Refining Targeting against Poverty Evidence from Tunisia

We introduce a new methodology to target direct transfers against poverty. Our method is based on estimation methods that focus on the poor. Using data from Tunisia, we estimate ‘focused’ transfer schemes that highly improve anti-poverty targeting performances. Post-transfer poverty can be substantially reduced with the new estimation method. For example, a one-third reduction in poverty severity from proxy-means test transfer schemes based on OLS method to focused transfer schemes requires only a few hours of computer work based on methods available on popular statistical packages. Finally, the obtained levels of undercoverage of the poor are particularly low.


I. Introduction
The issue Transfer schemes are among the main policy tools against poverty. Cash transfers are the provision of assistance in cash to the poor or to those who face a risk of falling Å We are grateful to the INS (National Institute of Statistics of Tunisia) that provided us with the data. This study is a revised version of the paper 'Focused Targeting against Poverty. Evidence for Tunisia'. The research has been supported by the ESRC Grant R000230326, which funded the employment of the second author as a research assistant. The first author is also grateful for the financial support by Spanish Ministry of Sciences and Technology, Project SEJ2005-02829/ECON, and by the Instituto Valenciano de Investigaciones Económicas. We thank G. Kingdon, J.-Y. Duclos, J.-M. Robin and participants in seminars in the Universities of Oxford, Alicante, Nottingham, Sussex, GREQAM and DEFI at Aix-Marseille II, Yonsei University in Seoul, University of Cergy-Pontoise, DIW in Berlin, University of Paris I and diverse conferences. Usual disclaimers apply. into poverty. Many of these schemes, called 'proxy-means tests' (PMT), are based on predictions of household living standards used to calculate the transfers. Such predictions are obtained by using household survey data for regressing the living standard variable on household characteristics that are easy to observe. However, the errors in using OLS for PMT against poverty are large, a key shortcoming of PMT. In this study, we show how these errors can be substantially reduced by using other statistical approaches.
Many countries have been using PMT to target transfers, particularly in (i) Latin America and the Caribbean, such as Chile for many years under the Ficha CAS system, Columbia under SISBEN , Mexico under the Oportunidades Program, Nicaragua, Jamaica, etc.; and (ii) Asia, such as India, Indonesia, China, Thailand and Philippines. In these countries, many theoretical and practical issues related to PMT have been studied. The performance of the estimated transfer schemes is quite variable (Coady, Grosh and Hoddinot, 2004). Raising their impact on poverty is of paramount importance as stressed in De Janvry and Sadoulet (2006b). However, the statistical foundations of these programmes have not received the attention that it deserves. We fill this gap in this study.
Concerned with improving anti-poverty transfer schemes, we propose an estimation method of anti-poverty PMT that focus on the poor and the near-poor, thereby dramatically enhancing the scheme performance. We evaluate different approaches to determine scores for PMT schemes. We apply our new method to Tunisia and find significant improvement when compared with traditional methods.

What is targeting?
Although living standards are measured with household surveys, they are generally badly known for the households that are not surveyed. Many authors have studied assistance to poor people based on targeting when some characteristics of individuals can be observed, but not income. 1 Recently, Coady, Grosh and Hoddinott (2004) reviewed 122 targeted anti-poverty programmes in 48 countries. Cash transfers based on PMT are generally found to provide the best results, although there is an enormous variation in targeting performances. They also find that targeting performance is better in rich countries and where governments are accountable. Lindert et al. (2005) measure the redistributive power of 56 transfer programmes in eight countries. They find that public transfers can be an efficient way of redistributing income, but often fail to do so. Moreover, the coverage of the poor is found far from 100% for the studied programmes. Some transfer programmes are conditional on prespecified behaviour by beneficiaries (e.g. child school attendance or child vaccination). We do not deal transfer, while poor. The Type II error arises where benefits are awarded to ineligible people under perfect targeting. The Leakage of programme benefits is a monetary assessment of this error, obtained by adding (i) the transfers given to those whose pretransfer living standard is above the poverty line, and (ii) the transfers received by pretransfer poor who are unnecessary because the post-transfer living standards exceeds the poverty line. 4 Unnecessary transfers are those in excess for all households lifted up above the poverty line, as from this level of living standards they are no longer poor. If the aim is minimizing poverty, there is no justification to transfer cash to households once they have been lifted up to the poverty line as this would not change the final poverty level. The Leakage ratio is obtained by dividing the Leakage indicator by the available budget. A last measure of the programme efficiency is the reduction in a poverty measure due to transfers. 5

Living standard predictions
In practice, anti-poverty targeting can be based on predictions of household living standards, generally obtained from ordinary least squares (OLS) regressions on observed characteristics (e.g. Joliffe, 2005, using data from 1997 Egypt). However, the OLS method is centred on the mean of the dependent variable (e.g. household living standard) and should provide accurate predictions around this mean only, which is often located far from the poverty line. Then, the predicted living standards of the poor and near-poor may be inaccurate. This explains why significant Undercoverage of the poor is common (as in Grosh and Baker, 1995).
