Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics



the market and other factors add more price variability around the trend. Therefore, this
stochastic trend model is also fitted to price data.

The model consists of one measurement equation and two transition equations:

(6)


yt = μt + εt

μt = μt-1+ βt1+ ηt

βt = βt-1 +ςt

where yt is the independent variable indexed by time t ;



is the state vector; εt is the random


error describing the short run randomness with mean zero and variance σε2 ;3

2
ση
I 0



σ2


is the error vector describing the long run randomness in the


transition equation that governs the evolution of the state vector. Both of the errors in the
measurement equation follow normal distributions and are independent of each other.

In the basic specification, μt, the mean component of the dependent variable, is shown
as a random walk with a drift. Therefore the final generalization shows that the mean of the
dependent variable grows at a random rate.

3 The model also allows for a non-normal errors when εt is assumed to be generated by an inverse

hyperbolic sine transformation from normality: et= (τt-δ)~N(0,1), and

τt =θ-1 ln θεt+



where δ is the non-centrality parameter; δ0(< 0) denotes the


distribution is skewed to the right (left) and if δ = 0 the distribution is symmetric. θ is associated with
the degree of kurtosis with
θ0 denoting a kurtotic distribution. Thus, the error term can be expressed

as εt


eθτt


e-θτt


2θ


12




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