We turn next to the progress that has been made in estimating the costs of achieving high performance standards. We begin by examining explicit attempts to generate cost estimates and then turn to what has been learned about the productivity and cost of a key educational input: the quality of teachers and teaching.

Existing Attempts to Estimate the Cost of Educational Outcomes

Researchers are dealing more explicitly with the links between costs and outcomes in a school finance context. Several approaches have emerged, and in this analysis we review each in turn. The approaches vary in terms of their degree of emphasis on economics, and we have ordered the discussion such that we move from approaches with the least to approaches with the most economic content. In particular, we examine the educator judgment model, the unit cost of inputs model, the cost of prevailing best practices model, and the cost function model, with and without adjustments for efficiency.

Educator Judgments

The goal of this approach is to assess the cost of providing an "adequate" education for students based on a consensus among educators over adequacy's relevant components and realistic best practices. These agreed-upon components and practices are then assessed in terms of their cost and totaled into an estimate of the full cost. The approach takes into account the inefficiencies associated with funding the expansion of actual practice to meet outcome standards (recall how large TC(AP) was presumed to be relative to TC(RBP)), but the search for the relevant benchmark tied to realistic best practices is based on judgments from panels of disinterested educators about what is appropriate under a given set of circumstances. One could argue that this is the default approach states have relied on for years as they have designed school finance formula, but in recent years there have been more explicit attempts to look at these judgments from a cost-resource perspective. The resource cost model that was developed by Jay Chambers and Thomas Parrish for Illinois and Alaska (Chambers and Parrish 1994) is a sophisticated and quite ambitious version of this approach. More recently, Guthrie et al. (1997) developed a version of this approach for Wyoming.

The approach relies heavily on the judgments of educators to ascertain the components of realistic best practices based on years of professional experience in different settings. There is no formal link with outcomes other than the available wisdom based on practice from those participating in the process. Although efforts are made to make the panels "disinterested," questions remain about the accuracy of such judgments as well as about potential conflicts of interest because there is likely to be an understandable underlying agenda to justify additional resources which support unmet educational needs of students. We also note that these efforts have not been informed by clear statements from the states or other standard setting bodies about the features of Matrices A and A*. None of the key elements of what constitutes adequate outcomes (see the list of items 1-5, previously) are specified. In this light, the necessary implicit judgments, estimates, and guesses of the various S_ijks are all the more difficult to deduce.

There have also been some recent attempts to "cost-out" innovative programs that purport to reflect realistic best practice that are sensitive to both the underlying circumstances educators face as well as the kinds of outcome standards that are being established. These models include "Success for All," accelerated schools, and the School Development Program, among others. Cost assessments of these models to date include King (1994) and Barnett (1996). Chaikind and his colleagues (Chaikind, Danielson, and Brauen 1993) reported the use of similar approaches to estimate the cost of special education. We include these efforts under the educator judgment heading because the models are adopted because of professional judgments about their appropriateness in a given setting and because they include judgments about how to best adapt the requirements of each model to local circumstance. The resulting cost estimates therefore reflect an attempt to achieve benchmark efficiency standards that lie between the two extremes that we have identified (TC(IBP) and TC(AP)).

Unit Cost of Inputs

Efforts have also been made to focus on differences in the unit cost of key inputs into the educational system. A number of different approaches have been employed, some relying on a market basket strategy (e.g., McMahon 1996) in which the focus is on how much a given basket of inputs costs in one place compared with another, and others in which the emphasis is on underlying models of supply and demand with allowances for compensating differentials such as the fact that teacher salaries tend to be lower in places with favorable working conditions, all else being equal. These latter models are called hedonic wage models and have been studied extensively by Jay Chambers (1997, 1998). These hedonic models are particularly interesting for our purposes because they include explicit distinctions between influences on the unit prices of inputs that are within and outside of the control of local school officials. Recall that this is the essence of the distinction we emphasized between the realistic and idealized best practice standards.

