above those from the NBS sample) so that 16 Ths comparson s only possble for ncome, snce there are no measures of dsperson of consumpton per capta avalable from offcal data. 15

16 mean ncomes based on the CHIP sample equal those based on the NBS sample. Ths scalng has no effect on estmates of Gn coeffcents and other measures of nequalty whch are ndependent of scale. 4. Transent poverty measures and certanty equvalent adjusted ncome dstrbuton measures In the next secton we report estmates of the urban-rural ncome gap, the Gn coeffcent and other summary measures of the ncome dstrbuton for the whole of Chna based on both observed and certanty equvalent rural ncomes. We frst, however, report measures of total poverty and ts transent and chronc components for our sample data usng the JR methodology. We replcate Jalan and Ravallon (1998) and L, Wang and Yue (2005) usng our data set, and frst confrm n our data the JR result that transent poverty accounts for a large porton of total poverty n rural Chna. Our estmates of decomposed poverty ndces from ths replcaton also support the relablty of data used n our study. Snce our decomposton estmates are broadly consstent wth results from earler work, t suggests that our data on ncome and consumpton generated by recall may be relable enough to use n an analyss of certanty equvalent ncomes. Any comparson of estmates of poverty ndces between earler work and ours can not be made precsely because our data dffers from that used n prevous work both n terms of the sample of households used and the survey perod. Data n Jalan and Ravallon (1998) come from four provnces n Southern Chna: Guangdong, Guangx, Guzhou, and Yunnan and cover a sx year perod between 1985 and Ther sample 16

17 covers 38,951 ndvduals. Data used n L, Wang and Yue (2005), on the other hand, come from a Poverty Montorng Survey, whch covers 592 natonally desgnated poor countes and covers a perod between 1997 and Ther sample s more than 70,000 ndvduals. In contrast, data used here covers 8,808 households and 36,206 famly members drawn from 22 provnces, and covers a perod between 1998 and Our sample s more comparable to that used by L, Wang and Yue (2005) than JR due to a closer matchng of the tme perod across the two studes and the use of the same poverty lnes and welfare measures (see dscusson below). When calculatng poverty ndces, a measure defned over ether ncome or consumpton can be used. In addton, the poverty lne used n prevous works on rural Chna poverty also dffers. The choce of measure and the assocated poverty lne also s also an ssue so as to facltate as close a comparson as possble of decomposton results wth our sample wth prevous studes. Jalan and Ravallon (1998) uses consumpton as welfare measure and employs poverty lnes compled by Chen and Ravallon (1996), whch gave two separate poverty lnes: a lower and a hgher one for each of four provnces. 17 Except for a hgher poverty lne for Guangdong n 1990, all of the lower and hgher poverty lnes le between the Chnese offcal poverty standard and that used by the World Bank of one dollar per day. L, Wang and Yue (2005) use both ncome and consumpton as measures and employ two poverty standards, an offcal Chnese poverty lne and the World Bank poverty lne of 625 Yuan and 874 Yuan at 2000 prces. Followng L, Wang and Yue (2005), we use both ncome and consumpton as measures and employ two poverty standards used by Chnese offcal agences and the World Bank. 17 Chen and Ravallon (1996) calculate a poverty lne for 1988 usng provncal food bundles and extend ths to other years usng provncal consumpton prce ndexes. Jalan and Ravallon (1998) dd not report whch of ther lower and hgher poverty lnes for each provnce they use when estmatng poverty ndexes. 17

18 These poverty lnes n 2002 prces (rather than 2000), are 628 Yuan and 878 Yuan respectvely. Both ncome and consumpton per capta are translated nto 2002 prces usng provncal consumpton prce ndces. 18 Table 2 reports total poverty ndces and ther chronc and transent components usng of our data for both ncome and consumpton. As can be seen, total poverty based on consumpton for the two gven poverty lnes s hgher than that based on ncome. Ths reflects savngs by households. Usng consumpton as ther measure of welfare, Jalan and Ravallon (1998) report 49.3 % percent of poverty as transent. Ths les between our estmates based on both the offcal poverty lne and the poverty lne used by the World Bank. Ths s broadly consstent wth estmates based on our sample data reported n Table 2, even through our sample perod s 10 years later than that of Jalan and Ravallon. Poverty as reported n L, Wang and Yue (2005) s larger than n Table 2 because ther study covers the poorest regons n rural Chna. Our shares of transent components of total poverty are below thers for each of four cases (two poverty lnes and measures), but our data s also lkely to slghtly underestmate fluctuatons n ncome and consumpton over tme due to the use of data based on recall. Earler studes of transent poverty also present ndces for each sub-group of the total sample populaton dvded by the number of household members and educatonal attanment of the head of households. 19 Jalan and Ravallon (1998) fnd that chronc poverty ncreases wth the sze of the household, whle the total poverty ndex s U- shaped and lowest at a famly sze of 5 and 6. L, Wang and Yue (2005) show smlar 18 Data on provncal consumpton prce ndces comes from Natonal Bureau of Statstcs (Chna) (2003). 19 Besdes the numbers of households and educaton of the heads of households, Jalan and Ravallon (1998) also stratfy ther sample by the mean yeld of land and by wealth. L, Wang and Yue (2005) also use a regonal populaton breakdown and the age of the head of the household. 18

