7
Decomposing the Productivity Linkages Paradox

Robert D. Pritchard

The productivity paradox can be stated as follows: How can improvements in performance that occur at one level of analysis seem to disappear when performance is measured at broader levels of analysis?

Many interventions developed by behavioral science and the more technological disciplines are geared to improving the performance of individuals and groups. Those disciplines have frequently been satisfied with claiming success for an intervention when it can be shown that measures of the performance of the users have improved. Thus, if a group-based intervention shows that group output has improved, the claim is made that the intervention will help organizations function better. The assumption is that if the group performs better, the organization will function better.

The productivity paradox calls this assumption into question. Indeed, it calls into question the very foundation of much of the work done to improve organizational functioning. Typically, the ultimate justification for work in such areas as personnel selection, training, equipment design, motivation, task design, group structure, and feedback systems is that it will help the organization function better. The paradox suggests the possibility that "successful" interventions can actually have no effect on organizational functioning in that the positive effects of the intervention are somehow being absorbed or negated somewhere in the organization.

The panel's focus on organizational linkages is based on the premise



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Organizational Linkages: Understanding the Productivity Paradox 7 Decomposing the Productivity Linkages Paradox Robert D. Pritchard The productivity paradox can be stated as follows: How can improvements in performance that occur at one level of analysis seem to disappear when performance is measured at broader levels of analysis? Many interventions developed by behavioral science and the more technological disciplines are geared to improving the performance of individuals and groups. Those disciplines have frequently been satisfied with claiming success for an intervention when it can be shown that measures of the performance of the users have improved. Thus, if a group-based intervention shows that group output has improved, the claim is made that the intervention will help organizations function better. The assumption is that if the group performs better, the organization will function better. The productivity paradox calls this assumption into question. Indeed, it calls into question the very foundation of much of the work done to improve organizational functioning. Typically, the ultimate justification for work in such areas as personnel selection, training, equipment design, motivation, task design, group structure, and feedback systems is that it will help the organization function better. The paradox suggests the possibility that "successful" interventions can actually have no effect on organizational functioning in that the positive effects of the intervention are somehow being absorbed or negated somewhere in the organization. The panel's focus on organizational linkages is based on the premise

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Organizational Linkages: Understanding the Productivity Paradox that to understand why the paradox occurs, one must look to the linkages between the levels of analysis. If performance improves at one level but does not show up in the next, there is something about the linkage between the levels that is causing the disappearance of the affect. Understanding the linkages between levels of analysis can lead to a much better translation of improvements at lower levels in the organization into improvements at higher levels in the organization. In other words, if the design and evaluation of improvement interventions are grounded in an understanding of the linkages and their effects, they will have a more positive impact on overall organizational performance. LINKAGES DEFINED An organizational linkage occurs when the outputs from one organizational subsystem are combined with the outputs of another subsystem into broader outputs. Consider the example of a small manufacturing firm of the type exemplified in Figure 7-1. The firm has three levels of analysis above the individual: the unit, the division, and the total organization. The firm comprises a production division, a marketing division, and such other divisions as personnel, maintenance, purchasing, and accounting. The production division includes a design unit and a manufacturing unit. All units and divisions are managed by a top management group. If a new product is being considered, top management makes the decision to allocate resources to develop the new product. The design unit develops the design for the product, the manufacturing unit makes it, and the marketing division sells it. This organization can be thought of as a set of linked subsystems. There are several levels of subsystems in this organization. According to Katz and Kahn (1978) and Naylor et al. (1980), as well as Chapters FIGURE 7-1 Example of an organizational structure.

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Organizational Linkages: Understanding the Productivity Paradox FIGURE 7-2 Organizational subsystem structure. NOTE: I = inputs; P = processing of inputs; O = outputs. 4-6, a subsystem has inputs, it does processing of some sort with those inputs, and it generates outputs. The individuals in each unit are themselves systems that become subsystems for the broader organization. This is depicted graphically in Figure 7-2, which shows the production division from the example above. At the bottom of the figure are the individuals. These individuals have inputs (I) in the form of materials, equipment, training, information, and so on. The individuals process (P) the inputs to produce outputs (O). An individual in the design unit might produce the output of an idea for one aspect of the new product's design.