It is worth noting that the unit cost approach to date has not made an explicit connection to the outcome standards reflected in Matrices A and A*. The question is more along the lines of asking how much more it costs to hire the same input in one place compared with another. Clearly, this is a relevant question. It bears directly on one of the key sources of cost difference between the various services that might be employed to produce a given gain in a given area of learning (i.e., S_ijk versus S_{ij(k +1)}). But, it should be clear how far short this approach falls of specifying all of the possible sources of cost difference and contingency that need to be dealt with in a comprehensive calculation of what it will cost in a particular place to reach a prespecified set of outcomes. As we shall see in the discussion about cost functions, it is possible to build unit cost indices into more comprehensive measures of the costs to produce educational outcomes.

Costs of Observed Best Practices

Under this rubric can be found explicit attempts to link outcome standards to comprehensive conceptions of cost. In other words, costs are not restricted to differences only in the unit prices of individual types of inputs, and the formulation deals directly with learning outcome phenomena. The outcome standards are specified in terms of performance on examinations, and the question becomes one of identifying places that seem to be producing these outcomes with admirable levels of efficiency.

The strategy is intuitively straightforward. Districts are identified that have reached a pre-specified minimally acceptable level of performance, and efforts are made to control for gross differences in the contextual reality of the identified districts. For example, districts with extraordinarily high or low levels of wealth and expenditure might be excluded on the grounds that they are highly atypical. The next step involves carefully reviewing practices that exist within the identified districts with an emphasis on identifying efficient results. For example, it might be found that some districts in the group are able to reach the outcome standard with a given set of class sizes and characteristics of instructional personnel. The costs of these various approaches can be estimated and interest can be focused on those successful places with the lowest level of cost. These districts and their practices can become benchmark standards. The associated cost estimates can then be used as the basis of a school finance system that is designed to cover the costs of adequate programs in which adequacy is rooted in outcome standards. A number of states have explored one version or another of this approach in recent years including Ohio (Augenblick 1997), Illinois (Governor's Commission, 1996), Mississippi (Augenblick, Myers, and Anderson 1997), and New York (Monk, Nusser, and Roellke 1998).

The implicit reasoning within this approach is that if some places can produce the desired test score results at a given (low) level of cost, it follows that it is possible for others to do so as well and that we can scale up the system by providing only those resources that would be necessary if the observed best practices were employed. In other words, the resources commensurate with TC(AP) should not be provided, and policymakers can rest easy knowing that they are not facilitating the kind of internal inefficiency that is suggested by the high cost shown for TC(AP) in figure 4.

Of course, the key piece in this reasoning is whether the prevailing best practices in settings in which they are observed are realistically available to places in which they are not currently in place. The approach includes efforts to adjust for differences in extenuating local circumstances, but the adjustments to date are not very sophisticated.

Our conclusion is that the cost of the observed best practice approach represents an important step in defining the middle ground efficiency benchmark that needs to be established in any serious attempt to estimate the costs of outcome performance standards, but that it is based on a crude set of adjustments. The approach moves the field in the correct direction, but the distance traveled is modest. Although there is progress to report, it needs to be recognized that this progress can have adverse effects at individual sites. For example, a given site may be seriously disadvantaged in its efforts to secure funding if it is expected to achieve an observed best practice that is not realistic for understandable reasons. Of course, this begs the question of what the "understandable reasons" are, but this is the crux of the problem facing analysts who work in this area.

Other problems lie in the approach's heavy reliance on existing test scores as the basis of the outcome standards. The available test score indicators are far removed from the kinds of outcome standards implicit in Matrices A and A*. The approach enjoys the virtue of an explicit emphasis on outcomes, but is limited by the narrowness and crudeness of the available indicators.

Cost Functions

In defining cost functions, economists have been the most active with ambitious models that attempt to take into account differences in unit prices of inputs as well as differences in how the inputs are being combined, all with effort to provide sophisticated controls for district structural characteristics in order to avoid the criticism we just made of the observed best practice approach.

The cost function approach makes use of econometric estimating techniques including explicit attempts to model simultaneous and other endogenous effects as well as nonparametric techniques such as data envelopment methods. These models represent some of the most promising work to date in the effort to establish the costs of outcomes and warrant a careful assessment. The models are potentially of great interest to policymakers because they establish conceptual links between outcomes and resources, and also because they have the potential to give concrete dollar estimates of the costs of achieving adequacy.

Let us begin with a general overview of the approach. The idea is to estimate a cost function. A cost function, when properly estimated, reveals the minimal cost necessary for achieving a given result. Presuming we can specify adequacy in terms of Matrices A and A*, and in theory we should be able to ascertain the idealized minimal cost of doing so—namely, TC(IBP), thanks to the construction of a cost function.

