(4) Now we see that harvest is a function of the ex-vessel price of fish, a vector of harvest input costs, the state of the biomass and stochastic error terms impacting harvest and effort. On the demand side the ex-vessel price of fish depends on harvest level, the export price of fish , the cost of processing, transportation, etc. (represented by the vector X) and other stochastic error factors impacting ex-vessel price . We write the population price equation as: (5) Equations (4) and (5) represent the population structural model for the fishery. The second stage is to make assumptions on the functional forms used in estimation (linear), clearly define the endogenous variables (harvest and ex-vessel price) and exogenous variables (input costs, current biomass, export price, and costs of processing), and most importantly what empirical variables are available to write-up the sample regression equation. We do have information on harvest, ex-vessel and export price, but the data available to proxy Z and X are sparse. We do have the real price of fuel that we will use to proxy the harvest input costs (Z) but we have no information on the vector X. In addition, we do not have stock estimates and will proxy the stock using a trend and trend squared variables. With these assumptions and data restrictions we can write down the sample harvest function as: (6) where . The residual also represents sampling variation in the data.
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