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Organizational Linkages: Understanding the Productivity Paradox The design unit is also a system in itself. An important part of its inputs is the outputs produced by the individual. This is shown in the figure by the line going from the outputs of the individuals to the inputs of the design unit. These and other inputs are processed by the design unit, which produces outputs in the form of designs for the product. The design unit is also a subsystem in the production division. The outputs of the design unit are combined with the outputs of the manufacturing unit to be inputs to the production division. Finally, there is the entire organization as a system. One major source of its inputs is the outputs of the production division. Thus, the organization can be considered as a series of related systems from the individual to the entire organization. The outputs of the more molecular subsystems become inputs for the next-level system. To return to the definition, a linkage occurs when the outputs of one subsystem are combined with the outputs of another subsystem into the outputs of broader organizational units. In the example, a linkage occurs when the outputs of the individuals must be combined to produce the inputs the design unit uses to produce a new product design. Another linkage occurs when the outputs of the design unit must be combined with those of the manufacturing unit to produce a product of sufficient quality to meet customer needs. Finally, a linkage occurs when the outputs of the production division must be combined with outputs of other parts of the organization to form the outputs of the total organizational system. It is important to recognize that this definition indicates that what is combined in a linkage is the outputs of a subsystem. It is the outputs that are combined with other subsystems' outputs to generate broader organizational outputs. The refrigerator is made by combining compressors with electric motors and painted panels. It is not outputs relative to inputs (efficiency) or outputs related to expectations (effectiveness) that are being combined in the linkage. While one might measure efficiency, effectiveness, or one of the other aspects of performance discussed in Chapter 6 and aggregate it across organizational levels, that is a measure of organizational functioning, not what is being combined across a linkage. In order to understand why the productivity paradox occurs, the paradox must be decomposed. In order to decompose it, the factors that could produce it must be examined. Many of the factors that could produce it have been discussed in earlier chapters. In Chapter 3, for example, Goodman and his colleagues identified a series of intra-and intertask factors that could produce the paradox. My approach in this chapter is to break down the possible factors

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Organizational Linkages: Understanding the Productivity Paradox into three groups. The first group contains structural characteristics. These factors are fairly permanent organizational characteristics that by their very nature would produce the paradox. The second group involves side effects from organizational interventions that could reduce or eliminate the positive effects of an intervention. The third group comprises measurement issues. The first two groups of factors have been discussed in earlier chapters and thus are only touched on briefly here for the sake of completeness. Structural Factors Structural factors are characteristics of the organization itself that could produce the paradox. Time lag is one such factor. Because of the structure of tasks in an organization, improvements in one subsystem sometimes take considerable time to show up in the combined outputs of the broader system. Other structural factors are slack, bottlenecks in the availability of needed inputs, the centrality of the task to the overall functioning of the organization, and the degree of interdependence of people and subsystems in producing the output. (See Chapters 2–4 for discussions of structural factors.) Structural factors have two important things in common. First, they are natural and unavoidable aspects of organizational functioning. Second, they all reduce the one-to-one correspondence between the outputs of one subsystem and the outputs of a broader subsystem. That is, they will in and of themselves produce data that look like the productivity paradox. Thus, to the extent that the paradox is caused by structural factors, there is no real paradox. This leads to the following hypothesis: The greater the presence of structural factors that naturally reduce the one-to-one correspondence between the outputs of subsystems that combine their outputs, the greater the likelihood of the appearance of a productivity paradox. Intervention Side Effects The second group of effects that could produce the paradox consists of unintended consequences of the intervention. It could be that direct measures of the effects of an intervention indicate improvement, but other effects of the intervention have a negative consequence at a broader level of analysis. There are several types of such side effects. One type occurs when the intervention changes the focus of the effort from one unit of analy

