# Methods of estimating productive efficiency for the enhancement of plan decision making.

I. ApproachIn elaborating current sectoral plans, workers in the administrative apparatus detail planning tasks, the distribution of material, labor, and financial resources, the formulation of production programs, and the fixing of norms and standards. The quality of these decisions depends on the experience of the planners, the volume of useful information, and its reliability. Administrative workers who rely on traditional technologies are able to utilize a relatively limited amount of information. Due to time constraints on the acquisition of supplementary information, processing is properly restricted to those calculations that are most critical for decision making. Under these circumstances, it is not always possible to reach the desired level of economic efficiency and accuracy.

The transition from traditional to man-machine planning technologies [Suvorov, 1987] permits the administrative apparatus to utilize more information in plan decision making. The use of this supplementary information in a standardized form facilities the estimation of productive efficiency and potential, which provide a useful basis for sound plan decision making.

Estimates of comparative sectoral efficiency are often used in elaborating current plans. For example, consider two types of plan decisions. First, the determination of the proportions in which productive tasks and resources are distributed to various enterprises within sectors. Second, the planning of the intensity with which diverse technologies are employed in enterprises.

Estimates of technical productive efficiency which in accordance with Danilin, et al., [1987] are understood here as measures of joint factor productivity determining the volume of output, can be used as a basis for making these decisions.

Comparative estimates of technical enterprise efficiency can be used as a basis for decisions of the first type. Decisions of the second type involve the estimation of the efficiency of various technological processes in enterprises. Consideration, therefore, must be given both to diverse methods of estimating technical productive efficiency at the sectoral and enterprise levels which can be utilized in man-machine procedures of sectoral planning.

Production functions provide the broadest approach to estimating technical productive efficiency. This approach can be applied in practice at the sectoral level in two primary ways. First, production functions can be used to estimate the efficiency of individual enterprises. Second, it can formally describe the technological potential of entire productive entities, which take account of the scale of production and the degree of homogeneity. The approach under consideration can be used to measure the technical efficiency of production of individual goods in multiproduct firms. The aggregate technical potential of the firms can also be estimated, together with the estimation of the relative productive efficiency of each product. The methodology in question thus allows one to estimate the level of productive efficiency by sector, enterprise, and product.

The classical definition of the production function with parameters [Theta]O portrays F(X,[Theta]) as an upper technologically determined output frontier, given assigned resources X. It encompasses a set of n enterprises, producing homogeneous goods, each of which is characterized by a vector of resource costs [X.sub.i],i=1,...,n and an output value [Y.sub.i]. If the general form of the production function is specified, then the task of constructing it under classical conditions amounts to discovering those values [[Theta].sub.*] of the parameters that yield

[Mathematical Expression Omitted]

given the constraints

[Mathematical Expression Omitted]

Productive efficiency in this case is the magnitude

[Mathematical Expression Omitted]

the deviation of the actual output level from the one indicated by the frontier technology F(X,[[Theta].sub.*]). It should be noted with regard to the constraints in equation (1) that only derivations below the frontier, that is positive magnitudes [[Theta].sub.i], are possible.

This deterministic approach is rarely used in practice. The parameters [[Theta].sup.*] of the production function are affected by random errors, connected with changes in the magnitudes {[X.sub.i],[Y.sub.i]}, and are affected similarly by random influences indirectly connected with production technology.

The stochastic approach to constructing a production function provides a good alternative. It describes the average aggregate technological potential of the enterprise. Least squares estimating techniques are usually applied in this framework. The vector of parameters [[Theta].sup.*] is chosen to achieve

[Mathematical Expression Omitted]

It is well known that the random variable [Epsilon],

[Mathematical Expression Omitted]

is a measure of productive efficiency that is normally distributed with a mathematically expected value of zero.

The stochastic approach to estimating a production function permits one to derive values for the parameters [[Theta].sup.*], using data from individual enterprises. However, this constitutes a departure from the traditional characterization of the production function as an entity that reflects progressive technology. In reality, deviations in output above the production function are just as probable as deviations below. Therefore, the production function in specific cases actually reflects average production possibilities.

