ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH

heteroskedasticity and/or autocorrelation in single and multiple equation specifications. The technique is
based on assuming that an expanded form of the Johnson Su family of distributions (Johnson, Kotz, and
Balakrishnan) can approximate the true underlying error term distribution. The Johnson Su family has been
previously applied by Ramirez to simulate non-normally distributed yield and price distributions for
agricultural risk analysis. Through Monte Carlo simulation assuming a variety of scenarios, it is shown
that when the underlying error term is non-normally distributed and non-i.i.d., the proposed estimator can
substantially increase slope parameter estimation efficiency in comparison to OLS, GLS (normal-error
ML), and all other partially adaptive estimators available in the econometrics literature. The proposed
technique is also validated and illustrated through two agricultural time series modeling applications.

The Estimator

The proposed partially adaptive estimator is obtained by assuming that the model’s error term (U)
follows the following expanded form of the Johnson Su family of distributions:

(1) Y = Xβ + U,

(2) U = σ{sinh(ΘV)-F(θ,μ)}∕{θG(θ,μ)}, V ~ N(μ,1),

F(Θ,μ) = E[sinh(ΘV)] = exp(Θ²/2)sinh(Θμ), and

G(Θ,μ) = [{exp(Θ²)-1}{exp(Θ²)cosh(-2θμ)+1}∕2θ²]¹/²;

where Y is an n×1 vector of observations on the dependent variable; X is an n×k matrix of observations on
k independent variables including an intercept; β is a k×1 vector of intercept and slope coefficients;
-∞<Θ<∞, -∞<μ<∞, and σ>0 are transformation parameters; and sinh(x) and cosh(x) are the hyperbolic
sine and cosine functions, respectively. Using the results of Johnson, Kotz and Balakrishnan (pp. 34-38) it
can be shown that in the model defined above:

(3)     E[U] = 0, Var[U] = σ²,

Skew[U] = E[U³] = S(Θ,μ) = -1/4w'''(w-1)²|w{w'2!siiili(3())-3snili(())|/G^,Li),
Kurt[U] = E[U⁴] = K(Θ,μ) = {1∕8{w-1}²[w²{w⁴+2w³+3w²-3}cosh(4Ω)+4w2{w+2}
cosh(2Ω)+3{2w+1}]∕G(Θ,μ)2}-3;

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