FISHERY BULLETIN: VOL. 86, NO. 2 



tion since demand is a discrete choice, and there 

 are individuals or firms which do not purchase a 

 vessel. 



Rather than attempt to deal with these difTi- 

 culties which do not appear to have widely ac- 

 cepted solutions, it is assumed that there are 

 underlying structural equations of demand and 

 supply which permit the derivation of the reduced 

 form equation. Moreover, the direct specification 

 and estimation of the reduced form is the more 

 commonly used approach to estimate the value of 

 a commodity as a function of its characteristics 

 (Bockstael et al. 1986). Last, the use of the re- 

 duced form should not create a problem since the 

 hedonic function is a joint envelope in character- 

 istic space of demander's bid schedules and sellers 

 offer schedules, and thus, the observed implicit 

 price locus is a reduced form equilibrium vector 

 reflecting both supply and demand influences. As 

 a result, shifts in both market demand and supply 

 are incorporated into the reduced form equi- 

 librium vector. 



The Capital Stock Model 



As previously indicated, it is common practice 

 to use the acquisition price as a measure of capital 

 stock. By the hedonic approach, the capital stock 

 or acquisition price of a fishing vessel is postu- 

 lated to be a function of several vessel character- 

 istics. The following general specification is con- 

 sidered: 



C = f(LN, CS, YEAR, FI, AGE, DNO, HPWR, GRT), 



(2) 



where C is the list or advertised price or the ac- 

 quisition price of a vessel, LN is length, CS is hull 

 type (1 = steel, = other), FI is fishery or gear 

 tj^e,' AGE is age of vessel, DNO is a dummy 

 variable for new and used vessels (DNO = 1 for 

 new and for used), HPWR is engine horsepower, 

 and GRT is gross registered tonnage. The vari- 

 able year equals the year of the observation. It is 

 included to incorporate technological changes 



'^Gear type is an integer valued variable set equal to the gear 

 codes used by the Northeast Fisheries Center. This may influ- 

 ence the results similarly to the use of nonbinary dummy vari- 

 ables (Kmenta 1971). The use of this variable implies that the 

 cost difference between gear types is equal to a scalar multiple 

 of the lowest integer valued gear code. Thus, statistical rejection 

 of cost differences due to gear type is actually a rejection of 

 differences not being equal to scaleir multiples. However, the 

 large number of gear codes prohibits their separate treatment. 



over time, such as the introduction of electronics 

 and stern trawling, and structural changes in the 

 industry such as changes in organization of capi- 

 tal and fish markets and changes in public regu- 

 lation. 



Functional Form 



Several functional forms could be specified for 

 Equation (2). Alternatively, generalized Box-Cox 

 (Box and Cox 1962) transformations could be used 

 to determine the functional form. However, the 

 selection of functional form is mostly concerned 

 with obtaining the relationship between the de- 

 pendent variable and individual independent 

 variables. This study is primarily concerned with 

 estimating the capital stock. Moreover, it may be 

 quite difficult to estimate capital stock from Box- 

 Cox transformations or other functional forms 

 since the conditional expectation is often of a com- 

 plex form (Smallwood and Blaylock 1986). Also, 

 Dadkhah (1984) noted that predictions based 

 upon some transformations and functional forms 

 result in biased predictions and asymmetric confi- 

 dence intervals. 



Since this study is primarily concerned with 

 estimating capital stock and investment rather 

 than estimating the implicit prices for character- 

 istics, a linear functional form is proposed for 

 Equation (2). The capital stock equation is speci- 

 fied as a second-order polynominal in order to 

 provide an approximation to an unknown, under- 

 lying hedonic function. This is equivalent to 

 specifying a generalized quadratic flexible func- 

 tional form and imposing zero valued restrictions 

 on the cross product coefficients or interaction 

 terms (Lau 1978). Flexible functional forms are 

 widely used in economic studies concerned with 

 determining the underlying economic structure 

 because they impose very little structure on the 

 economic equations of concern (Blackorby et al. 

 1978). 



Postulated Relations 



The postulated relations between cost and each 

 of the explanatory variables is as follows: 1) the 

 coefficients for the first order terms of vessel ton- 

 nage, length, and engine horsepower should be 

 positive since costs should increase as the size 

 characteristics increase; 2) the coefficient for 

 steel-hulled vessels should be positive since steel 

 vessels are generally more expensive than wood 

 or fiberglass vessels; 3) the dummy variable coef- 



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