19 results that lowest total poverty occurs for households wth 3 famly members. The upper panel of Table 3 reports results from our data that are smlar to those of L, Wang and Yue (2005). Both earler studes showed that both transent and chronc poverty ndces declned wth the educatonal level of the head of the household. The proporton of transent poverty n total poverty by these characterstcs s the same n our data as n Jalan and Ravallon (1998), but there s a weaker trend evdent wth educaton levels compared to L, Wang and Yue (2005). These results mply that chronc poverty declnes more quckly than transent poverty as the heads of households acqure educaton. Our estmates of the relatonshp between educaton level and poverty, shown n the lower panel of Table 3, are close to those of L, Wang and Yue (2005), except for the hgher educaton level. In summary, calculatons from our data of the relatve mportance of transent and chronc poverty are broadly consstent wth those that of prevous studes, and confrm the earler fndng that transent poverty accounts for a large proporton of total poverty. We vew ths approxmate consstency as an ndcaton that the panel data used n our study, even though collected by recall, s approprate to use n our analyss. 5. Certanty Equvalent Rural Incomes and the Urban-Rural Gap We now report our calculatons of certanty equvalent ncome for the rural populaton for 2002 usng the CHIP data descrbed above, and the mpacts these certanty 19

20 equvalent ncomes have on measures both the urban-rural gap and other dstrbutonal summary statstcs for the whole of Chna. Table 4 reports both summary statstcs for the dstrbuton of certanty equvalent rural ncome and the mpacts on the measured urban-rural ncome gap. We report results for alternatve values of γ (the coeffcent of relatve rsk averson) between 0.9 and These reflect the lterature range reported by Chetty (2003). A γ value of 1.0 yelds no well defned utlty functon. We frst report the mean of certanty equvalent ncomes relatve to the mean of observed rural ncomes for Wth a value of 0.9 the mpact of ncome volatlty s to reduce certanty equvalent ncome by around 3%, but wth a γ value of 10 certanty equvalent ncomes fall by much more. We also report the standard devaton and relatve mnmum and maxmum ncomes (1.0 as a maxmum ndcates no volatlty). The mpacts on measures of the rural ncome gap are reported as the far rght hand sde panel n Table 4. The unadjusted urban-rural ncome gap based on observed ncome s Dependng on the value of γ, the urban-rural ncome gap ncreases from to The Chetty (2003) preferred estmate for γ s n the hgher end of the range 0.9 to On ths bass we nterpret Table 4 as suggestng that a correcton for certanty equvalence of rural ncome n Chna can have the effect of ncreasng the urban-rural ncome gap by around 20%. These results thus underscore the pont that explctly correctng rural ncome n Chna for ncome volatlty worsens rather than amelorates relatve poverty, as uncertanty reduces the certanty equvalent value of ncomes. Exstng decompostons of poverty ndcate that transent poverty s a sgnfcant component of poverty, pontng to 20

21 poverty as a less serous problem. The results n Table 4 also suggest, n contrast, that the effects of drect adjustment for volatlty worsens measured nequalty, and can be sgnfcant. Table 5 report results for consumpton for smlar ranges of γ, usng consumpton rather than ncome data and a utlty of consumpton functon. The mpact of adjustng for certanty equvalence s more pronounced for consumpton than for ncome, and also produces larger adjustments to the urban-rural consumpton gap. These dfferences reflect a large number of households for whom there s greater volatlty n consumpton than n ncome n the underlyng survey data. The theme of results remans that volatlty n the rural sector sgnfcantly ncreases measured nequalty. Tables 6 and 7 report comparsons of other nequalty measures based on both observed and certanty equvalent ncome (Table 6) and observed and certanty equvalent consumpton (Table 7). We report cases for certanty equvalent measures usng values of γ between 0.9 and 10.0 as before. Upper panels report the measures and the lower panel reports the mpacts n relatve terms of usng certanty equvalent ncome. Usng certanty equvalent ncome ncreases all reported measures n Table 6 (the ncome case). The Gn coeffcent ncreases by around 7% usng a γ value of Ths s a smaller ncrease than for the urban-rural ncome gap, but the Gn coeffcent s known to be a relatvely nsenstve poverty measure. Table 7 reports results for consumpton. Wth the excepton of CRRAvalues of γ = 0.9 and γ = 1. 1, 20 all nequalty ndces used ncrease wth the value of γ. Ths s 20 Ths may reflect the feature that the use of certanty equvalent measures has an effect both across the urban-rural sub-populaton whch serve to ncrease nequalty, but also wthn the rural populaton. The combned effect s ambguous. For these low values of n these cases, the wthn rural sub-populaton effects domnate. 21