Alternative estimation methods are possible for our purpose of improving the schemes. For example, a semi-parametric estimation of the income distribution could be implemented by using kernel estimation methods in which correlates are parametrically incorporated (e.g. Pudney, 1999). Even full nonparametric estimation of conditional distributions of living standards could be adapted to the problem at hand. However, nonparametric methods suffer from slow consistency, inaccurate estimation of the distribution tail and are subject to the 'multidimensional curse' requiring unavailable large information. These are serious issues because of the numerous correlates included in proxy-means tests. Moreover, analysts in national statistical institutes favor simpler estimation methods. Accordingly, Deaton (1997) emphasizes methods that can be actually implemented in the relevant institutions.
For these reasons, we investigate two simple restrictions of the predictive regressions: (i) censoring the dependent variable to eliminate observations located far from the poverty line; and (ii) using quantile regressions. The knowledge of the quantile regressions centred on all observed quantiles is equivalent to the knowledge of the empirical conditional distribution. This distribution is the main information missing to make imperfect targeting optimization identical to perfect targeting optimization, of which solution will be presented in section II. It is therefore what is needed to solve optimally the targeting problem. However, there are too many quantiles to consider for a practical procedure, although good results may be obtained by just trying one quantile around the poverty line. Then, focusing on the poor means that the predictions are calculated by defining the quantile regression or the censorship threshold in terms of living standard levels representative of the poor.
Assume that the equation used to predict living standards has the form y i = X i b + u i , where y i is the living standard of household i, X i is a vector of exogenous correlates of living standard for household i, u i is an error term and b is a vector of parameter to estimate. OLS estimates correspond to imposing the restriction E(y i |X) = X b, which implies E(u i |X) = 0. Quantile regression estimates centred in quantile correspond instead to the restriction q (y i |X) = X b, where function q denotes the conditional quantile function of order , conditional on the values of the variables X. This restriction implies q (u i |X) = 0. That is, the quantile on which a quantile regression is centred relates to error quantiles. Thus, the vectors b differ when different quantiles are specified.
In that case, what is predicted is a chosen quantile of the distribution of the living standards conditionally on the correlates. This method has two shortcomings. First, if the error terms are approximately normal, some efficiency may be lost when compared with OLS (the MLE under normality). This matters for targeting purposes as large variance of predictions may yield poor predictive performance for any social indicator. Secondly, the focus is conditional on the set of correlates. That is, the chosen quantile is not that of the dependent variable, but the quantile of the error in the estimated equation. However, that is precisely the quantile of the error that may matter most if one is interested in the prediction error that affects the transfer scheme's performance.
Quantile regressions, centred on the poverty line, should improve targeting, when compared with OLS, precisely because they are centred on the distribution location that identifies the poor, i.e. the poverty line threshold. Indeed, typically in regression methods, the prediction error is minimal at the central tendency used to define the regression method (mean for OLS regression, median for least-absolute deviation regression, a given quantile for quantile regression), whereas it increases quadratically with the distance of the data from the chosen central tendency. As the living standards of the poor are usually quite different from the mean living standard in a population, OLS predictions are mediocre for the poor. In contrast, if the centreing quantile is chosen close to the poverty line, the prediction errors for the poor should be moderate with quantile regressions. Even if absolute prediction differences among methods may be reduced when running regressions of log-living standards, they become inflated again when using the exponential function to recover predicted living standards.
Another important issue is that OLS predictions for anti-poverty schemes are degraded by: presence of outliers, non-normality of error terms with finite sample size, heteroscedasticity and other misspecifications. These issues matter for targeting purposes as they are likely to occur with typical household survey data. Quantile regressions deal with these concerns for robustness (Koenker and Bassett, 1978), which are crucial in poverty analysis because of: (i) outliers generated by transaction omissions in consumption surveys; and (ii) the non-robustness of many poverty measures (Cowell and Victoria-Feser, 1996). Censored quantile regressions have been found useful to obtain robust explanations of chronic and seasonal-transient poverty (Muller, 2002b).
As mentioned above, a better focus of the scheme can also be obtained by censoring part of the income distribution (the wealthiest households for example) from the prediction. This suggests using Tobit regressions and censored quantile regressions instead of OLS and quantile regressions respectively.
Another interest of focused targeting is that it is directly related to the theoretically optimal transfer schemes, in which the transfers are concentrated towards the poorest of the poor, the richest of the poor or both (Bourguignon and Fields, 1997). From this theoretical perspective what needs to be well determined are the transfers to these subpopulations. Then, focused predictions of the living standards of the poor and near-poor may generate more efficient transfers.

Comparison with Elbers, Lanjouw and Lanjouw
Another field where living standard predictions obtained in a first regression stage using household survey data are subsequently used in a second stage for poverty simulation is the small area literature. For example, Elbers, Lanjouw and Lanjouw (2003), ELL from now, combine census data and household survey data. We do not deal in detail with this approach as it raises additional and specific difficulties.
Although transfer programmes based on PMT rely on observable household characteristics, in contrast with ELL they use neither census data nor the locality-specific variables (local census enumeration area). Should they use such information? Perhaps, but there are reasons to doubt it. First, information on many household characteristics from census data is infamously known as being of mediocre quality. Second, using accurate location for designing transfer schemes may lead to migrations from households attempting to capture the transfers. Third, in the household living standard survey used to estimate the predicted incomes, only few local areas are observed. The non-use of census data and location-specific variables constitutes a major difference of our approach with that of ELL.
Furthermore, we deal with model error and sampling error in different ways than ELL. We are interested in model error in that it determines transfers, but not for estimating the accuracy of poverty estimators or transfer performance estimators.
