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The Estimation Strategy
The procedure entailed in the empirical construction of PAMs can be seen by rewriting the letter entries of PAM in terms of price and quantity variables. The PAM can be described as follows:
where p= price of output, pi= price of tradable input i, qi = quantity of i per unit of output (Q), wi = price of factor input j, li = quantity of i per unit of output, and pi = profit. A superscript D is used to indicate that the value of the variable is observed under existing (private) price incentives; superscript S denotes the value that the parameter would assume under social price incentives. The above PAM describes costs and revenues as values per unit of output; the q; and li represent input-output coefficients. But the matrix values can be equally well presented as values per hectare, values per firm, or in terms of any other unit of observation. The q; and li need only to be multiplied by the relevant output measure.
To estimate PAMs, representative systems are first identified. Next, for each system, observable data for prices, output levels, and input use are collected, and the first line of the PAM is estimated. Third, the price and quantity observations are modified to reflect the social values appropriate to the second line of the matrix. The necessary social prices may be observed directly (world prices for tradable outputs and inputs) or they may be derived indirectly (for example, using information about divergences to estimate social factor prices from private factor prices). Finally, the observed quantities of inputs and outputs are altered to their "social" values, using econometric information about price response or engineering information about alternative technologies. If fixed input-output coefficients are assumed, the latter step is omitted.
The particular PAM that has been discussed so far represents revenues and costs for a commodity system-a chain of farming, processing, and marketing activities that characterize the production and delivery of a commodity to a wholesale market. But PAMs for commodity systems are not estimated directly. Instead they are composites of PAMs for each activity in the chain. For the purposes of data collection and organization, the PAM framework defines a commodity system to include four activities-farm production, delivery from farm to processor, processing, and delivery from processor to the wholesale market.
Figure 8.1 illustrates the structure of the commodity system model. Each of the activities in Figure 8.1 is described by a PAM matrix, made up of price and quantity variables. The PAM for the commodity system is derived from aggregation of revenues and costs across the representative activities. In some cases, these elements cannot be directly added to one another but must be adjusted to avoid double-counting of revenues and costs. Summation of output revenues for each activity, for example, would involve multiple counting of the principal output.
Additional calculations are needed to adjust for differences in the commodity units or numeraries used by different activities. Cost and revenue data for the activity budgets are collected initially in whatever form is most convenient. Farm-level costs of wheat production are commonly estimated on the basis of land area (such as costs per hectare). Farm-to-processor costs, such as transportation services, are mea-sured on a per metric ton (or some other weight or volume
meaure) basis.
Budgets for processing and processor-to-market activities might use different numeraires as well.
Conversion to a common numeraire is achieved with conversion ratios. Figure 8.2 describes the adjustment process for a wheat flour production system. In the top half of the figure, the system costs and revenues are expressed in currency units per physical unit (Portuguese escudos per metric ton) of wheat flour, the final product of the com-modity system. If farm activity costs and revenues are measured initially as currency units per land area (escudos per hectare), these entries need to be adjusted to final product equivalents. Two conversion ratios are necessary-the inverse of farm yield (hectares per metric ton of wheat) and the inverse of the processing outturn ratio (metric tons of wheat per metric ton of flour).
When farm-level costs and revenues are multiplied by these two conversion ratios, the farm-level entries are converted to an escudos per metric ton of flour basis. For the farm-to-processor activity, only the inverse of the processing outturn ratio is needed as an adjustment factor. No adjustments are needed for the processing and processor-to-market activities, because these costs and revenues are already denominated in escudos per metric ton of flour. The choice of a numeraire is entirely arbitrary. The bottom half of Figure 8.2 illustrates the activity adjustment procedure for the calculation of system costs and revenues on a per hectare basis.
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