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IV
MODELS

Part IV addresses issues involved in the modeling of teacher supply, demand, and quality phenomena. The focus is on models developed to project teacher supply and demand variables for use in estimating prospective teacher shortages and surpluses. One purpose is to identify, review, analyze, and compare the most promising of such models that have been developed at the state, regional, and national levels, as well as to review research relevant to modeling teacher supply and demand variables. The range of alternative approaches is described, and the strengths and limitations of the best examples of alternative types are analyzed. Another purpose is to relate the models to information needs of policy makers in dealing with teacher work force issues and to analyze the potential of these models to yield useful information about such issues.



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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. IV MODELS Part IV addresses issues involved in the modeling of teacher supply, demand, and quality phenomena. The focus is on models developed to project teacher supply and demand variables for use in estimating prospective teacher shortages and surpluses. One purpose is to identify, review, analyze, and compare the most promising of such models that have been developed at the state, regional, and national levels, as well as to review research relevant to modeling teacher supply and demand variables. The range of alternative approaches is described, and the strengths and limitations of the best examples of alternative types are analyzed. Another purpose is to relate the models to information needs of policy makers in dealing with teacher work force issues and to analyze the potential of these models to yield useful information about such issues.

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. Models for Projecting Teacher Supply, Demand, and Quality: An Assessment of the State of the Art STEPHEN M. BARRO INTRODUCTION Although concerns about future teacher supply and demand seem to be perennial, their content changes to suit the times. The alarms heard not so long ago about an imminent general teacher shortage have receded, to be replaced by increasing attention to the adequacy of prospective supply in science, mathematics, special education, and other particular teaching fields. Discussions of adequacy are now at least as likely to focus on teacher quality as on teacher numbers. The lesson seems to have been absorbed, after much contention over whether there will be "enough" teachers, that quantity per se is not the central problem. Given the willingness to pay and/or sufficient flexibility about standards, we can always hire enough people—and usually enough nominally qualified people—to fill the classrooms. But whether we can find teachers good enough to produce the educational performance gains the nation so urgently needs or to reach the ambitious national education goals that high officials have recently proclaimed are quite different matters. In these respects, the adequacy of the teacher supply is very much in question, and the future supply-demand balance is a major policy concern. Policy makers' questions about prospects for staffing the schools have stimulated efforts over the years to generate better information on the outlook for teacher supply and demand. Many of these efforts have focused on creating the data bases on which supply and demand analysis necessarily depends—data on the size and makeup of the teaching force, on teacher assignments and career patterns, on persons trained and certificated to teach,

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. on teacher training institutions and programs, and on the agencies (mainly local school districts) that recruit, employ, and seek to retain teachers. At the same time, other efforts have focused on creating, and then applying, the analytical tools needed to make the data meaningful and to provide policy makers and other users with the information they need—not just the facts, but estimates, inferences, and judgments as to what the facts imply. Prominent among these tools are the teacher supply-demand projection models reviewed in this paper. Ideally, state and federal officials, equipped with such projection models, should be able to monitor and assess developments in the teacher market, estimate trends, and anticipate imbalances or deficiencies (whether quantitative or qualitative) in time to take remedial action. How well these functions can be accomplished with current supply-demand models and how models can be improved to accomplish them better are the principal questions addressed in this assessment.1 Teacher Supply-Demand Models and their Characteristics A teacher supply-demand projection model consists of a set of mathematical relationships with which future levels of supply, demand, and (in principle) quality can be estimated and (ideally) linked to future economic and educational conditions and policies. Such models have been constructed for particular states by state education agencies and various research organizations: a regional model covering the New England states and New York is under development; and different types of national models have been introduced over the years by the National Center for Education Statistics (NCES). Although these models differ in important respects, all share a common basic structure. A complete teacher supply-demand model consists of three main components or submodels: (1) a submodel for projecting the demand for teachers. (2) a submodel for projecting the supply of continuing or retained teachers (or, equivalently, a model of teacher attrition), and (3) a submodel of the supply of potential entrants into teaching. The latter two components, taken together, should yield projections of the total teacher supply, which one should be able to juxtapose to, and compare with, projections of total demand.2 As will be seen, however, many current models offer incomplete treatments, or no treatments at all, of the supply of potential entrants, a situation that seriously limits their usefulness for assessing the overall supply-demand balance. The types of questions that can be addressed and the types of information that can be generated with a teacher supply-demand projection model depend on several key model characteristics. One is the extent of disaggregation of teachers by teaching field or subject specialty. Some models deal only with teachers in the aggregate (or only with such broad subgroups as