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Organizational Linkages: Understanding the Productivity Paradox sis to another. For example, giving each person is a unit a personal computer could result in people working individually rather than in groups. If the task for the unit requires high interdependence if it is to be done effectively, the shift from group to individual activity could decrease the combined, integrated output of the group while increasing the output of each individual. Another type of side effect is that the intervention could lead to changes in communication patterns. The new technology or work process could result in changes in the work structure that would disrupt a well-established informal communication pattern. It might take considerable time to reestablish a new pattern that is as efficient as the old one. Thus, although some output measures increase due to the changed technology, the decrease in communication effectiveness could decrease the unit's overall output. These and other unintended side effects were discussed in Chapters 2–4. The important thing to note for the purposes of this chapter is that this class of factors exists and can be part of the paradox. Unintended side effects can produce the paradox in that performance can improve in one aspect of the work, but decreases that occur in other aspects of the work can eliminate the positive effects when the aggregation to a higher level of analysis occurs. This leads to the following hypothesis: To the extent that unintended negative side effects of a successful intervention occur, they will reduce the overall output of the subsystem and thereby produce the appearance of a productivity paradox. Measurement Issues The third group of factors that can explain the paradox involves measurement issues. A major point in this chapter is that measurement issues are a critical key to decomposing the productivity paradox. There are two classes of measurement issues. The first comprises issues that are natural phenomena in organizations, and although they should be recognized and understood, they are not a cause for particular concern. The second class of measurement issues comes to the fore when there are actual errors or conflicts in the measurement of organizational performance. This class of measurement issues is much more critical to organizational functioning than the first class and much more problematic for decomposing the productivity paradox. In the next two sections, I examine each class of measurement issues in detail.

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Organizational Linkages: Understanding the Productivity Paradox MEASUREMENT ISSUES: NATURAL PHENOMENA Different Measurement Purposes Organizational performance is measured in different ways for different purposes. This is true whether what is being measured is productivity, effectiveness, efficiency, or any other aspect of performance. There are five major purposes in measuring organizational performance, each of which has very different implications for what is measured (Pritchard, 1992). The first purpose of measuring is to compare large aggregations of organizations to each other. Examples would be comparing the national economies of the United States and Japan and comparing the health care and computer industries. This type of performance measurement may be used by government agencies in determining how to control monetary policy, by government officials who are negotiating trade agreements with other countries, or by researchers studying broad organizational trends. A typical measure used for this purpose is price-deflated gross national product divided by the number of worker hours used (e.g., Kendrick, 1984; Mahoney, 1988). The second purpose of measuring is to evaluate the overall performance of individual organizations for comparison with other organizations or with some standard. In this type of measurement, yearly sales figures, profit and loss margins, price/earnings ratios, and percentages of market share would typically be used. Performance measurement of this type might be used by individual investors to determine where to place their investment dollars. The third purpose of measuring is for use as a management information system. Here, the focus is on a single organization, and the measurement deals with the functioning of the human-technological system. The question to be answered is how the entire organization or major parts of it are functioning, and whether that functioning is improving or declining. This type of measurement is used by upper management to determine major resource allocations, long-range goals, strategic plans, and the like. The fourth purpose of measuring is to control parts of the organization. Although this type of measurement is often overlooked (Weiss, 1989), the control of the movement and timing of material resources and products is quite important to the efficiency of an organization. Under this heading are included such activities as production engineering and scheduling, quality control, materials distribution and management, and inventory control. The goals of this type of measurement include

