The productive function has become a fundamental competitive variable for business organizations, at least under equal conditions with the other functional activities of the same, because it represents the maximum amount of production that can be obtained by efficiently applying a given quantity of factors.
Within this context, the concept of productivity is closely related to that of production. They are parallel concepts between which similarities and differences can be established. Specifically, the concept of productivity, its methods and practical utility have acquired great interdisciplinary significance in production processes, especially in the production function, as elements that generate competitive advantages. Few areas of economics are as relevant and complex as measuring productivity. The importance lies in the most efficient and rational use possible of productive resources and in the relationship that it has with the well-being of the population, in particular with the levels of real income and employment.The objective of this article is to analyze from theoretical research the most relevant aspects of the concept of production function, productivity and its valuation; Frontier model: Data Envelopment Analysis (DEA) and Malmquist indices; subsequently, carry out a brief review of analysis on a group of type III clinics located in the state of Zulia, applying methods based on the production function and the border model using DEA and Malmquist.applying methods based on the production function and border model using DEA and Malmquist.applying methods based on the production function and border model using DEA and Malmquist.
Keywords: Production Function, Productivity, Productivity Measurement Methods, Frontier Model, Data Envelopment Analysis (DEA), Malmquist Indices.
- INTRODUCTION
Al enfrentarse a presiones competitivas cada vez más fuertes, las empresas tienen una mayor necesidad de coordinar las actividades principales en una estrategia coherente que integre todas y cada una de las perspectivas funcionales. Históricamente, una de las características típicas de los análisis estratégicos es que las funciones principales de las organizaciones interactúan de manera de individual dominante y no son tomadas en cuenta de forma integral para generar acciones y resultados exitosos (Hill, 1997; Ibarra, 2006). Tal es el caso, que la mayor parte de las empresas reconocen la necesidad de adoptar las perspectivas de mercado e identificar las limitaciones financieras, y pocas incluyen las perspectivas críticas de la administración de operaciones o de la producción.
The central point of the strategic approach is the need to identify the level of overlap, or lack thereof, between functional strategies. When planning a strategy, many companies do not have the way and sometimes, or the willingness, to incorporate some of the functional perspectives necessary to determine an appropriate strategic response. Such is the case of the productive perspective. Although the production function received privileged attention at the beginning of industrialization, later on it ceased to be critical and the top management of the company relegated it to the background, since they did not dedicate a special interest to it because their responsibility was exclusive to production managers (technicians, engineers), despite the fact that this function is linked to the bulk of the workforce,costs and investments of the company.
Traditionally, the productive function has been considered from a very technical point of view with an analytical approach, and especially at the academic level, with an optimizing approach dominated by Operations Research (Domínguez and others, 1998). In part, the main criterion for evaluating the performance of the company in terms of efficiency and cost was limited, the main tool for measuring global performance being cost accounting (Skinner, 1978; Fernández, 1993).
Although these approaches could be maintained during a certain historical stage, for years this conception has become untenable, requiring a radical change of orientation. Reality has subsequently shown that the production function represents one of the most solid bases for obtaining a sustained competitive advantage. It has also been proven, with fatal consequences for many companies when the management of operations is inadequate and limits the possible strategic options, it leads to business failure (Hill, 1997; Huge and Anderson, 1989; Domínguez and others, 1998; Irribarra, 2006).
Faced with this situation, the productive function has become a fundamental competitive variable for the organization (Hayes and Wheelwright, 1984), at least on equal terms with the other functional activities of the organization. The productive function, in short, must receive attention, if not a priority, similar to the rest of the functional areas, which will result in an improvement in the general competitiveness of the company. For this, the recovery of production as a source of competitive advantages must be accompanied by organizational changes and improvements. This approach becomes essential if the potentialities of business technological capacity and the advantages that it could derive are considered, even more so in an era plagued by technological, economic and market changes.
In the last two decades, many companies have discovered how, frequently, the secret weapon of their fearsome competitors was not based on a greater commercial power or a superior financial strength, but on the ability to produce their products in a more efficient way. more reliable and more accurate (Hayes, Wheelwright and Clark, 1988). Within this context, the measurement of efficiency and productivity, its methods and practical utility have acquired great interdisciplinary significance in production processes, especially in the production function, as elements that generate competitive advantages.
For his part, Ahumada (1987) argues that the importance that the concept of productivity acquired was due to the need that countries had to use productive resources as efficiently and rationally as possible, in addition to the relationship it has with the well-being of the population, in particular on the levels of real income and employment, despite the fact that labor productivity is a partial measurement, since it reflects the joint effect of various interrelated factors such as technological innovation, changes in capital per capita or in the use of installed capacity, changes in the scale of production, increases in the qualification and effort of the worker, improvements in business capacity, variations in labor relations and other multiple factors of a quantitative and qualitative nature.
Likewise, according to Ahumada (1987), labor productivity is an important element for studying changes in the use of labor, analyzing occupational mobility, projecting future labor requirements, determining the policy for training human resources, examining the effects of technological change on employment and unemployment, evaluate the behavior of labor costs, compare productivity gains between countries and study many other economic problems.
The objective of this article is to analyze from theoretical research the most relevant aspects of the concept of production function, productivity and its valuation; Frontier model: Data Envelopment Analysis (DEA) and Malmquist indices; Subsequently, a brief review is made with a case analysis on a group of type III clinics located in the state of Zulia, applying methods based on the production function and border model using DEA and Malmquist.
- THEORETICAL BASES
2.1. Production Features
The production functions are closely related to the concept of systems used in mathematics or in modern control theory.
The theory of production makes use of a systems approach developing an input-output analysis to model the behavior of a company.
From a purely conceptual aspect, in economic theory a production function is called the one that generates the maximum output that a company can produce with normal inputs. The concept of production function has a somewhat ethereal aspect, since the maximum potential output depends on many factors, both technological and organizational human.
If, for example, data are taken from a national group of similar companies and a production function is adjusted to them, there will certainly be an ideal function that explains the behavior of such data, a function that is taken as a measure for those that generate, provides valuable and valid information to compare performance between them and produce support for managerial decision making.
But it should be noted that it is not, in any way, the one that gives the maximum potential of the group, since when fitting the curve and trying to find the parameters that define the function by least squares, the classical fit, it will be seen that the curve passes through them, leaving some data above and others below it. If there are data above the production curve, it no longer functions as such, since according to the definition there cannot be data above it: it is the maximum possible output.
By collecting a series of input and output data for a group of years from a specific company and fitting a production function to them. This function will serve to find the productivity that the company has had throughout the period of data provided in the production function adjustment, as well as for future years. In the same way, if national or international company data are obtained and the production function is adjusted, in addition to knowing the productivity of each company for the year in which the data were used, an estimate of competitiveness will also be obtained. of it, because you can see how far your productivity is from the rest of them.