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. elementary teachers and secondary teachers) and consequently are of no use for assessing the prospective supply-demand balance in particular subject areas. Other models disaggregate in different ways and to different degrees, making it possible to respond to correspondingly more or less detailed policy questions. A second key characteristic is whether the model is mechanical or behavioral. Mechanical or "demographic" models are capable only of estimating what will happen in the future if established patterns or trends continue. For example, a mechanical model of teacher demand yields estimates of the numbers of teachers that will be required in the future if teacher-pupil ratios (or trends therein) remain constant, and a mechanical model of teacher retention predicts how many teachers will remain in the teaching force if the attrition rate for each type of teacher remains unchanged. Behavioral models, in contrast, link the demand and supply estimates to pertinent conditions and policies. Only behavioral models can be used to address what-if questions about the effects of hypothetical changes in circumstances on teacher supply and demand. A third critical attribute is whether and how the models deal with teacher quality. In fact, nearly all the current projection models focus on numbers of teachers only, avoiding the quality dimension entirely. This makes them at best only peripherally relevant for addressing the quality-related teacher supply and demand issues referred to above. Because of the growing urgency of quality concerns, this assessment places special emphasis on the initial tentative steps that have been taken, and the further steps that may be feasible, to take teacher quality into account. Models also differ in many characteristics of a more technical nature, including explicit and implicit behavioral assumptions, definitions of variables, statistical methods, types of data used, and length of the projection period. The assessment considers how all of the above affect the validity and usefulness of the supply and demand projections. Purpose and Scope The general purpose of this assessment is to determine whether the current teacher supply-demand projection models and methods (and some now under development) are well conceived, technically sound, and—most important—capable of satisfying policy makers information needs. More specifically, the assessment addresses the following issues: How adequate are the present models and methods for estimating future levels of teacher supply, demand, and quality? How adequate are they for analyzing the effects on teacher supply, demand, and quality of changes in pertinent conditions and policies?

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. Which current approaches to supply-demand projection modeling appear to be the most promising? What new or modified models, methods, and data bases might improve the quality of projections and the usefulness of teacher supply-demand analyses? The assessment covers national models and a selection of models developed by or for individual states. The national models in question are mainly those produced by or for NCES. The state-level models to be examined were chosen semisystematically from among models cited in the literature, models submitted by states to the National Research Council in response to a general request for teacher supply-demand studies, and models suggested by experts in the field. The coverage of state models is neither comprehensive nor necessarily representative; almost certainly, it is skewed in favor of the more elaborate and sophisticated modeling efforts. The specific state models discussed in this report are those for Connecticut, Indiana, Maryland, Massachusetts, Michigan, Nebraska, New York, North Carolina, Ohio, South Carolina, and Wisconsin. In some instances, however, the available state studies present only certain model components (e.g., only models of teacher attrition for Michigan and North Carolina) rather than complete supply-demand models. Organization The main body of this paper is organized around the three model components defined above. Thus, the next sections assess models of the demand for teachers, the supply of retained teachers, and the supply of potential entrants into teaching, respectively. The section on the supply of entrants also covers the approach taken within each model (if any) to analyzing the supply-demand balance. Each section includes a discussion of general issues pertaining to the model component in question; a series of descriptions and evaluations of individual state and national models; and a general assessment of the current state of the art, unresolved problems, and possible avenues of improvement. A final brief section provides an overview of the current state of the art and prospects for improved supply-demand projections in the future. MODELS OF THE DEMAND FOR TEACHERS The size of the teaching force in a state or in the nation is determined primarily by how many teachers school systems are able and willing to maintain on their payrolls—that is, by how many teachers the employers demand. Projections of demand are the logical starting points for assessing

