impact of a program expansion hinges on the political process that governs the allocation of program’s outlays. In particular, it depends on the ability of different socioeconomic to influence that process.

These political economy considerations led the authors to propose a simple regression model linking, for each quantile, the participation rate for a region within a given state<sup>31</sup> to an instrument for the state’s average participation rate. More precisely, quantiles are defined over the entire rural population ranked by total consumption per capita<sup>32</sup> (normalized by state-specific poverty lines). The assessment of marginal program incidence is based on the _marginal odds of participation_ . This is the increment in program participation rate of a given quantile associated with a change in aggregate participation<sup>33</sup> . Lanjouw and Ravallion (1999) note that, for a given quantile, variations of its participation rate across regions depend on the size of the program in the state to which each region belongs. The size of the program is measured by the state’s average participation rate. This latter variable is instrumented by the so-called “leave-out mean”, which is the state average participation rate computed without the participation rates for the specific region and quantile under consideration. Following Younger (2003) the underlying regression model can be written as follows: _pr_ , _k_ , _q_ = α _q_ + β _q xk_ + ε _q_ . The lefthand side is the participation rate for quantile **q** in region **r** of state **k** , and **xk** is the instrumental variable<sup>34</sup> . The coefficient β **q** measures the _marginal odds of participation_ for quantile **q** . Estimates of these coefficients are interpreted as the gain in subsidy the case if poor people live in remote areas and the program expands geographically starting with less remote regions.

> 31 The authors applied the methodology to rural India taking advantage of large observed differences across Indian states in the size of each program considered namely: (1) a means-tested credit scheme known as the Integrated Rural Development Program (IRDP); (2) the Public Distribution System (PDS) which is a food rationing program; and (3) a public works scheme.  There are 62 regions spanning 19 states.  The data used are from the 1993-1994 National Sample Survey (NSS).

> 32 Ajwad and Wodon (2001) propose a variant of Lanjouw and Ravallion (1999) approach.  The basic difference between the two methods lies in the ranking of households in order to create quantiles.  Instead of defining quantiles on the basis of the overall distribution of welfare, Ajwad and Wodon would define the relevant quantiles on the basis of distribution of welfare within each state.

> 33 The proportion of households in a given quantile that participate in the program is the average participation rate.  The average odds ratio of participation, for a given quantile, is equal to its participation rate divided by the overall average participation rate.

> 34 Using the state average participation including the region and quantile under consideration would create an endogeneity problem that would lead to biased estimates.  Younger (2003) suggests that when possible, one can use panel data on regions to control for regional fixed effects.  He also notes that grouping observations into regional and quantile averages entails a loss of efficiency in estimation.  He thus recommends the use of individual level data.

36