Of course, there are many difficulties which fall into different categories: (1) we are not very advanced in specifying the properties of Matrices A and A* (i.e., our outcome-oriented adequacy standards); (2) we suspect that there is a substantial amount of prevailing inefficiency in the field such that a survey of randomly selected sites could be misleading in terms of identifying best practices; (3) there is considerable endogeneity inherent in the system (i.e., features that have bearing on costs are related to other embedded characteristics and it can be difficult to disentangle the several different ways that influences on cost are connected); and (4) judgments need to be made about what is accepted as realistic versus idealized best practice.

Analysts have responded in various ways to these challenges, and we review their work in the order of the level of ambition and technical sophistication involved. An important step in the direction of estimating education cost functions was taken by Imazeki and Reschovsky (1998). They used multivariate methods to estimate a cost of education function for Wisconsin and took account of endogeneity by using instrumental variable estimating techniques. Imazeki and Reschovsky also included a teacher input cost index so that their model dealt with important unit cost differences as well as with costs associated with differences in how inputs can be combined to produce outcomes.

Imazeki and Reschovsky acknowledge the problem associated with uneven amounts of inefficiency across the observations in their data. This unevenness is problematic because it means that high levels of observed spending due to inefficient operation may be misinterpreted as unavoidable high costs of producing the outcomes in question. Concerns about the uneven levels of efficiency among observed schooling units has prompted some analysts to build "efficiency" adjustments in their cost function approach. William Duncombe and his colleagues have worked on this problem and have made use of data envelopment techniques to construct measures of individual school district's efficiency levels using New York state data (e.g., Duncombe, Ruggiero, and Yinger 1996). The logic is that the addition of a control for differences in efficiency across the sites in the sample establishes the long-sought realistic best practice benchmark that will ultimately permit the state to make aid adjustments that are sensitive only to bonafide differences in costs (higher expenditures due to circumstances over which there is no local discretion).

A central question is whether techniques like data envelopment are adequate to the task of generating a trustworthy efficiency adjustment-control. There are good reasons to exercise caution. First, the technique is similar in principle to what underlies the observed best practice method in which districts achieving similar results are compared and those doing so with the least amount of cost are singled out as examples of what, in theory, is possible for the others to achieve. A problem arises if what is possible for some is realistically not possible for others. The data envelopment method attempts to keep the analysis realistic by employing a linear optimization routine that compares districts facing similar exogenously determined environmental factors (e.g., size, wealth, composition of the student population, etc.). Although these environmental features are relevant and permit more sophisticated controls than those shown earlier for the cost of the observed best practice model, there is no doubt that they fall short of controlling completely for the circumstantial influences on what counts as realistic best practice (TC(RBP)).

As an example of how the statistical controls can fall short of the mark, consider the case of two school districts with very similar characteristics with the exception of their size. Suppose that the smaller of the two districts finds itself spending at higher levels to provide a comparable outcome for its students. Suppose also that the reason for these higher costs is a rancorous history of past attempts to reorganize the district into a larger unit. Finally, suppose that there is ample "blame" for this state of affairs, which is widely shared across and within the affected communities. It is hard to conceive of a statistical indicator which is going to capture the rancorous history that could have bearing on a decision to treat the higher spending in the smaller setting as a legitimate higher cost rather than as an instance of inefficiency that should not be offset by the state. We can reach different conclusions about what counts as "realistic" best practice in the smaller school setting, and an efficiency indicator that is based on the data envelopment methods that are currently available is not likely to resolve this question.

Second, the technique depends heavily on the specification of outcomes. Recall the emphasis we placed on the components of Matrices A and A* as the core of an outcome-oriented standard. The existing data envelopment methods are based on standardized test score outcomes and are insensitive to the kinds of important outcome specification questions that are included in these two matrices. This is important because there is a potential for the envelopment comparisons to be made across districts pursuing very different agendas in terms of outcomes. The higher spending that is observed in one place may reflect an efficient pursuit of higher standards (the results of which are not captured by the existing assessments), but the envelopment method could interpret the higher spending as evidence of a serious inefficiency. A clear specification of outcome targets and consensus about what the state-imposed adequacy standards are going to be is essential for the development of an accurate and dependable efficiency index.