It is well known that the stochastic frontier production function, which was first developed in Aigner et al.,[1977], combines the traditional concept of the production function and the stochastic approach to the appraisal of production possibilities.

The production potential of an enterprise, characterized by a production process that is assumed to be non-uniformly stochastic in the sense that exogenous disturbances affect individual differently, can be defined as the stochastic production frontier [F(X.sub.i],[theta])e.sup.vi. Here Here, i is the enterprise index; [F(X.sub.i,[theta)] the production potential which is determined by resource costs; and [sub. [v.sub.i the portion of production potential, conditioned by random events and errors of measurement. The stochastic frontier production function, it is assumed, reflects the technologically maximal level of output.

Enterprise output may not attain the stochastic frontier (inefficient production) or may coincide with it (efficient production). The disparity between the achieved physical level of production and the technological maximum is modelled with the aid of a one-sided probability distribution. To identify productive efficiency, a random variable [u.sub.i] is introduced to measure deviations below the stochastic frontier. The actual volume of output of enterprise i can be expressed as:

[Mathematical Expression Omitted]

where [epsilon].sub.i] = [v.sub.i] - [u.sub.i],[u.sub.i] [is greater than is equal to 0].

This approach permits one to take a new, qualitatively important step forward

in assessing productive efficiency. It makes it possible to distinguish random events, not directly connected with the productive process, and to identify the level of productive efficiency. In this way, the scholas production frontier [F(X.sub.i,][theta)] [epsilon]v.sup.i] truely determines progressive, technological possibilities.

With respect to measuring productive efficiency, the coefficient [mu] should be considered. It expresses the relationships between the actual volume of output and the output volume established by the stochastic production frontier:

[Mathematical Expression Omitted]

From equation (2), we have [mu].sub.i] = [epsilon].sup.-ui].

For every i, i = 1,. . .,n, from the condition 0 [is greater than or equal to] [u.sub.i] lesser than [infinity] it follows that 0 [is greater than] [mu].sub.i] [is greater than or equal to]1.

The appraisal of enterprise efficiency may be made with the assistance of various assumptions about the distribution of the random variables [v.sub.i] and [u.sub.i]. The most natural is the assumption of normally distributed variables:

The random variable [v.sub.i] is normally distributed with parameters (0,[sigma].sup.2.sub.v)]; the random variable [u.sub.i] is truncated at 0, and normally distributed with parameters ([mu],[sigma].sup.2.sub.u]); and the random variables [v.sub.i],[u.sub.i] are independent, i = 1,...,n.

If for every entity, the volume of output [Y.sub.i] depends on the quantity of utilized inputs [X.sub.i], the production function can be written:

[Mathematical Expression Omitted]

The task of determining the stochastic production frontier and the degree of its efficiency requires the identification of a vector of parameters [Theta] of the production function and parameters [sigma.]sup.2.sub.u] and [sigma].sup.2.sub.v],[mu] of random variables. For the purpose of establishing an identification criterion, consider the maximum likelihood function L. The vector of parameter estimates [beta].sup.*] = [[Theta.]sup.*], [sigma].sup.2.sub.u], [sigma].sup.2.sub.v,] [mu]] is determined by maximizing the logarithmic likelihood function

[Mathematical Expression Omitted]

given the restrictions in equation (3), where

[Mathematical Expression Omitted]

and G is a distribution function of standardized normally distributed random variables.

To discover the maximum values, a vector of parameters [beta.sup.*] must be found such that

[Mathematical Expression Omitted]

The method of maximum likelihood is the most advantageous because it allows the statistical significance of each estimate [beta] to be determined asymptotically by the covariance matrix

[Mathematical Expression Omitted]

The value [S.sub.1], determined by the formula [S.sub.i] [square root][B.sub.ii], is the standard error of the estimated parameter, and [t.sub.1] = [beta].sub.i]/[S.sub.i], are the t statistics.