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Organizational Linkages: Understanding the Productivity Paradox identifying whether problems are developing and assessing the effect of changes made in operations. The fifth purpose of measuring is for use as a motivational tool (e.g., Algera, 1989). The objective is to improve performance by encouraging behavioral changes in individuals. The assumption underlying this type of measurement is that the human resources of an organization can have a significant impact on the organization's performance. In other words, personnel can exert more effort, be more persistent in their efforts, and spend their efforts in more optimal ways, thereby working more efficiently and effectively. Although the last three purposes appear to be somewhat similar, there are important differences. Each measures performance in a single organization, but they focus on different things and at different levels of the organization. The management information system is concerned with the overall functioning of the organization or its major subsystems and deals with macro measures, such as the profitability of the total organization or the contribution of different units to some type of overall effectiveness. The measurement information is rarely given to lower-level personnel in the form of feedback. Data gathering for the control purpose is typically done on smaller-sized organizational units than for the management information system, and it uses less macro measures, such as the flow of resources to various units and how well work is being scheduled. In addition, it does not attempt to separate the effects due to personnel from the effects due to technology. Measurement for motivation is concerned with the performance of individuals or work groups and gathers data on the accomplishment of specific work objectives. It is done, ideally, so that the effects due to personnel can be separated from the effects due to the technology, and the results are typically given to unit personnel in the form of feedback. Different Measurement Purposes Require Different Measures What is most critical for the discussion here is that measuring for different purposes involves measuring different things. As one moves from measuring for motivational purposes to measuring the total organization, new causal factors come into play that will affect the values produced by the resulting measurement. This is illustrated in Figure 7-3. The middle section of the figure represents the transformation of outputs that is made from individual to unit, to division, to total organization. As noted above, the outputs of the more molecular levels become the inputs of the more molar levels. However, other inputs are added at each level in addition to the outputs of the more molecular level. The upper section of the figure shows some of the many factors

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Organizational Linkages: Understanding the Productivity Paradox FIGURE 7-3 Measurement levels and sources.

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Organizational Linkages: Understanding the Productivity Paradox that are added at each level of analysis in the form of inputs or constraints. In Figure 7-3, the behavior of the individual, the most molecular level, is combined with the existing technology to produce unit-level outputs. The supervision of the individual also influences the transformation of individual outputs to unit outputs. As an example, design engineer using a computer-assisted design (CAD) system produces specific designs for parts of a new product. Individual or submit outputs are combined through an integration and coordination function that is overseen by the supervisor. The combined effects of individuals, the technology, and the supervision function produce the unit's outputs. Thus, the designs of individuals or small groups are combined into an integrated, final design for the new product, which is the output of the design unit. The outputs of the manufacturing unit would be finished products. The outputs of the design and manufacturing units are then combined into outputs for the production division. To accomplish this, a coordination function is required so that the outputs of the units can be integrated effectively. The plans developed by the design unit, for example, must be manufacturable at a reasonable cost. In addition, a major resource acquisition process occurs when the person in charge of the division must acquire resources from top management. The more effectively this is done, the greater the outputs of the division tend to be. The entire division has its own outputs that relate to the finished product. To measure the performance of the division, measures might be taken of how long it took to develop a manufacturable product, how economically the product can be made in the future, and how well the product meets customer needs. What is critical here is that the measures of the division's performance include not only the outputs of the two units forming it, but additional causal factors as well. Specifically, the effectiveness of division management in getting resources, how well those resources are divided between the two units, and how well the coordination is done between the two units will all influence how well the division performs on its measures. The same process occurs for higher levels in the organization. One division's outputs are combined with those of other divisions to be inputs for the total organization. In this example, the outputs of the production division are combined with those of the marketing division to produce sales and revenues for the total organization. These are combined with the costs and revenues of other divisions to produce the organizational-level outputs. If the total organization is measured on such factors as return on investment, total revenues, net profits, and so on, new causal factors are again added to the performance measure. In Figure 7-3, the factors shown are the strength of the economy, govern