There are different types of production functions: Additive Production Function and CES (Constant Elasticity of Substitution) Function. For the purposes of this article, we will work with the last one:
The CES-like function maintains the following form:
For the case of an output "y" and two inputs: x 1, x 2.
As its name indicates, it is a function that maintains a constant elasticity of substitution between factors or inputs, but adjustable to any specific value.
A special case of this function is the Cobb-Douglas production function, the most widely used and popular of the production functions.
The Cobb-Douglas function has the following form:
In particular; yes
It has the property of a "constant" scale return. If this sum is less than one, the economy of scale will be “decreasing” and if it is greater than one, it will be “increasing”.
2.2. Definition of productivity
Approaches to the knowledge of the economic activity of any region, or sector, involve a study of the behavior that, over time, presents any economic variable related to the result of the value of the product. Among these, productivity is revealed as one of the key variables to measure the efficiency and evolution of economic sectors, or of the economy as a whole, since its improvements can lead to an increase in the standard of living of societies (Estiballo and Zamora, 2002).
The concept of productivity is simple to define, but extremely complex to analyze and understand in depth. Few areas of economics are so relevant and complex. From a social perspective, productivity is one of the determinants of the quality of life of the inhabitants of a country. From a macroeconomic point of view, it is one of the determinants of the profitability of the company and, consequently, of its success in a competitive market.
Productivity has, in general, two meanings (SENA, 2003): physical productivity and value productivity. The first refers to productivity as a basic quantitative unit and the second to the economic value created through a series of activities. Physical productivity as a base unit can be applied to a particular industry or to a specific operating process. This type of measurement, although important, has limitations when it comes to making intertemporal evaluations. On the other hand, productivity understood as the value created in a company can be compared with that of another company and between industrial sectors, despite their differences, since changes in the body of the body are incorporated into the value of goods or services. product or service.The value of these changes is revealed by the recognition that the consumer makes through the price he pays.
The concept of productivity is closely related to that of production. They are parallel concepts between which similarities and differences can be established. In this sense, production, whether gross or net, is, as Miguel (1959) points out, an absolute concept, from a quantitative point of view, while the concept of productivity is relative, since the idea of quantity is associated with quality (Estiballo and Zamora, 2002).
Productivity is defined as an indicator that reflects how well the resources of an economy are being used in the production of goods and services. Thus, a common definition of productivity is one that refers to it as a relationship between resources used and products obtained, and denotes the efficiency with which resources are used to produce goods and services in the market (Levitan, 1984; Martínez, 1998). In general terms, productivity is understood as the relationship between the product (s) and the input (s). Its measurement at the company level is, then, the quantification of the production obtained and the inputs used in the production process (SENA, 2003).
In past periods it was thought that productivity depended on labor and capital factors, however, today it is known that there are a large number of factors that affect their behavior. These include investments, the capital / labor ratio, scientific and technological research and development, the use of installed capacity, government laws and regulations, the characteristics of machinery and equipment, energy costs, the quality of the human resources, unions, etc.
Productivity analyzes are carried out in order to study some economic and social problems such as the allocation of resources, productive efficiency, the distribution of wages, the standard of living or improvements in competitiveness, which allow achieving better assignments by achieving, with the same effort, more and better results in the production process. Most of these analyzes study the participation that productive factors have in the production process through the elaboration of indices of partial productivity of a productive factor, or through indices of total or global productivity of the factors (Estiballo and Zamora, 2002).
The productivity of a company is measured through a series of related indicators and is evaluated by comparing it with that of other companies, those that produce the same goods or services and that are considered as leading companies for their organization and technology in relation to the average of the productive sector to which the company belongs. Another evaluation is the historical evolution of the indicators, their trend, and thus know the degree to which the company improves its productivity over time (SENA, 2003).
It should be noted that, in general terms, there are two forms of productivity measurement: on the one hand, there are partial measurements that relate production to an input (labor, or capital); and on the other, there are multifactorial measurements that relate production to a weighted index of the different inputs used (Martínez, 1998). Productivity indicators can be constructed at various levels of disaggregation or detail. It can be measured taking into account the productive factors mentioned above, or from the various economic activities that take place in a country. They can also be calculated at the level of any company or establishment that carries out some economic activity.
When talking about the measurement of the productivity of the different inputs, what is referred to is partial productivity, defined as the variation that is caused in the amount of product generated, caused by a change in the level of consumption of a product. only input in the production process. One of the advantages of being able to measure the different partial productivities of each of the production inputs is that it can be observed to what extent each of the production factors or inputs participated in the increase in the level of production, as could be due to the automation of the process, the training of the workforce, or any other factor.
The most widely used indicator of this type of productivity is related to the labor factor, that is, an indicator of labor productivity, which can be measured in terms of the number of people employed, man-hours worked (the most recommended variable because it is highly sensitive to changes in production, among other aspects).
Partial productivity of labor is a relationship between production and employed personnel, and reflects how well employed personnel are being used in the production process. In addition, it allows studying changes in the use of work, in occupational mobility, projecting future labor requirements, determining the policy for training human resources, examining the effects of technological change on employment and unemployment, evaluating the behavior of labor costs, compare productivity gains between countries. The quality of work is also one of the factors that explains influences the behavior of productivity (Ahumada, 1987).
The total factor productivity (TFP), however, is a simultaneous measurement of efficiency in the joint use of resources. In both the analysis of multifactorial productivity and labor productivity, it is necessary to bear in mind that both the capital factor and the labor factor are not homogeneous factors. In the case of the latter, human resources have different characteristics that are reflected in different qualities.
In this regard, Hernández (1993) states that although the most common indicator is labor productivity, it is also true that there are as many productivity indices as resources used in production. However, the partial productivities do not show the joint efficiency of the use of all the resources, so it is important to have a simultaneous measure of the efficiency in the joint use of the resources; that is, a measure of total factor productivity (TFP).
The concept of total factor productivity (TFP) was introduced in the economic literature by J. Tinbergen at the beginning of the 1940s. This concept was independently developed by J. Stigler, and later used and reformulated in the 1950s and 1960s by various authors, including R. Solow (1957), JW Kendrick (1961) and EF Denison (1962).). More recently, the contributions of H. Lydall, WE Diewert, LR Christensen and D. Jorgenson in this line of research stand out (Hernández, 1993).