For the latter stage, we examine only the sampling standard error of these estimators as the transfer schemes to compare are considered as given.
In footnote 5 of ELL, the authors claim that using quantile regressions give results non-significantly different from using OLS. As quantile regressions of living standard dependent variables have routinely been found to significantly vary across the centreing quantiles, we presume that they found this result using least-absolute deviation (i.e. median quantile) estimators or another arbitrary quantile. There is no mention of selecting a given quantile to focus the regression in their study.
Is it possible to improve anti-poverty targeting by using living standard predictors that focus on the poor? The aim of this study is to explore this question. However, our intention is not to propose a detailed reform of the anti-poverty policy in Tunisia nor to deal with all the practical implementation difficulties of such policy. Section II presents the anti-poverty transfer schemes. In section III, we apply our new method to the 1990 Tunisian household survey. In section IV, we discuss programme efficiency results. We find that: (i) focused targeting would reduce poverty much more than targeting based on OLS; and (ii) Undercoverage of the poor can be massively reduced. Finally, section V concludes.

II. Anti-poverty cash transfers
This study is based on the following popular poverty measures of the FGT class (Foster, Greer and Thorbecke 1984) because of their attractive axiomatic properties: P = z 0 ((z − y)/z) f (y)dy, where z is a pre-specified poverty line, f (.) is the density function of household income y (or household living standard) and is a poverty aversion parameter. 6 Naturally, our approach could be extended to other poverty measures. Given an anti-poverty budget, one must design transfers that optimally allocate this budget across households.
Let us first consider the situation when Y (the vector of incomes in a population before applying the transfers, t i , i = 1, . . ., N ) is perfectly observed. In that case, the optimal transfer allocation is the solution to: where N is the population size, B is the budget to allocate, t i is the non-negative cash transfer to household i and y i is its pretransfer income. The objective function can be weighed by the household size (or some equivalent scale) in each household to deal with poverty at the individual level rather than the household level. However, for expositional simplicity, we neglect for the moment the possibility that households may include several members. We do not consider how the budget B is funded. When Y is perfectly observable, the solution to this problem is referred to as 'perfect targeting' and denoted t i for household i. Fields (1990, 1997) show that perfect targeting minimizing the head-count ratio would start awarding transfers so as to lift the richest of the poor out of poverty (in a decreasing order of income until all the budget is exhausted, 'r-type transfer'): In contrast, if the aim is to minimize an FGT poverty measure satisfying the transfer axiom ( > 1), it is optimal to start allocating the anti-poverty budget to the poorest of the poor ('p-type transfer'). In that case, the transfer scheme would be: where y max is the highest cut-off income allowed by the budget. As the anti-poverty budget rises, y max increases up to the poverty line, z, and perfect targeting would permit to lift all the poor out of poverty. For the poverty gap ( = 1), both rules of transfer allocation are equivalent provided the poor incomes are never lifted strictly above the poverty line. Unfortunately, perfect targeting is not feasible because incomes cannot be perfectly observed. Nevertheless, as household living standards are correlated with some observable characteristics, it is possible, as in Glewwe (1992), to minimize an expected poverty measure subject to the available budget for transfers and conditioning on these characteristics. In practice, the approach followed in the literature or by practitioners for designing the transfer scheme is to replace unobserved living standards by predictions based on observed variables.
Let us first recall the standard procedure used in the literature for such predictions. Several empirical articles on anti-poverty targeting have appeared in the literature. 7 They generally follow a two-step procedure. First, the expectation of y i conditional on X i (the vector of living standard correlates for household i) is parametrically estimated by OLS. Then, if the budget allows it, each predicted poor household receives the difference between its predicted income and the poverty line. Other dependent variables could be used in such regressions, sometimes with different meaning of the objective function. Our method can be easily adapted to these cases. Some correlates might be modified by households, raising moral hazard problems. We deal with this issue by avoiding as much as possible endogenous regressors, and by considering alternative sets of correlates, defined by their increasing presumed sensitivity to moral hazard. What matters for anti-poverty targeting is the ability to predict the living standards of the poor. Our strategy is to focus on the poor when predicting living standards. We now turn to the estimation results, first by presenting the data used for the estimations.

III. Data and methodology
The data In Tunisia, targeting transfers to poor people has become increasingly urgent because structural adjustment programmes have imposed cuts in food subsidies (Tunisian Universal Food Subsidies Program), traditionally the main way to fight poverty. Since 1970, basic foodstuffs have been under subsidy to protect the purchasing power and the nutritional status of the poor. This programme was inefficient and expensive. Indeed, about 2.9% of GDP was spent in subsidies by 1990 (still slightly < 2% nowadays). Furthermore, non-poor households received much more from the programme than the poor. Improvement on subsidies has been limited by preference patterns, income inequality and the size of individual subsidies (Alderman and Lindert, 1998). In such situation, transfer schemes may alleviate poverty at a lower budgetary cost, provided that the method used to design the scheme performs well. This is consistent with one of the key challenges to meet the goals of the 10th Tunisian Economic Development Plan: to strengthen the performance of social programmes while maintaining budget balances (The World Bank, 2004). Meanwhile, maintaining social stability through a better safety net is still a major challenge in Tunisia (Hassan, 2006). A former government attempt at substituting food subsidies with direct cash transfers to the poor ended in riots in the 1980s because the proposed transfer system was perceived as leaving aside a large proportion of the poor. Other issues about social welfare, inequality and horizontal inequity could be raised about such policies in Tunisia (as in Bibi and Duclos, 2007). In this study we focus on poverty.