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Organizational Linkages: Understanding the Productivity Paradox ment regulations, and actions of competitors. These are factors that will influence the overall performance of the organization on its measures, but they are not a function of the actions of the organization's divisions. At the bottom of the figure, some of the different measurement purposes are listed. They indicate graphically that different factors are included when measurement is done for different purposes. Measurement for motivational purposes should measure only what the individual or the unit has control over. It will frequently measure up to the level of unit output, but it should try to remove the effects of the technology. The management information purpose encompasses individual behavior, the performance of the technology, how well supervision is done, the effectiveness of coordination of the individual units, and the effects of resource acquisition. Measuring total organizational performance typically includes all the factors shown in Figure 7-3, including those outside the organization. One should expect the productivity paradox to occur when measures collected for different purposes are compared. For example, suppose an organization introduces CAD technology and finds that its design engineers are able to create better designs and in less time. It then measures overall organizational outcomes, such as return on investment and gross profit and finds no change. This is an example of the paradox, but it really makes no sense that the two measures should be related. As Figure 7-3 illustrates, measures at the organizational level of analysis will be influenced in a very minor way by the design unit's producing the better designs. This leads to the following hypotheses: The more factors that are added to a measure of organizational functioning when it is aggregated from lower to higher levels of the organization, the weaker the relationship between the original measure and the composite measure will be. The more factors that are added to measures of organizational functioning when they are aggregated to higher levels of the organization, the greater is the likelihood of finding evidence of a productivity paradox. Different Aggregation Strategies The problem being discussed here can be seen as an issue of aggregation. The concept of linkages is by definition a cross-level issue—measures are aggregated across levels of analysis. In order to deal with cross-level questions, measures must be developed that go across levels

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Organizational Linkages: Understanding the Productivity Paradox Step 4: Create the Feedback Report The fourth step in developing ProMES is to create a formal feedback report. Once indicator data are collected, effectiveness scores can be determined based on the contingencies for each indicator. As can be seen in Figure 7-5, if 99.8 percent of the group's boards pass inspection, it would achieve an effectiveness score of +62. Continuing this process would result in an effectiveness value for each indicator. Once effectiveness values for each indicator are determined, they can be summed to determine the overall effectiveness score for that particular work group. This score represents the group's level of overall performance. A score of zero means that the group is meeting expectations; the higher the score is above zero, the more the unit is exceeding expectations. This information is presented to the unit in a formal written feedback report on a regular basis. Figure 7-6 shows an example of such a report. Another overall measure that can be derived from the system is the group's percentage of maximum effectiveness, that is the overall effectiveness score the group would receive if it was at the highest possible level on every indicator. The unit's actual overall effectiveness score for the period can then be expressed as a percentage of this maximum. For example, summing the maximum values for each of the indicators in the example yields a total possible score of 300. The example unit received a monthly score of +97. Thus, its percentage-of-maximum score was 97/300, or 32.3 percent. The closer the unit is to 100 percent, the Circuit Board Manufacturing Unit Date: July 19xx I. Production   A. Percentage of Boards Completed 98% +40   B. Percentage of High-Priority Boards Done 85% -5   Total Effectiveness: Production = +35     II. Quality   Percentage Passing Inspection 99.8% +62 III. Attendance   Percentage of Maximum Hours Worked 97% 0   Overall effectiveness = +97     FIGURE 7-6 Sample feedback report.

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Organizational Linkages: Understanding the Productivity Paradox closer it is to performing at the maximum performance level. If the unit's overall effectiveness is negative (i.e., below expectations), a negative value of the percentage-of-maximum score is calculated. The advantage of the percentage-of-maximum index is that it allows the performance of groups doing very different things to be compared. The group with the highest percentage-of-maximum score is the highest-performing work group. This comparison is valid even if the groups have different indicators because the contingency process scales all indicators on a common metric, overall effectiveness. The comparison between different groups is then based on this common metric. The ProMES methodology was first developed and evaluated in five units of an Air Force base (Pritchard et al., 1989). It resulted in large gains in productivity, and those gains were maintained for the entire time of measurement—at least 20 months. The methodology has also been successfully implemented in other organizations in the United States and Europe (Janssen and van Berkel, 1991; Jones, 1995; Kleinbeck et al., 1991; Kleingeld et al., 1991; Roth et al., 1995; Hedley et al., 1995; Schmidt, 1991; Stout and Jones, 1989; Thierry and Miedema, 1991; van Tuijl, 1991). ProMES and Linkage Issues ProMES is one methodology that can be used for dealing with conflicts in objectives that can produce the productivity paradox. The technique can be seen as a way of formally identifying organizational policy. Products, indicators, and contingencies reflect what the objectives of each subsystem are, what measures will communicate how well the subsystem is fulfilling those objectives, the relative importance of each measure, what is expected on each measure, and what level of output is defined as good or bad. This is a statement of policy. It is developed subjectively, but policy is by nature subjective. What ProMES does is to give organizational personnel a methodology with which to define policy in a way that people can understand, that people can agree with or not, and that can be communicated clearly. By going through the process of developing the system, incumbents, supervisors, and managers can come to terms with the fact that there are disagreements in policy. These disagreements almost always occur somewhere in the development of a system. However, because the system gives personnel a structured method for dealing with the disagreements, it can make reaching a satisfactory compromise easier. This approach can be used across organizational levels and at the same level. Through the process of getting incumbents and supervisors to agree on the elements of the system and then presenting those elements to higher management and gaining approval, disagreements in objectives and