Third, there are conceptually distinct degrees of efficiency, and data envelopment methods actually employ a relatively weak efficiency test. Ruggiero (1996) called attention to the difference between Farrell and Koopmans standards of efficiency. Passing the Farrell standard means that there is no way to reduce inputs equi-proportionally and maintain the same level of outcome. In other words, a school district will be Farrell efficient if it is impossible to reduce all inputs by some common percentage amount and maintain the same level of outcome. In contrast, within an inefficient district in a Farrell sense, it would be possible to reduce all inputs by, for example, 3 percent and have no adverse effect on outcomes. Koopmans efficiency requires that all slack be removed from the system such that it is impossible to reduce any input without adversely affecting the level of outcome. Thus, Koopmans efficiency is a more stringent standard in the sense that a district could achieve Farrell efficiency and still be able to make efficiency improvements by reducing the supply of one input relative to the others while holding the outcome constant.

The distinction between Farrell and Koopmans standards of efficiency is significant because data envelopment techniques make implicit use of the Farrell standard. In other words, while the data envelopment approach provides a control for differences in efficiency across the units in the sample, the efficiency of these units may still vary in the Koopmans sense, and it is possible for this variation to be substantial. The problem is that we are still left with a situation in which high expenditure levels in one place relative to another may be due to differences in Koopmans efficiency or differences in real costs. It is worth noting that this problem remains even if the other problems are resolved. Ruggiero (1996) has addressed this problem using a second stage (parametric) canonical regression technique that builds upon the data envelopment method to come closer to the identification of Koopmans efficient school districts.

These reasons for skepticism create a dilemma for policy analysts as well as for policymakers. We might agree that a cost function complete with a Koopmans efficiency index developed according to Ruggiero's specifications is conceptually preferable to a less sophisticated, observed best practice approach or a cost function with no adjustment for efficiency, but this conceptual progress comes with some potentially significant costs. It is more than a matter of making incremental progress toward a fixed goal, because there is real potential for efficient practices to be misinterpreted as inefficient practices. Districts that are working with realistic best practices could find themselves penalized wrongly because of remaining limitations in the techniques being developed. However, conceptual progress should not be discounted, and it is clear that further efforts need to be made to extend this work.

It is particularly important to make progress in terms of the specification of the outcomes (i.e., clarifying the properties of Matrices A and A*). We also see promise in approaches that blend elements of the educator judgment and the cost function approach. It could be possible, and quite desirable, to rely on sophisticated cost functions to generate first approximations of estimated costs with a given set of circumstances to reach the stipulated outcome standards but to then build in an explicit appeals or "clarification" process which would permit informed judgments about particular local circumstances that may make the first approximation results unattainable. We speculate that an iterative process that draws on professional judgments in the context of cost estimates emerging from sophisticated cost function offers the best hope of making progress toward identifying the true costs of adequacy. For an alternative view that places greater relevance on the professional judgement approach, see Guthrie and Rothstein (1999).

Teacher Quality Research

Although many types of inputs contribute to the production of desired educational outcomes, in this section we narrow our attention to address what is known about the impact of teacher quality. In other words, we shift our focus to studies that trade comprehensiveness for a more focused examination of a specific category of inputs. We have selected studies estimating relationships between teacher quality and educational outcomes for several reasons. First, teacher resources represent a large proportion of the total resources committed to education, and consequently can have a disproportionate effect on the productivity of the enterprise. Because teachers are a key component of almost all of the S_ijks in Matrix A, it makes sense to take stock of what is known about the productivity of this cross-cutting input. Second, several elements of this category of inputs, for instance, preservice teacher preparation programs and certification requirements, are particularly interesting from a policymaking perspective.

The studies included in our review vary in terms of how heavily they rely on formal economic models of production. Some use sophisticated econometric techniques to test hypothesized models of production. Others consider the costs and effects of various alternatives to teacher preparation. Still others test for relationships using simple bivariate correlational analyses. We include a variety of studies along this "methodological continuum" and also present findings from reviews that others exploring this literature have conducted. We contend that although all of this work does not fit squarely into the categories of production or cost function research, it is nonetheless important to consider given the lessons it provides regarding such a key input to the production process.

