regressions. Employment shares from the 2001 Census are used for estimating NSS 2004-05 employment shares, and employment shares from the 2011 Census for the NSS 2011-12 employment shares. The regressions are run separately for the rural and urban samples. The predicted employment shares from the first-stage regressions are then used in the second-stage Probit estimation of female labor force participation.<sup>7</sup> When applying this instrumental variables approach to Model D, the five hypotheses advanced in this paper hold (table 5, third column, Model D2). With minor nuances, the marginal effects are similar in size to the marginal effects in the original specification. Only a few differences with the main results in the previous section stand out. Among the household variables, on the one hand, the effect of having dependents in the family is diluted, but on the other, the effect of household size is negative and significant. Some of the location variables, captured by the rank variable, are no longer statistically significant. The survey variable is now slightly significant, but still three times smaller in magnitude than in Model C, where the local employment structure has not been controlled for. The gap variable is now statistically significant. While the effects of the employment variables are attenuated, they are still quite strong and highly significant. In particular, farming jobs have a higher marginal effect than other types of jobs. Regardless of whether there is a job deficit at the aggregate level in India, the gradual disappearance of farming jobs remains a highly significant determinant of the decline in female labor force participation.<sup>8</sup> The second potential problem with the empirical strategy of this paper, _endogeneity_ , arises if local employment levels ( Lj ) are correlated with the error term εij + φij . Consider a dynamic locality, where many firms operate and more of them are about to start operations. The participation variable ( Pij∗ ) and the employment variable ( Lj ) will be inflated by the unusually high number of women already at work in the locality. But the participation variable will be inflated even further by the unusually high number joining the labor force to seize the upcoming job opportunities. An analysis not controlling for the firms that are about to start operations will overestimate the effect of current employment on labor force participation. The problem would be symmetric if local unemployment was high.

The introduction of the indicator of labor market tightness at the local levels, ( Vj −Uj ), is supposed to address the two symmetric problems in this example. But it can be argued that it does not address endogeneity if the correlation between local employment levels ( Lj ) and the error term ( εij + φij ) occurs across the entire sample, and not only in particularly buoyant or declining localities.

> 7 The estimated coefficients in the first-stage regressions are significant at the conventional levels; the F-statistics are above 10 in all cases.

> 8 The hypothesis that the coefficients of all the employment variables are the same can be rejected at 1 percent significance level.

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