22 smlar to the case of ncome, but gven values of γ estmates of nequalty based on consumpton are greater than those based on ncome. Ths reflects two factors. Frst, there s a more pronounced mpact from adjustng for certanty equvalence for consumpton than for ncome. Second s larger nequalty measures for consumpton than for ncome based on observed data. Larger consumpton nequalty s also observed for UK households by Goodman and Webb (1995). Table 8 reports Atknson ndces for varous combnaton of γ (rsk averson) and ε (socal nequalty averson). We calculate Atknson measures both for observed ncome unadjusted for certanty equvalence, and for certanty equvalent ncome. Gven socal averson to nequalty of 2.0, the Atknson ndex s 0.55 when observed ncome data used, but dependng on γ can rse to 0.78 when γ of There s an approxmate 20% ncrease n the Atknson ndex to volatlty. For consumpton the ncrease s smaller. In summary, volatlty reflects tme varyng ncome (or consumpton), and wth lmted access to captal markets n rural areas for ncome (or consumpton) smoothng, volatlty reduces the value of the ncome stream relatve to ts certanty equvalent. Explctly adjustng measure of household ncome and/or consumpton for volatlty usng a certanty equvalent approach can ncrease nequalty measures for Chna such as the urban-rural ncome gap by around 20%. 6. Concludng Remarks Volatlty of ncome or consumpton streams has receved only lmted attenton n the lterature n terms of ts mpacts on relatve poverty (nequalty). Here we use longtudnal 22

23 rural data for Chna between 1998 and 2002 to adjust 2002 rural ncome for certanty equvalence, and show that volatlty n rural ncome worsens measures of relatve poverty n Chna. Dependng on the value used for the coeffcent of relatve rsk averson current estmates of the urban-rural ncome gap n Chna may need to be revsed by around 20%. We contrast these results to exstng decompostons of poverty n Chna nto chronc and transent components, whch pont to a large transent porton, wth the mplcaton that poverty vewed as a longer term problems s less serous n Chna than t may appear n annual data. A weakness wth our calculatons s the lack of longtudnal data on urban as well as rural ncome (and consumpton) n Chna. Volatlty n the urban sub-sample wll lessen the effect of the adjustments we make, but t s wdely beleved that rural ncomes are sgnfcantly more volatle than urban ncome. When such data becomes avalable a smlar methodology to that we set out here can also be deployed. Bblography Alderman, Harold and Chrstna H. Paxson, 1994, Do the Poor Insure?: A Synthess of the Lterature on Rsk and Consumpton n Developng Countres, n Bacha ed. Economcs n a Changng World: Volume 4: Development, Trade and the Envronment, London: Macmllan Press. Anand, Sudhr, 1983, Inequalty and Poverty In Malaysa: Measurement and Decomposton, publshed for the World Bank, Oxford Unversty Press. Atknson, Anthony B., 1975, The Economcs of Inequalty, Oxford: Clarendon Press. 23

24 Atknson, Anthony B. and Francos Bourgugnon, 2000, Introducton: Income dstrbuton and Economcs, n Atknson, Anthony B. and Francos Bourgugnon ed. Handbook of Income Dstrbuton, Vol. 1, Elsever. Chen, Shaohua and Martn Ravallon, 1996, Data n Transton: Assessng Rural Lvng Standards n Southern Chna, Chna Economc Revew, 7(1), Chetty Raj, 2003, A New Method of Estmatng Rsk Averson, NBER workng paper W9988. Chetty Raj, 2006, A Bound on Rsk Averson Usng Labor Supply Elastctes, forthcomng n Amercan Economc Revew. Foster, J., E. Greer, J., Thorbecke, E., 1984, A Class osf decomposable poverty measures, Econometrca, 52(3), Goodman, Alssa and Steven Webb, 1995, the Dstrbuton of UK Household Expendture, , Fscal Studes, 16(3), Jalan, J., and Ravallon, M., 1998, Transent poverty n postreform rural chna, Journal of Comparatve Economcs, 26(2), L, Sh, Pngpng Wang and Xmng Yue, 2005, The Causes of Chronc and Transent Poverty and Ther Implcaton to Poverty Reducton Polcy n Rural Chna, Fnal Report to Poverty and Economc Poverty (PEP) network, downloadable from L, Sh, Chulang Luo, Zhong We and Xmng Yue, 2005, The 1995 and 2002 Household Surveys: Samplng Methods and Data Descrpton, unpublshed ms. L, Sh and Xmng Yue, 2004, An Investgaton nto Urban-rural Dvde n Chna, Cajng Magzne, March/Aprl. (In Chnese) 24