The category of inputs associated with teacher quality is broad. For instance, teachers' pay scales are generally based on factors which include years of experience and degree level. In addition, characteristics such as course work taken to prepare for the profession, prestige of the institution at which one's degree was earned, and literacy or knowledge measured through the use of tests have been identified as attributes likely to contribute to successful teaching. In this section, we examine the impact of three specific indicators of teacher quality: (1) a teacher's preparation program, including degree level, links to state certification, and the presence of extended or other alternative teacher education programs; (2) the specific course work taken by teachers in preparation for the profession, with attention given to both the amount (e.g., number of courses, number of credits) and the type (e.g., pedagogical, content-specific) of courses taken; and (3)teachers' test scores indicating some aspect of teacher knowledge, proficiency, and level of literacy. All of the studies reviewed focus on preservice preparation rather than in-service professional development. The impact of these indicators of teacher quality has been measured in terms of a variety of educational outcomes including student achievement (general-composite as well as in specific subjects), principals' evaluations of teachers, teachers' perceptions of themselves and the quality and impact of their preparation, and teacher attitudes. We were able to draw several broad conclusions about the relationship between these teacher quality variables and educational outcomes from the numerous studies and research reviews that we examined.

Teacher Preparation/Certification Programs

One indicator of the quality of teachers concerns the "package" of their educational preparation, without attention to the individual components of that package (e.g., specific courses) or to the skills and knowledge acquired. This input has been studied in terms of the level of academic degree possessed by the teacher, the number of years of schooling, and whether or not the teacher has earned state certification to teach through traditional versus alternative routes. Much attention in the literature on teacher quality and preparation deals with the question of whether the quality of the candidates who are enrolled in, and graduate from, teacher education programs is lower than that of students in other degree programs, thus limiting the quality of the supply of teachers.

In general, the studies we reviewed pertaining to the impact of teacher education programs on teacher effectiveness offer several insights. First, "traditional" teacher education programs seem to make a difference with regard to a variety of measures of teacher quality and performance. Olsen (1985) found that graduates of education programs tend to be equal to or better than noneducation graduates in terms of their high school rank, math and English placement scores, and cumulative grade point averages in a variety of college subject areas. Hawk, Coble, and Swanson (1985) used a matched comparison design to demonstrate that student math achievement scores are higher for students whose teachers were certified in mathematics. Goldhaber and Brewer (1996) also report positive effects of subject-specific training programs on student math and science achievement. Darling-Hammond's (1990) review of the literature on the relationship between teacher education and teacher effectiveness found that fully prepared and certified teachers are generally more highly rated and more successful with students than teachers without full preparation.

In addition, several studies explore the impact of alternative teacher education programs such as requiring graduate education for teachers. Research shows that the relationship between graduate study and teaching effectiveness is modest (Domas and Tiedeman 1950; Goldhaber and Brewer 1996; Turner et al. 1986). Furthermore, several studies address the productivity of alternative routes to teacher certification through cost analyses concluding that alternatives such as extended year programs (Hawley 1987) and master's degrees (Knapp et al. 1991) may not be cost effective.

Teacher Course Work

Measures of the level and type of course work taken by teachers represent proxies for what teachers know and can do in the sense that course work indicates the degree of exposure individuals have had to particular areas of study (e.g., subject-specific content versus teaching methods). During the mid-1980s, the debate over the importance of subject matter versus education course work in teacher preparation programs took on new life (Ferguson and Womack 1993). This theme surfaces in a number of the studies we examined which consider course work as the indicator of teacher quality.

The studies we reviewed vary in terms of the measures, data, and methods used. Nonetheless, they are rather consistent in their findings. Most notably, they suggest that teacher course work in both content areas and pedagogy contributes to positive educational outcomes, but the relative impact of their effects varies. Subject matter preparation in the subject area taught is shown to be important in several studies (Perkes 1968; Hawk, Coble, and Swanson 1985), but investments appear to have diminishing returns after a certain point (Darling-Hammond 1990; Monk 1994). In contrast, course work in education methods is shown to have consistent positive effects that often outweigh those of content coursework (Ferguson and Womack 1993; Monk 1994). Further supporting this finding are a number of meta-analyses that emphasize the importance of pedagogical verses content course work in the preparation of teachers (Evertson, Hawley, and Zlotnik 1985; Ashton and Crocker 1987; Darling-Hammond 1990).

