SQUIRES: EX-VESSEL PRICE LINKAGES 



approach relying directly upon distributed lag rela- 

 tionships between dependent and independent 

 variables has led to three widely used tests: those 

 suggested by Sims (1977), the direct Granger test 

 forwarded by Sargent (1976), and the Modified Sims 

 test advanced by Geweke et al. (1983). 



The small-sample properties of the Sims (1972), 

 direct Granger, and Modified Sims tests have 

 recently been examined within Monte-Carlo frame- 

 works by Guilkey and Salemi (1982) and Geweke et 

 al. (1983). Although the two studies differ somewhat 

 in their specifications, both found that the Sims test 

 was outperformed by the other two. Since the Sims 

 test is more time-consuming and expensive to 

 employ and requires more decisions about param- 

 eterizations, both studies unequivocally recommend 

 against its use. 



The two studies reach slightly different conclu- 

 sions on the efficacy of the direct Granger and 

 Modified Sims test. These contradictory results can 

 be attributed to differences in research design. 

 Geweke et al. (1983) concluded that the two tests 

 essentially perform equally well. In contrast, Guilkey 

 and Salemi (1982) determined that the direct 

 Granger test consistently outperforms the Modified 

 Sims procedures by small amounts. Since the direct 

 Granger test is computationally the least expensive 

 of the three and results in the fewest degrees of 

 freedom lost from formation of leads and lags, 

 Guilkey and Salemi recommend its use over the 

 Modified Sims and Sims procedures. Nonetheless, 

 they do note that the Granger procedure's advan- 

 tage over the other two diminishes with increases 

 in sample size. 



Several additional findings of Guilkey and Salemi 

 (1982) are also worth reporting. They observed that 

 for sample size <200, the shorter versions of all 

 three tests are superior to the longer versions. 5 They 

 further noted that in their Monte-Carlo study the 

 direct Granger and Modified Sims procedures ac- 

 curately recover the coefficients of the relevant 

 population projections of the statistical model used 

 to generate experimental time series in small 

 samples. Consequently, it may be unlikely to observe 

 "large" coefficient estimates arising spuriously. 

 Finally, test performance is extremely sensitive to 

 sample size, strength of causation, and length of test 

 parameterization employed. 



The direct Granger test as applied in this study 



is based upon ordinary least squares regression of 

 the current observation of the time series of round 

 ex-vessel prices from one port upon its own past 

 observations and the past observations of the other 

 port's round ex-vessel prices for species k: 



4 J 



P2 k (t) = a, + I b kl D % + cLT + I d kj P2 k 



J 



x(t-j)+ Z f kj Pl k (t - j) + e kt . (1) 



Here, LT refers to a linear time trend, D t is the 

 zero-one variable for quarter i, Pl k (t) is the round 

 ex- vessel price of species k in month t in port 1, J 

 is the number of periods lagged, and e kt is a vector 

 of stochastic, white noise residuals. The presence 

 of lagged dependent variables in Equation (1) is 

 counted on to remove serial correlation from the 

 estimated residuals. 6 



The test of the null hypothesis that P\ k does not 

 cause P2 k is a test that f kj = 0, j = 1,2,. . .,J. 

 Guilkey and Salemi (1982) indicated that the F-test 

 statistic is calculated by estimating Equation (1) in 

 both constrained (f kj = 0, j = 1,2,. . . ,J) and un- 

 constrained forms, and may be written as 7 



F = 



(SSE C - SSEJJ 

 SSEJ(T - (2J + 2)) 



(2) 



where SSE U and SSE C are the residual sum of 

 squares from the unconstrained and constrained 

 regressions, respectively, and T represents the 

 number of monthly observations on round ex- vessel 

 prices. Under the null hypothesis, F is an F-test 

 statistic with J and T - (2J + 2) degrees of free- 

 dom. This procedure is then repeated reversing the 

 roles of P\ k and P2 k to test the null hypothesis that 

 P\ k does not cause P2 k . 



The direct Granger test requires selection of a lag 

 length, J, large enough to purge serial correlation 

 from estimated residuals. Several factors require 

 consideration before specifying the lag length. 

 Chilled fresh fish is a commodity that rapidly 

 deteriorates in quality. Consequently, definite limits 

 exist to the length of time which inventories of 



failing to reject the null hypothesis of independence of the two 

 series more often than the specified level of significance suggests. 

 Because of this limitation, the second basic approach is applied. 

 5 Longer versions of these tests include additional lead and lag 

 variables. 



"Serial correlation exists when the error terms from different 

 observations in a time series are correlated. Serial correlation tends 

 to give unbiased but inefficient estimators, and a biased sampling 

 variance, which then affects the results from significant tests such 

 as the F- or -t-tests. 



7 A constrained F-test includes one or more restrictions, such as 

 one or more coefficients constrained to zero. An unconstrained F- 

 test does not include these restrictions. 



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