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. the future supply-demand balance. Taken together with estimates of future attrition (discussed in the next section), demand projections indicate how many entrants into the teaching profession will have to be found to replace those who leave, to adjust to changes in enrollment, and to respond to new education policies. Likewise, disaggregated projections of demand by field or subject specialty provide some of the basic information needed to judge whether serious problems are likely to arise, as some have alleged, in finding enough teachers in such areas as science, mathematics, and special and bilingual education. Ideally, demand projection models should also be instruments for assessing the effects of future economic, fiscal, and demographic changes on the size and makeup of the teaching force; examining connections between teacher staffing and teacher compensation; and even exploring tradeoffs between numbers of teachers and teacher quality; but as will be seen, major advances in the state of the modeling art will be needed before any of these broader ambitions can begin to be realized. Unlike research on teacher attrition, which has progressed rapidly in the last few years, research on the demand for teachers has been minimal. Methods of projecting demand are little changed from what they were when the National Research Council last undertook reviews of teacher supply and demand models (Barro, 1986; Cavin, 1986; Popkin and Atrostic, 1986). The main noticeable advance is that demand estimates now seem more often to be disaggregated, and disaggregated in greater detail, by grade level and subject specialty; however, methods of projecting subject-specific demand are still rudimentary. Some of the more fundamental improvements called for in earlier reviews—most notably, a shift toward behavioral modeling—have been slow in coming. The importance of making models behavioral is regularly reaffirmed (see, e.g., Gilford and Tenenbaum, 1990), but real behavioral modeling remains, as it was five years ago, a hoped-for future development rather than a reality. Considerations in Modeling Demand Before reviewing specific projection models, I discuss briefly some of the major generic issues that arise in modeling the demand for teachers and certain key considerations in assessing present and proposed projection methods. The Definition of Demand The number of teachers demanded in a state or in the nation refers, both in standard English and in economics, to the number that school systems want to employ and are prepared to pay for at a given time. The everyday and economic definitions differ, however, in that the former is usually framed in terms of fixed requirements (e.g., predetermined teacher-pupil ratios),

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. whereas the economic definition treats the number of teachers demanded as contingent on such things as how much teachers cost and how much money the employers (school systems) have to spend. The economist, therefore. thinks of demand as a mathematical relationship or schedule—i.e., as a function rather than a number. A demand function relates the number of teachers that employers seek to hire—the quantity demanded—to such factors as the size and composition of enrollment, the level of education funding, and the prices that must be paid for teachers of various types and qualities. According to the everyday definition, a demand projection is an estimate of the number of teachers that will be "required" in the future (e.g., to maintain some stipulated teacher-pupil ratio), but, according to the economic definition, it is an estimate of how many teachers school systems will seek to employ, contingent on certain projected values of an array of underlying determinants of demand. The significance of this definitional difference is that the two concepts lead to different models and modeling strategies. The requirements notion of demand translates into mechanical (sometimes termed demographic) projection models, in which, typically, ratios of teachers to pupils (or trends therein) are assumed to be fixed and projections of numbers of teachers are driven by enrollment forecasts. In contrast, the economic definition points to behavioral models, in which projections derive from multivariate equations linking the number of teachers demanded to various economic, fiscal, and demographic causal factors. Thus far, the mechanical models dominate the field. As a result, the only demands that can now be projected are those that will materialize if no significant changes occur in any of the factors that influence school systems' ability and willingness to employ teachers. The Relationship Between Demand and Employment A crucial but often unappreciated consideration bearing on the validity of demand projections is the relationship between the number of teachers demanded and the number actually employed. In principle, both the economic concept and the requirements concept of demand allow for the possibility that the former could exceed the latter—that is, school systems might fail to find the numbers of teachers they are able and willing to pay for.3 In practice, however, analysts have almost always assumed (usually implicitly) that the number of teachers demanded is currently the same, and has been the same in the past, as the number actually employed. That is, the prevailing assumption is that the teacher market is characterized by supply-demand balance or excess supply—that there is and has been no excess or unfulfilled demand.4 The validity of demand projections depends strongly on whether the assumption of excess supply is correct. Invariably, the quantities referred to