Total factor productivity is not directly observable in an industry, therefore, the development of methodologies for its estimation has been a constant theme in the economic literature. The techniques used to estimate productivity can be classified into four categories. First, estimation of total factor productivity from aggregate data in an economy, second, estimation using panel data techniques, third, using semi-parametric techniques, and finally, using instrumental variables derived from demand conditions (González, 2004). Likewise, there is talk of input and output productivity. The first principle involves using the minimum level or amount of inputs (inputs) to produce a fixed amount of goods or services,and the second refers to the maximization of goods and services generated or produced when the same level of inputs or inputs is maintained.
2.2.1. Productivity concept using a production function.
The concept of productivity using a production function coincides with that used by the frontier model. The most general and the most widely accepted is:
Where the inputs are labor (L), capital (K), materials and supplies (M), and intermediate inputs (II). The outputs can be determined by the amount of product generated or the total sales made or value added of the product.
In the case of production functions, its definition is used to create an ad hoc concept of productivity; that is, productivity is defined as:
This is in the measure of productivity when a production function is used, the value given by the data of the real output is compared through a ratio with the value given by the production function for said input. Both ordinates enter into the definition of productivity and both concepts are also responses or outputs of the system before an excitation, stimulus or input of the same. Thus, the concept of productivity using production functions has an eminently "output" or "output" approach, unlike other techniques or methods that mix inputs and outputs. This way of analyzing productivity is then more nuanced in a way of maximizing the outputs before a specific input or input.
Since productivity is a quotient of two outputs, then, on the one hand, both must have the same units of expression; but on the other hand, they must be expressed in any of the possible measurement units, giving the method more generality.
The same observation extends to the inputs or inputs to the production process, aspects such as: labor, capital, materials and supplies and intermediate inputs; the classic inputs in any productivity evaluation model: as long as the inputs for each company are measured in the same units or there is a conversion factor between them, it is feasible to use any type of unit.
Finally, when what a company can potentially produce remains a mystery that challenges specialists in the area, the determination of the production function by least squares to the existing data generates a production function that is very useful in determining the the productivity.
2.3. Productivity measurement methodologies
Measurement is the collection and recording of data under typical circumstances:
- Usefulness: importance in the decisions made. Precision: it faithfully reflects the magnitude of the event to be analyzed. Decision-making before the unwanted abnormality occurs. Reliability; Measurement in the company is not a one-time act, we must periodically review the entire measurement system. Economy: proportionality that must exist between the costs incurred in the measurement.
Measurement can be sectoral or business:
- a) Sector measurement:
Productivity in the industrial field has focused on three types of approach:
- Indices Production functions Input-product.
- b) Business measurement:
The measurement of productivity in the field of companies is under development, having grown in recent years. There are several approaches.
- Economist: Suggests measuring productivity through indices, production functions or through an input-output relationship.Engineering: Proposes measurement through indices with an orientation towards utility and servo systems.Administrators: Considers that productivity should be measured through index arrangements and with financial ratios. Accountants: It is based on measurement through capital budgets and unit costs.
There are different methodologies to measure productivity, which have specific purposes that are useful in various cases. However, for the purposes of effective comparisons between companies, regions, chains or sectors, a standardized methodology is required (CPC and OITE, 2002). It is noteworthy that productivity is a concept that has been present in the analysis of many economists and that has developed historically. Thus, in the last century, two stages were broadly defined: one in which the authors were mainly concerned with theoretically developing the concept, analyzing which are the determining factors (incorporating or breaking them down); and the second, in which the research focused, fundamentally, on fine-tuning the measurement methods.
According to Botero (2006), the literature on productivity and efficiency measurement can be grouped into two main areas: on the one hand, that which is related to efficiency measures, which go back to Farrell (1957); the other, those that deal with the variation in total factor productivity (TFP), which mainly refer to Solow (1957).
The efficiency analysis was approached by Farell (1957) from two concepts technical efficiency and allocative efficiency. The first measures the production of a firm in relation to the production possibilities frontier; while the second determines the relationship between various combinations of inputs to achieve a level of production, given their relative cost. Farell's definitions of efficiency have given rise to measurement techniques applicable to individual productive units, which in turn can be classified into four broad categories (Pollit, 1994): non-parametric programming techniques (Data Envelopment Analysis); parametric programming techniques; deterministic statistical techniques; and stochastic border methods.
Among the methods for measuring productivity, the following stand out:
Indices:
- Total productivity, partial productivity Factor arrangements, multifactorial.
Functions:
- Production functions Cobb-Douglas functions Reasons: Financial ratios, added value Financial positioning Boundary models: Data Envelopment Analysis (DEA) Malmquist
2.4. Border Model
In this model, what is intended is to create an environment of competitiveness by incorporating companies from the same branch to compare all of them with each other, and have a real image of their productivity and competitiveness.
The border technique, as its name indicates, generates a surface or border in a space whose axes are the resources or factors of the productive system, and the products or services it generates as additional axes. The most common is to consider the total of inputs and products, added in the following headings:
Tickets:
Capital first axis
Second axis work
Third axis materials and supplies
Intermediate inputs fourth axis
Departures:
Total sales or quantity of
the products or services generated Fifth axis
or added value
The intermediate inputs take into account all those resources that are not clearly classified in any of the first three aspects, such as; medical and legal services, external maintenance for the equipment, external consultancy, etcetera.
Materials and supplies are considered as the variation of inventories that was recorded during the period in which productivity was analyzed; This is under the hypothesis that all the necessary purchases enter the warehouse and are registered for their subsequent distribution to the production process.
Thus, there is a five-dimensional space, one for each of the previously mentioned concepts.
The border technique is constructed in a segmented way with each of the data or companies that are analyzed, in such a way that the analysis is punctual and the border and other attributes are constructed through each piece of data and not the other way around.
The fundamental basis of this technique consists of generating a space whose axes are the inputs or inputs of the production process (x i) and the outputs or products (y i). In this way, each report or balance of a company in which there are both data (outputs and inputs) provides a point in said space which will be denoted as T; and it is called the set of production possibilities.
This space can be generated with different data from the same industry at different times, with which its productivity will be measured with respect to itself, or data can be obtained from different companies of the same national or international industrial branch, with which it will generate a national or international border against which the efficiency of any local data will be measured. Those with 100% productivity or efficiency will form the frontier against which any other data will be measured.
Therefore, as a point in space moves away from it, it will be more inefficient and on the contrary, the closer it will be, the more productive.
To determine the productivity and marginal rates of substitution, as well as the economy of scale, the technique builds a hyperplane that is tangent to the set of production possibilities T, and from this the required information is obtained.
This is essentially the frontier method, which can also provide economies of scale; the most productive TEMP or scale size, such as the one that maximizes outputs or production while minimizing the inputs required for it. It also generates the marginal productivities or variations of the output with respect to changes in the input and finally the marginal rates or variations of the output with respect to changes in the input and finally the marginal rates of substitution between inputs.
