Ray Production Function Estimates for the Maize-Bean Mixed Crop System in Madzuu

Doug Brown and Chris BarrettCornell University

  

March 15, 2004BASIS CRSP Project Annual Team Meeting

Nyeri, Kenya

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)

Method of AnalysisRay 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.

),,( 1 xfy

DataPlot-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 maize0.46 t/ha beans

input-output θ correlation = 0.077

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

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)

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.