ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH



numerically simulate the probability distribution from which they could have been drawn. Specifically, let

γi be the kx 1 vector of maximum likelihood estimators for Γi, the vector of true population parameters

^ ^

underlying the normal (i=N, k=10) or the non-normal (i=NN, k=14) regression model, and CM [ri ] be the
estimated covariance matrix for
γi. Then, the joint probability distribution of γi is simulated by:

~

(9)     Si= Z x Chol( CM[Γi ]) + Γi,

where Z is an mxk matrix of independently distributed standard normal random variables, Chol(.) denotes the
~                                          ^

Cholesky decomposition, and γi the kx 1 vector of parameter estimates obtained from γi. Equation (9) yields

~                      ^ ^

an mxk matrix of random variables with mean γi and covariance matrix CM[ri]. Since, under a correct

^                                ^ ^                              ^

model specification, γi is a consistent estimator for Γi and CM[ri] is a consistent estimator for CM[ri], Si
is a theoretically correct probabilistic statement about Γi. Thus, the boundaries of a (1-α)% confidence
interval for the expected price under the normal (non-normal) model at time period t can be obtained by
extracting the m sets of simulated parameter values from S
n (Snn), using them to obtain m “predicted” price
values for time t, and finding the (
a/2) x mth and the [(1-a)+a/2] x mth largest of these m price values.

Confidence intervals for the actual price realizations require simulation of m error term draws as well.
In the case of the normal regression model, these are obtained by extracting the m simulated values for the
standard deviation parameter (
σc or σs) from Sn and multiplying them by m independent draws from a
standard normal random variable. In the case of the non-normal model, the m sets of simulated values for
σc,
μ c and Θc (or σs, μ s and Θs) have to be extracted from Snn and coupled with m independent standard normal
draws. Then, m non-normal error term values are simulated by applying equation (2). The final step in
constructing the boundaries of a (1-
α)% confidence interval for the actual price observations is to add the m
simulated error term values to the corresponding m price “predictions” and find the (
a/2) x mth and the [(1-

15



More intriguing information

1. The name is absent
2. Effects of a Sport Education Intervention on Students’ Motivational Responses in Physical Education
3. ADJUSTMENT TO GLOBALISATION: A STUDY OF THE FOOTWEAR INDUSTRY IN EUROPE
4. The Challenge of Urban Regeneration in Deprived European Neighbourhoods - a Partnership Approach
5. Analyzing the Agricultural Trade Impacts of the Canada-Chile Free Trade Agreement
6. Testing Gribat´s Law Across Regions. Evidence from Spain.
7. The name is absent
8. The name is absent
9. The Role of Trait Emotional Intelligence (El) in the Workplace.
10. Partner Selection Criteria in Strategic Alliances When to Ally with Weak Partners
11. Reform of the EU Sugar Regime: Impacts on Sugar Production in Ireland
12. Prevalence of exclusive breastfeeding and its determinants in first 6 months of life: A prospective study
13. Road pricing and (re)location decisions households
14. A Location Game On Disjoint Circles
15. Education Research Gender, Education and Development - A Partially Annotated and Selective Bibliography
16. Olive Tree Farming in Jaen: Situation With the New Cap and Comparison With the Province Income Per Capita.
17. The name is absent
18. Developing vocational practice in the jewelry sector through the incubation of a new ‘project-object’
19. Food Prices and Overweight Patterns in Italy
20. Cross-Country Evidence on the Link between the Level of Infrastructure and Capital Inflows