The data also show some evidence that average costs fall with increases in output in joint wheat and maize institutes. The average cost per wheat variety is consistently lower in joint institutes than in wheat-only institutes. Similarly, the average cost per maize variety is consistently lower in joint institutes compared with maize-only institutes. For wheat , the cost per variety falls from 187,000 yuan in wheat-only institutes to 145,600 yuan in joint wheat and maize institutes. The same patterns also appear in data when the area-weighted output measure rather than number of varieties is used. Moreover, the evidence of economies of scope becomes stronger as the scale of research effort increases. Hence, our descriptive data provide evidence that economies of scope may be a source of efficiency differences among institutes. The evidence of economies of scope suggests a potential cost saving associated with combining a wheat-only institute and a maize-only institute into a bigger, joint, wheat and maize institute. Further analysis of the data also points to other factors that potentially could affect costs,plastic pots for planting although in some cases the descriptive statistics do not show a particularly strong correlation. The relatively low education level of China’s agricultural researchers has long been claimed to be one of the key factors limiting agricultural research productivity . Based on our data, the human capital in China’s wheat and maize breeding institutes is low compared with other countries . Our data also show that increases in the educational level of breeders help to reduce the cost of variety production. The institutes that have the highest average cost of variety production also tend to have the lowest proportion of breeders with post-secondary education .
Byerlee and Traxler suggest that efficiency in crop breeding increases when agricultural scientists from other disciplines work in conjunction with breeders. Although the share of scientists working on other agricultural disciplines in wheat and maize breeding institutes is quite high , compared to 30 percent in an average wheat improvement research program in a developing country , there is little difference in this share between institutes with low and high average costs. Finally, it is also unclear from visual inspection of the data in Table 3 whether breeding efficiency is affected by the source of a breeding institute’s genetic materials or the presence of retirees. In this section, we specify the econometric model to be used to study the efficiency of China’s crop breeding institutes, and discuss our strategy for estimating the model. We begin by specifying the relationship between costs and the factors that affect them in institutes that produce either one or two types of varieties . We also define measures for economies of scale, ray economies of scale, and economies of scope. Here we treat a breeding institute as a typical “firm” which applies inputs to produce research output . The total variable cost of an individual institute is expressed as a function of its research output, the price of its inputs and other institutional characteristics affecting the cost structure of crop breeding research.10 A wide range of different types of cost functions have been applied in the literature.We estimate economies of scale and scope in two ways: from a base model, where we estimate the relationship between cost and output taking account of the effects of annual salaries , time, province and institute type without the Z variables; and from a full model, which also includes the four covariates . In the final section we discuss the implications for economic efficiency of crop breeding that can be drawn from the estimated relationship between cost and output after controlling for other variables . We do so for both equation , the single-output cost function, and equation , the multiple-output cost function. Hence in our analysis we have four fundamental units of analyses: the base model for the single-output cost function ; the full model for the single-output cost function , and the base and full models for the multiple-output cost function.
We estimate the base cost function model with ordinary least squares to get initial estimates of economies of scale and scope. However, the OLS estimates of the parameters may be underestimated if there is measurement error in the construction of the output variable . One source of measurement error arises from the special nature of crop breeding and the decision making of its directors. The implicit behavioral assumption that underlies the cost function is that the research manager minimizes costs given the output of the institute. Such an assumption, even for a quasi-productive entity like a research institute, often has been made in cost analyses . While it is not difficult to imagine that the typical research manager in a breeding station strives to minimize the institute’s costs of given output, one characteristic that makes the plant breeding industry special is the long time lag between expenditure and the realization of the output. We are assuming that research managers make their cost-minimizing expenditure decisions based on the expected output of the breeding station. But the econometrician does not observe expected output; only actual output is measured. We measure actual output from a crop-breeding institute as the number of new varieties from that research institute adopted by farmers in the five-year period, 6-10 years after the research expenditure. This measure might vary systematically from the output that the manager was anticipating when expenditure decisions were made. One solution to measurement error is the use of instrumental variables . In order to account for the measurement error, we identify a set of instrumental variables and reestimate our model using three-stage iterative least squares. Since the relationship between output and cost basically depends on factors associated with supply-side decisions of the research institute, we turn to a series of demand-side factors in our search for exogenous IVs: farm-gate prices of wheat and maize, the prices of fertilizer and pesticides in input markets, the land-labor ratio in a region, the share of irrigated land to total cultivated land, and the multiple cropping index. We are also concerned with several other assumptions. In order to test for the effect of our assumption about the length of the lag between costs and research output , we conducted sensitivity analysis using data generated by an array of different lag structures. Further, the presence of unobserved heterogeneity may bias the estimates of our parameters of interest.
