The Cholesky values of the constrained model are equal to indicating that the extended Slutsky matrix S of equation is negative semi-definite and satisfies the rank condition of theorem 1. Hence, the PITP hypothesis is not rejected also in version 2 of the model. We notice that, in this case, the value of the log-likelihood function obtained using the GAMS program is higher than the one computed by SHAZAM. Again, this event may be due to the highly non-convex and nonlinear model and to the different algorithms used by the two programming packages. With the results of Table 3, the input biases were measured using equation . The results are reported in figure 7. The machinery biases indicate a factor-using TP prior to 1935 and then a constant level of factor-saving TP for the rest of the sample period. The labor biases exhibit a factor-using TP that decreases until WWII and then increases steadily for the rest of the sample period. The fertilizer biases show a factor-saving TP for the entire period. The land biases are factor-saving prior to world war II and the hover around a zero bias for the rest of the period. The different trends of input biases in the two sets of diagrams reveal the heavy dependence of these measures upon the estimated coefficients. Both patterns, however, are consistent with our PITP theory.A final aspect of the empirical results associated with version 2 of the PITP model deals with the pattern of substitution and PITP components of the input quantities obtained from the application of the extended Shephard lemma as reported in Figure 8. The machinery decomposition is similar to that one of Figure 6. The labor PITP component in Figure 8 is flatter than in Figure 6 but has a similarly rising end portion. The fertilizer PITP component of Figure 8 exhibits a much smaller size than its counterpart in Figure 6.

A radical difference lies with the PITP components in the land input of the two Figures. In Figure 8,large plastic pots the PITP component of the land input remains insignificant until the world war II years and then rises steadily until the year1980. The substitution component has a mirror pattern. Intuitively, the pattern of the land input in Figure 8 is more plausible than the one in Figure 6.There remain to comment upon the distributed lag relationships that explain the PITP components of the various inputs. We recall that the estimation of the version 2 model was carried out according to problem – with the distributed lag pattern for the various explanatory variables as indicated in Table 2. The four equations and their distributed lag pattern expressed a rather high level of fit with R-square measures of 0.90, 0.83, 0.95 and 0.98, respectively. It is apparent, however, that several alternative combinations of lags can achieve high levels of fit. In Table 4, therefore, we report a more refined exploration of fit that reveals a different pattern of distributed lags. Now, all the four relationships exhibit a high measure of fit, as indicated by the R-square, while maintaining a parsimonious specification . We note that in Table 4 the labor equation now contains significant lags of the extension and public R&D explanatory variables. The extension expenditures and the public R&D variables enter every equation. The private R&D expenditure enters only the fertilizer equation. It is difficult to attach any intuitive meaning to the individual coefficients and we refrain from it.We recall that this third version of the model was performed with the objective of evaluating the robustness of the input biases to a variation in the lag distribution. The input biases corresponding to the empirical results of Table 5 are presented in Figure 9. The pattern of the labor and land diagrams is substantially similar to the pattern presented in Figure 7. The land input is clearly characterized by a factor-saving TP throughout the sample period. Labor remains a factor-using input. This counter intuitive result is mitigated by our previous discussion about the difficulty of assigning a clear meaning of input-using .

The machinery and fertilizer input diagrams of Figure 9 exhibit trends which are opposite to those in Figure 7. Now, the machinery bias is factor-saving until WWII, becomes factor-using until 1980, and then returns to be factor-saving. The fertilizer bias is factor-using until WWII and then hovers around a zero bias for the rest of the sample period. These empirical explorations suggest that the biases of TP are very sensitive to the model specification and the values of the estimated parameters. This conclusion reduces the importance of the notion of input bias in evaluating technical progress, since all the patterns of biases exhibited in Figures 4, 7 and 9 are admissible under our PITP theory. Without a formal test of a null-hypothesis pattern of input bias, it is exceedingly difficult to make sense of any pattern, merely on the basis of “intuition.”The input decomposition for version 3 of the model is given in Figure 10. Although the pattern of decomposition is roughly similar to the pattern depicted in Figure 8, we must point to the quantitative aspect of machinery and land decomposition. The PITP machinery component acquires a substantial magnitude after World War II in both pictures, but its level is halved in Figure 10. The PITP land component in Figure 10 exhibits a trend that exhausts the entire amount of input by the end of the sample period. The land input, with its low variability, may admit many alternative patterns of decomposition.The essential points of the paper can be listed as follows: A) a novel theory of technical progress, complete of its comparative statics conditions, that re-interprets the relative price hypothesis of Hicks; B) within this theory, an extended Shephard lemma that provides a natural decomposition of the input quantities between a purely substitution component and a complementary amount attributable to the price-induced conjecture; C) an empirical application of the theory that requires a primal-dual approach to the corresponding econometric specification because of the necessity to estimate both the production function and the cost function jointly. The data dealt with in this paper involve a sample of 81 years of US agriculture with one aggregate output and four inputs, machinery, labor, fertilizer and land. Furthermore, private and public R&D series and extension expenditures were available.