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Organizational Linkages: Understanding the Productivity Paradox policy across levels are made clear. Where possible, they are resolved and a new, more congruent policy is developed. If agreement is not possible, at least people know where the disagreements are and why they exist. This seems to make it easier to cope with the conflict. The process of developing the system also helps resolve conflicts between units that must coordinate with each other. When the system is developed, it becomes clear where objectives are not consistent. In the design and manufacturing units in the example above, it would be clear from an examination of each unit's products and indicators that the two units are evaluating themselves differently. It then becomes the responsibility of higher management to work with the two units to bring products and indicators more in line with the objectives of the broader organization. One way this can be done is for each unit to have its own products, indicators, and contingencies as usual, but to have additional indicators that are a function of the joint efforts of the coordinating units. In the example, the common measures could be time to complete the final prototype, number of changes in the original design, and number of prototypes needed. These measures can only be highly favorable when the two units work closely together in developing the new product. These common measures would be added to the measurement system of each unit. If the two units want to look good on their measures, they must work together effectively. ProMES and Aggregation The point has been made that one way of avoiding the productivity paradox is to aggregate only measures that are influenced by the same set of causal factors. The ProMES methodology offers a way to do this through the percentage-of-maximum measure. This is the index that is the unit's actual overall effectiveness divided by the maximum possible effectiveness for that unit. It is a metric that is common across all types of units, no matter what work they are doing. One could calculate the percentage of maximum for a variety of different units. The mean percentage of maximum across the units would be the overall index of how well personnel are performing the organization's work. TOWARD A COMPOSITION THEORY OF LINKAGES While it is important to decompose the productivity paradox and suggest solutions for dealing with it, the larger objective must be kept in sight: learning about productivity linkages. The paradox is only an example of the importance of studying and understanding linkages between organizational subsystems. What is really needed is greater

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Organizational Linkages: Understanding the Productivity Paradox awareness and understanding of how outputs get combined and transformed across organizational levels. The solutions to decomposing the paradox suggested above are a start in this direction, but they are just partial solutions. What is needed in addition is more conceptual work that will enable researchers and practitioners to understand better the nature of organizational linkages. Specifically, a sound theory of aggregation is needed, that is, a theory for how organizational levels are related to each other and how that affects organizational productivity. Rousseau (1985) has cogently made the same point, arguing that when aggregation is done, what she calls a ''theory of composition" is necessary. A composition theory specifies what the relationship is between the variables of interest at each level of aggregation. In the case of productivity, the composition theory would describe conceptually how productivity at the individual level is combined to produce productivity at the group level, and how the productivity of the groups are combined to produce divisional and organizational productivity. A simplified example of such a composition theory is shown in Figure 7-7. The darker boxes in the middle of the figure show the linkages going from the individual to group to organizational level of analysis. Other levels would be needed for a complete theory, but the three depicted make the point. Above and below the middle of the figure are causal factors that will influence the transformation of outputs (i.e., linkage) from one level to the next. The theory might suggest that an individual's output is a function of abilities, knowledge gained through training and experience, motivation, and availability of materials/resources to do the work. These variables combine to produce individual output, the first box in the figure. However, since the individual's efforts must be combined with those of others, how well individuals work together will influence how well the individuals' outputs are translated into group outputs and, ultimately, group performance. In addition, if the supervisor does not provide sufficient materials and information and does not handle intergroup and intragroup relations well, group performance will be affected. Thus, the quality of supervision is also involved in the translation of individual to group performance. Another variable in this composition theory is the degree of interdependence of the individuals in the group. If each person works completely independently, moving to a higher level of analysis is more straightforward. Individual measures can be more easily aggregated because the work of one individual has little impact on the work of the others. If, however, there is a great deal of interdependence in the work, the situation is much more complicated. In this case, it is inap-

