An Econometric Model of Multivariate Stochastic Production Functions for Manitoba Crop Agriculture

Researchers: Barry Coyle, University of Manitoba

Research Summary

The primary objective of this research is to estimate an econometric model of crop production emphasizing the impact of input decisions on yield covariances as well as variances. This will address a major shortcoming of empirical stochastic production functions, which largely ignore impacts on yield covariances. Agriculture and Agri-Food Canada (AAFC) has a strong ongoing interest in simulating impacts of programs such as CAIS and Production Insurance (PI) on farm production decisions, and AAFC recognizes that such impacts depend critically on perceived yield risk, price risk and risk preferences. Theory of decision making under risk emphasizes the importance of risk covariances as well as variances (e.g. in diversifying portfolios of stocks or agricultural enterprises), so these extensions should be of considerable interest to AAFC. Indeed an ongoing study for AAFRC on impacts of CAIS and PI emphasizes estimation of coavariances of yield risk across crops, but assume constant correlations (Coyle, “An integrated economic and environmental impact analysis framework of CAIS and PI”, AAFC 2007), which may be an appropriate assumption within the context of AAFC’s CRAM model. However, more generally, input decisions presumably influence correlations of yield risk just as they influence variances, and it should be important to model this in various simulation frameworks. The study proposed here extends this AAFC research by estimating impacts of inputs on correlations of yield risk across crops in Manitoba. Thus this proposed study would be a timely extension of recent research with AAFC.

Significance of Research

This research will apply a recently developed methodology (Coyle, “On Modeling Multivariate Stochastic Technologies”, 2007). Following Just and Pope, studies of stochastic production functions have ignored production impacts on yield covariances, with a few minor and unsatisfactory exceptions. Building on insights in recent multivariate GARCH literature (especially Engle), Coyle presents a more satisfactory approach to modeling impacts on correlations of yield risk. The proposed study will use a large farm level panel data set on yields and physical levels of four fertilizer inputs (nitrogen, phosphorous, potassium, sulfur) provided by the Manitoba crop insurance agency. The study will focus on the five major crops for Manitoba (there is insufficient data to obtain robust estimates of stochastic production functions for minor crops). The AAFC study mentioned above has obtained more robust estimates with this data set of Just-Pope-type stochastic variance equations than in most of the literature, suggesting this is a quality data set. Moreover, preliminary study by Coyle suggests that extensions to model impacts on yield correlations are tractable and significant.

Summary of Research Results: Yet to come.