Marginal Benefit Incidence Analysis Using a Single Cross-section of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.

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1 Margnal Beneft Incdence Analyss Usng a Sngle Cross-secton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple method to conduct margnal beneft ncdence analyss wth a sngle cross-secton of data. Ther method enables the analyst to test whether the poor beneft more or less than the non-poor from program expanson. In ths note, we propose an alternatve to the method proposed by Lanjouw and Ravallon. An applcaton to access to basc nfrastructure servces n Latn Amerca llustrates the approach. EL classfcaton: D3, I0, I20 Key words: Beneft ncdence, Latn Amerca, poverty, electrcty, water Both authors are wth the Poverty Group n the Vce Presdency for Latn Amerca at the World Bank. Ths paper was prepared as a contrbuton to a regonal study on nfrastructure reform and the poor, funded by the Regonal Studes Program of the Offce of the Chef Economst. We benefted from the comments of Vven Foster, Peter Lanjouw, and Martn Ravallon. The vews expressed here are those of the authors, and they do not necessarly represent those of the World Bank, ts Executve Drectors, or the countres they represent.

2 . Motvaton Beneft ncdence analyss s a popular tool used by polcy makers to evaluate the dstrbuton (e.g., accordng to a welfare ndcator such as per capta ncome) of the benefts from publc programs and expendtures. In most emprcal applcatons, the analyst looks at the dstrbuton of current publc spendng. However, as noted by Lanjouw and Ravallon (999), the dstrbuton of addtonal spendng need not be smlar to the dstrbuton of exstng spendng. If publc expendtures reach the rch before reachng the poor, and f there s some level of saturaton n the servces that can be provded to the rch, then the poor may beneft more from an ncrease n spendng than from exstng levels of spendng. Lanjouw and Ravallon proposed an nnovatve methodology to measure margnal beneft ncdence analyss usng a sngle cross-secton of data. Ths note presents an alternatve to ther approach for estmatng the so-called tmng of program capture usng a sngle cross-secton. The dfference between Lanjouw and Ravallon s approach and our alternatve les n the way the groups of households are defned accordng to ther poston n the ncome dstrbuton. Lanjouw and Ravallon defne fve untles by groupng households 2 accordng to ther poston n the overall dstrbuton of ncome of a country. In an emprcal settng smlar to that of Lanjouw and Ravallon, we defne the untles to whch households belong not accordng to the poston of the households n the overall country-wde dstrbuton of ncome, but rather accordng to ther poston n ther departmental dstrbuton of ncome, wth the country beng dvded nto several departments. The mplcaton of ths modfcaton s that wth our method, the poorest household n the rchest department s classfed as belongng to the poorest untle together wth the poorest household n the poorest department, even though the poorest household n the rchest department may belong to a hgher untle n the overall dstrbuton of ncome. One case n whch our method could be of use s when well-beng s relatvely defned. Accordng to relatve deprvaton theory, households take nto consderaton not only ther absolute level of welfare, but also ther level of welfare relatve to others. If for any gven group of households, the peer comparson group conssts of other households lvng n the same geographc area, the relatvst approach for the analyss of the dstrbuton of publc spendng would lead to our way of rankng households usng ther poston n the departmental rather than natonal dstrbuton of ncome. That s, one would frst be nterested n assessng whether wthn a gven department, poor and rch households beneft n the same way from an ncrease n publc spendng. Next, when aggregatng the results at the natonal level, as already mentoned, a poor household n a rch regon would be gven the same treatment as a poor household n a poor regon. Ths relatvst lne of reasonng would dffer from an absolutst percepton of well-beng, accordng to whch all households should be ranked natonally by ncome level.