Several of the more sophisticated multivariate studies reviewed demonstrate some of the complexities associated with the education production function. More specifically, the production process appears to depend on a number of factors including student characteristics, teacher attributes, and subject area (see, for examples, Druva and Anderson 1983; and Monk 1994). In addition, Monk and King (1994) looked at multiple levels of schooling to conclude that it is the cumulative effect of the set of teachers a student has had over time, rather than the subject matter preparation of the entire faculty, that affects student mathematics and science achievement.

Teacher Test Scores

Test scores are arguably the best measure of what a teacher knows and can do because they go beyond exposure to programs and specific courses to assess the knowledge and skills that individuals have actually acquired. However, test scores are also arguably the least policy manipulable relative to the other indicators of teacher quality discussed in this paper. Although policymakers can require that certain tests be taken and passed by teacher candidates, it is far more difficult to influence the degree to which individuals excel on these tests, particularly broad proficiency assessments like literacy tests. The debate over the role and relevance of teacher test scores received a great deal of attention in the late 1970s through the 1980s. One explanation for this may be that the legality of using the National Teacher Examination (NTE) for certification purposes was upheld by the United States Supreme Court in N.E.A. versus South Carolina in 1978 (Stedman 1984).

Given the role of the NTE as a potential gatekeeper for teachers, the predictive validity of this instrument has been the object of study. Although Ayers and Qualls (1979) found that NTE scores are significantly related to grade point averages and scores on the ACT, correlations between NTE scores and principal and pupil ratings were found to be quite low. Likewise, Quirk, Witten, and Weinberg (1973) demonstrate that NTE scores are not highly correlated with supervisor ratings during the student-teaching period or during the first year of teaching. Pugach and Raths (1983) make several recommendations about the use of the NTE that argue against using this test as an end-of-program criterion for teacher candidates.

Other studies suggest that some test scores seem to predict high levels of teacher performance and desired educational outcomes. More specifically, tests that assess the impact of literacy levels or verbal abilities of teachers tend to show positive effects (Coleman et al. 1966; Ehrenberg and Brewer 1995; Ferguson 1991). In contrast, studies of the impact of the NTE (as noted above) and other state-mandated tests of basic skills, teaching abilities, or both (Guyton and Farokhi 1987) do not appear to be strong predictors of teacher performance. Finally, these studies also reinforce the complexity of the education production process in that the impact of what teachers know and can do as indicated by test scores depends on factors like student attributes (Ehrenberg and Brewer 1995; Strauss and Sawyer 1986).

Lessons to Learn About Indicators of Teacher Quality

The central goal of this review was to organize the existing research concerning the productivity of teacher inputs to demonstrate how education productivity research can inform policy decisions. We chose to focus on teacher quality given the large proportion of educational resources attributable to this type of input and the relevance that findings in this area have for policy. Indeed, numerous policymakers have called for various reforms related to the preparation of teachers (Bush 1987). For instance, in its call for improved teacher preparation, the National Commission on Excellence in Education (1983), in their report A Nation at Risk, stated "teacher preparation programs are too heavily weighted with courses in educational methods at the expense of course in subjects to be taught." The Carnegie Foundation for the Advancement of Teaching recommended that teacher education programs require a 3.0 grade point average for admission, and that teachers complete courses in an academic core in four years and then spend a fifth year learning about education (Boyer 1983). Likewise, the Holmes Group (1986) advised that all major universities with substantial enrollments of preservice teachers should adopt the four-year liberal arts baccalaureate as a prerequisite for acceptance into their teacher education programs. Most recently, the National Commission on Teaching and America's Future has focused on accreditation, recommending that these issues be left to professional organizations. Clearly, the studies reviewed in this section have implications for these types of policy decisions, and improving the overall productivity of the educational enterprise.

