13th Annual International Management Conference Proceeding

A production function portrays an important input-output relationship. It describes the rate at which
resources are transformed into products (Doll and Orazem, 1984). Cobb-Douglas production function has
been the most common production function in use.
It provides the following benefits (1) adequate fit if data, though sometimes it may fail hence the need to
perfume model selection tests before endorsing the use of the model (2) computational feasibility and (3)
sufficient degrees of freedom are used to allow for statistical testing. Due to these numerous advantages of
the Cobb- Douglas type of production function, it has been widely used in agricultural studies and in this
study.
The major shortcomings have been identified as, mis-specification, input measurements and multicollinearity.
These have led to unreliable biased results in most cases and have necessitated precautionary
measures for reliable results to be achieved.
Multicollinearity and the Cobb-Douglas production function
The Cobb-Douglas production function estimated by least squares method has been widely applied in
agriculture, but estimates based on cross sectional samples of farms, most typical elasticities of labour and
land are negative. These negative coefficients have been attributed to the existence of multicollinearity in
random sample or non-stratified farm samples where farms with large labour inputs are also those with larger
inputs of land and various forms of capital (Roy et al. 1975). In addition, reporting or measuring bias and
other inadequacies of labour have been similarly attributed to the cause of multicollinearity. Doll (1974)
confirms that modern theory suggests that multicollinearity may lead to problems of structural estimation
and specification errors.
Many studies have proposed ways of minimizing the effect of multicollnearity. Heady (1968) cited many
ways like combining variables in the same units, developing an index of sets of related variables through use
of principle component analysis and inserting the index into the regression as a proxy for the original
variable. However, Doll (1974), noted that if inputs are not perfectly correlated no aggregation is needed.
Similarly, many others have proposed aggregation as one of the ways of overcoming multicollinearity within
variables. Unfortunately, there has not been any standard way of aggregating inputs and consequently Earl
(1961) realized that a high degree of aggregation may imply that the resultant function may be of little
relevance in decision-making. Though aggregation serves the purpose, the categorization should depend on
the investigator’s assessment of the strategic inputs in the production process. Faced with these constraints, it
is important to dwell on the procedures for input use and measurement while applying the Cobb-Douglas
type production function.
To be able to counteract the problem of muliti-collinearity in this study a procedure of aggregating inputs,
which have the same measurement unit, was adopted. For instance all tools and equipment were grouped into
one variable. Family and hired were assumed to be homogenous and so were represented by a proxy for total
labour measured in person-days. During data analysis a test for collineraity among all the independent
variables was done and variables were found to have very weak relationships.
Input use and measurement
Labour use measurement
Many methods of estimating the cost of labour have been put forward. Krause (1982) gave an alternative of
adding up family and hired labour then multiply by the average area wage rate and length of time required
for all operations. Considering that hired labour becomes a purchased input the wage rate represents the unit
cost as stated by Martin (1973). Mahmood et al. (1979) suggested that the wage rate for family labour
obviously must be an imputed rate, and the imputation used was that chosen by the respondents. Therefore,
this study considered average area wage rate as the labour cost per person-day.
Land use measurement
Heady et al. (1969) notes that the major difficulties in measuring land are so inflexible not like in measuring
labour and capital. For example, differences in land quality are likely to be indicated by the market value. In
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