We use data from the 1990 Tunisian consumption survey conducted by the INS (National Statistical Institute of Tunisia). This is the most recent national consumption survey data available in Tunisia, where official data dissemination rules are stringent. The survey provides information on expenditures and quantities for food and non-food items for 7,734 households. Usual additional information from household surveys is available, such as the consumption of own production, education, housing, region of residence, demographic information and economic activities.
Because estimated equivalence scales based on cross-section data has often been criticized, 8 and in order to concentrate on the issue of imperfect targeting, we assume that living standard based on per capita consumption expenditure is an adequate indicator of each household member's welfare. Other equivalence scales have been tried and provide qualitatively similar results.
In Table 1, we define the correlates of living standards used for the predictions. The correlates are grouped according to increasing difficulties of administrative recording and increasing ease of modification or hiding by households. Set I contains regional dummies. Using it along with OLS corresponds to 'regional targeting'and the regional poverty profile estimated in Muller (2007). 9 Set II includes regional and demographic information on households and characteristics of the household's dwelling. Set III adds information on occupation and education of the household's head to that in Set II. The correlates in Set II are unlikely to be manipulated by households and could be cheaply recorded, yet those added in Set III are easier to conceal. So, Set II would be the set to include in the regression analyses based on the need for these to be verifiable by programme offices and not easily manipulated by households.
It has been found that price differences across households may affect poverty measurement (Muller, 2002a). In order to correct for this, account for substitution effects caused by the elimination of price subsidies (which is the origin of the budget for cash transfers) and control for spatial price dispersion, we estimate the equivalent-gain from food subsidies. The calculus of the equivalent-gain is explained in the working paper by Muller and Bibi (2006). It is derived from our estimation of a quadratic almost ideal demand system. Both income and poverty line are converted into equivalent-incomes. Our reference price system is the one without subsidies as the subsidies' budget is assumed to be reallocated to cash transfers.
On the whole, there are four stages of estimation: (i) the estimation of a demand system to infer equivalent-incomes that enter the definition of living standard variable; (ii) the predictions of living standards from observed characteristics; (iii) the calculus of the optimal transfers corresponding to the predicted living standards, using perfect targeting optimization; and (iv) the simulation of the welfare effects of the transfer scheme. Let us turn to the living standard predictions, which is the stage where we introduce our focused estimation. Table 2 shows the descriptive statistics of the main variables used in the estimation. Mean total expenditure per capita is TD 804 (Tunisian Dinars), while mean equivalentincome (i.e. correcting for subsidies and spatial price variations) is TD 746. The first decile values for the equivalent-income variable are shown together with the mean equivalent-income and the mean log equivalent-income globally and for the first five decile groups, and finally with the poverty lines and logarithms of the poverty lines. Tables 3 presents the results of OLS regressions, quantile regressions (anchored on the first decile) and censored quantile regressions (censored at 50% and based on the  HH, household head. Zone 1 corresponds to Greater Tunis, the most prosperous region and largest industrial centre. Zone 5 corresponds to the Middle East (Sousse, Monastir, Mahdia), which is the second economic region of Tunisia. It is reputed for its thriving tourist industry. As Zones 1 and 5 are omitted, the sign of the coefficients of the other zones should be negative in the prediction equation of living standards. Zone 2 is the Northeast (Nabeul, Bizerte, Zaghouen), which is the third-most important economic region of Tunisia. We expect the coefficient of this variable to have the smallest magnitude among the zone coefficients in the prediction equation. Zone 3 corresponds to the Northwest where the highest poverty incidence is. Its coefficient should have the largest magnitude among the zone coefficients. Zone 4 is the Middle West, which is also very poor. Zone 6 is the Sfax area, which is economically prosperous as one the main industrial centre after Tunis and the Middle East. Zone 7 is the Southwest where Tozeur oasis stands as an important producing area of dates. It is also an increasingly prosperous tourism centre. Other important towns in this area are Gafsa (with a declining production of phosphates) and Kbelli. Zone 8 is the Southeast, which includes Gabes (relatively wealthy although less than Sfax), Mednine and Tataouine. Its coefficient in the prediction equation should be negative. As for the housing characteristics, the number of rooms per capita should be correlated with living standards. The omitted category for the housing type is 'villa'. Therefore, the coefficients of the remaining categories should have negative signs, especially for 'arab house' and 'hovel'. Arab's houses are traditional houses that do not satisfy standard requirements of modern houses. Walls may not be straight. Construction materials used for roof, walls and floor are often of poor quality. The activities of members are likely to matter for living standards. The number of participants in the household budget (nbbud) and the number of male and female active members (respectively actifm, actiff) should be positively correlated with the living standard. The categories for professionals, managers, industrials and traders are omited in the prediction equations. Then, except for the categoryAgrifar (farmer), the included professional categories should have negative coefficients. The sign of the coefficient for farmer may be ambiguous because the questionnaire does not distinguish small and large producers. Moreover, no information on the cultivated areas or on the agricultural activity is available. Education variables are often correlated with living standards. We omit the categories corresponding to university or the second cycle of the secondary level (at least 4 years of secondary education beyond the 6 years of primary education) for the education of the HH. The remaining categories are denoted: Illiterate (no education), Prim (6 years of primary education or less) and Sec1 (3 years of secondary education or less). The coefficients of these dummy variables should be negative. Nbetud denotes the variable indicating the number of students in the household. As education is likely to be a normal good, we expect its coefficient to be positively correlated with the household living standard.  