# **Supplementary Online Appendix**

# **A Tale of Two Programs: Assessing Treatment and Control in NREGA Studies**

# **Girish Bahal**

## **S1. Oster (2019) test**

Here, I conduct Oster (2019) test for omitted variable bias that is based on information contained in the change in coefficient and the change in R-squared when moving from an uncontrolled regression (column 1 of table 1 in the main article) to a controlled regression (column 4 of table 1). The test is based on Altonji et al. (2005) and shows that given the degree of selection on unobservables relative to observables ( _δ_ ), one can estimate an identified set of the true treatment effect [ _βcontrolled, β_ ( _δ, Rmax_ )]. Alternatively, one can estimate the coefficient of proportionality that is required to explain away the result (under a hypothetical regression with all controls). Following Oster (2019), I establish a theoretical _Rmax_ of 0 _._ 9402 by regressing log wage measure on its lag (together with fixed effects and heterogeneous trends). As can be seen from table S3, if we assume unobservables to be equally important as observables ( _δ_ = 1), the true _β_ is estimated to be between [0 _._ 023 _,_ 0 _._ 026] which suggests that the _β_<sup>�</sup> reported in column 4, table 1 is likely a lower bound of the true general equilibrium effect of public workfares on private wages. Alternatively, if I assume the true _β_ to be equal to zero, this requires _δ_ = _−_ 12. In other words, unobservables need to be an order of magnitude more important than observables. This is a very strong assumption, especially because observables explain more than 92% of the variation in wages.

## **S2. Stability of elasticity estimates**

In this section, I check for the stability of the elasticity estimate as obtained in equation 2 in the main article). Until now, the effect of program expenditure on wages is assumed to be similar for both programs. Although I allow the level of wages to be different (on average) under the NREGA regime by controlling for _NREGAd,t_ , the elasticity of wage is assumed to be constant for both the programs. I now check whether wages have become more or less responsive under NREGA by estimating separate elasticities for SGRY ( _NREGAd,t_ = 0) and NREGA ( _NREGAd,t_ = 1) regimes. For comparability, column 1 of table S4 reports the elasticity of wage estimated under the preferred specification in table 1 in the main article. Column 2 reports separate elasticities for the two programs by interacting _NREGAd,t_ with _sinh_<sup>_−_1</sup> ( _ed,t_ ).

The elasticity of wage under the SGRY regime is 0 _._ 06 (significant at 1% level). In contrast, the elasticity of wage under NREGA is approximately 0.02 (insignificant at 5% level). Prima facie, it appears that expenditure under the older program drives the overall results. However, it is important to note the larger standard errors in the second specification due to the smaller sub-samples. I cannot reject the equality of the two coefficients, even at 90% percent confidence level. Hence, we cannot reject the null of similar aggregate effects due to the two programs.

Next, I test whether there is any sub-sample heterogeneity based on how well the employment programs were implemented. A useful criterion to measure program implementation’s intensity is the annual average per-capita expenditure incurred in a district. Table S5 reports separate elasticities for sub-samples divided on the basis of district-wise _low_ and _high_ annual average (per capita) expenditure, respectively. This is achieved by interacting an indicator variable _Iexp_ which takes the value one (zero) if the average expenditure of a district is above (below) the median value of the series (<sup>�2010</sup> _t_ =2001<sup>_ed,t_)</sup><sup>_/_10.The elasticities for</sup><sup>_low_and</sup><sup>_high_average expenditure groups</sup> are estimated to be around 0.01 and 0.03, respectively. Based on the coefficient size alone, this suggests the