3 Another case n whch our method could be employed s n the evaluaton of Government polces usng mult-country data. If we have regonal data for, say, Latn Amerca, and f we use margnal beneft ncdence analyss n order to analyze whether on average n the regon, Governments are pro-poor n ther spendng allocatons at the margn, we would need to rank households accordng to ther poston n ther own country s ncome dstrbuton rather than accordng to ther poston n the regon-wde dstrbuton. Wth mult-country data, the absolutst approach would be of lmted value for polcy dscussons because decsons are clearly made at the country rather than regonal level. A smlar case could occur f offcals n the central Government of a federal entty were to assess the dstrbuton of spendng wthn federated enttes n a decentralzed context whereby the federated enttes have the power and autonomy to allocate budgetary resources. In ths note, we do not wsh to suggest that the relatvst approach s necessarly better or worse than the absolutst approach n all cases. The choce of one approach versus the other wll depend on the context and data avalable. But f the relatvst approach s desred, then a dfferent econometrc method from that used by Lanjouw and Ravallon s reured. 2. Method Let us frst revew the method proposed by Lanjouw and Ravallon. The authors use an Indan data set wth two types of geographc enttes, namely states and regons. Contaned n the data are,, N states and a number of regons wthn each state. The regons (whch are taken as proxes for the households wthn these regons) are ranked by a measure of per capta ncome on a natonal bass and assgned to one of,, ncome bracket ntervals. We denote by x j the beneft ncdence of a program n regon j belongng to nterval of state. The mean beneft ncdence n nterval for state s denoted by and the overall state mean s denoted by. If nterval of state, the two means are respectvely eual to: s the number of regons n x / [] j j j x j / [2] Although they do not wrte ther emprcal model explctly, Lanjouw and Ravallon conduct the margnal beneft ncdence analyss by runnng regressons as follows: ˆ α ε for,, [3] 2 Lanjouw and Ravallon use aggregate sub-natonal data rather than household data, but the dea s the same. 2

4 where ˆ s obtaned from the ftted-values of the followng regresson: xj x j j j γ δ ν Euaton [3] enables beneft ncdence n nterval to be analyzed wth respect to the varaton n the state s mean beneft ncdence. However, the mean state beneft ncdence depends on the ncdence n nterval. Ths endogenety s avoded by usng as an nstrument n the estmaton n [4], the leave-out mean, whch s the state level mean for all the regons except those belongng to nterval. In our approach, we also defne,, N geographc unts, whch n the emprcal llustraton are sx Latn Amercan countres. But t s wthn each country rather than wthn the Latn Amerca regon as a whole that households are ranked by household ncome and assgned to one of,, ncome bracket ntervals. We classfy households nto ncome decles, so that 0. We denote by the beneft ncdence of a program n household j belongng to ncome nterval of country. The beneft [4] x j ncdence n nterval for country s denoted by, the country overall country mean s denoted by and s the number of households n nterval of country. We conduct the margnal beneft ncdence analyss by runnng regressons as follows:, xj x j, j j α ε for,, [5] In the frst and poorest nterval (), ths yelds a regresson of the mean level of program partcpaton n the poorest households n the varous countres on the mean level of program partcpaton n the country as a whole. To avod endogenety (standard country means would be obtaned over all the households n the country, ncludng those n the frst nterval), we defne the rght hand sde varable at the country level drectly as the mean on all the households except those belongng to nterval. Assume now that all the ntervals wthn a gven country have the same number of households,. For nstance, wth 0, the bottom decle n a country wth 20 households has 2 observatons, whle the correspondng nterval n a country wth 30 households has 3 observatons. Whle the sze of the ntervals may dffer between countres, they do not dffer wthn countres. Wth can smplfy [5] as follows: for all, we 3

5 4 ε α for,, [6] The coeffcents can be nterpreted as margnal beneft ncdence measures only when the number of ntervals s large. To see ths, note that snce, we have. Hence: ε α for,, [7] Droppng the error term and rearrangng the terms yelds: ) /( ) / ( α for,, [8] Partally dfferencatng, we get: for,, [9] The margnal beneft ncdence estmates are the values of /(- ). The change n program ncdence for decle followng from a one unt ncrease n the aggregate ncdence of the program s eual to only when the number of ntervals tends to nfnty. We now turn to the estmaton of the coeffcents. To estmate a sngle regresson, we pool all the observatons from the varous ntervals together and rewrte the system of regressons [7] as: ε α [0] In [0], the ntercepts and slopes are allowed to dffer for the varous ntervals subject to an mplct restrcton. The restrcton s that the mean margnal beneft ncdence estmates for the ten groups must be eual to one. Totally dfferentatng ) / ( yelds ths restrcton: [] Wrtng, the parameter for the last nterval, n terms of the other parameters yelds:

