13 circumstance vector in our panel cross-country analysis to be non-trivial. Naturally, a higher dimension ( _J_ ) for the circumstance vector ( _C_ ) allows the analyst to better capture the possible sources of inequality of opportunity. Although the resulting measure, I��μik�� , is still a lower bound on actual inequality of opportunity, as noted earlier, fewer omitted circumstances is likely to mean a smaller underestimation.

In an attempt to address this problem, we extended our analysis to an additional sample of countries and household surveys, by drawing on the Demographic and Health Surveys (DHS), where additional circumstance variables were available. The DHS sample contains 42 developing countries from Africa, Asia and Latin America (see table A2 in the Appendix for details). The earliest survey used is from 1986 and the most recent from 2006. The DHS are designed to provide in-depth information on health, nutrition, and fertility. In addition, the survey includes socioeconomic information of household members and access to services. As noted earlier, the DHS does not typically contain estimates of household income or expenditure, so we construct a wealth index as the first principal component of a set of indicators on assets and durable goods owned, dwelling characteristics, and access to basic services. The list of indicators included may vary somewhat from country to country, but we maintain the same set of variables within countries across time.

For all women aged 15 to 49, the DHS collects relatively detailed information on circumstance variables. We define the types based on the following indicators: region of birth, number of siblings, religion, ethnicity, and mother tongue. Mother’s and father’s education are available in some countries for some years, but never for all years, so this variable could not be included in our set of circumstances. Since not all indicators are available in all surveys and the number of categories in each variable also varies, the number of types differs from country to country (but, again, remains the same within countries across time). Details of the DHS data set are also reported in Table A2.

# **5. Estimation and Results**

Equations (5) and (6) can be estimated using a variety of techniques. First, they can be estimated with the classical OLS estimator. However, the OLS can suffer from biased coefficient estimates due to the fact that the lagged outcome variable can be correlated with the fixed effect in the error term, especially when T is small, violating the underlying consistency assumption for OLS. Therefore, a second technique to estimate our model is by using a fixed effects (FE) estimator. The OLS and FE estimators are presented in columns (1) and (2) in Tables 3-6. For comparison with other studies on inequality and growth, such as Marrero and Rodríguez (2013), we also estimate a ten-year OLS, which regresses growth during the latest 10-year period we have in each country on initial conditions at the beginning of that period, excluding the time dummies.<sup>23</sup> These estimates are presented in column (3) of each regression table.

However, the FE estimator does not solve the endogeneity problem. Using the within-country variability, the lagged dependent variable and the error term are still correlated, violating the assumption of independence between the regressors and the error term. Whereas the OLS is biased in one direction,

> 23 We would ideally like to run a long-run OLS, as in Marrero and Rodríguez (2013), examining growth over a long period of time as a function of initial inequality. However, the durations of long-run periods vary widely in our data sets. Hence, we chose to examine growth during the latest available 10-year period as a function of initial inequality in our data set for consistency.