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Gelson Tembo is lecturer I, Department of Agricultural Economics
and Extension Education, University of Zambia, Lusaka; B. Wade Brorsen
is regents professor and Jean & Patsy Neustadt chair; Francis M.
Epplin is Charles A. Breedlove Professor, Department of Agricultural
Economics at Oklahoma State University; and Emilio Tostao is assistant
professor, Division of Agricultural Economics at Universidade Eduardo
Mondlane, Maputo, Mozambique. The authors thank professor William R.
Raun, for providing access to data and information regarding the
experiment, and Francisca G.C. Richter for helpful comments and
technical assistance. Journal paper AEJ-245 of the Oklahoma Agricultural
Experiment Station, Projects H-2237, H-2403.
Table 1. Summary of Regression Results for
Wheat Yield Response Functions
Estimates and
Standard Errors by
Type of Response
Function (a)
Linear response
Statistic Symbol Stochastic Plateau
Intercept [[beta].sub.0] 26.32
(0.93)
Level of nitrogen (lbs) [[beta].sub.1] 0.40
(0.02)
Expected plateau yield
(bus) [[mu].sub.m] 41.78
(0.82)
Nitrogen at expected
plateau (lbs) [x.sub.m] 38.32
(2.70)
Variance of plateau
yield [[sigma].sup.2.sub.v] 163.92
(28.85)
Variance of year random
effect [[sigma].sup.2.sub.u] 75.81
(10.39)
Variance of error term [[sigma].sup.2.sub.
[epsilon]] 28.51
(1.46)
Variance correlation [rho] 0.39
(0.041)
Log-likelihood (b) -2,722.45
Estimates and Standard Errors
by Type of Response Function (a)
Linear response Switching
Statistic Plateau Regression
Intercept 26.31 24.54
(1.51) (0.77)
Level of nitrogen (lbs) 0.27 0.22
(0.02) (0.02)
Expected plateau yield
(bus) 42.06 39.73
(1.45) (0.91)
Nitrogen at expected
plateau (lbs) 57.71 70.56
(3.54) (6.48)
Variance of plateau
yield 205.22
(16.46)
Variance of year random
effect 68.93
(17.01)
Variance of error term
53.49 53.70
(2.66) (1.82)
Variance correlation 0.28
(0.17)
Log-likelihood (b) -2,920.45 -3,390.8
(a) Standard errors are in parentheses.
(b) The null hypothesis that the nonstochastic plateau is the correct
model (i.e.. [H.sub.0]: [[sigma].sup.2.sub.v] = O) is rejected at any
conventional level of significance based on a likelihood ratio test.
The calculated value of the likelihood ratio statistic is 396, which
is considerably above the [[chi square].sub.(1,0.01)] critical value
of 6.63. Pollack and Wales's (1991) likelihood dominance criterion for
testing nonnested models indicated that the stochastic plateau model is
about 668 times more likely than the switching regression model.
Table 2. Maximum Expected Profit Per Acre, Assuming the Linear
Response Stochastic Plateau Is the Correct Model and the Price
of Wheat Is $3 Per Bushel
Profit by Price of Nitrogen (r)
Model $0.01 $0.02 $0.06
[lb.sup.-1] [lb.sup.-1] [lb.sup.-1]
Linear response stochastic
plateau (a) 124.08 108.12 87.01
Linear response plateau (b) 118.39 107.42 84.34
Switching regression (c) 116.78 89.86 70.46
Perfect information (d) 124.96 117.68 102.35
(a) For the stochastic plateau model, the optimal quantity of
nitrogen is 114.40 lbs/acre, 69.20 lbs/acre, and 38.65 lbs/acre when
r is equal to $0.1 [lb.sup.-1] 11. $0.2 [lb.sup.-1], and $0.6
[lb.sup.-1]. This is translates into an expected yield, E(y|x), of
72.47 bu/acre, 54.23 bu/acre, and 41.91 bu/acre.
(b) For the nonstochastic plateau model. at all three prices,
[x.sub.m] = 57.71 bu [acre.sup.-1], which translates into
E(y|x) = 42.58 bu/acre, and 24.54 bu/acre.
(c) For the switching regression model, the optimal quantity of
nitrogen is 216.9 lbs [acre.sup.-1], 102.4 lbs [acre.sup.-1],
and 0.0 lbs/acre when r is equal to $0.01 [lb.sup.-1],
$0.2 [lb.sup.-1], and $0.6 [lb.sup.-1]. This translates into an
expected yield, E(y | x), of 71.22 bu/acre, 46.58 bu/acre,
and 24.54 bu/acre.
(d) For the perfect information case the average optimal quantity
of nitrogen at all prices is [x.sub.m] = 38.32 lbs/acre, and the
average plateau yield of [u.sub.m] = 41.78 bu/acre is obtained.
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