It is advisable to estimate technological potential with the function

[Mathematical Expression Omitted]

the most general form of the class of two-factor production functions that exhibit constant elasticity of substitution and nonhomotheticity. Here, K is the average annual fixed capital stock; L is the number of productive industrial personnel; [Theta] = ([c.sub.1], [c.sub.2],[gamma].sub.1] [gamma].sub.2,][rho]) is a vector of parameters. The well-known CES and Cobb-Douglas production functions are special cases of this function.

To carry out the designated task, a program was developed for the EVM series ES [Afanas "ev and Skokov, 1984]. The designated task requires a nonlinear program, which has n + 8 variables and nonlinear constraints. Using a separable functional form for the constraints in equation (3), with respect to magnitudes of the deviations [epsilon].sub.i] = [v.sub.i] -[u.sub.i], the task was reduced to unconditionally maximizing the objective function with respect to the parameter vector [beta]. In each iteration of the calculation of the function and its gradient, [epsilon].sub.i] was computed from equation (4) using the Newtonian method for homogeneous nonlinear equations. The task of maximizing the function 1nL for the parameters [beta] was solved with the program package PAOEM [Skokov, et al., 1980]. The program provides an effective method for estimating the reduced gradient, using a combination of the quasi-Newtonian method and the conditional gradient.

With the assistance of the [beta] parameters, the general stochastic deviations [epsilon].sub.i] can be determined without their division into indicators of efficiency and the impact of exogenous disturbances for each enterprise and division. The values of [v.sub.i] and [u.sub.i] can be estimated in the second stage of the identification procedure.

If the density of the distribution [P.sub.u][(center dot)] and [P.sub.[epsilon] ([center dot]) are known, the average values of of [u.sub.i] can be estimated as the mathematically expected values E(u.sub.i/v.sub.i - u.sub.i)]. The estimates [v.sub.i,u.sub.i] can be determined as the maximum probability of their joint distributions that generate the maximum liklihood estimates. In Materov [1981], it is shown that the most probable values [v.sub.i] and [u.sub.i] are are attained, if they satisfy the condition:

[Mathematical Expression Omitted]

given the restrictions

[Mathematical Expression Omitted]

The analytic solution to this task has the form,

[Mathematical Expression Omitted]

The following section examines practical applications of this technique more thoroughly.

II. An Appraisal of the Technical Efficiency of An Enterprise

Information on output volumes and primary factor costs is required in order to carry out real calculations. In accordance with production theory, data on fixed capital formation and labor costs should be used to measure primary productive factors. In sectors and enterprises which produce comparable products, output ought to be considered in natural terms. This will prevent the inclusion of differential price effects in the model. In sectors where prices are the common denominator for compiling enterprise products, output ought to be measured in value terms. Prices in this case must be considered as additional factors at an analytical level.

The volume of primary productive factors is expressed in value terms. Labor costs can be evaluated in norm-hours, spent on the production of output.

Source data for the calculations are arrayed in three vectors.

[Mathematical Expression Omitted]

Here, n is the number of enterprises considered in each; [Y.sub.i] is the volume of output of each enterprise i (in natural or value terms); [K.sub.i] is the volume of fixed capital in value terms; and [L.sub.i] is labor costs.

Each enterprise characterized by the data is measured in one and only one time period, typically a year. The source data entered are processed sequentially [Mathematical Expression Omitted]

For convenience in the computational process, normalized values of [Y.sub.i],[K.sub.i], and [L.sub.i] are utilized. The normalization is automatically carried out for enterprise data by indexation i=n after the information is inputed into the EVM. after the normalization, calculations are performed with the magnitudes

[Mathematical Expression Omitted]

moreover,

[Mathematical Expression Omitted]

The convenience of normalization lies in the fact that the sum of estimated parameters [c.sub.c1] and [c. sub.2] of the production function, which corresponds with the maximum of the likelihood function in this case, approximates unity. The meaning of the other parameters is not altered by normalization.

The results of these computations are illustrated in Table 1.

