versely related to the expected implicit rental 

 price of these vessels. Similar equations could be 

 developed for other inputs used in the shrimp 

 fishing effort. 



Desired Net Investment in Fishing Vessels 



New fishing vessels are acquired by Gulf 

 shrimp fishermen both to expand their productive 

 capacity and to replace losses in the productive 

 capacity of existing vessels. This partitioning of 

 observed gross investment into net investment 

 and replacement investment for the j^^ category 

 of fishing vessels can be expressed definitionally 

 as follows: 



Njt = Kj, - K,, 



h - ^jt 



(5) 



where 7,7 represents the level of real gross invest- 

 ment in the 7'^ category of fishing vessels in year 

 t while Rf is the real replacement investment 

 needed to offset annual capacity depreciation of 

 these vessels. The variables K; and K/- 1 represent 

 the productive capital stock of the 7'^ category of 

 fishing vessels the end and the beginning of the 

 year, respectively. Given Equations (4) and (5), 

 the following relationship between the desired 

 stock of the j^^ category of fishing vessels and 

 current real net investment in these durable 

 inputs can be defined: 



A^ 



jt 



QjiK*j, 



Kj,-i) 



(6) 



where < 0^ < 1 and where 0^ represents the par- 

 tial adjustment coefficient that describes the 

 speed of adjustment of actual stocks to desired 

 levels for thej'^ category of fishing vessels. Sub- 

 stituting Equation (4) into Equation (6) and as- 

 suming an adaptive expectations hypothesis for 

 (pXICj)t, the following compound geometric ex- 

 pression is obtained: 



A^^, = 0^ \^jUpXICj)t + (1 - ^j)Njt-i 



+ %{l - \j)Kjt-2 



0A 



Jt-l + \^Jt 



(7) 



where \j is the adaptive expectations coefficient 

 and [Xji represents the error term. Since Kjt-2 is 

 equal to Kjt^i - Nf-i, Equation (7) reduces to the 

 following estimating equation: 



A^,, = bjo + bji (pXICj)t + bj2 Kjt-i 



where 60 is the intercept, 61 = 8 px, 62 = -8X, 

 63 = (1 - \) (1 - 0) and \xt is once again the ran- 

 dom disturbance term. The estimates of the 61 

 and 63 coefficients are expected to be positive 

 while the value of 62 is expected to be negative.^ 

 Equation (8) thus represents the general form of 

 the equations to be econometrically investigated 

 in this study. 



Data 



The time series data used in this study consist 

 of annual observations for each variable in Equa- 

 tion (8) over the 1965-77 period. This time period 

 represents the only period for which investment 

 expenditure information is available. 



The productive capital stock of the^'^'^ category 

 of fishing vessels is comprised of a series of differ- 

 ent vintages of vessels or 



Kj, = Ijt + (1 - hj^)Ijt.^ + (1 - A,i - hj2)\^_^ + . . . 



+ (\-hj^-hj2- .. .- hjr,)Ijt-n (9) 



where /i^, is the fraction of thej*^^ category of fish- 

 ing vessel's original productive capacity lost in 

 the i^^ year of its service life. The value of A, is 

 represented by (1 - <}>)'" ^, where <t> = 2/n and n is 

 the assumed service life.^ In a related matter, 

 the present value of the stream of capacity de- 

 preciation of a vessel {Fj) was computed as fol- 

 lows: 



+ bj3Njt-i + iXjt 



(8) 



6The net investment model expressed in Equation (8) can be 

 seen as a part of a simultaneous equation system that includes 

 other investment equations as well as supply equations for all 

 inputs and the production function for the fishing industry. The 

 specification of the complete simultaneous system of equations 

 and measurement of time series data needed to simultaneously 

 estimate the 6, coefficients in Equation (8) are beyond the scope 

 of this study. Since the disturbance terms for this set of invest- 

 ment equations are likely correlated, the seemingly unrelated 

 regression equations estimator was employed. The disturbance 

 terms given by this estimator were also examined for autocorre- 

 lation. The estimated rho coefTicient in this small sample was 

 shown to be insignificant in all cases. Finally, the predicted 

 rather than actual value of A'^, _ j was used in estimating Equa- 

 tion (8) to address the pyossibility of correlation between the 

 lagged dependent variable and the disturbance term. 



''While a geometric decline in productive capacity has been 

 assumed for fishing vessels, recent studies indicate that the 

 productive capacity of equipment and machinery deteriorates at 

 a lower rate in the early period than in latter years. Coen (1975) 

 suggested that equipment and machinery deteriorate as they 

 age, though not necessarily at a geometric rate. For farm trac- 

 tors, a concave decay pattern represents the best proxy for the 

 capacity depreciation pattern suggested by engineering consid- 

 erations (Penson et al. 1981). The true pattern which underlines 

 actual capital spending decisions in the fishing industry could 

 not be examined due to inadequate data. 



153 