2.4.1. Boundary Model Results
Among the main results of this model, it is worth mentioning (Mercado and Col. 1998):
- Input productivity
The horizontal distance from a particular point to the border represents the degree of inefficiency or misuse of the company's resources. It means what could be saved on inputs and still maintain the same level of finished product.
In other words, as a company moves horizontally away from the border, its input productivity will be lower; that is, in other words, the company will be consuming a greater quantity of inputs to produce the same output. This happens when the company generates a lot of waste or there is excess rework or scrap lots. A thorough analysis of its organization and production techniques will be necessary to correct this problem and reduce the horizontal distance that the company has from the efficient frontier.
- P roductivity output
Similar to the interpretation of input efficiency or productivity, there is the concept of output productivity.
This represents the number of outputs or products that the company could increase by consuming the same current resources.
A strategy of maximizing outputs using the same amount of inputs would be indicated when it is not feasible to obtain a greater amount of resources for the purchase of inputs, but there is an unsaturated market to which it is possible to increase the supply. The emphasis would now be to optimize marketing and consumer service programs in order to increase sales and decrease inventory volumes. Collaterally, specific programs must be developed to avoid rework or waste parts, as well as rejected batches, monitoring key points on the production lines.
- Most Productive Scale Size (TEMP)
This is another characteristic of the frontier method and represents the position in the space of production possibilities in which it is more convenient for the company to be located, since in such a situation it will be minimizing resources or inputs and maximizing the outputs it generates. In this position the company works with an economy of increasing scale, that is, it produces more outputs than the resources or inputs it requires. The model determines, for each company in the database, what its position should be if it is desired to operate under these characteristics.
- Overall efficiency
Technical and scale efficiency, known as global efficiency, is determined as follows:
Overall efficiency = MN / MA
With this quotient, the current inputs that the company is requiring are compared with that hypothetical company generated with a hypothetical frontier, a line that runs from the origin, is tangent to the set of production possibilities and touches the efficient frontier, which assumes that the set of companies work with a constant economy of scale.
- Technical efficiency.
Technical efficiency is given by the following equation:
Technical efficiency = MB / MA
This efficiency compares the company with that located on the efficient frontier. Here we see the current situation of the company versus the one it would have if it were on the efficient frontier, minimizing the inputs it uses and working in an environment in which diseconomies are admitted.
- Scale efficiency
Scale efficiency is defined by:
Scale efficiency = MN / MB
This value represents how far the efficient frontier (with feasible diseconomies) is from the hypothetical one formed (companies working with a constant economy of scale).
- Economies of scale.
Using the frontier technique it is relatively simple to determine whether the economy of scale under which a company is operating is increasing, constant, or decreasing for points that lie on the frontier. Remember that an economy of scale measures the proportion in which the outputs vary as inputs vary. This economy of scale is obtained by generating a hyperplane tangent to the projection at the boundary of the point of interest and observing its intersection with the axis of the outputs. If the intersection is positive (above the origin) it is said that the company operates with a decreasing economy of scale; if it passes through the origin then it is constant and, finally, if it intercepts in the negative part, the economy of scale is said to be increasing.
- Marginal rates.
Even though the model allows evaluating the changes in the output or finished product when there are variations in the inputs and the substitution rates between inputs, in practice very small values are observed for each of the substitution rates, making it difficult or little useful its economic interpretation.
2.4.2. Data Envelopment Analysis
Starting from the ideas of Farell (1957) and, Charnes, Cooper and Rhodes (1978), the Data Envelopment Analysis (DEA) was developed, which seeks to establish which organizations in the sample determine the envelope surface or efficient production frontier. Interest in the analysis of economic efficiency frontiers has grown rapidly in recent times. There are numerous methodologies and applications with reference to the measurement of effectiveness.
In recent years, Data Envelopment Analysis has become the Benchmarking method widely used by companies. The main advantage of DEA is that it is not based on knowledge of the production function. It corresponds to a non-parametric method, thus allowing richer models that are not dependent on the knowledge of the prices of the production factors. DEA finds the set of efficient companies from which, through linear combinations, it obtains the envelope or frontier. This represents an advantage due to its greater flexibility, although for many its fundamental drawback lies in the lack of statistical properties of the results obtained with linear programming. However, in its favor is the feasibility of incorporating economies of scale into the analysis;important advantage that justifies their choice (Raffo and Ruiz 2005).
The DEA method consists of measuring efficiency radially. That is, it is considered that productivity increases by a certain volume only if all products are increased simultaneously by that same volume without consuming more inputs, or, alternatively, that there is a saving of a part of the resources only if all the Inputs are reduced to the same extent without reducing production. In practice, to check whether there have been improvements in productivity, each productive unit is compared with the production frontier formed by the units for which the best performance is observed. Figure N ° 01 illustrates the application of the CCR model to the case of a single input (X) and a single product (Y), so that each point represents the values corresponding to a single productive unit.
In the previous graph, unit 2 (defined by the intersection of Y 2 and X 2) is the only efficient one, since it presents the smallest ratio between inputs and outputs, defining, therefore, the efficient frontier with which they are to be compare the other two units. Thus, if the productivity of the other two units were equal to that of unit 2, they would maintain their output levels, Y 2 and Y 3, with respective inputs of X 1 e and X 3 e, lower than those observed (X 1 and X 3), so the efficiency indices will be X 1 e / X 1 and X 3e / X 3. The efficiency index takes a unit value for efficient units (in the example, unit 2) and tends to zero as they become less efficient.
Figure N ° 01
The DEA method
The information provided by the DEA method is static in nature and, obviously, in historical studies it is essential to offer a temporal analysis.
2.4.3. Malmquist Productivity Index
Caves, Christensen, and Diewert (1982) developed a multilateral index that is useful for measuring total factor productivity with firm-level data, which they called the Malmquist Productivity Index. The index is constructed as the difference between the logarithm of the company's output and the weighted sum, by the profit sharing, of the company's inputs. To ensure a consistent comparison between observations for different firms, output and inputs are expressed as deviations from a single point of reference.
According to the following equation, the productivity index from one period to another can be measured as:
If the production function has one good and several inputs, only the numerator is directly observable. The denominator, on the other hand, must be calculated from the aggregation of inputs.
