**Table 6:** Machine Learning algorithm ensemble fit for the first sample split simulation. For illustration, we show the linear fit coefficients or predictive importance of selected variables for each ML algorithms chosen in the ensemble

||LASSO|Random forest|Gradient boosting trees|
|---|---|---|---|
|log SR yield|0_._190|35_._628|0_._132|
|Enumerator reported damage on the crop-cut|_−_0_._011|22_._164|0_._0001|
|Farmer reported percentage of crop loss on plot|0|9_._744|0_._0001|
|Agricultural implementation index|0|8_._963|0_._002|
|Village dummy|0|5_._701|0|
|Plot acquisition type|0|0_._414|0_._085|
|Sowing date 1st half June x rain fall 1st half June|0|0_._269|0_._131|
|Sowing date 1st half June x rain fall 2nd half May|0|0_._158|0_._132|
|Plot is owned by household|0|0_._103|0_._131|

_Notes:_ The ML model set up used log CC yield as the dependent variable and the covariates included log SR yield. The ML ensemble fit for the first sample split simulation comprised the predictions of LASSO (weight = 0.594), random forest (weight = 0.273), and gradient boosting trees (weight = 0.133). We show the variables selected (with non-zero coefficient) by LASSO and the top 5 most important variables in terms of predictive power for random forest and gradient boosting trees.

To put the accuracy of our ML measure in perspective in context, we also show the _R_<sup>2</sup> and _ρ_ for SR and crop cut-calibrated satellite yields, which we obtained from Lobell et al. (2019). These results are consigned in the bottom panel of Table 7. Our ML-based imputed CC yields, in comparison to SR yields, explains unambiguously more of the variation of in CC yields, and even more impressive finding is that the _R_<sup>2</sup> and _ρ_ of the are on-par with that of the CC-calibrated satellite yields.

# **4.2.3 Empirical assessment of the yields and inputs relationship using predicted yields**

We replicate bi-variate and multivariate regressions of yields as a function of key inputs, with competing measures of yields, including SR, CC and ML yields. We use our preferred model specification of ML in the first sample split simulation in the test sample. Since we are working with predicted measures, the standards errors for the regression coefficients are bootstrapped. Further, as a robustness check, we also use the method introduced by Chernozhukov et al. (2018) to compute de-biased regression coefficients and conservative standard errors when the number of control parameters is large as it is the case of the relationships of interest between yields and key inputs.

The regression results are reported in Table 8. We note that in the test sample, the observations that we previously made concerning the difference between the coefficients of the inputs when using SR or CC are still valid. For example, in the multivariate case, the quantity of seeds per hectare is positively correlated with yields but carry a stronger coefficient when the yield measure is SR, as opposed to CC. The regressions based on ML yields yield new findings. The coefficients obtained with ML yields are similar to the ones obtained with CC yields and the coefficient pairs are not statistically distinguishable, irrespective of the agricultural input in question. This is better seen in the bottom panels of Figure 21