[TABULAR DATA OMITTED]

The information which is contained in the ith line in Table 1 characterizes enterprise i, i = 1,...,n. The magnitudes [Y'.sub.i], [K'.sub.i], and [L'.sub.i] are normalized outputs volumes, fixed capital, and labor, respectively. The magnitude of the deviation [[epsilon].sub.1] determined from equation (4) given the parameters [Theta] * corresponds to the maximum of the likelihood function. Given this magnitude [e.sup.[epsilon].i] is the relationships of the actual volume of output to the volume [Y.sub.i], which is determined by the costs of the productive factors and the estimated production function

[MATHEMATICAL EXPRESSION OMITTED]

Note that equation (6) follows from equation (4) given [epsilon] = 0. The magnitudes [v.sub.i] and [u.sub.i], which satisfy the condition [epsilon.sub.1] = [v.sub.i] - [u.sub.i], are determined according to formula (5).

The function [Ye.sup.v], computed from [Ye.sup.v.sub.i], models technical productive potential. In this case, the magnitude v derived from [v.sub.i], i = 1,...,n serves as a measure of the random disturbances in the production process and the influence of measurement errors in the source data. Moreover, the deviation in the determined composite Y from the stochastic frontier is measured by [e.sup.v.sub.i]. The random value u, computed from [u.sub.i], characterizes the actual deviation of the volume of output from its technical potential [Ye.sup.v]. Given this magnitude, [e.sup.-u] measures productive efficiency.

Table 2 contains the value components of the gradient vector and the value parameters of the model resulting from the maximization of the likelihood function. Their values are shown by the following parameters:

[Mathematical Expression Omitted]

Table 2 Gradient Vector and Value Parameters Number Gradient Functional Parameters 1 [G.sub.1] [[beta].sub.1] . . . . . . . . . 8 [G.sub.8] [[beta].sub.8]

Next, an impression of the symmetric matrix of the second derivatives of the log likelihood function is provided by

A ([beta] = [[alpha].sup.2]lnL/[[alpha].sub.[beta]] [[alpha].sub.[beta']]

and the covariance matrix of parameters estimates

B ([beta]) = [[-A ([beta])].sup.-1]

As already observed above, the magnitudes [Mathematical Expression Omitted] provide the standard errors of the parameter estimates, where [B.sub.ii] are the diagonal elements of the matrix B; [t.sub.i] = [[beta].sub.i]/[S.sub.i] and [t.sub.i] are t statistics.

The following information should also be considered. The significance of the logarithm of the likelihood function; the average coefficient of technical efficiency

[Mathematical Expression Omitted]

the elasticity of input substitution 1/1 + p; the elasticity of nonhomotheticity

[[gamma].sub.1] - [[gamma].sub.2]/1 + [rho]

and the elasticity of output with respect to increased capacity of capital [[gamma].sub.1]/[rho] and of labor [[gamma].sub.2]/[rho].

A graphical representation of the level of technical productive efficiency is provided in Figure I. The number of the enterprise is designated on the absissa, the value of the deviation [epsilon] (indicated by the sign *) and [e.sup.-u] (indicated by the sign +) on the ordinate.

As a result of these calculations, the entire set of enterprises can be divided into two groups: enterprises with negative deviations [epsilon] and those in which [epsilon] [is greater than or equal to] 0. It can be anticipated that the number of enterprises with negative deviations will exceed those in which [epsilon] [is greater than or equal to] 0. This is explained by the fact that the technical potential, determined by the stochastic frontier, exceeds the average sectoral technical possibilities computed with least squares.

The production function (6) defines the technical potential and is determined by the expenditure on productive factors. It is the best practice standard for the entire enterprise.

If [[epsilon].sub.i]] [is greater than or equal to] 0, the corresponding enterprise is efficient. In this case in accordance with equation (5) [u.sub.i] = 0, and actual output coincides with technical potential set by the stochastic production frontier. The value of the coefficient [e.sup.-u] is thus 1. If the actual output level exceeds the determined level Y, defined by formula (6), it is caused by a positive, random factor. If [epsilon] < 0, in accordance with the equation (5), there are two possible cases: [u.sub.i] = 0 and [u.sub.i] > 0.