Consider, for example, the case in which there are two inputs and one output, and the production function Y = A t f (X 1, X 2), which is illustrated in Figure 3, in which two levels are represented (f 0, f 1) of a production function for a product (y) and two inputs (the vector x). Equilibrium in the first case occurs at the point x 0, while x 1 is the final equilibrium. A first measure of the variation of the inputs is "t0", the factor by which the inputs used must be divided into "1", so that with the initial production function y 0. A second measure is “t1”, the factor by which the inputs used must be multiplied in “0”, to obtain y 1 with the final production function. The Malmquist-type index of variation of inputs is defined as the geometric mean of “t0” and “t1”. More specifically, and for the case of n inputs, the values “t0” and “t1” must be calculated such that (Botero, 2006):
And the Malmquist-type index of variation of inputs is:
It should be noted that the calculation of Malmquist-type indices implies the prior estimation of the production function.
With the information from this index, a new measure of productivity can be calculated:
Figure N ° 02
Malmquist Productivity Index
The Malmquist Productivity Index, which is also based on the DEA method, provides such a dynamic perspective.
2.5. Type III Private Clinics
A private clinic is considered to be an entity that provides medical and specialized care, both ambulatory and hospital, with high technology application that identifies the use of medicine to study patients in their diagnosis phase, where it is necessary to carry out observation and research, with the support of intermediate and terminal services, (outpatient consultation, emergency, nursing, hospitalization, intensive therapy, rehabilitation). In addition to existing nosological entities circumscribed to specifically outpatient care, with the presence of numerous sub-specialties, which are supported by auxiliary services, in some cases with rehabilitation (laboratory, X-rays, pharmacy, pathological anatomy and Blood Bank).
It is classified as type III clinic because they provide comprehensive medical care services at the three levels (primary, secondary and tertiary medical care), are located in populations greater than 60 thousand inhabitants, with an area of influence of up to 400 thousand inhabitants, with capacity between 150 and 300 beds. In addition, they have Departments of Medicine, Nephrology, Rheumatology, Gastroenterology, Physical Medicine and Rehabilitation, Surgery in all their specialties (Traumatology, Urology, Otorhinolaryngology, Ophthalmology, Gyneco-Obstetrics and Pediatrics), each having Heads of Department.
On the other hand, it is important to point out that primary medical care is called those establishments with simple equipment such as diagnostic support (stethoscopes, tensiometers, ENT equipment (otorhinolaryngology), hammers, mechanical equipment (microscopes) that have direct accessibility by of the users.
Secondary medical care refers to simple but larger establishments, with equipment such as diagnostic support of regular complexity, such as: X-rays, laboratory, specialized medical equipment and the presence of specialist doctors. Likewise, another characteristic is that the care is carried out based on a referral system (referral of patients).
Finally, tertiary-level medical care concentrates those larger establishments with the incorporation of complex equipment as diagnostic support (computerized equipment, in addition to electromedical and radiation) and whose care is carried out, as in the previous case, based on a referral system. Within these health centers, medical sub-specialty services are offered.
General Considerations of the Health Sector in the state of Zulia
Approximately a decade and a half ago, type III private clinics were going through a boom period, since they were a valid alternative due to the terrible care and serious problems that arose in public health centers. Many of these organizations grew and consolidated within the sector.
However, today the circumstances have changed, the return to personalized attention at home, through programs such as "neighborhood inside I and II", "neighborhood by neighborhood", the bringing of Cuban doctors to assist in health campaigns Public services, among others, have contributed to generating a healthcare crisis at the level of private provision of the service.
Of course, there are still advantages in the private provision of comprehensive care to patients, such as: the high prestige that many of these institutions have, having highly qualified personnel, having cutting-edge technology, infrastructure and environments, among others. However, economic policies such as exchange control, generalized inflation in the imported component of health purchases and the high financial costs of care, become threat devices that threaten the sector.
It is not the purpose of the authors of this research to make a detailed preliminary diagnosis of how this sector has developed in recent years, but to make known some general considerations that may affect productivity and efficiency levels that are evidenced within of the same.
One of the main weaknesses that private clinics must face is the increasingly difficult task of recovering bad debts and offering services that are available to a middle class whose incomes are increasingly depleted. This limits the possibility that clinics can offer quality services, obtain financing to make investments in state-of-the-art technology and allow permanent training of personnel.
On the other hand, the study in its initial phase seeks to specify the parameters of the inputs under a Cobb Douglas production function, which within the current conditions in which the clinics operate and during a financial year (2005) provide the generation levels of services capable of offering each one of them, by increasing the use of the productive factors identified as, work or labor, capital and supply.
In its second phase, it was sought to know the competitive position of each of the health organizations, according to the DEA technique, which relies on mathematical programming to build a frontier made up of clinics that show better behavior and, from of them, the efficiency of the rest can be determined and measured.
Finally, through the analysis, it is intended that the clinics can fulfill their prospective vision: "To be institutions that offer comprehensive health services, reference centers at the national and international level that plan to expand their activities and coverage through openings of other dependent and similar establishments, providing the optimal cost-benefit ratio that allows them to develop integrated production processes, to meet the demands of users with the use of advanced technology to achieve market positioning in the coming decades, supported by the highest scientific and academic level ”.
- METHODOLOGY
For the development of the following research, seven (7) medium-sized private clinics were selected, located in different municipalities of the Zulia State. In order to respect the anonymity of said institutions, which so graciously provided the required data, pseudonyms were placed on it, since the information collected is from the financial statements of the fiscal year corresponding to the year 2005.
Given that this information was provided at current prices, the financial statements were indexed or deflated by using the consumer price index (base year 1997). In this way, we work with data at constant prices for the year indicated above.
Subsequently, the production functions for the 7 clinics were created, for which accounting criteria were used to define which items would make up Labor, Capital and Supplies. After consulting experts in the area, it was established that the "work" would be made up of the expenses made by the clinics for remuneration of the labor factor, regardless of the type of personnel; the “capital” would be made up of the depreciation fund, understood as a flow through the use of the equipment, facilities or any other fixed asset in the health service production process and, finally, the “supplies” would be made up of the expenses both in direct and indirect materials that the clinics carry out to develop their activities.
Once the information had been tabulated, the runs were carried out using the EMS as basic software, for the production function the "Statgraphics" package and for the analysis of borders (Data Envelopment Analysis and Malmquist Productivity Indicators). For the analysis, a clinic was selected from the sample as the basis for it. In the specific case of this work, the clinic to study and compare with the rest of this group is “San Rafael” (Clinic N ° 03).
In the first software, individual runs were carried out to obtain the production function of each of the clinics, by applying multiple regression applying logarithms to the variables for conversion into a Cobb-Douglas type production function; which allows to measure the efficiency of the use of productive factors and determine the level of contribution of inputs to production levels.
For the DEA or efficiency frontiers model, the data was consolidated according to input and output for one year (2005), which allowed us to identify the points where the clinics are efficient or not. Those that were located within the efficiency frontier yielded coefficients of 100 percent, on the side of the outputs and on the side of the inputs.
