Graduate Thesis Or Dissertation
 

Separability tests on wheat production functions in Oregon

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  • Many natural resources such as water and forests have become more intensively used in recent years. Often, this has made it necessary to reallocate these resources from less to more efficient productive usage. The knowledge of the existing tradeoffs between alternative uses are necessary to make reallocative decisions. However, these resources also have strong public property character and are not usually amendable to demand analysis to determine willingness to pay. When the "price" is institutionally set, the productivity measurement often must be based on direct production function estimation. For sectoral reallocation of resources, some aggregate productivity measures are required. Such measurements are feasible when aggregate production functions are estimated. The aggregate production functions are however beset with a host of difficulties arising from their aggregate nature. The resulting aggregation bias must be eliminated if any aggregate productivity measure is to be the basis of policy recommendation. The improvement of the results of aggregate productivity analysis hinges on the methods which reduce aggregation bias. There are two major conditions under which the aggregation bias is minimized or eliminated altogether. These conditions are a) relative prices are fixed amongst factors that are aggregated and/or b) the aggregated factors are weakly separable from others in an economic sense. The first condition relates to Hicks' Aggregation Theorem and the second to Leontief Separability. The latter condition appears to be directly relevant from the practical standpoint, since relative prices are seldom fixed amongst all aggregated factors. Thus the existence of valid aggregate input indices in an aggregate production scheme can be assured only when there exists separability between these inputs in each aggregate input indices. The present study attempts to test for separability amongst inputs going into wheat production using county level Oregon Census of Agriculture data. There is strong empirical evidence of weak separability amongst the biological process inputs such as fertilizer and the husbandry process inputs such as capital and irrigation service. And furthermore, a weather variable, rain, is found to be separable from both biological and husbandry process inputs. The tests were conducted utilizing the TRANSLOG type second order Taylor approximation to a general functional form. The separabilities imply various linear and nonlinear restrictions on the estimated coefficients of the translog function; and these restrictions were tested in conjunction with the usual F-distributed statistics of linear and non-linear restrictions on quadratic expressions. The results from linear restrictions were however ambiguous between inseparabilities among fertilizer and irrigation and among capital and irrigation. Similarly, for nonlinear restrictions, ambigueity resulted between inseparability amongst capital and fertilizer and capital and irrigation. However, in both cases inseparability amongst capital and irrigation does marginally better in terms of the sum of the squared error terms. A logarithmic cubic approximation function was used to test for Sadan's perfect process complimentarity between biological and husbandry processes. This test using quadratic approximation models was rejected. However, the strongest evidence from the cubic approximation model was that the model with inseparability amongst capital and irrigation is the only one consistent with Sadan type high process complimentarity. Thus the implication is that, at the micro-level biological and husbandry process functions are valid because of Sadan's perfect process complimentarity, and,at the macro-level, wheat production function can be defined for aggregate inputs of capital and irrigation service, and fertilizer, precipitation, etc. In conclusion, the results appear to be supportive of the lay notion that wheat production consists of biological and the husbandry processes which are highly complementary to each other.
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