procedure on the unweighted data. In all cases the reported z-statistics have been adjusted to account for the fact that one is using<sup>_T_ˆ</sup> _i_<sup>rather than</sup><sup>_T_</sup> _i_<sup>in the outcome equation.</sup> The IV results in Table 11, for 2004, show a positive but not statistically significant impact of the VRF on expenditure and income. In rural areas the measured effects are negative. Curiously, the impact on farm income, and on non-farm income, are separately large and positive. The results for 2002 show that VRF borrowing raised expenditure by 9.9%, and income by 8.4%, although the latter effect is not highly statistically significant.

These results are not particularly robust. The middle rows of Table 11 show the effect on the IV estimates of adding other instruments. The first instrument is “anydebt”, which equals 1 if the household in 2004 has any outstanding debt. This is strongly correlated with whether a household borrows from the VRF, but weakly associated with the outcome variable (e.g. simple correlation with expenditure per capita of -0.035; weighted correlation of -0.109). The inclusion of this instrument raises the measured impact of the VRF to a statistically significant 16% for income and 20% for expenditure, levels that are certainly on the high end.

It might be objected that “anydebt” is not exogenous, if households borrow from the VRF when they would not otherwise have borrowed. Alternatively one could use a measure of “non-VRF debt”, set equal to 1 if the household has debt other than VRF debt. With this instrument the measured impact of VRF borrowing on household spending rises to an implausible 46%, but even here it might be argued that the new instrument is not truly exogenous.

Finally, we also add, as an instrument, the interest rate charged by the VRF. It is plausible that a higher interest rate would deter borrowing – indeed, the weighted correlation coefficient is -0.054 – and be essentially unrelated to the log of expenditure per capita (correlation of 0.046). The inclusion of this instrument raises the measure of the impact of VRF borrowing to unrealistically high levels. But it is by no means a fully satisfactory instrument: when it is included, the sample size falls, because interest-rate information is only available for villages that have an operating VRF.

In sum, the results of our IV analysis are not very sharp and are partly contradictory. It does seem reasonable to conclude, however, that the most satisfactory models just use the inverse of the village size as an instrument; and in this case, the marginal impact of the VRF on expenditure and income is minimal. Combined with the propensity score matching results, it appears that the VRF raises spending and income on average, but is experiencing diminishing returns at the margin.

Our results are broadly in line with those found by Kaboski and Townsend (2006), who also used an instrumental variables approach, but with data from the 2003 and earlier rounds of a panel of 960 households surveyed in four rural provinces. They checked for robustness by applying a variety of econometric specifications (levels, changes, and estimates with and without outliers). Their main findings are that greater use of the VFR was associated with somewhat higher levels of household expenditure, and perhaps an _Village Fund, draft of June 29, 2009_ _Page 17 of 34_