# _4.5 The Potential Role of Village Heterogeneity_

We find robust evidence that initial village inequality has a long-lasting, but fading, effect on household growth rates, but as we noted in Section 3.2, this is insufficient evidence to establish a causal link between inequality and growth. While we can rule out a large set of mechanical and other endogeneity explanations, our most serious reservation is that inequality reflects other initial conditions that are correlated with both inequality and growth, which we denoted θ _vt_ −1 . The conventional approach for dealing with that sort of unobserved heterogeneity is to control for village fixed effects through a firstdifferenced implementation of the growth equation.<sup>29</sup> If we can track repeated episodes of growth, i.e., first-difference growth rates, then this exercise is potentially informative. As is well known, however, there are significant limitations to examining growth rates over short periods in first-differenced models because the covariation of high-frequency measures of growth and inequality after controlling for villagelevel unobservables may not be sufficient to identify the relationship between inequality and growth. Inequality is a slowly-evolving variable, and even with national-level samples, period-to-period changes may be driven largely by measurement error. In the context of rural China over this time period, measurement error is an obvious concern. Moreover, we are also concerned about simultaneity bias, as growth itself may change the income distribution (a “Kuznets Process”).<sup>30</sup> Moreover, some of the core implicit assumptions about the error term necessary for the panel-based approach to work may be violated in our data. Nevertheless, the exercise is worth conducting, as it helps to reveal important aspects of the inequality-growth relationship.

Consider the base village-level equation: where growth is defined as that between period _t_ -1 and _t_ , ln _yvt_<sup>−ln</sup><sup>_y_</sup> _vt_ −1<sup>. Note that in keeping with the</sup> focus on household growth, we examine the average household growth rate, not the growth in average incomes. Our empirical objective is to determine whether our estimate of α _v_ is robust to controlling for village “fixed effects.” Implementation requires addressing two immediate concerns: constructing a village-panel data set, and using an estimator that accounts for the potentially dynamic error structure implicit in Equation (4). To construct the village-panel we use the balanced panel of households to construct the growth-rate and mean log income variables for each period, symmetric with the household regressions, and the larger non-attritted samples to construct the key village covariates like village

> 29 See, for example, Forbes (2000) and Banerjee and Duflo (2003) for a discussion of the merits and pitfalls associated with the panel-data (“fixed effects”) approach in cross-country data. 30 See Kuznets (1955). Ravallion and Chen (2007) explore precisely this question as they investigate linkages between growth rates and various measures of poverty and inequality using nationally representative NBS data. Panel analyses using state-level data from the US also finds evidence of a Kuznets process leading to a positive association between inequality and growth (Frank, 2009).

_Inequality and Growth in Rural China_ , Page 19