first decile) of the logarithm of the household consumption per capita respectively, on Sets I, II and III of explanatory variables. 10 The regression predictions are applied to the whole sample, here and throughout the study. The dependent variable is the logarithm of the equivalent income (i.e. with living standards corrected with the true price indices inferred from the estimated demand system). 11 Other conventions, for censorships and quantiles, lead to results in agreement, 12 as well as not adjusting for prices or correcting by Laspeyres price indices. The censored quantile regression estimator for dependent variable y i and quantile is obtained as the solution to the minimization of

Results for living standard predictions
where [u] ={ − I [u < 0] }|u|, X i is a matrix of regressors and is a vector of parameters. Quantile regressions correspond to replacing max(0, X i ) with X i . Powell (1986) and Buchinsky and Hahn (1998) analyse these estimators. The estimation is obtained by using a linear-programming algorithm and subsample selection at each iteration of the optimization. We estimate the confidence intervals of the censored 10 Other estimation methods could be used such as Probit models of the probability of being poor, or nonlinear specifications for the right-hand-side variables. We tried a variety of such methods. However, to limit the length of the article, we only show some of the better performing and more relevant estimates. 11 To remain close to common practices, we did not weigh the estimation by the sampling scheme. However, we checked that using sampling weights in this case yields similar results, in part because the sampling probability at each sampling stage of this survey is almost proportional to population sizes. 12 The censorship at quantile 50% of the censored quantile regression is chosen because of two requirements. First, censored quantile regression estimates are inconsistent if too few observations are present in the uncensored subsample (a condition is needed, which is unlikely with a too small sample). Second, excessive censoring leads to disastrous loss of accuracy in the estimation.   quantile regression estimates with the bootstrap method proposed by Hahn (1995) and 1,000 bootstrap iterations. 13 Let us take a look in Table 4 at the ratios of the variance of the prediction errors over the variance of the logarithm of the living standards. 14 These ratios measure the prediction performance of the estimation methods for the mean of the logarithms of living standards. They are provided for three subpopulations: the whole population of households, the households in the first quintile of the living standards and the households in the first and second quintiles.
The results show that quantiles regressions (centred at the first decile) perform much better than the other methods for predicting the logarithms of living standards of the poorest households (here defined as belonging to the first or second decile of the living standard distribution), to the exception of censored quantile regressions that perform better for the households with living standards below the first quintile. In contrast, the best method for predicting the mean of the logarithms of living standards in the whole population is the OLS method. Finally, the predicting performance of the censored quantile regressions is disappointing for the whole population, and 13 We also tried with a Tobit model. However, this yielded mediocre prediction performance as Tobit estimates are generally inconsistent. Indeed, first the normality assumption on which the Tobit model is based is often rejected. Second, heteroscedasticity is likely to arise from household heterogeneity. Finally, the threshold y max may be unknown. All the results associated with the Tobit estimates are provided in the study of Muller and Bibi (2006). 14 The interpretation of the R 2 as a percentage of variation explained is dependent on the use of OLS to compute the fitted values. This is why we use instead the ratio of variances as our prediction performance indicator. For the OLS only, the considered ratio is equal to 1 − R 2 . dominated for the households with living standards below the second quintile by that of the quantile regressions. This is worrying as realistic poverty lines in Tunisia lie between the first and second quintiles. Moreover, censored quantile regressions rely on algorithms difficult to implement in most national statistical offices. Then, if our business is predicting the logarithms of living standards of the poor, the quantile regressions look like the most promising method.
Beyond general prediction performance, we shall show that using quantile regression predictions is useful if the aim is to improve transfer schemes.Appropriate assessment will come from estimating the schemes with different methods and examining the results. Let us first briefly turn to the results of the prediction equations in Table 3, which are related to typical living standard explanations in Tunisia. The signs of most coefficient estimates (significant at 5% level) correspond to the expected effects of variables and are consistent across all estimation methods. In the next section, the predicted household living standards are used to simulate targeting efficiency measures resulting from the considered schemes.

IV. Programme efficiency results
The calculation of the transfers in the simulations requires the determination of the cut-off income, y max . The p-type transfer is: y max minus the predicted income, for each household predicted poor, and zero for households predicted non-poor. Under perfect targeting, the y max permitted by the budget currently devoted to food subsidies is TD 358, greater than the poverty lines typically estimated for Tunisia. 15 However, even if the budget is sufficient to eliminate poverty under perfect targeting, under imperfect targeting additional resources are needed and the budget is exhausted.
We use a poverty line equal to TD 250 to estimate targeting efficiency measures, consistently with the most credible poverty line in The World Bank (1995), corresponding to a head-count index of 14.1%. This poverty line corresponds to an equivalent poverty line of TD 280 without subsidies. However, the qualitative results of this study go through with poverty lines at reasonable levels, as it is illustrated in the poverty curves corresponding to the stochastic dominance analyses shown in Muller and Bibi (2006).