It is important to make the caveat, that the veracity of the information could be questionable, since there is no absolute guarantee that the organizations have provided the real information of their financial statements. However, the method applied to test the productivity of companies is guaranteed through the use of data enveloping analysis and malmquist indices.
3.1 CASE N ° 01: Production Function of the San Rafael Clinic
The production function of the San Rafael clinic is presented below, made up of the production factors Labor (T), Capital (C) and Supply (S):
Y = a + b T + c C + d S
Where:
Y = Production or Generation of the Service
a, b, c, d = Parameters of the equation
T = Work or payment to total personnel (managers, doctors, employees and workers)
C = Principal (interest payment + depreciation fund)
S = Materials and Supplies
3.1.1 Information on Production Factors:
| San Rafael Clinic (6) | ||||
| Months | Production | Work | Capital | Supplies |
| January | 32,083,895 | 4,669,431 | 1,635,393 | 25,779,071 |
| February | 31,003,124 | 4,748,731 | 1,502,228 | 24,752,166 |
| March | 31,520,918 | 4,700,672 | 1,569,349 | 25,250,897 |
| April | 30,989,373 | 4,537,441 | 1,570,592 | 24,881,339 |
| May | 29,651,524 | 4,563,257 | 1,429,626 | 23,658,641 |
| June | 29,732,774 | 4,561,218 | 1,438,343 | 23,733,213 |
| July | 28,501,111 | 4,324,941 | 1,394,379 | 22,781,791 |
| August | 29,512,878 | 4,564,553 | 1,415,472 | 23,532,852 |
| September | 29,730,425 | 4,444,272 | 1,476,702 | 23,809,450 |
| October | 29,704,878 | 4,305,328 | 1,520,025 | 23,879,526 |
| November | 30,338,786 | 4,477,416 | 1,525,993 | 24,335,378 |
| December | 30,624,474 | 4,517,213 | 1,541,143 | 24,566,119 |
| Totals | 363,394,160 | 54,414,472 | 18,019,246 | 290,960,442 |
3.1.2 Results of the Multiple Regression Model run (Software: Statgraphics):
Dependent variable = LOG (Production)
| Regular T | ||||
|
Parameter |
Estimate | Error | Statistical | P - Value |
| Constant | 0.114802 | 0.0 | 0.0 | 0.0 |
| LOG (Labor) | 0.0554933 | 0.0 | 0.0 | 0.0 |
| LOG (Capital) | -0.072106 | 0.0 | 0.0 | 0.0 |
| LOG (Supplies) | 1.01661 | 0.0 | 0.0 | 0.0 |
The results were the following:
R 2 -Square = 100%
R 2 -Square adjusted by df) = 0%
Statistical Standard Error = 0%
Absolute meaning of the Error = 1.97039E-7
Durbin-Watson test statistic = 1.85279 (P = 0.3202)
Lag 1 residual auto-correlation = 0.00637317
P-Value = 0.0000
3.1.3 Analysis of the Results of the Multiple Regression Model
This analysis is derived from the production function:
Log (Y) = 1.302528 + 0.0554933 x Log (T) - 0.072106 x Log (C) + 1.01661 x Log (S)
This equation shows that the production of the San Rafael clinic depends positively on the work factor (T) and the supplies (S), that is, production increases as larger units of work and supply are added. In the same way, it is evident that as units of the capital factor (C) are added, production is decreasing (financing expenses).
Regarding the value of the parameters of the independent variables, the results show that the supply factor is the one with the greatest significance in the production of the service, because its absolute value is the one with the highest or highest value (1.01661), followed by the capital factor (0.072106) and the labor factor (0.0554933).
With the execution of the multiple regression model, the following statistical results were obtained after running the data of twelve (12) observations that represent the information of one year of the financial year in the "Statgraphics" software:
- As the value of "P - Value" is 0.0000 in the ANOVA table (analysis of variance) and this is less than 0.010 then there is a statistically significant relationship between the variables that have been selected to represent the model. In this particular case, this means that the production model of the San Rafael clinic has a confidence level of 99 per The coefficient of determination (R 2) indicates that in the model the controllable independent variables express the variation in production 100%. For this reason, the production of the service is expressed as 100% by the variables or factors of production labor, capital and supply. Regarding the adjusted statistic or adjusted determination, it is observed that it has no variation because its value is 0.0%. The standard error presents a value of 0.0%. This indicates that the multiple regression model has a reliability of 100% and that it can be used to predict future behavior of the variables. The mean absolute error is 0.0%, this value expresses the average reached by the residuals. develop the Durban Watson test or statistical test of residuals,It is determined that if there is any significant correlation based on the order of how the data are presented, the results obtained show a statistical value of DW = 1.85279 for a P = 0.3202; which is greater than 0.05; then it is stated that in this model there is no serial autocorrelation between the residuals. To determine if the model can be simplified, it was observed that the highest value of the P-Value of the independent variables are all "0", therefore it is not possible not to you can simplify the model or remove any of its variables.It was observed that the highest value of the P-Value of the independent variables are all "0", therefore it is not possible to simplify the model or remove any of its variables.It was observed that the highest value of the P-Value of the independent variables are all "0", therefore it is not possible to simplify the model or remove any of its variables.
3.1.3 Interpretation of the results obtained from the Cobb Douglas function at the Socrates Clinic:
Cobb Douglas - San Rafael Clinic:
The results obtained by the multiple regression model are presented below, once the logarithms have been applied for each of the independent variables. The purpose of the logarithmic application was to convert the model into an exponential production function. The final results were as follows:
Y = J. T a. K b. S c
Where: Y = Production; T = Work; K = Capital and S = Supply. A, B and C are coefficients of factor utilization and J = a coefficient of technological change.
So:
Y = 0.1302528. T 0.0554933. K -0.072106. S 1.01661
- A = , 0554933; measures the coefficient of elasticity of the labor factor, as this is less than 1 (0.05 <1), it is said that in order to cause significant changes in the value of production, substantial modifications are needed in the use of labor, since the levels of health service production are inelastic in the face of changes or percentage variations in this factor. On the other hand, to increase 1% (unit) of the production of the service, the labor factor must be increased by 0.0554933. This is an indication that the labor factor needs to be increased more than proportionally if it is desired to increase production at a level higher than the unit level. B = -0.072106;measures the coefficient of elasticity of the capital factor. Note that its value is negative, therefore, this factor decreases the production levels of the service. But in absolute terms 0.072106 is less than 1 (0.072 <1), therefore, an increase of 1% in the value of the capital factor causes a less than proportional decrease in the levels of production of the service. This can be positive (the capital factor being inelastic) since it allows the clinic to increase its capital amortization funds and depreciations without generating such a strong negative impact on the production levels of the service. C = 1.01661;It reflects the coefficient of elasticity of the factor. Since its value is the highest, with respect to the other parameters, and is positive, then it is the parameter that has the greatest positive effect on the levels of production of the service. In absolute terms 1.01 is greater than 1 (1.01 ›1) this factor is said to be elastic. For each unit of production of the service, the supply factor must be increased by 1.01661. J It measures the incidence of technology with respect to productive factors, that is, it allows determining technological changes. As for the San Rafael clinic, it was located at a value of 0.1302528.