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Organizational Linkages: Understanding the Productivity Paradox FIGURE 7-7 Simplified model of composition theory.

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Organizational Linkages: Understanding the Productivity Paradox propriate simply to sum individual measures. Specific group-level measures that will capture the interdependencies would be needed. Role accuracy is another variable that influences the translation of individual output to group performance. This variable is conceptualized as the accuracy of the match between what the individuals see as important in expending their time and effort and what is important to the broader group. Other variables influence the translation of group-level performance to organizational performance. Inputs from other units are the outputs of other units that are needed to translate group-level performance to organizational performance. They could include other components of the final product, direct services (e.g., marketing), or staff functions of various types. Match of group to organizational objectives is analogous to role accuracy, but at the group level. It is the degree of match between group objectives and organizational objectives. Factors outside the organization include the economy and government regulations. Once the variables in the theory of composition are identified and defined unambiguously, the next step would be to develop quantitative operationalizations of each variable. For example, degree of interdependence could be operationalized as the correlation of mean individual output and total group performance over time. If personnel in the group are truly independent, their individual outputs can simply be summed to arrive at total group output. In this case, if one calculated the correlation between mean individual output and group output over time periods, the correlation between the two measures over time would be 1.0. Thus, if this correlation is close to 1.0, the individuals are highly independent. If there is dependency between group members, the outputs of one individual influence the outputs of others. In a case of interdependence like this, the mean outputs of the individuals cannot simply be added to get total group output. Consequently, the correlation between mean individual output and total group output over time will decrease from 1.0. The greater the interdependency, the greater the decrease from 1.0 toward 0. Once the operationalizations have been developed, the next step would be to estimate mathematical functions that capture how the separate variables are related to each other. For example, the interdependence coefficient, which ranges from 0 to 1.0, could be a multiplier between total individual output and group performance. An interdependence coefficient of, for example, .50 would mean that increasing individual output would improve group performance, but not as much as when interdependence is lower (e.g., a coefficient of .8).

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Organizational Linkages: Understanding the Productivity Paradox Advantages of a Theory of Composition While this theory of composition and the example functions are simplistic, they illustrate what a theory of composition for productivity linkages might be like. A great deal of work would be needed to develop a comprehensive theory, but the work would be well worth it because of the advantages of such a theory. One major advantage of such a theory would be that it would enhance understanding of productivity linkages and cross-level organizational analyses in general. Researchers and practitioners have been very naive in their approach to organizations, assuming that changes in one level of the organization will automatically be apparent at higher levels of the organization. It is commonly implied, for example, that better selection of entry-level personnel will improve organizational productivity. The argument is that if the mean productivity of individuals is improved by, for example, 10 percent, the productivity of the unit will improve by 10 percent. This sort of argument ignores all the factors that the theory of composition indicates influence the translation of individual to group productivity. If the output of a group of programmers is increased by 10 percent through better selection, but the work flow between programmers is not managed so as to utilize the improved individual performance, the increase could easily be lost. A clear theory of composition would make the fallacy of the assumption very clear and indicate the factors that intervene in the linkages. Once there is even a basic mathematical model of the linkages, several other benefits become possible. One advantage will be the ability to predict the relationships between components of the theory. Not only will this allow the theory to be tested, but once supported, the theory can then be used to predict what to expect when components of the model are changed. One application of this capability of the model is to predict whether productivity gains at one level will be lost or wasted in their translation to higher levels. For example, it may be possible to predict that with the level of slack that exists in a given unit, improving the efficiency of one group will simply increase the amount of slack, not improve the broader unit's performance. Another application is to do "what-if" and sensitivity analyses to compare productivity improvement strategies. For example, one could compare the expected gain in performance at the group and organizational levels from (1) improving personnel selection, (2) clarifying roles, and (3) changing technology. Being able to approximate the gains that would occur with different strategies could be of great benefit in deciding among alternatives.

