adequately control for regional effects. In addition, the agro-ecological zone variables continue to be jointly significant in the presence of district dummy variables, suggesting that one set of variables is not a substitute for the other; that is, neither is dispensable. The two RPP indicators, however, become jointly insignificant in the presence of the district fixed-effects.

As discussed above, it is possible that by including too many fixed-effects (for AEZs, RPPs and districts), the effect of any meaningful or genuine variation in the extension supply variable may be reduced to the point of making it redundant. The large drop in the magnitude of the extension coefficient and its significance, thus, warrant some further investigation. To determine whether the base-case result represents the genuine impact of extension or a spurious result due to omitted factors, a series of tests were performed. These included dropping the AEZ and RPP indicators to test the sensitivity of the coefficient on the extension supply variable. As noted above, including the district fixed-effects makes the RPP indicators jointly insignificant. Hence, it is not surprising that, when the RPP indicators are dropped, all coefficients and their standard errors remain virtually unchanged relative to the full fixed-effects model (model II) in table 1. Next, the set of AEZ indicators was dropped (despite their joint significance noted above). Again, there were no substantive (or significant) changes in the standard production parameters or in the extension coefficient. Further, the overall model fit is better with district fixed-effects and without AEZs (adjusted R<sup>2</sup> of 0.70) compared to the base-case model (adjusted R<sup>2</sup> of 0.65). Finally, dropping all the RPP and the AEZ indicators, the model fit continues to be superior (adjusted R<sup>2</sup> of 0.70), while the estimated coefficients are not substantively different from the full fixed-effects model.

These tests reveal the importance of the district-specific effects in explaining the productivity differences across households. They also provide confidence that, while it is theoretically possible that too many fixed-effects can be more of a nuisance than an aid in statistical inference, in this empirical application such is not the case.

To test the hypothesis that extension may be differentially efficient across districts, and hence that the district effects are obscuring the extension impact, model III in table 1 presents the results of the regression including cross-terms between district effects and extension. Two of the districts (Mlachakos and Muranga) have positive and statistically significant coefficients, while one (Kisumu) has a statistically significant negative coefficient. All of the remaining districts have an insignificant coefficient but the sign is negative. While the signs on the individual district effects are possibly interesting in themselves, from the evaluation point of view, the overall impact of extension is of greatest interest. Towards this end, the two tests mentioned above are performed. One is the sum of the coefficients on the seven cross-terms, which turns out to be small (0.037) and insignificant. A more appropriate test is the significance of the weighted sum of district-specific extension effects, where the weights are the sample shares of each district in total output. The results of including cross-terms between district effects and extension indicate a negative overall extension impact (-0.246), which is statistically insignificant.

As sketched above, a number of modifications need to be made to the variables used in the analyses reported in table 1. These include: the new indicators (dummy variables) for medium and low potential zones; the AEZ classification available in the 1982 RHBS data set; respecification of household head's education status to dummy variables for primary and higher levels of education; updated cluster-level means for non-farm income, production, farm holding 10