6 ( ) [2] To take nto account the restrcton [], we rewrte [0] as: α ε [3] ( ) Euaton [3] can then be estmated wth non-lnear least suares. 4. Results To llustrate the method, we use household survey data on access to electrcty and water from sx Latn Amercan countres. We conduct the margnal beneft ncdence analyss wth household surveys for 986 n Brazl, Honduras, Mexco, and the Republc Bolvarana de Venezuela, and 989 n Chle and Guatemala. Thereafter, to test whether our method s relable, we compare the results obtaned wth our method on the bass of a sngle cross-secton wth the actual changes n beneft ncdence observed between the frst pont of data and a second pont whch corresponds to the year for 996 n Brazl, Honduras, Mexco, and the Republc Bolvarana de Venezuela, 998 n Chle, and 999 n Guatemala. Table presents the mean (rather than margnal) beneft ncdence for access to water and electrcty n urban and rural areas. Not surprsngly, households at the bottom of the dstrbuton wthn each country have much lower access rates than households n the rcher decles, and the dfferences tend to be larger n rural areas where access rates are lower. Table 2 presents the estmated margnal beneft ncdence analyss for urban and rural areas separately obtaned usng euaton [3]. The upper panel gves the estmated slopes for water, whle the lower panel gves them for electrcty. All coeffcents are sgnfcant at a 5 percent level. The 95 percent confdence ntervals are ncluded for convenent comparson of statstcally sgnfcant dfferences between the coeffcents. Fnally, table 3 presents the margnal mpacts /(- ) whch are constructed usng the slope estmates n table 2. Whle the poor have lower access rates than the rch (table ), they often beneft more than the rch from margnal ncreases n access rates (table 3). For water, a one standard devaton (0.22) ncrease n urban access rates ncreases access n decle two by 0.20 ( ) and n decle nne by In rural areas, a one standard devaton (0.73) ncrease n water access rates ncrease access rates by 0.20 n decle two and by 0.4 n decle nne. For electrcty, a one standard devaton (0.090) 5

7 ncrease n urban access rates ncreases access by 0.55 n the second decle of a typcal country and by n the nnth decle. In rural areas, a one standard devaton (0.270) ncrease n electrcty access rates ncreases access n decle two by and n decle nne by How good are our estmates? Snce we have two data ponts for each country, we can compute the actual ncreases n access rates between the two years n each of the countres for the two nfrastructure servces for both urban and rural areas. The actual average ncreases n access rates, n decle across the sx countres between tme t and tme t- are defned as: ~ N N, t, t, t, t for,... [4] Table 3 presents the estmated and actual values of the margnal mpacts, and fgure presents the results graphcally. The plan lnes represent the estmates and the dashed lnes the actual values. In most cases, the estmates are farly good approxmatons of the actual values, whch suggests that cross sectonal data can ndeed be used to conduct beneft ncdence analyses wth reasonable accuracy. To conclude, we have provded a new method for conductng margnal beneft ncdence analyss whch can be useful n a number of settngs, ncludng those characterzed by the use of cross-country data. We have tested the method usng data on household access to basc nfrastructure servces n sx Latn Amercan countres. The estmates obtaned wth our method are farly close to the margnal beneft ncdence actually observed from the late 980s to the late 990s. From a substantve pont of vew, we have shown that although the poor have much lower access rates to electrcty and water than the rch, they often beneft more from ncreases n access rates than the rch. ~, Reference Lanjouw, Peter, and Martn Ravallon, 999, Beneft Incdence, Publc Spendng Reforms, and the Tmng of Program Capture, World Bank Economc Revew, 3:

8 Table : Mean access rates to electrcty and water by ncome decle n sx Latn Amercan countres Water Electrcty Decle Urban Rural Urban Rural Mean Source: Authors estmatons from household survey data. Table 2: Margnal beneft ncdence regresson coeffcent estmates for electrcty and water Urban Rural Decle Coeffcent Std. Err. 95 % Confdence Interval Coeffcent Std. Err. 95 % Confdence Interval Water Electrcty Source: Authors estmatons from household survey data 7

9 Table 3: Margnal beneft ncdence estmates /(- ) and actual values ~ for electrcty and water Urban Rural Water Electrcty Water Electrcty Decle Estmated Actual Estmated Actual Estmated Actual Estmated Actual Mean Source: Authors estmatons from household survey data 8

10 Fgure : Comparson of margnal beneft ncdence estmates wth actual changes n access [The dashed lnes are the actual values ~ and the plan lnes are the estmates /(- )] 2.0 Water Urban 2.0 Water Rural Electrcty Urban.6 Electrcty Rural Source: Authors estmatons from household survey data 9