1. Ray Production Function Estimates for the Maize-Bean Mixed Crop System in Madzuu Doug Brown and Chris Barrett Cornell University March 15, 2004 BASIS CRSP Project Annual Team Meeting Nyeri, Kenya

2. Core Issues Estimating production response when (i) multiple outputs share common inputs - which inputs are limiting? - what’s the optimal crop mix? (ii) there may be non-convexities associated with use of inputs inaccessible to some farmers (e.g., livestock, inorganic fertilizers)

3. Method of Analysis Ray Production Function (Löthgren 1997,2000) Use the Euclidian norm – the multi-dimensional distance – ║ y ║ as dependent variable and the polar-coordinate angles – the direction in multi-output space –  i, as regressors. For a two-crop (maize-bean) system, one estimates the multi-output production function: Allow for interactions that can create local nonconvexities and exact second-order approximation of true prod’n fn: we use a generalized quadratic, w/ normalized variables. Try with directions in both output and seed space.

4. Data Plot-level input and output data, long rains 2002, from Madzuu, Vihiga District 129 maize-bean intercrop plots, 112 hhs Mean yields: 0.97 t/ha maize 0.46 t/ha beans input-output θ correlation = 0.077

5. Very preliminary results Using θ based on outputs, yields are: - convex in livestock holdings and joint N- P application rates - declining in plot size - concave in N application rate - monotone increasing in labor - increasing as reduce maize/beans ratio - increasing in soil quality at acquisition

6. Very preliminary results Using θ based on seed, yields are: - declining in plot size - concave in N and P application rates with complementarity between them - monotone increasing in labor - increasing as reduce maize/beans ratio - increasing in soil quality at acquisition (livestock no longer have significant effect)

7. Conclusions and Practical Implications Madzuu farmers err in direction of maize cultivation Soil quality very important, with P more limiting than N, but the two complement each other Labor availability limits output Although inverse yield-size relation, total output grows with size Ability to apply fertilizer, keep labor and perhaps livestock increases yields … access to finance and human health central to productivity and incomes, consistent with poverty trap idea.