 measurement of household income may simply contaminate our estimate of initial inequality _IQvt_ −1( _i_ )<sup>. For</sup> example, “outlier” households may generate a high-level of apparent inequality combined with high initial income. With mean-reversion of household incomes, such villages will appear to have lower growth rates, even if there is no link between inequality and growth. Alternatively, the greater degree of noise in _IQ_  _vt_ −1( _i_ )<sup>may result in conventional attenuation bias. In principle, this type of measurement error</sup> is relatively straightforward to address with instrumental variables. The most obvious candidate instrument for _IQ_  _vt_ −1( _i_ )<sup>is an alternative measure of inequality that is robust to outliers and measurement</sup> error. We use the 90-10 ratio for this purpose, jackknifed in the same way as other village-level variables, _RAT_  _vt_ −1( _i_ ) = _y_  _vt_ 90−1( _i_ ) _y_ 10 _vt_ −1( _i_ ) .

_Attrition_ . Our best estimates of village-level initial conditions are based on the largest sample of households surveyed in 1987, which because of attrition is significantly larger than the balanced panel of households observed continuously between 1987 and 2002. The attrition rate is about 30 percent over the 15 years. While this hurts the sample size, our greater concern is that household attrition may be correlated with both initial inequality and subsequent growth. For example, there may be selective outmigration, with households more likely to leave slow-growing villages. The key question is whether such migration is correlated with initial inequality. If out-migration was more common in the high-inequality, low-growth potential villages, then depending on which households leave, we might observe a spurious link between initial inequality and the growth rates calculated on the basis of the initial sample collected in 1987, and the revised (attrition-affected) sample in 2002. In our empirical work, we explore the issue of attrition in detail, and ultimately present our main results adopting the “Inverse Probability Weighting” procedure recommended by Wooldridge (2002).

_Omitted Variables Bias_ . Our greatest concern is that even measured perfectly, _IQ_  _vt_ −1( _i_ )<sup>may be</sup> correlated with a village-level unobservable component of _ui_ , _vT_ , which we denote as θ _vt_ −1 . No matter how many covariates we include to control for initial conditions, there would always be the suspicion that inclusion of a better proxy for θ _vt_ −1 could eliminate the apparent impact of inequality (e.g., see Kanbur (2005) for a summary). Perhaps the initial income distribution is related to policies in place at _t_ - 1 that affect future growth? What characteristic of θ _vt_ −1 might be of particular concern? Suppose that θ _vt_ −1 is a long-standing village taste, or predisposition, for low inequality. This is of concern only if θ _vt_ −1 is also related to growth, for example, if egalitarian villages are more likely to invest in growth-enhancing public goods like schools, or to keep growth-distorting taxation to a minimum. From an interpretation standpoint, if θ _vt_ −1 drives the inequality-growth relationship, then our conclusions will only be accurate from an “historical” descriptive perspective: unequal villages in our sample grew more slowly. If it is the _Inequality and Growth in Rural China_ , Page 9