hectare, the logarithmic transformation of the number of days of household labor per hectare. _P_ is a vector of plot characteristics including inputs other than seeds and household labor, _O_ is a vector of objective measures of plot characteristics (including geospatial variables). _H_ is a vector of household characteristics, _M_ is a vector of plot manager characteristics. _V_ is a vector of dummy variables for villages (village fixed effects) and _εi_ the error term.

The coefficients of interest are the _β_ ’s. A negative and statistically significant _β_ 1 would be in support of the inverse scale-productivity relationship at the plot-level. A positive and significant _β_ 2 would indicate that increasing the quantity of seeds per hectare is correlated with higher yields, suggesting that one the potential way to increase yield is to increase the quantity of seeds per hectare. Finally a positive and significant _β_ 3 would indicate that more labor per hectare could potentially increase yields. From a policy perspective, a negative _β_ 1, and positive _β_ 2 and _β_ 3 plead in favor of agriculture intensification to improve yields.

Our empirical analysis confirms our expectations, as presented in the preceding section. Table 5 presents the regressions coefficients of key agricultural inputs, as obtained from the bivariate and multivariate regressions of SR and CC yields. The IR is always confirmed when using SR yields, with a statistically significant negative coefficient associated with plot area. More specifically, it appears that a 1 percent increase in GPS-based plot area results in a .2 percent reduction in sorghum yield. The relationship disappears, however, when using CC yields.

**Table 5:** Regressions results of SR and CC measures of yields for selected inputs

|||||Measu|res of Yi|elds|||
|---|---|---|---|---|---|---|---|---|
||SR|CC|SR|CC|SR|CC|SR|CC|
|GPS measured plot area|_−_0.268<sup>_∗∗_</sup>|0.138|||||_−_0.304<sup>_∗∗∗_</sup>|_−_0.045|
||(0.109)|(0.122)|||||(0.085)|(0.099)|
|Quantity of Seeds|||0.574<sup>_∗∗∗_</sup><br>(0.128)|0.051<br>(0.139)|||0.366<sup>_∗∗∗_</sup><br>(0.068)|0.185<sup>_∗∗_</sup><br>(0.086)|
|Days of household Labor|||||0.417<sup>_∗∗∗_</sup>|0.078<sup>_∗∗_</sup>|0.159<sup>_∗∗∗_</sup>|_−_0.040|
||||||(0.058)|(0.033)|(0.058)|(0.045)|
|Multivariate Framework?|No|No|No|No|No|No|Yes|Yes|
|Village Fixed efects?|No|No|No|No|No|No|Yes|Yes|
|Observations|577|577|577|577|577|577|577|577|
|R<sup>2</sup>|0.033|0.009|0.081|0.001|0.144|0.005|0.443|0.424|
|Adjusted R<sup>2</sup>|0.031|0.007|0.079|_−_0.001|0.143|0.003|0.391|0.371|

_Notes:_ Errors clustered at the enumeration area. Dependent and Independent variables shown here are log transformed. Full multivariate regression results are shown in Table A3 Significance levels: *p _<_ 0.1; **p _<_ 0.05; ***p _<_ 0.01 In sum, assuming that CC yields do not suffer from NCME, the errors in SR yields create spurious relationships between yields and key inputs in the context of smallholder farmers. The policy implications of these results are very concerning if agricultural initiatives are to be motivated by the analysis of these relationships. In fact, examining the full regression results in Table A3, it is striking how sensitive our estimations are to whether we use SR or CC yields. Using SR yields, plots with more intensive input use have higher yields, suggesting that the focus should be on agricultural intensification 16