The direct effect of disembodied technical change in the food processing industries, possibly induced by changing output demand, has clearly been MA-saving, even adapted for the conflicting forces from innovation, and rigidities in the agricultural sector, that have affected the virtual prices of agricultural materials and capital.Our goal is to evaluate costs, input demand , and output price behavior in the U.S. food processing industries, and their dependence on various pecuniary and technological forces. A cost function specification recognizing virtual prices, and augmented by an output pricing equation, provides the foundation for this exploration. Such a framework assumes that cost minimizing input demand behavior based on observed input prices and output demand characterizes firms in the food processing industries. The potential for imperfect markets from quasi-fixity and deviations from perfect competition is incorporated through the virtual price specification. The resulting cost structure representation allows us also to characterize profit maximizing output prices and quantities through an equality of the associated marginal cost and marginal revenue. More formally, the technology and cost-minimizing behavior underlying the observed production structure are typically represented by a total cost specification of the form TC, where Y is output, p is a vector of variable input prices, and r is a vector of exogenous technological determinants. Impacts on this cost relationship of changes in components of the p and r vectors,plastic seedling pots and thus on the implied overall costs and input-specific demands, can be derived via 1st- and 2nd-order elasticities with respect to these arguments of the cost function. The ability to reach minimum possible production costs, as implied from such a cost function specification, is often recognized to be restricted by adjustment costs, which severs the equivalence of the observed input price, pk, and its true economic return.
Alternatively, something that looks like internal adjustment costs may stem from increased factor prices due to some other type of input market imperfection. This could arise from, for example, imperfect competition in the factor market, external adjustment costs or unmarketed characteristics.This representation is particularly appealing if the interaction terms from the former model seem uninformative, but an imperfect market gap, lk seems to exist .If instead Zk appears well approximated by pk, or lk» 0, one can reasonably assume that rigidities or other input market imperfections are not binding constraints on, or determinant of, measured cost structure patterns. We have adopted such a virtual price framework as that most consistent with our data, from preliminary investigation of estimation patterns. Evidence was found, however, for deviations between observed and effective or virtual prices for capital and agricultural materials . The virtual price of capital was therefore defined as p*K=pK+l K, with lk¹ 0 potentially attributable to capital rigidities or unmeasured taxation or quality impacts. Various forms for the deviation between pK and ZK=p*K were tested to establish their empirical justification in terms of significance of the parameters, robustness of the overall results, and plausibility of resulting elasticities. The finding that lMA¹ 0 is plausible for a variety of reasons. In particular, if the processing industries perceive some control over MA prices, the marginal than average price drives MA input demand behavior and lMA>0. This is of interest since the potential for processing facilities to depress prices paid to farmers, has often been recognized as a policy concern. In reverse, embodied technical change could imply lower effective prices of agricultural materials compared to their measured values . The variables in the r vector reflecting the industry’s technological base include the time counter t, as well as t2, to represent disembodied technical change trends and further structural change shifts in the 1980s as compared to the 1970s .
A capital equipment to structures ratio, , is also used to represent technology embodied in the capital stock.6 And dummy variables for the different industries, DI , are included to capture fixed effects.Output supply/pricing decisions are also accommodated in this cost-based model by specifying a pricing mechanism that allows for a difference between output price and marginal costs, or average and marginal cost. This extension of the cost function framework is founded on imposing the standard profit maximizing condition underlying output choice, MR = MC , and assuming that any gap between output price pY and MR results from a dependency of pY on output levels; pY. Alternative treatments with lY specified as a function of other exogenous variables were also tried, with no significant impact.10 To empirically implement this model of the production structure of the U.S. food processing industries, we use a panel of input and output quantities and prices we have constructed from the Census of Manufactures, the NBER productivity database, the Bureau of Labor Statistics, and the U.S. Department of Agriculture. In particular, we distinguished cost shares for three materials aggregates – agricultural materials, food materials , and other materials. To accomplish this, we used Census of Manufactures data to calculate the share of each materials aggregate in the industry value of shipments for which cost information is available.These shares were then adjusted in two ways to arrive at our final estimated materials shares. First, in some food industries, the industry value of shipments includes substantial amounts of materials resales – materials that are purchased but not processed before being resold. We subtracted resales from the value of shipments, to better capture manufacturing output. Second, some small establishments are not required to separately report individual materials purchases, but instead report all materials in an “n.s.k.” category.
