The current world food crisis has necessitated alternative policy actions in most countries, including increased investment in agricultural research and development. This study uses duality theory to obtain allocative and cost efficiency from the parametric stochastic distance function, and results are then compared to estimates from the non-parametric distance function. The study further evaluates the impact of technological innovations and other policy variable on technical, allocative and cost efficiency from both approaches in a second-stage endogeneity-corrected Tobit regression model. Mean technical, allocative and cost efficiency ranges from 80.1 per cent to 86.7 per cent, from 57.8 per cent to 73.8 per cent, and from 50.3 per cent to 62.3 per cent respectively. The analysis of technical, alloctive and cost efficiency with respect to technological innovation and other policy factors is robust. Results show that policies aimed at maize technology development and its timely dissemination, as well as improvements in education and access to credit and extension, could promote technical, allocative and cost efficiency, reduce yield variability, enhance farm income and food security and reduce poverty in Nigeria.