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. as demand projections in teacher supply-demand studies are projections of employment rather than demand per se. The implicit assumption is that school systems were able, historically, to find as many teachers as they wanted, and hence a projection of employment and a projection of the number of teachers demanded are one and the same thing. If this were not true—if past levels of employment were determined by numbers of teachers available (supply) rather than by demand—then projections of employment would be supply rather than demand projections. It would become meaningless, then, to speak of the projected supply-demand balance. The distinction between numbers of teachers demanded and numbers actually employed is especially critical when it comes to projecting disaggregated demand by teaching field, for reasons spelled out below. Disaggregation by Field of Teaching Recently, concerns about general teacher shortages have receded, and attention has focused instead on the supply-demand balance in particular fields of teaching, especially fields in which difficulty is anticipated in finding enough qualified teachers. To respond to these concerns, many state models offer disaggregated, subject-specific demand projections. The standard approach to disaggregation is to apply to each subject area exactly the same method as is used to project demand in the aggregate: namely, to multiply projected enrollment in the subject area by an extrapolated, subject-specific teacher-pupil ratio. However, this approach suffers from two serious but often unappreciated conceptual limitations. First, it presumes that the excess-supply assumption holds for each subject area separately—i.e., that the number of teachers demanded in each field is the same as the number actually employed. This assumption, even if approximately correct for teachers in the aggregate, is less likely to hold for teachers in particular fields. We have been hearing for some time, for example, that there are ''not enough'' teachers in such fields as physics, chemistry, mathematics, and special education. If this is true, it cannot be correct to project future demands for such teachers on the basis of current and past employment. For example, if the number of physics teachers currently demanded were 2 per 1,000 high school students but the number actually employed were only 1.5 per 1,000 because too few qualified applicants were available, then it is logically the former ratio rather than the latter that should be used to project future demand. This is admittedly a difficult prescription to implement because the actual teacher-pupil ratio is observable, while unfilled demand is neither observable nor readily inferred. Nevertheless, the issue is unavoidable: it would be logically inconsistent to say that there is excess demand for physics teachers today but then to project the future demand for physics teachers from the number currently employed.

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. Similarly, subject-specific demand projections based on historical patterns of course enrollment rest implicitly on the assumption that past course enrollment patterns were wholly demand-determined rather than jointly determined by both demand and supply. It is quite likely, however, that past levels of enrollment in some subjects were constrained by limited course offerings, which in turn reflected the limited availability of teachers. At the high school level, in particular, the pattern of course taking gives the appearance of being largely demand-determined, in the sense that it reflects the pupils' own choices, but pupils can choose only among courses that are offered and for which teachers exist. Consider, for example, what would happen if one attempted to project the demand for teachers of Japanese from data on the number of such teachers currently employed. The estimate obtained from such a projection would undoubtedly be very low, but this would reflect the limited present availability of Japanese teachers and the consequent rarity of Japanese as a curricular offering. It seems quite likely that if teachers of Japanese were abundant, many more Japanese courses would be offered, more teachers would be employed, and projected demand would be considerably higher than in the present supply-constrained situation. A further obstacle to producing valid disaggregated projections of demand is that neither data bases nor methods have been developed for projecting future rates of course taking by subject. The present models merely reflect the assumption that current or recent distributions of course enrollments by subject area will remain unchanged for the indefinite future—an assumption that is often demonstrably false, given the changes that have been taking place in state curricula and graduation requirements. To my knowledge, no methods of projecting changes in subject-specific course enrollment rates have yet been demonstrated. It appears, however, that some data bases are now available that would make such projections possible. Certain states (e.g., California and Florida) maintain detailed pupil-level data bases that include information on enrollment by subject and could be used to study changes in course taking over time. National studies of course-taking behavior based on samples of high school transcripts may also be useful for projecting subject-specific demands.5 This particular unexplored area of demand modeling appears to be ripe for substantial progress. The Demand for Teacher Quality Even the most sophisticated projections of numbers of teachers likely to be wanted in the future would not meet the needs of those concerned with issues of teacher quality. The quality dimension of demand has received very little attention (apart from acknowledgments of its omission) in sup-

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. ply-demand studies. No demand projection model, to my knowledge, takes any quality-related attribute of teachers into account. This situation is unlikely to be rectified soon. Nevertheless, certain aspects of the quality issue are worth addressing, even if for no other reason than to indicate what is missing from, and may be misleading about, projections that do not take teacher quality into account. States and school districts are clearly not indifferent between teachers of higher and lower quality—however quality might be defined—and there is good reason to believe that districts are willing to pay more to acquire teachers with the quality-related attributes they value. For example, some school systems (usually the more affluent ones) generally do not hire inexperienced teachers but instead recruit higher-priced teachers who already have taught elsewhere. Some districts (again, usually the more affluent) appear to offer higher salary schedules than neighboring districts specifically to attract large pools of applicants among whom they can choose. The fact that teacher salary schedules almost universally reward teaching experience and training is evidence in itself that qualifications matter to employers, and that all teachers are not viewed as essentially interchangeable labor. Thus, it is clearly meaningful to speak of a demand for teacher quality, just as one normally speaks of a demand for quantity. Two related aspects of the demand for teacher quality that merit investigation (and that could conceivably be reflected in a future generation of demand projection models) are (1) the nature of the quality-price relationship (how much extra are school systems willing to pay for valued attributes of teachers?) and (2) the nature of quantity-quality tradeoffs (to what extent would school systems be willing to accept lower teacher-pupil ratios to get higher-quality but presumably more expensive teachers). The possibility of quantity-quality tradeoffs raises serious concerns about projections of numbers of teachers. For instance, a state that has been shifting its emphasis toward higher teacher quality may be employing fewer teachers (but better ones) than would have been projected on the basis of earlier data. With a demand model that takes no account of quality or price, such a development would either be missed or misconstrued. Moreover, even a behavioral demand model would yield misleading results if it lacked a quality dimension; for example, a tradeoff of quantity for quality could be misinterpreted as a reduction in the number of teachers demanded in response to rising cost. Interstate comparisons of teacher demand also remain problematic without methods of taking quality differentials into account. Ideally, one can envision a model that projects both the number of teachers and the quality of teachers demanded in a state, but the obstacles to creating such an analytical tool are formidable. Quality measurement is only one major problem. It is actually less of a problem in connection with demand projections than in other contexts because what counts in a demand

