_(4) Yhd, =_ at _+ Xhd P + yFd +_<sup>_6_</sup> _Fd_ I(t= I ) _l + hdt,_ using the full sample of panel and non-panel households. To see how the parameters in (4) should be interpreted, assume for the moment that funding is either received or not received, so that Fd takes on one of two values, 0 or 1. In this case, y measures the difference in the outcome variable across households in funded and unfunded districts (given _Xhd,)_ in time period 0, prior to the expenditure. We can therefore refer to it as the "targeting" effect. The sum of y and 6 measures the difference across funded and unfunded districts in period 1, after the program is conducted. The parameter 8 is the "difference-in-difference", which measures the impact of FONCODES funding between period 0 and 1. When Fd is a continuous variable, these parameters represent marginal rather than level differences (see, for example, Angrist and Lavy, 1997, or Duflo for applications of similar methods to the evaluation of education programs).

The difference-in-difference estimate will be biased if there are unobserved factors (such as poverty, or tastes for education, or local capacity) which have components that vary over time and are correlated with Fd. For example, the demand for education could change, due to (unobserved) changes in local labor markets, prompting households in a village to apply for funding and to keep their children in school longer, with or without the help of FONCODES. A solution to this problem is to estimate the model using instrumental variables (IV). In the case of FONCODES, the _allocation_ of funds to districts is a good instrument for actual expenditures. The instrument must meet two well-known conditions: it must be correlated with expenditures, and uncorrelated with the error term. The first condition can be tested in practice, while the second seems plausible since allocations during the years in question were developed from formulae based on the 1981 and 1993 censuses-both of which took place before the period covered in the analysis. It is therefore unlikely that allocations are correlated with unobserved changes in "tastes" for education between 1994 and 1997.13 Several potential problems with the strategies discussed above should be kept in mind when assessing our results. The 1994 LSMS is not a true baseline survey: it was conducted after FONCODES had made expenditures in 1992 and 1993. In what follows, our measure of FONCODES expenditure Fd consists of (per capita) expenditures made in 1994, 1995 and 1996. We include 1994, since lags between project approval, disbursement of funds, and actual school

> **_13_** However, it is still possible that the allocation of funds is correlated with other (unobserved) factors that affect school attendance. For example, it could be that other programs spend more or less money in districts that have been allocated more by FONCODES, or that there are macroeconomic shocks that are correlated with allocations and happen to affect attendance. As we discuss in more detail below, including controls for the amount spent by other programs on school infrastructure does not alter our results. Still, without more years of data, and more information on other programs, we cannot rule out all problems of this type.

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