In the first case production is similarly efficient. The fact that the actual output is less than the determined level Y, defined in accordance with equation (6), is interpreted as the consequence of the negative ([v.sub.i] < 0) disturbance resulting from random factors on the production process.

In the case where [[epsilon].sub.i] < 0 and [u.sub.i] > 0, output is inefficient. Together with the negative effect of the random variable, there is a systematic factor which depresses efficiency. These factors condition the decline in the output level by the multiplicative term [e.sup.-u] (or with respect to lower case u, by u percent). The influence of systematically influential factors facilitates the subsequent analysis.

The possibility of computing the array [{u.sub.i}].sup.n.sub.i] = 1 holds great interest for the study of the influences of various technical economic factors on the degree of productive efficiency. For example, the construction of the functional dependence u = [pi](K) showing the effect on the variable u of [K.sub.i] engineering personnel from among the general productive industrial labor force of the enterprise, can enable the establishment of the best composition of K * facilitating maximum efficiency. Analogous research may be carried out on other technical economic factors which influence the technical efficiency of production.

Table 3 considers the results of a computational experiment performed on enterprises in the cotton-refining industry in the USSR. The parameters [THETA] * of the production permit one to measure the elasticity of substitution and nonhomotheticity, and other important characteristics of production. However, primary interest lies in the possibility of computing the degree of productive efficiency for each of the 151 enterprises.

TABLE 3 An Experiment Using Data for 151 Cotton-Refining Enterprises in the USSR in 1977 The optimum value of the function 1n L is 1n l = -36.38 Gradient Functional Parameter 1. -3.81469727E+00 7.51296100E-03 2. 1.66893005E+00 4.36051960E-01 3. 1.43051147E+00 4.32705438E-01 4. 0.00000000E+00 2.26090440E+00 5. -9.53674317E-00 2.23765706E+00 6. -1.43051147E+00 3.65123005E-00 7. -2.14576721E+00 4.57538820E-02 8. -2.38418579E-01 9.55278743E-01

Among the 151 enterprises, 125 have negative values of [[epsilon].sub.i] which testifies to the progressiveness of the technologies constituting the stochastic frontier F(X,[THETA])[e.sup.v.sub.i]. In the accordance with the hypotheses about the normal distribution of the random variable, truncated at 0, the deviations [[epsilon].sub.i], which have positive values for 26 enterprises, are attributed to the effect measurement errors and random disturbances have on the production process. In this case [v.sub.i] = [[epsilon].sub.i] and [u.sub.i] = 0.

Negative values of the deviations [[epsilon].sub.i] can be represented as [v.sub.i] - [u.sub.i]. It should be noted that fully 98 of the 125 enterprises for which [[epsilon].sub.i] < 0 had positive values of [u.sub.i]. The degree of productive efficiency for 27 of the enterprises was equal to unity.

The mathematical expectation of the random variable [u.sub.i] is equal to E([u.sub.i]/[[epsilon].sub.i]) = 0.2089. The average value of the indicator u for the 125 enterprises where [[epsilon].sub.i] < 0 is [SIGMA][u.sub.i]/125 = 0.2080. The closeness of these values testifies to the usefulness of the method of decomposing the deviations [[epsilon].sub.i] into the components [u.sub.i] and [v.sub.i]. The coefficient of productive efficiency for the entire aggregate [mu] = [e.sup.-0.2089] = 0.81.

For comparative purposes, an experiment was performed using the very same data to estimate the [THETA] * parameters from function equation (3) by means of the least squares method. The following parameter estimates were obtained: [c.sub.1] = 0.001; [c.sub.2] = 0.617; [[gamma].sub.1] =1.452; [[gamma].sub.2] = 1.452; and [rho] = 4.368.

The normally distributed random values of the deviations [[epsilon].sub.i] are characterized by the parameters (0; 0.104). As might be anticipated, only half - 70 enterprises - displayed negative deviations [[epsilon].sub.i] < 0 from the production function, and 81 were positive.