The best performance of quantile regressions may be attributed to the focus properties of this method. However, an alternative interpretation could be that the robustness of the quantile regressions is what matters in practice. To control for this, we ran Huber robust regressions, which yielded almost the same results than OLS whether for the estimated coefficients or the poverty curves. So, using Huber regressions does not modify the coefficients obtained with OLS-based predictions, and therefore does not improve the quality of predictions. The best performance of the quantile regressions is therefore not due to robustness. However, poverty curves provide only qualitative insights. We now turn to quantitative estimates of targeting efficiency. Table 5 presents simulation results for: (i) two measures of targeting accuracy (Leakage and Undercoverage, as defined in Section 1.4); (ii) the levels of poverty severity (P 2 ) reached with the transfer schemes; and (iii) the share of transfers to the targeted population. As mentioned above, a poverty line of TD 280 per capita per year without subsidies is used, corresponding to TD 250 with subsidized prices. We also show qualitatively similar conclusions for two other poverty lines in the Appendix. To concentrate the discussion on targeting performance, we discuss the poverty results for P 2 only. Results for other poverty indices and results under price subsidies are in provided in the study of Muller and Bibi (2006).

Estimates of targeting performance
In our comments, we emphasize the comparison among transfer methods. The sampling standard errors of poverty and targeting indicators were obtained by bootstrapping, taking as given the demand estimation and prediction procedures. That is, we compare given PMT schemes, without incorporating the uncertainty involved in all the stages necessary to develop the PMT formulae. The standard errors suggest that the estimated targeting indicators significantly vary with the prediction methods. This is indeed generally what we found when we implemented tests of null differences, as obvious with bootstrap confidence intervals. If the aim is to reduce poverty measured by the axiomatically appealing poverty severity measure P 2 , quantile regressions anchored on the first decile are best. Moreover, Leakage and Undercoverage are also lower with this method.
However, the picture slightly changes when we extend the set of regressors. With regressor Set II, which adds information on dwelling and demographic characteristics to the information on regional dummies of Set I, substantial improvements can be reached whether in terms of poverty statistics, Leakage or Undercoverage. Remember also that Set II is our chosen set of correlates for actual programme offices. With Set II, the quantile regression based on the first quantile remains the best approach for reducing P 2 and Undercoverage. Low Undercoverage indicators may be related to desirable political conditions as policies leaving aside a large proportion of the poor are unlikely to be implementable in Tunisia. Censored quantile regressions would allow even larger reduction of Undercoverage.
Using information on education or occupation of household head gains little ground. The quantile regressions based on the first decile (and sometimes the censored quantile regressions) remain preferable if the aim is to alleviate P 2 , whereas OLS are better if the aim is just to cut the number of the poor down (see results with the head-count index in the study of Muller and Bibi, 2006). Using censored quantile regressions anchored on the first decile would lead to the lowest Under- The living standard variable is the equivalent income. Set I of independent variables includes only regional variables. Set II includes, in addition to Set I, demographic and dwelling variables. Set III includes, in addition to Set II, occupation and schooling level of household head. OLS 1: Transfers based on OLS 1: Set I variables. OLS 2: Transfers based on OLS 2: Set II variables. OLS 3: Transfers based on OLS 3: Set III variables. QR10 1: Transfers based on quantile regressions centred on quantile 0.1 with Set I variables. QR10 2: Transfers based on quantile regressions centred on quantile 0.1 with Set II variables. QR10 3: Transfers based on quantile regressions centred on quantile 0.1 with Set III variables. QR30 1: Transfers based on quantile regressions centred on quantile 0.3 with Set 1 variables. QR30 2: Transfers based on quantile regressions centred on quantile 0.3 with Set II variables. QR30 3: Transfers based on quantile regressions centred on quantile 0.3 with Set I variables. QRC01 1: Transfers based on censored quantile regressions centred on quantile 0.3, censored at quantile 0.5, with Set I variables. QRC01 2: Transfers based on censored quantile regressions centred on quantile 0.3, censored at quantile 0.5, with Set II variables. QRC01 3: Transfers based on censored quantile regressions centred on quantile 0.3, censored at quantile 0.5, with Set III variables. Pro-poor Uniform OLS3: Uniform transfers based on OLS 3: Set III variables. Pro-poor Uniform QR10 3: Uniform transfers based on quantile regressions centred on quantile 0.1 with Set III variables. Each of measures presented in this table has been multiplied by 100 for easy interpretation. 7734 observations. Sampling errors in parentheses.
coverage. Meanwhile, quantile regressions based on the first decile, which are simpler to implement, still yield low Undercoverage of 8.7%, a remarkably low result. The other methods may produce disastrous Undercoverage outcomes.
However, if the aim is to reduce Leakage, although quantile regressions based on the first decile perform better than OLS, using censored quantile regressions may be very slightly preferable.As a matter of fact, no prediction method generates substantial fund savings through Leakage reduction. Leakage always remains high (above 68%) whatever may be the used method.
