FISHERY BULLETIN: VOL. 78, NO. 2 



The Durbin-Watson statistic (0.731) is below the 

 lower critical value (d/ = 0.86 for 21 observations 

 and 4 parameter estimates), indicating sig- 

 nificant serial correlation in the errors of the de- 

 mand model. As suggested above, this serial cor- 

 relation may be caused by incorrect specification 

 of a static model when a dynamic adjustment 

 model would be more appropriate, or it may 

 reflect true serial correlation in the errors which 

 may in turn be due to some other source of mis- 

 specification. 



Following the suggestion by Griliches (1967), a 

 regression equation with lagged dependent and 

 independent variables was computed (Table 5). 

 The F-statistics for the four hypotheses as- 

 sociated with the serial correlation model range 

 from 0.119 to 6.516. The critical value for each 

 hypothesis (withP<0.05 and for 1 and 11 df) is 

 4.84. Clearly, only one of the four hypotheses, the 

 one associated with the soybean price, can be re- 

 jected with great confidence. Even this may be 

 misleading, because the probability of wrongly 

 rejecting at least one of four hypotheses at the 5% 

 level is 0.183"*. Due to the provisional nature of 

 the test procedure and the inconclusiveness of the 

 result, it is useful to consider both the static and 

 distributed lag models as plausible representa- 

 tions. 



The distributed lag model [Equation (8)] was 

 estimated by ordinary least squares for several 

 values of the transformation parameter A. Re- 

 gression coefficients and pertinent statistics for 

 the distributed lag model are listed in Table 6. 

 The log-likelihood function is greatest for k = 



"The probability of type 1 error in a single test is 0.05. If four 

 tests are made the probability of making at least one type 1 error 

 is one minus the probability of making no type 1 errors, i.e., 1 - 

 (0.95)". 



Table 5. — Estimates for demand function parameters with all 

 variables lagged.' Transformation parameter, A, equals -0.55; 

 and all symbols are as explained in Table 4. R^ = 0.855. 



Variable 



Estimated 

 coefficient 



SE 



F-statistic^ 



Pfit) 



Pfit-n 



Ps(f-I) 



Pc'C) 



Pc(f-I) 



Op(f-I) 

 q-{t-n 



0.455 



6.516 



0.119 



4.006 



'q-(f) = ao + a,P]{t) + b,P){t - ■)) * azP'sU) * b2P■,(t-^) - a^P.d} 

 + bjPc{t-n + a,Op{t) + b,0p(f-1) + a5q-(/-l) 



^The hypotfiesis to be tested is (b; ^ a, a^) = 0; and the corresponding 

 F-statistic is F, = {b, + a, as)^/Var(b, + a, a^). 



-0.3, and the approximate 95% confidence inter- 

 val for A is -1.0 to 0.22. As in the earlier nonlag- 

 ged model, the coefficients of the independent 

 variables have the appropriate signs. Since the 

 coefficient of the lagged dependent variable can 

 be interpreted via Equation (5) as one minus the 

 rate of adjustment parameter, the partial ad- 

 justment parameter is 0.503. This implies an av- 

 erage lag of slightly less than one. As expected, 

 buyers of fish meal generally adjust to changing 

 conditions and prices within a year. 



DISCUSSION 



Both the static demand model and the partial 

 adjustment model provide reasonable levels of 

 statistical fit to the historical data series and the 

 signs and magnitudes of the regression 



Table 6. — Regression equations for determining maximum log-likelihood of distributed lag form of 

 demand function. Pf = price of fish meal, P^ = price of soybean meal, P^ = price of com feed, Q„ = 

 poultry and egg production index, <7^_i = quantity offish meal, lagged. Superscript* indicates Box- Cox 

 transformation expressed in Equation (1). 



'Indicates maximum likelihood estimate (f-values in parentheses). 



274 