The stability of the parameters of the production function with respect to the data of the individual firms ought to be noted. Thus, the computations for 148 of the enterprises (data for three enterprises were excluded because the corresponding values for [[epsilon].sub.i] fell outside the aggregate) indicated that the change in the estimated values of the [[epsilon].sub.i] deviations compared with the results for the 151 enterprises, fell within the range [10.sup.-3].

The possibility of comparing estimates of intertemporal technical productive efficiency is particularly interesting. A comparison of findings permits the establishment of: the change in productive efficiency by an entire sector (with regard to all aggregate entities) and the change in relative productive efficiency for each entity.

The volume of output, determined by the costs of productive factors and the defining function (6) can serve as a primary indicator for comparing the efficiency of the aggregate entities under consideration. In this case relative productive efficiency for each entity varies with the value [e.sup.v.i]. For example, a comparison of the results for 108 cotton-refining enterprises in Uzbekistan during 1982-83 revealed that technical potential increased by 3 percent [Afanas"ev, 1988]. However, the relative efficiency of enterprises did not change proportionally because the number of efficient enterprises fell by eight. The rate of their efficiency growth was slower than in the group considered as a whole.

Sectoral rates of scientific and technical progress ought to be taken into account in forecasting the development of enterprises during the five year plan and for periods of longer duration. Enterprises in given sectors are established at different times, and exhibit different rates of capital growth. Looked at from the standpoint of equation (2), the achieved output level can be expressed as

Y = F(X, [THETA])[e.sup.[epsilon] + [lambda] (t - [t.sub.1]]

where [lambda] is the sectoral rate of scientific and technological progress; t is the year being investigated; and [t.sub.i] is the year the enterprise was founded. This expression allows the author to take separate account of capital growth. Additional source data pertaining to the vector [{t.sub.i}.sup.n.sub.i = 1] must be introduced for this purpose. The maximum value of the liklihood function is then determined not by 8, but by 9 parameters, one of which is [lambda].

For example, the estimated rate of scientific and technological progress for 151 cotton-refining enterprises was

[lambda] = 0.0088.

(0.0018)

The approach under consideration can be used to determine the technical productive efficiency of the aggregates entities, each of which is represented not from one, but from many perspectives characterizing the relationships linking inputs-outputs at various moments in time. This situation is described by the technical productive efficiency estimates for groups of entities, each of which is characterized by data for the five year plan period.

[Mathematical Expression Omitted]

In this case the number of tests increases fivefold. However, this approach does not take the rate of sectoral scientific and technological progress adequately into account. The source data must be made comparable for the time period in question (e.g., the final year of the period being considered) for each enterprise. This can be accomplished by means of the transformation

[Mathematical Expression Omitted]

where [t.sub.0] is the base year and [[lambda].sub.i] are the growth rates of productivity in enterprise i for the period [Mathematical Expression Omitted], ascertained individually for each enterprise. Regression analysis can be used to compute the coefficients [[lambda.sub.i] for each enterprise.

It ought to be noted that the designed method does not always allow the presence of systematic causal factors which diminish productive efficiency to be established. But, in an experiment performed with data on three enterprises in the American energy sector, the parameter estimates for [THETA] and [[sigma].sup.2 sub.v], obtained by the methods of maximum liklihood and least square, were largely coincident. This shows that the enterprise data in the American energy sector are sufficiently precisely described by the laws of normal distribution. In this case, the actual deviation of output from the value fixed by the deterministic production function (6) can be reconciled with the influence of random factors. Naturally, in building models of technological potential in this case, it is appropriate to utilize the relatively simple method of least squares.

III. The Estimation of the Technical Efficiency of Productive in Enterprises

Information on the volume of outputs and primary factor inputs for each technological process is required to perform disaggregated calculations. Technological progress is specific to the production of each product type. For comparative purposes, source information on the output ought to be measured in the value terms.

