mean enrollment for children ages 13-16 in the PROGRESA sample is 71 percent, compared to 56 percent for the same age group in the BDH sample. Since the program effects estimated for the BDH are based on instrumental variables, it is also possible that the returns to “compliers” in the Ecuador sample are particularly large; however, it seems unlikely that any difference between LATE and average effects of BDH transfers would be large enough to account for the estimated difference in magnitude between PROGRESA and the BDH.

Another way to benchmark the BDH program effects is to compare them with estimates of the elasticity of enrollment with respect to expenditures. In a regression of a dummy variable for enrollment at baseline on the log of total household expenditure in the BDH evaluation sample, without controls, the coefficient on expenditure is 0.108, with a standard error of 0.016; when the extended set of controls is included the coefficient is 0.049, with a standard error of 0.014. These values are comparable to those found in other developing countries—see the review in Behrman and Knowles (1997). The monthly transfer of $15 made by the BDH is equivalent to 7.2 percent of expenditures for the mean household in our sample. As a first pass, one might therefore expect that the transfer would have a positive effect of roughly 0.78 percentage points (0.108*7.2) on enrollment. Yet the instrumental variables estimates in Table 5 suggest an impact of between 8.6 and 11.6 percentage points—more than a full order of magnitude larger. Moreover, one would not expect households receiving BDH transfers to increase expenditures by a full $15 per month, for a variety of reasons: First, households may save part of the transfer, or may offset it with reductions in labor supply—in either case a $15 transfer would translate into a smaller amount in terms of per capita expenditure. Second, the banking records suggest that some households did not collect the full amount of transfers for which they were eligible.

There are of course a variety of concerns with simple regressions of enrollment on expenditures. Measurement error in expenditures is likely, but simulation results suggest it would have to be implausibly large to cause attenuation bias of more than 90 percent;<sup>15</sup> reverse

> 15 Suppose the measure of observed log total household expenditures at baseline were “true” expenditures Xi*, uncontaminated by measurement error.  Mis-measured expenditures Xi can then be simulated by adding a normally distributed measurement error ei, so that Xi* = Xi + ei, where ei is N~(0, σ ), and σ is given by the observed standard deviation of log expenditures at baseline (0.521).  The reliability ratio can then be calculated from a regression of Xi* on Xi (Angrist and Krueger 1999).  The mean coefficient on Xi from one hundred repetitions of this simulation is 0.496, implying proportional attenuation of 0.504 in the estimated cross-sectional relationship between enrollment and log household income.  When the same simulations are conducted with more measurement error, so that ε i is N~(0, 2 σ ), the mean estimated reliability ratio is 0.199.  Clearly, log household expenditures would have to be very

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