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Organizational Linkages: Understanding the Productivity Paradox DIRECTIONS FOR FUTURE RESEARCH Attempting to understand linkage issues leads to a series of ideas for needed research. First, the most general need is for research that further explains the importance of linkages and the impact they have on attempts to improve organizational performance. It is easiest just to focus on a single intervention at a single level of analysis, but as this report makes very clear, such a strategy is overly simplistic. Second, future researchers need to avoid the temptation to try to identify the "proper" criterion for assessing organizational performance. It make no sense to talk about organizational performance or effectiveness as if it is a concept that has a universal meaning. It is like asking whether an individual is a good performer. The obvious answer is a good performer at what? What constitutes organizational performance is what the measurer wants to assess the organization on. Researchers must be very careful that they do not fall into the trap of assuming that there is a set of agreed measures or even that one set of measures is somehow better than another. Third, in order to attack the linkages problem in a systematic fashion, researchers should develop a master list of variables that could influence the translation of outputs across linkages. The chapters in this report are an excellent source for such a taxonomy. Such a listing could group the factors by type. For example, this chapter breaks down factors into structural effects, intervention side effects, and measurement effects. Within each type, the factors could be grouped by the type of solution needed to address the linkage issue. For example, variables that are the natural consequence of organizational structure (e.g., slack), which cannot and should not be considered problems, would be grouped together. Fourth, empirical research is needed to identify the major linkage variables and their relative importance. To do such research, multiple units within multiple organizations must be studied in a longitudinal design. As a first step, improvements in outputs at the most molecular level must be shown to have occurred because of an intervention, and then those improvements must be traced through the various organizational linkages to the broadest organizational level. The idea would be to measure each explanatory factor as identified in the linkages taxonomy, along with the amount of loss of output across the linkage. For example, explanatory variables such as slack and conflict in objectives would be measured directly. Then, the importance of each could be assessed empirically. Ideally, the data would be collected so that the variance accounted for by each explanatory factor could be assessed. The most important types of linkage variables are those that result

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Organizational Linkages: Understanding the Productivity Paradox in the actual loss of outputs from one level to the next. This represents waste, and to the extent it exists, its elimination will improve organizational functioning. Thus, the next step in the research program would be to use interventions to change the factors that are decreasing the translation of outputs across levels and assess the effectiveness of the interventions. For example, if conflict in the objectives of different units is causing the linkage loss, interventions to make the objectives consistent would be employed. The evaluation would be to assess the effectiveness of different types of intervention and to determine if the linkage loss can be eliminated. Finally, a theory of composition is sorely needed. As argued in this chapter, this is a theory that indicates what the major linkage variables are and how they affect the translation of outputs from one level of the organization to the next. This would be a major research program that would take a great deal of work. However, if it could be done successfully, the payoffs would be enormous. CONCLUSION It is clear from the issues raised in this chapter that the productivity paradox is of great significance in that it highlights the importance of a much clearer understanding and appreciation of the linkages among levels of the organization. Researchers and practitioners have been very simplistic in thinking that changes at one level in the organization will be translated in a simple manner to higher levels. There are many possible explanations for the paradox, the importance of which is to enhance understanding of organizational linkages. This and other chapters in this report suggest many factors that must be considered in understanding these linkages. The challenge is to use these ideas to further understanding of linkages and, from that, to learn how efforts to improve productivity can be facilitated. AUTHOR'S NOTE I would like to thank Margaret Watson for her contribution to an earlier version of this chapter. Steven Worchel suggested several of the ideas in the section on unintended side effects of organizational interventions. I would also like to thank Amie Hedley-Goode, Karlease Clark, and Anthony Paquin for their helpful comments on an earlier draft of the chapter.

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