Omitting price correction or deflating with household Laspeyre price indices gives similar results. On the whole, the quantile regression based on the first decile is best for diminishing P 2 and perhaps Undercoverage. Sometimes, the censored quantile regressions anchored on the first decile with a 50% censorship dominate the quantile regressions based on the first decile for reducing Undercoverage, but they seem unlikely to be used in most applied contexts as this method is not available in standard statistical packages. 16 Three important points may be noted. First, the gaps between the estimated reductions in P 2 with different prediction methods are considerable. The statistical method used to design the transfer scheme is a crucial ingredient of the performance of the scheme. When compared with other cash transfer methods, substantial improvement of the poverty situation measured by P 2 can be obtained (with our preferred estimation based on Set II: from 0.385% with the best OLS method to 0.272% with the best quantile regression method -centred in the first decile). Moreover, the percentage of excluded poor households from the scheme dramatically falls (to 8.6%) when compared with what is obtained with OLS predictions based on geographical dummies (for which it is 41.6%). Second, the usually employed method, based on OLS estimates, appears as the worst performing approach in contrast with methods focusing the predictions on the poor. However, when considering only the number of the poor, the OLS may provide acceptable predictions for the richest of the poor that are not in that case discounted when compared with the poorest. With limited budget, one could push still further the transfer performance by using quantile regressions centred about the poverty line for r-type transfers and centred on small quantiles for p-type transfers, consistently with the theoretical definitions of these transfer types.
The censorship of the wealthier half of the sample is statistically too crude to make much impact on the performance of anti-poverty schemes through censored quantile regressions. They generally yield worse results than what can be obtained with quantile regressions, except for Undercoverage.
On the whole, using prediction methods focusing on the relevant part of the living standard distribution substantially raises transfer efficiency. Even better results could be reached by trying a large set of quantiles instead of using arbitrarily the first and third deciles to centre the regressions. Systematic search of the centreing quantile, although time-consuming, could be implemented in any context where a household living standard survey is available in order to optimize the transfer performance.
As shown in the Appendix, robustness checks based on two other poverty lines yield similar qualitative results. In Muller and Bibi (2006), stochastic dominance tests show that the qualitative results for poverty measures can be extended to a broad range of poverty lines.

Uniform transfers and graphs of targeting errors
Results shown in Table 5 also indicate the performances of uniform transfers to the poor respectively based on OLS predictions and (first decile) quantile regression predictions, in both cases using the largest set of regressors. The performances are disastrous with OLS-based uniform transfers yielding the worst reached levels of P 2 and Undercoverage. They are better for quantile regression-based uniform transfers, while with mediocre level for P 2 (although only slightly less good than with optimal transfer based on OLS). The lowest Undercoverage can be obtained with uniform transfers based on quantile regressions. This is because all the identified poor receive transfers, whereas with optimal transfers some well-identified poor are not covered for the lack of sufficient funds.
As mentioned before, we prefer to estimate Leakage statistics that do not include 'unnecessary' transfers in the sense that they would raise households above the poverty line. Indeed, such transfers would not diminish any usual poverty index (satisfying the focus axiom). If this point is taken into account in the Leakage statistics, then even under uniform transfers, Leakage and Undercoverage are not mirror images. As expected, estimated Leakage statistics under uniform transfers remain high.
Another possible indicator of target efficiency is the share of transfers going to the targeted population, shown in the last column of Table 5. For all estimation methods, this share rises with the size of the set of used correlates in the living standard prediction equation. The more information used, the greater the share of transfers going to the initially poor. However, this indicator is a mediocre measure of anti-poverty targeting as can be seen by further examining the estimates. Indeed, the estimated share with OLS appear to be systematically greater than the estimated shares for the tried (censored or not) quantile regressions. This is unexpected as the latter methods have been found more efficient for anti-poverty targeting than OLS, for all other efficiency criteria. This surprising result is due to several features. First, the transfers sent to pretransfer poor households are not relevant when they lift the households' living standards above the poverty line. Then, high shares of transfers to the poor may characterize an inefficient outcome if some poor receive excessive amounts, whereas other destitute households are left below the poverty line. Second, we have shown the importance of accounting for the heterogeneity of living standards among the poor. Identifying who is poor is far from being enough for anti-poverty transfers. What really make the policy efficient are accurate estimates of the living standards of the poor. For the latter task, OLS perform badly, while they may be enough to just identify the poor, as illustrated by their corresponding high shares of transfers to the poor for uniform transfers. What happens is that using OLS leads to giving too much to many poor or non-poor, whether because the transfer lifts them above the poverty line, or because still poorer households receive less and therefore the budget is not employed optimally. All these yield high estimated shares of transfers going to the poor, an indicator hiding the actual misallocation of funds.
Finally, we show graphs of targeting errors against initial living standard levels for z = TD 280, following Coady and Skoufias (2004) (see Figure 1). On the left of the poverty line, the curve shows the percentage of the pretransfer poor not reached by transfers. On the right of the poverty line, it shows the percentage of the pretransfer non-poor unduly receiving transfers.
One can see that OLS and quantile regressions essentially differ by their capacity to calculate accurately transfers for the extremely poor households, whereas their performances are closer for households around the poverty lines. On the other hand, the OLS would better target non-poor households if it were useful. These features are apparent if optimal transfers are calculated (in Graphs 1 and 2) or if pro-poor uniform transfers are used (in Graphs 3 and 4).  These graphs allow the visual separation of the performances of the pure uniform targeting transfer schemes (Graphs 3 and 4) from optimized transfer schemes (Graphs 1 and 2). Additional post-transfer targeting errors may occur during the adjustment of the transfer levels to the predicted living standards. Indeed, with optimized transfers and a given available budget, not all households can generally be served by the transfer scheme. In contrast, with uniform transfers all households identified as poor are served, but they receive amounts that are not related to their living standard.