The sample data analyzed in this paper constitute an unusual amount of information with prices and quantities for every commodity. We attempted to utilize all the available information because this condition is a fundamental requirement toward achieving efficient estimates. Three versions of the general model were formulated using a translog specification for both the production and its associated cost function. The first version dealt exclusively with expected relative prices and the results indicated that the conjecture of price-induced technical progress could not be rejected based upon a test of the comparative statics conditions that characterize our PITP theory. The analysis of the input biases associated with this version shows that three of the four inputs have minimal biases at the end of the sample period. Only the labor input exhibits a significant level of bias at that point. This version of the PITP model allowed a preliminary analysis of the conjecture that a distributed lag of relative prices, R&D and extension expenditure could explain the portion of inputs attributable to technical progress in the extended Shephard decomposition. A second version of the model incorporated lagged R&D private and public expenditures as well as lagged extension expenditures. The lags were suggested by the regression analysis of Table 2 and produced estimates of the PITP model that cannot reject the price-induced hypothesis of expected relative prices entering the production function. The pattern of input biases of version 2 differs from that of version 1 in ways that are both satisfying and against intuition. In either case, however, those patterns do not contradict the necessary and sufficient conditions of our theory. A third version of the model incorporated the lag structure presented in Table 4 and was carried out mainly to assess the robustness of the input biases to a variation of the lag distribution. With a truly dynamic theory of TP, this ad-hoc sensitivity analysis can be avoided. The translog functional form may have a determinant role in the shape of the input biases, but the evaluation of this conjecture is left for another occasion. Two aspects of this paper should be kept distinct: the PITP theory and its empirical implementation. The theory generalizes many traditional specifications of models dealing with technical progress and provides its own specific comparative statics conditions. The particular implementation of the PITP theory that was executed in this paper is certainly imperfect. Yet, the empirical results have given more than a glimpse of the ability of the primal-dual approach to interpret the available information.

There are many ways to examine the benefits as- sociated with agricultural production and to measure the impact of agriculture on the economy. Traditionally,raspberry container the agriculture sector was considered to include only eco- nomic production and employment associated with crops, livestock, forestry, fishing, hunting, trapping, and support activities for each of these outputs. Today, many econo- mists take a broader approach and include food processing and marketing as part of the agriculture sector, and some even go as far as to consider restaurants as part of the this sector. To identify the impact of the agriculture sector on California’s economy, one can measure agricultural rev- enue generated and jobs created. The gross value of Cal- ifornia’s agricultural production of $38.3 billion in 2006 makes the state the agriculture leader for the U.S. and a top producer in the world . The gross value of production includes all farm production, whether sold or used on the farm where it was produced. In addition to generating revenue, agricultural employment in 2002 was more than 2.7 million in California. Rural agricultural employment was greater than urban agricultural employment as a percentage of total employment . California produces a large variety of crops, but the gross value of farm production is heavily concentrated in 20 top agricultural commodities. These 20 commodities accounted for more than 80% of the state’s gross value of farm production in 2006. Eight of these commodities grossed over $1 billion in revenue, including milk and cream , grapes , nursery and greenhouse products , cattle and calves , almonds , lettuce , strawberries , oranges and hay . The state ranks first in the nation for the production of dozens of crops such as avocados, grapes, and processing tomatoes and is the sole producer of many of the nation’s crops, such as almonds, artichokes, figs, olives, and walnuts . In 2002, more than 27 million acres were used for farmland . Regionally, farmland uses vary across the eight California agriculture statistics districts that include North Coast, North Mountain, Northeast Mountain, Central Mountain, Sacramento Valley, San Joaquin Valley, Sierra Nevada, and Southern California districts. For example, the San Joaquin Valley district produces the majority of the state’s production of agriculture and grows much of the state’s fruit, nut, and vegetable products, whereas the North Coast district produces a lower dollar amount of agricultural products and specializes in cattle and calves, milk products, and some fruit tree products . For example, Fresno County alone produces 12.5% of the state’s total agricultural output. Many counties, such as Mono or Mariposa, produce less than 1% of the state’s output . Agriculture has always been negatively impacted by pests whose feeding and/or other damage can lead to a loss of agricultural output or reduction in output relative to potential output . Pests in California agriculture are diverse and include vertebrates, such as coyotes, rodents, birds, and feral hogs; invertebrates, such as the glassy-winged sharpshooter, avocado thrip and the Mediterranean fruit fly; plants, fungi, and other pathogens. It has been estimated vertebrate pests alone cause $944 million in damage to U.S. agriculture annually . The agriculture sector is fundamental to regional economies because it not only contributes substantially to the general economy and employment of the region, but it is additionally linked to almost all other sectors in the economy as a source of inputs.