Hernck and Squires Measuring fishing fleet productivity 



93 



Kirkley. J. 



1984 Productivity in fisheries. Discussion pap., Woods Hole 

 Lab.. Natl. Mar. Fish. Serv., NOAA, Woods Hole, MA 02543, 

 20 p. 



McFadden, D. 



1978 Cost, revenue, and profit functions, /h Fuss, M., and 

 D. McFadden (eds.). Production economics: A dual approach 

 to theory and applications, vol. 1, p. 3-109. North-Holland 

 Press, Amsterdam. 



Nelson, R. 



1981 Research on productivity growth and productivity dif- 

 ferences: Dead ends and new departures. J. Econ. Lit. 

 19:1029-1064. 



Norton, V.. M. Miller, and E. Kinney 



1985 Indexing the economic health of the U.S. fishing in- 

 dustry's harvesting sector. NOAA Tech. Memo. NMFS- 

 F/NEC-40, Northeast Fish. Cent., Natl. Mar. Fish. Serv., 

 Woods Hole, MA 02543, 42 p. 



Schaefer, M.B. 



1957 A study of the dynamics of the fishery for yellowfin tuna 

 in the eastern tropical Pacific Ocean. Bull. 6, Inter- Am. Trop. 

 Tuna Comm., La Jolla, CA 92038, p. 247-285. 

 Scott, A. 



1954 The fishery: The oLijectives of sole owiiership. J. Political 

 Econ. 63:116-124. 

 Solow. R. 



1957 Technical change and the aggregate production func- 

 tion. Rev. Econ. Stat. 39:312-320. 

 Squires, D. 



1988 Index numbers and iiroductivity measurement in multi- 

 species fisheries: An application to the Pacific coast trawl 

 fleet. NOAA Tech. Rei:.. NMFS 67, Natl. Oceanic Atmos. 

 Adm., Natl. Mar. Fish. Serv., 34 p. 

 Squires D., and S. Herrick, Jr. 



1988 Productivity measurement in common property resource 

 industries: An application to the Pacific coast trawl fishery. 

 Mimeo rep.. Southwest Fish. Cent., Natl. Mar. Fish. Serv., 

 NOAA, La Jolla, CA 920:38, 34 p. 

 Tornqvist, M.A. 



1936 The Bank of f^inland's consumption price index. Monthly 

 Bull. Bank of Finland 10:27-34. 



Appendix 



The growth-accounting framework is developed by dif- 

 ferentiating Equation (1) with respect to time t: 



dY(t) 

 dt 



N+l 



= I 



6F_ 



6F 

 6B(t) 



dX;{t) 



dt 

 dt 



6F 



dA(t) 



dA(t) 

 dt 



(A.l) 



where (/i'(^ )ldt represents the growth rate of output 

 (i.e., extraction rate) due to technical progress. Putting 

 the left side of Equation (A.l) into percentage terms 

 (and suppressing the notation for each time period / ) 

 gives: 



dYl 

 dt Y 



1 

 F 



Af-fl 



y 6F^dX, 6FdA 6FdB 

 ,T"i 6X, dt ^ 6A dt '^ 6B dt 



(A.2) 



J 



To obtain proportionate growth rates for all vari- 

 ables, substitute [dYldt \ [1/7] = YIY, [dX,ldt ] [1/A',] = 

 A',/A',. [dAldt] [IIA] = AIA, and [dBldt] [IIB]^B/B 

 into Equation (A.2) to give: 



Y 



N+l 

 = I 



6FB 

 6B F 



B 



b' 



(A.3) 



In equation (A.3), by convention (Denny et al. 1981, 

 Solow 1957) the term [6FI6A ] [AIF] is the proportional 

 shift in the production function with time and is set 

 equal to unity. Thus a 1% increase in the index of tech- 

 nical progress increases the flow rate of output by 1%. 

 This shifting of the production function through time 

 is called technical change or the time rate of growth 

 of technical progress. The term [dFI6B] [BIF] is set 

 to unity because it is a technology-shift parameter for 

 a Schaefer (1957)-type production technology in which 

 catch rates are proportional to resource abundance for 

 any given vector of inputs. i- 



Define E, = [6FI6X,] [X,IF]. This is the output 

 elasticity of input A', , representing the proportional 

 change in output flow for a given change in A, within 

 some level of resource stock abundance and state of 

 technological progress. Substituting the output elas- 

 ticity expression into (A.3) gives the long-run rate of 

 output growth as: 



Y 

 Y 



X ^1 + + - , 



,=1 A, A B 



(A.4) 



^This corresponds to the production function siiecified by Schaefer 

 (1957), }' = FlE.B) = qEB. where q denotes the catchahility coef- 

 ficient and E represents effort or an aggregate input index so that 



E = 3(A', Xy^ I ), where g is a linearly homogeneous aggi-egator 



function and the A' -i- 1 A', are the inputs. Thus, di'/dB = 1. We are 

 grateful to Jim Kirkley who pointed this out to us. Moreover, the 

 Schaefer production function implicitly assumes constant-returns- 

 to-scale in inputs, because dVldE = 1, so that a proportionate in- 

 crease in £ generates an equal proportionate increase in Y. In addi- 

 tion, changes in the resource stock affect the production function 

 in a Hick's-neutral manner, similar to technical progress. 