Computational experiments estimating the efficiency of technological processes were conducted on 41 different kinds of confectionary products, manufactured at the Kaunasskoi confectionary factory (using data for 1982).

The following data were employed: 1) Commodity production valued in wholesale prices (prevailing); 2) Labor intensiveness statistics for each product, obtained from the labor use schedule (kart trudoemkosti); and 3) Capital intensity statistics.

The calculations generated the following results: the optimal value of the likelihood function 1n L = -91.30; the parameter estimates are

[Beta] * [0.6808; 0.3172; 0.0227; 0.00029; 0.161; 0.5061; 0.0781; -0.2812] (0.012) (0.013) (0.015) (0.0016) (0.0085) (0.0654) (0.0011) (0.38)

The [THETA] * parameters of the production function permit the elasticity of substitution an nonhomotheticity and other important characteristics of production to be determined. However, the primary interest lies in the possibility of computing the degree of productive efficiency of individual technological processes.

From a group of 141 activities 121 had negative values for [[epsilon].sub.i], confirming the progressiveness of the technologies which characterize the stochastic frontier F(X,[THETA])[e.sup.v.sub.i]. In accordance with the hypothesis of a normal distribution truncated at 0 for the random variable u, the deviations [[epsilon].sub.i], which have positive values for 20 technological processes, are imputed to the effect measurement errors and random disturbances have on the production process. In this case, [v.sub.i] = [[epsilon].sub.i] and [u.sub.i] = 0.

The negative values of the disturbances [[epsilon].sub.i] as mentioned above, can be represented as [v.sub.i]-[u.sub.i]. It should be noted that 113 of the 121 processes for which [[epsilon].sub.i] < 0 have negative values of [u.sub.i]. The degree of productive efficiency for eight of the 121 technological processes estimated with the method utilized is nearly unity. The efficiency level of the remaining 113 processes are distributed in Table 4.

Aggregate confectionary production, manufactured at the Kaunasskoi confectionary factory, is dependent on the type of raw materials and the variety of goods that are divisible into six assortment groups: candy and boxed candy, wrapped candy, chocolate and chocolate products, drops, toffee, and marmalade-pastila (a kind of fruit fudge).

The improvement of technological efficiency of productive activities, given data on input costs, can be secured in the first instance by observing the relative efficiency with which productive

[TABULAR DATA OMITTED]

capacity and normed working capital are utilized, and similarly with reference to labor use. The linkage between indicators of technological efficiency with indicators of the rate of capital return and labor productivity is shown in Table 5, using the first assortment group (candy and boxed candy) as an example. Analogous dependencies are obtained for the whole factory and for other assortment groups. It should be noted that the tendency for the technological efficiency to decline is positively correlated with decreases in the indicators of the return on capital and labor productivity.

For all assortment groups manufactured at the factory one can compute the average technical efficiency coefficients. The results are illustrated in Figure II. The least technically efficient activities are candy drops, marmelade-pastila products, and candy and boxed candy. Chocolate is the most efficient. These results will be scrutinized further by basic assortment group.

As shown by these findings, improvement in the production of confectionary products in the diverse assortment groups is influenced by the general technical efficiency of production at the Kaunasskoi candy factory. It is simultaneously influenced by the efficiency with which primary productive factors, labor, and fixed and working capital are utilized. Therefore, in devising the current plan, it is important to estimate the technical efficiency of production for all confectionary goods manufactured in the factory.

It is desirable that technical productive efficiency be directly correlated with economic efficiency, otherwise technical efficiency could be utilized in the production of unwanted consumer goods. Therefore, for a more detailed analysis of the computer results by individual assortment groups, estimate of quality and demand for each products should be utilized.

The first assortment group - candy and boxed candy - is the most popular among buyers in the Lithuanian SSR. Of the 36 varieties, 28 have high quality, good taste characteristics, and attractive external appearance. The boxing of candy at the factory is not completely mechanized and requires considerable manual labor. This is consistent with the relatively low estimated efficiency of this group of goods (Table 5). Therefore, from the standpoint of expanded future distribution, it is essential to contemplate measures for increasing the productive efficiency of boxed candy in the plan. Candy and boxed candy can be subdivided into two smaller subgroups - candy samplers and individual types of boxed candy.

