inequality. We have seven available two-year periods: 1987-88, 1989-90, 1991-93, 1995-96, 1997-98, 1999-00, and 2001-02.<sup>31</sup> In all specifications we include the core set of village covariates (controls for initial mean log income, education, land, dependency ratio, composition of village income, geography, and province dummies), but we also add period dummies. We address the dynamic panel data issues through the use of a variety of estimators, and discuss details in Appendix 2.

The key results are presented in Table 5. We vary the estimation in two main dimensions: First, by estimator, and second by the length of the difference. Longer differences may be more robust to highfrequency variation of inequality driven by noise, and may better capture the “long run” effects of inequality on growth.<sup>32</sup> We also show results for both measures of inequality used in the cross-section analysis: the Mean Log Deviation, and the 90-10 ratio. In the first column we report the pooled OLS estimates of Equation (4), with no account for fixed effects but with standard errors clustered at the village-level. The estimated effect of inequality is negative, but very small, and statistically insignificant. Growth from one period to the next is unrelated to previous inequality when we pool growth and inequality from the entire period. In the second column, we take first-differences to sweep out the fixed effects. Whether we take short (one period) or long (up to four period) differences, we find no significant effect of growth on inequality. If anything, the effect is positive, though insignificant, as one might expect if growth caused inequality. Accounting for dynamic panel data issues does nothing to change the conclusion: when we difference to eliminate the village fixed effects, there is no relationship between inequality and growth.

On the surface, this suggests that unobserved village-level heterogeneity may be driving our previous results. However, the evidence is more complicated. As a starting point, note that the inequalitygrowth relationship vanishes _before_ we control for village fixed-effects in the pooled OLS specifications of Table 5. Admitting evidence of the impact of inequality from periods _after_ 1987-88 seems to diminish the estimated effect of inequality. Alternatively, it could be that short-run estimates of growth are less affected by inequality. That is unlikely to be true, however, as we saw in Table 2 that the effect of inequality is strongest early in the growth trajectory. To address this question we break apart the villagepanel into a series of pair-wise cross-sections, and estimate the village-level cross-section specification with varying beginning and endpoints. The results are quite striking and reported in Appendix Table 3. We find a significant negative relationship between growth and inequality in 1987-88 and every endpoint, except 2001-02 (as in Table 2), though even for 2001-02 the result is significant for the 90-10 ratio. However, when using pairs of endpoints with the starting period after 1987-88, we do not find a

> 31  Note that there was no survey in 1992 or 1994, so the period 1991-93 is constructed slightly differently from all of the other periods with adjacent years (1991 and 1993 being non-adjacent).

> 32 Note that with the longer differences, given that the IV-based procedures are based on lagged observations, it is not possible to properly implement the FD-IV or WG estimators given the short duration of our series.

_Inequality and Growth in Rural China_ , Page 20