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. about the dependence of teacher supply on economic conditions affecting other college-trained workers in the same area. It was considerations like these that guided our NCES-sponsored work at RAND in redesigning the Schools and Staffing Survey to enhance their utility for making assessments of the condition of teaching across the nation. Our 1988 RAND report Assessing Teacher Supply and Demand, coauthored with Linda Darling-Hammond and David Grissmer, spells out our rationale for the linked surveys of districts, schools, principals, teachers, and former teachers that were subsequently implemented. Since NCES adopted the survey instruments that we devised almost without change, most of our specifications of data desiderata for a national data base on teachers can be inferred from an examination of the questionnaires themselves. The district and private school questionnaires asked for detailed staffing breakdowns to permit estimating teacher stocks by state, sector, level, and field. The school surveys also elicited information on teacher turnover by field that can be aggregated to provide key turnover estimates at any level of aggregation or used to augment the individual data on samples of teachers in the same schools. In addition to providing individual data for profiling teachers along numerous dimensions, the teacher surveys contained a sequence of items pertaining to the teachers' work histories to identify sources of entry into teaching and to pinpoint the nature and timing of subsequent transitions. Since the items include current and previous year's statuses (full-time, part-time, itinerant teacher, substitute, etc.), year of entry into full-time teaching, total years of service, years at present school, number of breaks in service, and main activity during the year prior to current teaching assignment, the items extract the key information needed to support analyses of employment patterns and their linkages to school policies, family characteristics, and economic factors. As the first step in implementing a one-year follow-up survey of teachers and ex-teachers, we recommended going back to the school representatives in the SASS school sample and asking them to fill out a checklist encoding the current statuses of all teachers who participated in the base year survey, including their reported reasons for leaving and current main activities. In effect, this created polytomous outcome measures for updating the work histories of the base year participants to support detailed analyses of "competing risks" in teacher turnover. Hence, the SASS surveys were specifically designed to allow analyses of teachers' career patterns along numerous dimensions—attrition, field-shifting, mobility, longevity, breaks in service, retirement, etc. For the most part, the individual data for these analyses are right-censored observations of continuing sojourns of teaching activity, i.e., most SASS participants will

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. continue teaching for one or more years. The data can be analyzed by adapting standard procedures for fitting year-to-year transition rates (e.g., by logistic regression) or by using nonparametric or semiparametric procedures that have been especially tailored to handle censored failure-time or event-history data in demographic and biostatistical contexts (Elandt-Johnson and Johnson, 1980; Kalbfleisch and Prentice, 1980; Cox and Oakes, 1984; Tuma and Haanan, 1984). It is also important to undertake the kinds of analyses of teacher stocks, flows, and utilization needed to assess the condition of teaching across the nation today and to pinpoint shortcomings, trouble spots, and signs of erosion that could worsen over the next few years. Here, I am not just referring to the basic information needed to fill in the blanks in manpower planning models, such as those discussed in Bartholomew and Forbes's Statistical Techniques for Manpower Planning (1979), but also the information about teachers' characteristics, qualifications, working conditions, family status, future plans, and attitudes that is needed to profile the teaching work force along many other dimensions that bear directly or indirectly on teacher supply, demand, and quality. In my view, the SASS survey instruments were well designed to gather the necessary information to meet these objectives. But merely asking the right questions is not sufficient, because the surveys are restricted to probability samples of districts, schools, and teachers. The requisite statistical infrastructure has to be in place to allow extrapolations from SASS samples to the entire population and to permit linkages with other data bases. For the public schools, NCES's Common Core of Data, the repository of annual censuses of districts, is the main linkage between the SASS files and the population; it provides the sampling frame and subpopulation counts needed to support the sampling plan. The SASS files can be viewed as augmentations to the Common Core, which serves as the central data base on public schools. Since the state data systems and studies that Barro cites are also additions to the same data base, the linkages in the combined data base can be exploited provided that the data elements in the various segments are commensurate. Regrettably, there is no similar census or sampling frame for the private schools, so that statistical underpinnings of the SASS private school data are less firm. By providing detailed information on the employment patterns of teachers and principals, the SASS files also provide data for examining flows into, within, and out of a sizable segment of the college-educated work force. Most teachers, especially those with science, mathematics, and business backgrounds, have highly marketable job skills. Analyses of the flows of college graduates into and out of teaching can shed light on the non-teaching opportunities for teachers, circumscribe pools of workers that have some propensity to enter teaching, and identify economic factors related to

