# 5.3.  SENSITIVITY ANALYSES

As noted earlier, the crucial assumptions for the validity of the aggregate decomposition include overlapping support and ignorability. The key assumptions additionally required by the detailed decomposition are additive linearity and zero conditional mean. A methodology that is proposed by Imbens and Rubin (2009) to assess the feasibility of the overlapping support assumption is centered on the idea of calculating a scale-free normalized difference for each covariate. They assert that the overlapping support across the groups of interest, in our case female- vs. male-managed plots, is adequate if the scale-free normalized differences across the covariates are less than 0.25. Table A.1 in the Appendix<sup>32</sup> presents the scale-free normalized difference of the variables used in the regressions. Only 2 out of 29 independent variables have a normalized difference greater than 0.25.

In trying to lend support to ignorability and zero conditional mean assumptions, we use all available data and econometric tools at our disposal, and first rely on an empirical approach that was pioneered by Altonji (1988), Murphy and Topel (1990), and Altonji et al. (2005), based on the idea that the amount of selection on observable variables provides a guide to the extent of selection on unobservable counterparts. We use an informal version of the methodology applied by Acemoglu et al. (2001) and Altonji et al. (2005), and incorporate into our base specification, in a phased-in fashion, thematically-grouped control variables such that each regression is estimated with a different set of additional independent variables and that the results are compared to those from the base specification. Our purpose is to gauge the stability of the key regression coefficients that underlie our decomposition results. If the coefficients on the covariates included in the base specification, including the female plot management dummy in the pooled regression, are stable subsequent to the incorporation of additional covariates, they are less likely to change if we are able to take into account potentially missing omitted variables.

To perform this analysis, we consider the following sets of variables: (i) district fixed effects, (ii) plot geospatial characteristics informed by GIS data, (iii) other plot characteristics solicited by the IHS3, (iv) additional household characteristics, and (v) additional community characteristics. Table A.2 in the Appendix includes the detailed list of the variables included in each set. Tables 5, 6 and 7 present the base regression results and the estimates from the regressions including the additional controls for the pooled, male-managed, and female-managed plot samples, respectively. An overwhelming majority of the coefficients, with respect to the base specification, are stable across the specifications and the plot samples, and do not change sign or significance. This suggests that the assumptions of ignorability and zero conditional mean might not be unfounded.

> 32 The Appendix including the results from the sensitivity analysis referenced in Sections 5.3 and 7.2 are available upon request from the authors or could be downloaded at http://tinyurl.com/mwgenderandagriculture.

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