The greatest demand among buyers is for samplers of mixed candies. The sampler contains various types of chocolate covered candy, which are prepared from the best quality and most expensive ingredients. The external appearance of the candy is attractive and has good taste characteristics. Therefore, it is not surprising that it is so popular among consumers. It appears that the most technically efficient element of this subgroup is the candy sampler "Assorti." This is explained by the fact that its boxing line is semi-automated with comparatively small labor intensity. All the remaining candy samplers are technically less efficient (Nos.27-36, Table 5).

[TABULAR DATA OMITTED]

Increasing the efficient use of labors resources in the first assortment group requires that an effort be made to enhance the technology of packing candy in boxes and mechanizing the process of decorating the candy boxes. This will facilitate an increase in the productive efficiency of confectionary factories and create conditions for the fuller satisfaction of the growing demands of the population for this product.

The analysis of the results of the experiment in estimating enterprise efficiency and technological progress shows that the stochastic frontier production function can be used to model the technical potential in formulating current and five year plan. Efficiency estimates [mu] = [e.sup.-u.sub.i] can be used in reviewing wholesale prices for individual items. The possibility of determining new progressive sectoral technological norms and standards is especially interesting. Capacity norms can be applied to standard products which have suitable productive technologies that are characterized by the stochastic frontier production function.

The stochastic frontier production function F(X,[Theta])[e.sup.-v] can be considered as the potentially achievable level for forecasting enterprise development from the standpoint of technological efficiency. If production is inefficient,i.e.,if [u.sub.i]>0, then a way must be found which can remove the influence of these systematically negative factors.

REFERENCES

M. Afanas"ev "Experimental Estimates of Enterprises Efficiency in the Cotton Refining Industry," unpublished manuscript 1988. M. Afanas"ev and V. Skokov, "Programma otsenki effektivnosti funktsionirovaniia predpriiatii na osnove rascheta stokhasticheskikh granits proizvodstva," (A Program for Estimating the Efficiency of Enterprises on the Basis of Computing Stochastic Production Frontiers), in Sistemy programmnovo obespecheniia resheniia zadach optimal' novo planirovaniia (Systems of Program Techniques for Solving the Task of Optimal Planning), ed., Moscow, TsEMI, 1984. D. Aigner, K. Lovell, and P. Schmidt, "Formulation and Estimation of Stochastic Frontier Production Function Models," Journal of Econometrics, No.5, 1977. V. I. Danilin, K. Lovell, I. S. Materov, and S. Rosefielde, "Normativnye i stokhasticheskie metody izmereniia i kontrolia effektivnosti raboty firmy i predpriiatiia," (Normative and Stochastic Methods for Measuring and Controlling the Efficiency of Labor in Firms and Enterprises), Ekonomika i matematicheskie metody, T. XUSH, No. 1, 1982 P. Materov, "K probleme polnoi identifikatsii modeli stokhasticheskikh granits proizvodstva" ("Concerning the Problem of the Full Identification of the Model of Stochastic Production Frontiers," Ekonomika i matematicheskie metody, T. XUII, No. 4, 1981. V. Skokov, Iu. Nesterov, and I. Purmal', Paket analiza optimizatsionnykh ekonomicheskikh modeli PPP. "PAOEM ES EVM." (A Package for the Analysis of Optimal PPP Economic Models "PAOEM ES EVM." Nonlinear Programming, Moscow, TsEMI, 1980. Boris P. Suvorov, ed., Osnovy optimizatsii tekushevo otraslevovo planirovaniia, (Principles of Optimization for Current Sectoral Planning), Moscow, Nauka, 1987.

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Author: | Afanas, Mikhail Iu.; Rosefielde, Steven |
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Publication: | Atlantic Economic Journal |

Date: | Mar 1, 1992 |

Words: | 5771 |

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