advantages to using household-level data.<sup>2</sup> Most importantly, we can control for a host of household-level variables–notably flexible functions of initial household income–that may be confounded with local inequality. This helps rule out some potential explanations for the inequality-growth relationship, in particular those that rely on the aggregation of non-linear effects of own-income. With household-level data we are also able to explore “within-village” heterogeneity of the impact of inequality on growth: Are the poor hurt more than the rich? Are households with higher educated members immune to the impact? We are also able to broaden the set of outcomes from “income growth” to other economic variables, like the composition of income, e.g., concentration in agriculture, or participation in off-farm employment, that inform the question of how inequality may affect growth.

Repeated observations at the village-level allow us to evaluate the stability and consistency of the “treatment” of higher inequality: We examine whether all variation in inequality is the same. First, we explore the impact of cross-sectional differences of initial inequality across villages. We then determine whether rising inequality within villages, or changing inequality across villages, affects household growth in the same way. These multiple sources of “treatment” provide identifying information on the nature of any causal relationship between inequality and growth. The village-dimension of the panel also allows us to address whether unobserved heterogeneity confounds the impact of initial inequality.

While we are able to provide robust estimates of the correlation between village inequality at the outset of reforms and subsequent growth, there remain disheartening limits as to what we can learn from even these data. Paramount among these limits, the endogeniety problem is intractable: Solving it requires finding instruments that predict initial income inequality, but are otherwise excludable from a growth equation, and in particular are uncorrelated with _any_ institutions that may be related to subsequent growth. The next best thing is to trace the correlation of income inequality through various _observable_ institutional channels that affect growth. While we previously attempted this (Benjamin, Brandt, and Giles, 2006), we were unable to find any robust linkages between inequality and measured institutions at the outset of reforms. Again, this problem is thorny to solve, as initial inequality in a village in 1987 will reflect not just the immediate institutional structure of the reform period, but the entire history of the village throughout the occasionally tumultuous post-1949 period, e.g. land reform, collectivization, the Great Leap Forward, the Cultural Revolution, as well as its pre-1949 socio-economic structures. Moreover, “village” inequality will reflect “local” conditions beyond the village, at the township and even county-level, making it difficult to pin down the precise institutional mechanism.

> 2 Ferreira (2010), among others, has highlighted the importance of using micro-level data to shed light on those mechanisms driving the growth-inequality relationship that cannot be addressed by the cross-country macroeconomics literature.

_Inequality and Growth in Rural China_ , Page 2