In general, the wide range of studies reviewed here suggest several broad conclusions regarding teacher quality. First, teacher education programs seem to make a difference, but alternative routes to certification such as extended programs or the requirement of a master's degree for certification can be questioned on cost-effectiveness grounds. Second, although teacher course work in both subject matter and pedagogy have been shown to contribute to positive educational outcomes, investments in the area of subject-matter preparation may have diminishing returns after some point. Third, some teacher test scores, particularly those that measure broad qualities like literacy or verbal ability, appear to be associated with high levels of teacher performance. Finally, and perhaps most important, several of the more methodologically sophisticated studies demonstrate the complex nature of the education production process. Factors associated with students, teachers, and courses have been shown to affect the impact of teacher quality variables on educational outcomes. Also, other issues such as the alignment between teacher preparation and teacher assignment have begun to emerge in the literature as important issues that have an impact on the productivity of teacher resources (Hawk et al. 1985, Monk and Rice 1998).

Implications for Policymakers and Researchers

Education policymakers face contentious choices in a climate of limited resources. They are responsible for making wise decisions about how to get the most productive use of these resources. The resource allocation model we presented in this paper provides a starting point for framing and even guiding the decisions that must be made. The distinction between actual practice and best practice, particularly realistic best practice, is important to maintain as efforts are made to make efficient progress toward attaining new outcome standards. The greater the discrepancy in the cost associated with realistic best practice and actual practice, the more productive the system can become. These considerations are important for policymakers at many different levels of the decision-making structure.

It is heartening to see the progress that has been made toward mapping the path to greater levels of productivity in the education arena. Efforts to estimate the magnitude and nature of the links between education outcomes with their costs are becoming more sophisticated as well as more informative and useful. Furthermore, knowledge about the productivity of key cross-cutting inputs such as teacher quality is becoming more conclusive, providing insights that can lead policymakers toward improved practice.

What are the next best steps to take in the quest to realize more productive use of resources in schools and school systems across the country? We see three promising steps that need to be taken in the near term.

First, further work needs to be done to establish the conceptual link between outcomes and costs. The matrices we introduced provide useful insights, but we recognize that more needs to be done, particularly with respect to efficiencies that can be realized by providing services to multiple students at once as well as by providing services that meet multiple goals simultaneously. The model is built on the premise that different students benefit more or less from different kinds of services with respect to particular educational outcomes, and this has implications for the cost of the service alternatives. However, it is reasonable to expect that what works best for one student may also work well for others in ways that make it possible to realize additional efficiencies. Similarly, the model specifies services with respect to individual educational goals, but clearly some types of services are intended and can be expected to promote multiple outcomes simultaneously. These issues of aggregation are important to consider as we operationalize this model because schools and school systems are bound to serve groups of students and routinely seek to meet multiple goals simultaneously.

Second, policymakers need to be clearer about the content of their high performance standards, particularly with respect to the number and types of standards and, even more important, with respect to the degree to which those standards are expected to be universal. Departures from universality may involve applying the standard to only a subset of the student population, or allowing the standard to be met at different levels for different students. The specification of outcome standards is a key step in the further development of the resource allocation model and the linking of costs to outcomes. Policymakers need to do more than generate and salute vacuous rhetoric. Hard decisions need to be made about the degree to which we aspire to universal versus differential outcomes across students. The resource allocation model makes it clear that answers to questions about the costs of adequacy presuppose clear pictures of what the outcome standards entail.

Finally, we were impressed with the potential for iterative cost calculation methods to generate the most useful estimates of cost. We think the key is to draw upon educator judgments that are informed by the results of sophisticated cost and production function estimations. We were similarly impressed by the progress being made toward estimating the productivity of teacher resources, although we share in the frustration of many regarding the existing limits on the availability of direct indicators of teacher quality. There are important implications for the collection of the next generation of data for cost-productivity research. It is essential to more directly measure the capabilities of teachers. Crude proxy measures for teacher quality, such as degree level, years of experience, and even numbers of courses taken are inadequate substitutes for direct measures of teacher content knowledge and teaching capabilities. It is also essential for the next generation of data for cost-productivity research to include sophisticated measures of pupil outcome gains. Value-added test score measures may be the best that can be expected in the near term, but we dare to hope that progress can be made toward the developing assessment instruments that are well aligned with the outcome standards embodied in Matrices A and A*.

Footnotes

^{1 Alternatively, we could introduce the idea that in addition to the 0 versus 1 question that is dealt with by Matrix A, the expected degree of learning might vary among the students who are expected to learn in a given area. In other words, among the 1s in a given column of Matrix A, there may be variation in the degree to which each of the students is expected to perform.}

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