Second, because the decision on the FAIS allocation by the central government is based on information provided by the latest available population census available, the use of the lagged value of the FAIS circumvents any mechanical correlation between the contemporaneous welfare measure applied and the FAIS. This decision guarantees that, at any period, the outcome measure relies on information from the census at year , while the FAIS is defined using information from the previous census or count, at _t_ − 1. tt However, this specification still suffers from endogeneity because of the presence of simultaneity bias. FAIS allocations are targeted to improve welfare. If the FAIS is sufficiently flexible to respond to local welfare shocks, one will observe more resources being allocated during periods of lower welfare. Not accounting for this simultaneity may result in a downward bias in the estimates, 1. One may even observe a negative effect of the FAIS on welfare that is only explained by the opportune response of the FAIS to local welfare shocks, but not ββ by an actual negative effect of the resources allocated through the FAIS, which may be difficult to explain.<sup>15</sup> To circumvent such a simultaneity bias, the analysis relies on an instrumental variable strategy that exploits the centralized component of the FAIS allocation across municipalities, which should be exogenous to local welfare shocks. The actual allocation of the FAIS is defined in two steps. First, the federal government suggests a formula-based allocation that considers welfare information derived from the latest available population census. The second step is defined by a set of factors that operates at the local and state levels and that may respond to contemporaneous local welfare. The analytical instrument is therefore the predicted FAIS allocation that would have been forthcoming if the allocation had followed only the lines of the federal formula. This allows the analysis to exploit the variations in the FAIS that are not endogenous to local welfare.<sup>16</sup> By design, the formula-based FAIS allocation is highly correlated with the actual FAIS allocation. The firststage estimates produced by the analysis confirm the existence of a strong relationship and validate the relevance of the analytical instrument. The exclusion restriction of the instrument relies on two characteristics of the formula-based component: First, the formula-based component is determined at the central level, and the formula applies to all municipalities; hence, the component cannot be correlated to unobserved local factors. Second, because the formula relies on information derived from the latest population census that is available at the time of the federal decision on the formula-based allocation, any local welfare change that occurs between censuses cannot affect the allocation.

A potential threat to the integrity of the identification strategy revolves around the fact that the initial welfare conditions considered in defining the formula-based allocation also affect contemporaneous welfare levels. This identification threat is countered in two ways. First, because the main reasons for the persistence of poverty across time involve unobserved structural characteristics that change only in the long run, the inclusion of municipality fixed effects can account for these characteristics. Second, because the FAIS allocation is a nonlinear function of the initial welfare conditions, the initial welfare conditions can be included as additional controls without generating multicollinearity, and, after a robustness check, the results will remain qualitatively similar.

> 15 See, for instance, Ramones and Prudencio (2014), who estimate the impact of the FAIS using a simple ordinary least squares (OLS) strategy.

> 16 Other authors have used the instrumental variable approach to address the endogeneity problem in estimating the effects of the FAIS. Díaz-Cayeros, Estévez, and Magaloni (2016) use geographical variables—rainfall, access to railroads, access to cities, and rugged terrain—to instrument expenditure allocations and explain changes in the provision of public goods.

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