From the analysis of the elasticity coefficients, it can be concluded that the coefficients of the productive factors Labor and Capital are inelastic, therefore, to generate growth in the levels of production of the service, the use of these must be increased more than proportionally. that have a positive relationship with respect to production. With respect to the coefficient of the Supply factor, it is elastic, for each unit of production of the service the supply factor must be increased by 1.01661
3.1.4 Determination of Returns to Scale - Cobb Douglas:
The sum of the parameters thrown by the model allows to calculate the level of scale of production of the clinic. In another sense, in relation to the scale performance of the organization, it is pertinent to mention given that the sum of the parameters or coefficients of the production factors is equal to 0.999 ≈1, which means that it is equal to 1, the San Rafael clinic it is operating with constant returns to scale.
3.2 CASE N ° 02: DEA CLINICA SAN RAFAEL BORDER MODEL (06)
The border model technique generates a border in a space whose axes are inputs (X) or factors of production and outputs (Y) or products or services generated. The total of production factors (labor, capital and supplies) are considered as inputs and the total services produced sold as exumes. For the following analysis, information from the results statements of seven clinics in Zulia state was taken as a reference, specifically the analysis will focus on the San Rafael clinic (06).
In the present work the two non-parametric border analysis techniques were used: Data Envelopment Analysis (Data Envelopment Analysis –DEA-) and Malmquist Indices.
3.2.1 Data Envelope Analysis (DEA)
DEA is a methodology that allows to establish and compare the efficiency of similar organizational units, that is, where the set of units analyzed are homogeneous; in order to determine those that are more efficient by comparing the performance of all, which allows to establish which organizations in the sample determine the envelope surface or efficient production frontier. The comparison is made taking into account the relationship between outputs and the inputs used to generate them as a measure of efficiency. This measure is calculated with the results of the different entities analyzed.
3.2.1.1 Output Productivity Analysis
This analysis represents the number of outputs or products that the company could increase by consuming the same current resources.
The following table presents the database for DEA:
| DEA Analysis Results Outputs | ||||||
| Weather | Clinics | Production Value (Y) | Total Inputs (X) | Ф | ∆Y | I = ∆Y + Y |
| T1 | one | 1,161,846,192 | 1,022,372,875 | 118.42% | 214,012,069 | 1,375,858,261 |
| T1 | two | 687,215,995 | 566,960,104 | 111.03% | 75,799,924 | 763,015,919 |
| T1 | 3 | 515,548,610 | 383,081,531 | 100.00% | - | 515,548,610 |
| T1 | 4 | 573,235,130 | 435,957,937 | 102.35% | 13,471,026 | 586,706,156 |
| T1 | 5 | 552,147,549 | 410,540,049 | 100.06% | 331,289 | 552,478,837 |
| T1 | 6 | 475,322,279 | 363,394,160 | 102.89% | 13,736,814 | 489,059,093 |
| T1 | 7 | 526,398,984 | 425,281,571 | 108.73% | 45,954,631 | 572,353,615 |
According to the data presented, it is inferred that the group of clinics that are on the frontier of efficient cannot grow more in their products (Ф = 100%) and the further away they are from it, the more unproductive and inefficient it will be. The scale efficiency (Ф) indicates how far clinic N ° 06 is from the efficiency frontier. In this sense, in general terms only clinic No. 03 (100%) is located within the efficiency frontier; very close to the border are clinics No. 05 (100.06%), No. 04 (102.35%) and No. 06 (102.89%); Clinic No. 01 (118.42%) being the furthest from the border. Because of this, it can be said that the efficiency level of the analyzed group is very close to the border, despite the fact that only one clinic is within the efficiency border (No. 03).
Clinic No. 03 is located on the frontier of output efficiency with exumes (Y) of Bs. 515,147,549 and a total of supplies (X) of Bs. 383,081,531. For its part, the current production value of clinic No. 06 (San Rafael) is Bs. 475,322,279 (Y) with inputs of Bs. 363,394,160 (X), to be projected to the efficiency frontier must increase Bs. 13,736,814 (∆Y) for a total of optimal exumos of Bs. 489,059,093 (Yo).
The results obtained with the execution of the EMS software for output productivity are presented below in the following table. It shows how the benchmarks suggest comparing in terms of scale efficiency with clinic No. 06 with technical efficiency with No. 03; and in terms of technical efficiency, clinic No. 06 has no comparison.
| DMU | $ | $ | ||
| OUTPUT PRODUCTIVITY | ENVELOPE OUTLETS | |||
| TETA Ф | BENCHMARKS | TETA Ф 1 | BENCHMARKS | |
| Clinic 1 | 118.42% | 3 (2.67) | 100.00% | 3 |
| Clinic 2 | 111.03% | 3 (1.48) | 103.03% | 1 (0.26) 5 (0.74) |
| Clinic 3 | 100.00% | 6 | 100.00% | 0 |
| Clinic 4 | 102.35% | 3 (1.14) | 100.74% | 1 (0.04) 5 (0.96) |
| Clinic 5 | 100.06% | 3 (1.07) | 100.00% | 3 |
| Clinic 6 | 102.89% | 3 (0.95) | 100.00% | 0 |
| Clinic 7 | 108.73% | 3 (1.11) | 107.68% | 1 (0.02) 5 (0.98) |
Technical Efficiency (Ф 1) makes it possible to compare clinic No. 06 with that located on the frontier of efficiency. As shown in the table above, clinics No. 01, 03, 05 and 06 have a technical efficiency of 100%. This means that the technical utilization coefficients of the productive factors labor, capital and supplies are adequately combined.
