HUPPERT: ANALYSIS OF UNITED STATES DEMAND FOR FISH MEAL 



Ho:(6, +sa,) = 0. (13) 



An approximate sample variance for ib, + sa^) is 

 computed by the "delta method" described by 

 Saber (1973). The expression for approximate 

 variance of a function of a vector of random vari- 

 ables, G(x), is 



v[G(x)] = Zy(x,)(|^y 



+ 221: COY (jc 

 i<J 



Mm 



dG 

 dx. 



(14) 



Assuming that the estimate of (6, + sa^) from the 

 regression equation is approximately normally 

 distributed, the following ratio will be approxi- 

 mately distributed as anF-statistic with 1 and (n 

 - r) df (where r is the number of regression 

 parameters estimated): 



ib, +sa,)2/v[6, + sa,]^F(l,n-r). 



(15) 



Since the serial correlation model requires each 

 of the four hypotheses to hold, a definite rejection 

 of one or more of the hypotheses may be taken as 

 evidence against the serial correlation model and 

 in support of the partial adjustment model. Be- 

 cause of the lack of rigor in the suggested testing 

 procedure, however, caution must be exercised in 

 drawing conclusions. 



RESULTS 



Ordinary least squares estimates of the static 

 demand Equation (2) were computed for a range 

 of values for the transformation parameter A. The 

 regression coefficients and statistics of most in- 

 terest are listed in Table 4. A value of \ = -0.55 

 maximizes the log likelihood function, but the 

 95% confidence interval for A is 0.2 to -1.4. The 

 interval includes the logarithmic transformation 

 (A = 0), but not the linear transformation (A = 1). 

 The negative value of A, which implies a price 

 elasticity of demand that decreases as quantity 

 decreases, conforms to expectations. The signs of 

 all the coefficients are also consistent with prior 

 expectations; demand is diminished by increasing 

 price of fish meal or corn meal, and is increased 

 by increasing price of soybean meal and by ex- 

 panding poultry and egg production. Application 

 of ^-tests to the coefficients of the equation with A 

 = —0.55 indicates statistical significance with 

 99% confidence for the coefficients of fish meal 

 price and corn meal price, and with 90% confidence 

 for the coefficient of soybean meal price. The poul- 

 try and egg production index appears to be an 

 insignificant influence on fish meal demand by the 

 ^-test. But this is insufficient reason for elimi- 

 nating a theoretically important variable from the 

 equation. 



The squared multiple correlation coefficient, r^ 

 = 0.73, indicates a reasonably "good fit" for a de- 

 mand equation estimate from time-series data. 



Table 4. — Regressions for determining maximum log-likelihood of static demand function. P, = price 

 offish meal,Pj = price of soybean meal.P^ = price of com feed, Qp = poultry and egg production index. 

 Superscript * indicates Box-Cox transformation expressed in Equation (1). 



' D-W stands for Durbin-Watson statistic. 



^Indicates approximate 90% confidence interval for a. 



^Indicates maximum likeiitiood estimate (f-values in parenthesis). 



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