25 Knght, John and Lna Song, 1999, The Urban-Rural Dvde: Economc Dspartes and Interactons n Chna. New York: Oxford Unversty Press. Morduch, Jonathan, 1995, Income Smoothng and Consumpton Soothng, The Journal of Economc Perspectves, 9(3), Newbery, Davd and Joseph Stgltz, 1981, The Theory of Commodty Prce Stablzaton, Oxford: Oxford Unversty Press. Natonal Bureau of Statstcs (Chna), 2003, Chna Statstcal Yearbook 2003, Chna Statstcal Press, Bejng. Ravallon, Martn, 1988, Expected Poverty Under Rsk-Induced Welfare Varablty, The Economc Journal, 98(393), Rodgers, R., Rodgers, L., 1993, Chronc poverty n the Unted States, The Journal of Human Resources, 28(1), Scular, Terry, Xmng Yue, Bjorn Gustafsson and Sh L, 2006, The Urban-Rural Gap and Income Inequalty n Chna, forthcomng from Revew of Income and Wealth. 25

26 Table 1: A Comparson of Summary Statstcs between CHIP and NBS Sample of Rural Income, Income Consumpton Year per capta n Chnese Yuan Gn coeffcent Per capta n Chnese Yuan CHIP sample , , , , , , , , , ,897 % Change NBS sample , , , , , , , , , ,834 % Change CHIP sample as a % of NBS sample Note: 1 See text for more detal of these two sample survey sources. 2 Ths denotes the annual compound growth rate between 1998 and 2002 at current prces. 26

27 Table 2: Poverty Indces and the Dstrbuton between Chronc and Transent Poverty by Poverty Lne and Income/Consumpton Measure usng CHIP data Poverty Poverty ndex Shares of Poverty lne Chronc Transent Total Chronc Transent Total Income per capta Consumpton per capta Table 3: Poverty Indces and Ther Dstrbuton by Household Characterstcs Poverty ndex Share Chronc Transent Total Chronc Transent Total Number of household members Educatonal attanment of the heads of households Illteracy and sem-llteracy Prmary school Mddle school Hgher school College and above

28 Table 4: The Impacts of Certanty Income Equvalent Rural Income on the Urban-rural Income Gap Rato of urban to rural per capta ncome after adjustng Summary statstcs of the certanty ncome for certanty equvalent ncome scale ( s ) equvalence and relatve to the γ unadjusted urban-rural ncome rato* Mean S.D. Mn. Max. After Index relatve to unadjusted rato (100) Note: * the unadjusted or observed rato of urban to rural per capta ncome s Table 5: The Impacts of Certanty Consumpton Equvalent Rural Consumpton on the Urban-rural Consumpton Gap Rato of urban to rural per capta consumpton after Summary statstcs of the certanty adjustng consumpton for equvalent consumpton scale ( s ) certanty equvalence and γ relatve to the unadjusted urban-rural ncome rato* Mean S.D. Mn. Max. After Index relatve to unadjusted rato (100) Note: * the unadjusted or observed rato of urban to rural per capta consumpton s

29 Table 6: Comparson of Chna-wde Inequalty Measures Based on Observed and Certanty Equvalent Income γ Coeffcent of varaton Gn coeffcent Thel ndex Mean logarthmc devaton Observed data Relatve measures (measure based on observed data=100) Observed data

30 Table 7: Comparson of Chna-wde Inequalty Measures Based on Observed and Certanty Equvalent Consumpton γ Coeffcent of varaton Gn coeffcent Thel ndex Mean logarthmc devaton Observed data Relatve measures (measure based on observed data=100) Observed data

31 Table 8: Atknson ndces of nequalty of both observed and certanty equvalent ncome and consumpton usng CHIP data γ Observed ε data Income Consumpton