To eliminate the unwanted covariance between the unobserved factors and the other regressors we took advantage of the panel nature of the data, using both fixed- and random-effect methods. Finally, it is also possible that the cost minimization assumptions that underlie cost function analyses may not all be valid. As noted above,plant pot drainage these assumptions are avoided— albeit, at the expense of some other disadvantages—when we use a production function approach rather than a cost function approach. As a check on this aspect, we also estimated a Cobb-Douglas production function model, and found that the main findings regarding returns to scale are quite similar between the two approaches . The base model produced remarkably robust estimates of many of the parameters . The quadratic specification fits the data well with R2 estimates ranging from 0.53 to 0.75 for wheat and 0.52 to 0.72 for maize . The goodness of fit measures, however, systematically demonstrate that, for both wheat and maize, the models that use the area-weighted and area-yield weighted outputs have a significantly better fit. In all of the models the effect of an increase in wages on costs is positive and significant, in keeping with expectations and theory. All of the variables were normalized by dividing at their sample mean such that we can interpret the regression coefficients as elasticities at the mean. Economies of Scale After controlling for wages, region and year effects, and the institute type, the measures of economies of scale calculated from the estimated parameters are all much less than one and significantly so . The estimates of SCE for wheat institutes range from 0.22 to 0.26; those for maize institutes range from 0.14 to 0.32. The results imply that at the mean levels of research output and other explanatory variables, strong economies of scale exist for both wheat and maize institutes. If output increases by 10 percent, costs would increase no more than 3.2 percent. Evidence of such strong economies of scale from the multivariate analysis is consistent with the descriptive evidence and reflects the patterns in Figure 1. The elasticities of cost with respect to output are relatively small compared with those found in studies of non-profit institutions . The strong economies of scale are largely unchanged when we control for other institutional factors. Comparing results in Tables 4 and 5, after controlling for the four Z factors and their interactions with output, the SCE elasticities still fall in a similar range . Although the coefficients on variables representing several of the institutional factors are significant and suggest that there are other ways to affect breeding efficiency , the remarkably low and highly significant measures of SCE indicate that significant cost savings could be attained if the scale of China’s breeding institutions were expanded. Accounting for a number of the potential econometric problems does not significantly alter the magnitude or significance of the measures of economies of scale, as can be seen in Table 6.
To address concerns of measurement error, exclusion restriction tests of the validity of our demand-side instrumental variables show that they meet the statistical criteria required for identification. Using these instrumental variables and the 3SLS estimator does not substantively change the estimates of the economies of scale parameters. The economies of scale parameters range from 0.12 to 0.26. The results hold for both wheat and maize in both the base model and the full model. Allowing for lags of different lengths, or controlling for the unobserved heterogeneity also does not materially affect the estimates of economies of scale.11 Similar to the results generated by the parameter estimates of the single-output cost function, results based on the multiple output cost function also imply high and statistically significant estimates of ray economies of scale. The estimates of SOEray, which range from 0.33 to 0.39, mean that if wheat and maize institutes double their output of both wheat and maize varieties, the total variable cost of wheat and maize breeding would increase by only 33 to 39 percent. The strong ray economies of scale are also not affected by alternative estimation strategies or model specifications. While not as strong or as robust as the evidence of economies of scale, our multioutput cost function models show the existence of economies of scope between wheat and maize variety production, as summarized in Table 7. The estimates of SOE based on the parameter estimates of the base model indicate that there would be cost saving of about 10 percent if a wheat-only and maize-only breeding institute were combined into a joint wheat-maize institute. Bootstrapped confidence intervals show that the measured elasticities are statistically significantly different from zero. Unlike economies of scale, however, economies of scope are affected when other institutional factors are added. For example, if we control for the educational level of breeders, the cost savings from merging wheat and maize institutes drops from 10 to 5 percent, and it drops to only 3.8 percent when both human capital and spill-in variables are added to the model. In addition to the cost efficiency associated with the scale and scope of wheat and maize variety production, the statistical analysis supports the early descriptive findings and shows that economic efficiency is also affected by other institutional variables, as can be seen in Table 5. For example, except for one case, the coefficients on the interaction between breeder’s education and output are negative and significant. The magnitudes of the coefficients show that if research managers can increase the share of breeders with college and more education by 10 percent , the marginal cost will fall by around 1.0 percent. An increase in the proportion of genetic material used in breeding that comes from outside the province also increases efficiency .