For uniform transfers, the bulk of targeting errors from OLS are below the poverty line and large. They are much less substantial for optimized OLS transfers, for which the errors elicit a smooth peak at the centre of the graph. In contrast, decile-regression targeting errors are much smaller at the left of the poverty line, whether for optimized or uniform transfers. Meanwhile, on the right-hand side of the poverty line, these errors are larger than from OLS. However, decile-regression targeting errors do not differ very much when considering optimized and uniform transfers. This is because with the considered transfer budget and poverty line, only about 3.5% of households are simultaneously identified as poor (using quantile regressions based on Set III) and cannot be served because of budget exhaustion. It appears that the main gain obtained from moving from uniform to optimized transfers, as far as targeting based on decile regressions is concerned, occurs around the used poverty line. The graphs make clear that the use of quantile regressions is important for better targeting of the poor, whether for uniform or optimized transfers.

Policy consequences
What are the policy consequences of the new focused transfer schemes? The first one is that improving existing schemes is concretely and easily possible. Lower poverty levels, smaller Leakage and Undercoverage statistics can be attained by focusing the estimation of transfer schemes. In Tunisia of 1990, the gain of efficiency, notably in terms of Undercoverage, is so large that it should deserve serious practical consideration. In terms of poverty severity, 3.9% is already the level reached with the best OLS method. Another half reduction in poverty requires only a few hours of simple statistical work easy to do with common package (e.g. Eviews: Quantitative Micro Software, LLC, 4521 Campus Drive, #331, Irvine, CA, 926122621, USA; Stata Corp LP, 4905 Lakeway Drive, College Station, Texas 77845, USA). Moreover, this reduction is much larger than that obtained by adding education and occupation variables to the list of regressors in OLS regressions.
There is already a small transfer scheme in operations in Tunisia: the 'Programme des Familles Nécessiteuses' (République Tunisienne, 1991). However, a large trans-fer programme would necessitate raising large funds. A possible consequence of our results is that the transfer of some public funds allocated to price subsidies towards a national focused transfer scheme may be easier with our new technique.
Previous attempts at eliminating subsidies in Tunisia ended in riots. Indeed, as all the poor benefit from price subsidies, an alternative system of cash transfers may not only further alleviate aggregate poverty, but also leave aside a large proportion of the poor. If this risk is perceived as high by the population, social unrest may follow. Therefore, replacing subsidies by OLS-based PMT transfers is likely to meet political obstacles as about between one-quarter and one-fifth of the poor would be excluded from the benefits. Another possibility would be to replace food subsidies with targeted food subsidies based on PMT programmes. However, this seems difficult as it would imply to administer expenditure transactions by targeted households.
However, using focused cash transfers would allow the government to reduce Undercoverage to such a low level that: (i) the reform may be politically viable; and (ii) the reform would not generate severe risk for a large proportion of the poor. As a matter of fact, it seems exceptional that such a small proportion of the population would suffer from a large social reform. Moreover, considering the gain in efficiency caused by eliminating price distortions, and the saving of public funds, the actual percentage of the poor suffering from the reform may even turn out to be negligible in the end.

V. Conclusion
Leakage to the non-poor is often substantial from universal food price subsidy programmes directed to the poor. Because of their large budgetary cost, many governments have moved away from them towards better targeted methods, such as PMT cash transfers. Indeed, benefits can be awarded to the poor contingently on their characteristics. However, transfer schemes may be inaccurate because the statistical predictions involved in their design are centred on the mean of the living standard distribution and not enough oriented towards the potentially poor.
This study improves on past methods by focusing on the poor and near-poor for the design of transfer schemes based on estimated living standard equations. 17 This is achieved by using quantile regressions. Moreover, the method can be adapted to any social programme based on 'household assessment', that is, predictions of household characteristics (as in Case andDeaton, 1998, or Hanmer et al., 1998).
Our estimation results based on data from Tunisia reveal potential for poverty alleviation with our new approach. The improvement is also substantial when compared with usual targeting schemes based on OLS predictions: with our method based on quantile regressions, poverty could be massively reduced in Tunisia. Moreover, large reduction in Undercoverage is possible, even when compared with the best OLS-based transfers. In contrast, censoring the living standard distribution does not improve the performance of transfer schemes, except sometimes for reducing Undercoverage. On the whole, with the new techniques, targeting by indicators may be relatively cheap to implement, when compared with the huge financial burden of price subsidies. 18 Other ways of focusing on the poor are possible, for example by using nonparametric regressions, shading the shape of the living standard distribution. It is unclear what the optimal econometric techniques to use to implement this focus concern are and we conjecture that they may depend on the data at hand. On the whole, the important point in our approach is the adaptation of the estimation method for household living standard predictions in order to improve the performance of the anti-poverty targeting scheme. Using quantile regression improves this performance dramatically in the case of Tunisia. However, other variants and improvement are probably possible and left for future work.
Finally, future research should be applied to repeated cross-sections from household budget surveys separated by a few years. It would tell us how badly targeting efficiency degrades when targeting rules derived from a survey in year T are applied to data in year T + s. Final Manuscript Received: September 2009 Appendix: Robustness checks with two other poverty lines 18 It is likely that poverty mapping can be improved by estimating methods focusing on the poor. We leave this question for future work. Finally, the assessment of the welfare impact of public spending (Van de Walle, 1998) could be based on focusing statistical approaches.