We assumed that these establishments allocated n.s.k. shipments to agricultural, food, and other materials categories in proportions equivalent to those reported by the larger institutions. Materials input price series were constructed primarily from commodity PPIs from the Bureau of Labor Statistics. In cases where an industry consumed several specific agricultural or food materials, an aggregated materials price index was constructed from the constituent materials indexes, with each price index weighted by its expenditure share in the Census aggregate. In the few cases where PPI indexes were not available, we constructed indexes from average price series maintained by USDA’s National Agricultural Statistics Service. The resulting data panel covers 5-year intervals from 1972 through 1992, for the 40 4- digit SIC industries in the U.S. food processing sector . The remaining data on output and input prices and quantities were taken from the 4-digit manufacturing NBER productivity database, which is often used as a foundation for production structure studies. Although instrumental variables procedures are often used in the literature on which this study is based, to accommodate potential endogeneity or measurement errors in the data, we did not rely on them for a variety of reasons. First, IV techniques require a somewhat arbitrary specification of instruments, which can be problematic. In addition, models of this form are typically estimated with time series data, and often use lagged values of the observed arguments of the function as instruments. But this is not conceptually appealing for our application due to the short time series,container size for raspberries as well as the 5-year gaps between data points. Although some preliminary investigation was carried out to determine the sensitivity of the results to other IV specifications, the results from these models were more volatile and not as plausible as those from the basic SUR model, which was therefore relied on for the final estimation. Our specification of the arguments of the r vector also warrants additional comment. Including ES as a determinant of the cost structure in addition to the standard time trend t initially seemed important for explaining cost and input demand patterns; the ES parameters, interpreted as the impact of technical change embodied in the capital stock, tended to be significant and plausible. When t2 was also included to capture the potential impact of structural changes in the 1980s, the t2 parameters became statistically significant but the ES parameters tended to be less definitive. Both variables thus seem to capture changes in the 1980s – perhaps toward greater capital- or high-tech- intensity of production. Since the ES parameters remained jointly statistically significant, however, they were retained in the final specification. The parameters estimated from the cost-based model specification TC are presented in Appendix Table 1. The dummy terms are not included in the table since there are too many to be illuminating, but they are primarily statistically significant.
The overall explanatory power of the model is indicated by the high R2 ’s for the estimating equations, including the TC equation which was not estimated but was fitted to determine the implied R2 . Also, many parameter estimates that are not individually statistically significant are jointly significant, such as the ES parameters mentioned above.These estimates were used to construct the cost, input demand, and output supply elasticity and contribution estimates from the decompositions outlined in the modeling section. The measures were averaged across the whole sample, and separately for 1972-1982 and 1982- 1992, and by 3-digit industry, to distinguish temporal and industrial patterns. The elasticity estimates were constructed by computing the indicators for each data point and then averaging across the sample under consideration. Statistical significance of these measures was imputed by constructing elasticity estimates instead over the averaged data; values significantly different from zero at the 5% level are indicated by an asterisk. In most cases the significance implications were not data-dependent, although for some estimates the data point at which the measure was evaluated contributed to evidence of significance. To begin our investigation of agricultural materials use in U.S. food processing industries, we first assess MA demand implications from the decomposition presented in the first panel of Table 1 for the full sample . Recall that such a decomposition weighs the estimated elasticities by the observed changes in the arguments of the function to determine their contribution to observed changes in the dependent variable .First consider the elasticities. The largest MA demand elasticity as well as contribution is from its own price. The own elasticity of eMA,pMA = –1.138 for U.S. food processing industries implies MA demand is fairly elastic; pMA increases have motivated a movement up the demand curve to a lower MA demand level that more than compensated for the price change in proportional terms. Based on observed pMA price changes, this provided a negative contribution of CMA,pMA = -0.062% to the overall observed increase in MA use of 0.038 ; other factors outweighed the negative own-demand effect.By contrast, if the indirect implications from the deviation between the effective and observed input prices are taken into account this effect appears quite a bit smaller; p*MA changed by only 0.036% as compared to the pMA change of 0.055%,21 so the total contribution weighted by this price change would be C*MA,pMA = -0.041. The lesser apparent growth in p*MA than pMA could derive from various factors – including augmented quality that is not captured in the measured values – but is inconsistent with increases in market power.That is, l MA appears to capture some form of technical change or productivity embodied in MA, that represents the impact of technical innovation in agricultural markets transferred to the next level of the food chain – food processing.This effect will be evaluated more explicitly below in the context of the indirect components of the t impact within the CMA,t decomposition. All other inputs are substitutable with MA, as is apparent from their positive price elasticities, and the observed increases in these input prices over the sample period thus imply positive shift effects on MA demand that in sum seem to more than compensate for the own price effect. In particular, MA seems somewhat substitutable with both MF and MO, but the contributions of pMF and pMO changes to observed MA demand adaptations are not substantial since the price changes have not been large; CMA,pMF=0.0035 and CMA,pMO=0.016. Rising relative prices of labor and energy – which have been experienced in these industries for most of the recent past – have also had positive effects on MA use, although their contributions are limited by smaller substitution elasticities; CMA,pL=0.012 and CMA,pE=0.004. The statistically insignificant elasticities for pL and pMF suggest that MA-MF substitution is driven more by demand than price impacts. The contribution of pK increases to MA demand is much greater than the price effects associated with other inputs, especially if adjustments in effective pK, p*K, are recognized.