3.2.1.2 Input Productivity Analysis
This analysis represents the amount of inputs or inputs that the company could decrease by producing the same current services. The following table presents the database for DEA:
| DEA Input Results | |||||||
| Weather | Clinics | Production Value (Y) | Total Inputs (X) | θ | Xo | ▼ X = X-Xo | 1- θ |
| To | one | 1,161,846,192 | 1,022,372,875 | 84.44% | 863,291,656 | 159,081,219 | 16% |
| To | two | 687,215,995 | 566,960,104 | 90.07% | 510,660,966 | 56,299,138 | 10% |
| To | 3 | 515,548,610 | 383,081,531 | 100.00% | 383,081,531 | - | 0% |
| To | 4 | 573,235,130 | 435,957,937 | 97.70% | 425,930,904 | 10,027,033 | two% |
| To | 5 | 552,147,549 | 410,540,049 | 99.94% | 410,293,725 | 246,324 | 0% |
| To | 6 | 475,322,279 | 363,394,160 | 97.19% | 353,182,784 | 10,211,376 | 3% |
| To | 7 | 526,398,984 | 425,281,571 | 91.97% | 391,131,461 | 34,150,110 | 8% |
According to the data presented, it is inferred that the group of clinics that are on the efficient frontier cannot decrease more in their supplies (θ = 100%) and the further away they are from it, the more unproductive and inefficient it will be. The scale efficiency (θ) indicates how far clinic N ° 06 is from the efficiency frontier. In this sense, in general terms only clinic No. 03 (100%) is located within the efficiency frontier; Very close to the border are clinics N ° 05 (99.94%), N ° 04 (97.7%) and N ° 06 (97.19%); Clinic No. 01 (84.4%) being the furthest from the border. Because of this, it can be said that the efficiency level of the analyzed group is very close to the border, despite the fact that only one clinic is within the efficiency border (No. 03).
Clinic No. 03 is located on the frontier of entry efficiency with inputs (X) of Bs. 383,081,531 and a total of exumes (Y) of Bs. 515,548,610. On the other hand, the value of the current supplies of clinic N ° 06 (San Rafael) is Bs. 363,394,160 (X), being the lowest of the analyzed group, and some supplies of Bs. 475,322,279 (Y), to project to the efficiency frontier it must decrease by Bs. 10,211,376 (▼ X) for a total of optimal inputs of Bs. 353,182,784 (Xo).
The results obtained with the execution of the EMS software for input productivity are presented below in the following table. It shows how the benchmarks suggest comparing in terms of scale efficiency with clinic No. 06 with scale efficiency with No. 03; and in terms of technical efficiency, clinic No. 06 has no comparison.
| DMU | PE | PE | ||
| SCALE EFFICIENCY | TECHNICAL EFFICIENCY | |||
| TETA θ | BENCHMARKS | TETA θ 1 | BENCHMARKS | |
| Clinic 1 | 84.44% | 3 (2.25) | 100.00% | two |
| Clinic 2 | 90.07% | 3 (1.33) | 96.32% | 1 (0.22) 5 (0.78) |
| Clinic 3 | 100.00% | 6 | 100.00% | one |
| Clinic 4 | 97.70% | 3 (1.11) | 99.02% | 1 (0.03) 5 (0.97) |
| Clinic 5 | 99.94% | 3 (1.07) | 100.00% | 3 |
| Clinic 6 | 97.19% | 3 (0.92) | 100.00% | 0 |
| Clinic 7 | 91.97% | 3 (1.02) | 91.99% | 3 (0.70) 5 (0.30) |
Technical Efficiency (θ 1) makes it possible to compare clinic N ° 06 with that located on the frontier of efficiency. As shown in the table above, clinics No. 01, 03, 05 and 06 have a technical efficiency of 100%. This means that the technical utilization coefficients of the productive factors labor, capital and supplies are adequately combined.
3.2.2 Malmquist Productivity Indices
Malmquist productivity indices for the case of an input and a product, for the “San Rafael” clinic, obtained by the EMS, considering as time 0 the date of January 2005 and as time 1 the data corresponding to December 2005, are as follows:
| Times and / or Distances | Malmquist Productivity Indices | Interpretation |
| D0 (x1, y1) | 204.89% | Represents the distance in time one from the efficiency frontier at time zero |
| D1 (x0, y0) | 134.12% | Represents the distance at time zero with respect to the efficient frontier at time one |
| D0 (x0, y0) | 178.68% | Represents the distance in time zero with respect to the efficient frontier of that same moment |
| D1 (x1, y1) | 153.79% | Represents the distance in time one with respect to the efficient frontier of that same time |
| Malmquist Average | 1,6797 | Greater than unity, which means that productivity has improved from period t0 to t + 1. |
- FINAL CONSIDERATIONS
The pressing reality of the global environment is the age of competition and information, the business challenge is the need to significantly improve productivity; As predicted by Drucker (1993), productivity will dominate the managerial environment for decades, determined by the competitive performance of firms, the quality of life in each country, and the true structure of society.
Within this context, the productive or production function is a fundamental competitive variable of the organization that generates various advantages, because through it the efficiency and profitability of the productive factors and economic activities of a country can be determined.. From this important function, they have developed various definitions and methods for measuring efficiency and productivity, which are of great interdisciplinary significance. Understanding productivity as the relationship between resources used and products obtained, which denotes the efficiency with which resources are used to produce goods and services in the market.
As could be seen, productivity can be studied as a quantitative basic unit and as an economic value. The usefulness of productivity analysis lies in the fact that it serves to study some economic and social problems such as the allocation of resources, productive efficiency, the distribution of wages, the standard of living or improvements in competitiveness, which allow achieving better allocations to the economy. achieve, with the same effort, more and better results in the production process. Hence the importance and significance of this concept.
This diversity of analysis makes the concept of productivity go from being something simple to define, to something extremely complex to understand. Specifically, productivity measurement methodologies have evolved over time, existing multiple types with different types of application and degree of complexity and precision, which have arisen or originated from the contributions of Farell (1957) and Salow (1957).
At present, the two most used methodologies in estimating efficiency through the boundary function are mathematical programming using Data Envelopment Analysis or DEA (Seiford and Thrall, 1990) and what is called econometric boundary (Battese, 1992). Both methods allow estimating the average efficiency level of the sample as well as the efficiency index of each company. A good treatise on the most relevant aspects of this matter can be found in the works carried out by Álvarez (2001), among others.
For its part, the total measurement of the factors of production has concentrated efforts on the most common indicator is labor productivity, it is also true that there are as many productivity indices as resources used in production. However, the partial productivities do not show the joint efficiency of the use of all the resources, so it is important to have a simultaneous measure of the efficiency in the joint use of the resources; that is, a measure of total factor productivity (TFP).
Orienting the Venezuelan economy towards the field of productivity and competitiveness is an urgent task, specialists in the field have coinciding opinions on a number of decisions that must be taken, even more so when these concepts are linked to improving quality life of societies. According to the above, the national competitive culture must be stimulated, created and developed to achieve business success. Hence the importance of substantial improvement of production functions and the application of precise and consistent production measurement methodologies, which allow organizations to make the pertinent adjustments and continuous improvements.
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