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. shifts into or out of teaching. The major vehicles for tracking the entire labor force are the Current Population Survey (CPS) and the decennial censuses. The Bureau of Labor Statistics (BLS) relies on CPS data to make the projections of demand by occupation that are cited in several publications, including its two series entitled Occupational Outlook Handbook and Outlook 2000. Perhaps because the complicated BLS projections methodology suffers from some of the expositional problems that I mentioned earlier, it is difficult to determine how the projections of teacher supply and demand were generated, and the information in the Handbook about the outlook for teachers is vague. Nevertheless, the CPS and SASS files provide the data and the linkages for extending examinations of teacher mobility into more general studies of employment decision making in the college-trained labor force, and this opportunity should be exploited. REFERENCES Bartholomew, D.J. 1973 Stochastic Models for Social Processes. Second edition. New York: John Wiley and Sons. Bartholomew, D.J., and A.F. Forbes 1979 Statistical Techniques for Manpower Planning. New York: John Wiley and Sons. Bureau of Labor Statistics 1989 Outlook 2000. Bulletin 2352, November. Washington, D.C.: U.S. Department of Labor, Bureau of Labor Statistics. 1990 Occupational Outlook Handbook. Bulletin 2350, April. Washington, D.C.: U.S. Department of Labor, Bureau of Labor Statistics. Cox, D.R., and D. Oakes 1984 Analysis of Survival Data. London: Chapman and Hall. Elandt-Johnson, R.C., and N.L. Johnson 1980 Survival Models and Data Analysis. New York: John Wiley and Sons. Feistritzer, Emily 1990 Profile of Teachers in the U.S.—1990. Washington, D.C.: National Center for Education Information. Freedman, David A. 1987 As others see us: A case study in path analysis. Journal of Educational Statistics 12(2)(Summer):101–128. 1991 Adjusting the 1990 census. Science 252(May):1233-1236. Haggstrom, Gus W., Linda Darling-Hammond, and David W. Grissmer 1988 Assessing Teacher Supply and Demand. May. R-3633-ED/CSTP. Santa Monica, California: The RAND Corporation. Kalbfleisch, J.D.. and R.L. Prentice 1980 The Statistical Analysis of Failure Time Data. New York: John Wiley and Sons. Keyfitz, Nathan 1972 On future population. Journal of the American Statistical Association 67(338)(June):347-363. Tuma, Nancy B., and Michael Hannan 1984 Social Dynamics: Models and Methods. New York:Academic Press.

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. Discussion RONALD E. KUTSCHER The rose-colored glasses that my remarks will be filtered through are those of an economist specializing in the labor market and, in fact, most of my professional career has been devoted to projecting the labor market, so, what I say has been through that filter. I really have no quarrel with the paper that Steve Barro has prepared. Most of what I hope to bring to you is explicitly or implicitly in his paper. Perhaps I will rephrase them in a somewhat different way, and by doing so provide some additional insights. I would like to begin by asking a question. Why are supply and demand projections of teachers being developed? I think we must begin with that question because it is a very important issue in determining how much to invest in improving the models used in these projections. That is, if these supply and demand projections of teachers are to be used for information and indicative purposes only, then the cost to users of errors in the projections may be relatively low. If these projections are used to make very concrete decisions such as expanding teacher training programs or institutions, adding to or constructing new buildings, or adding or subtracting staff, then the cost of errors in these projections becomes much higher. If the cost of errors is very large, then we should be willing to spend more time, money, staff, and effort in exploring means of improving the projections. The principal cost of improving projections is in defining the types of data needed and in collecting underlying data necessary for estimation of new or improved models. The model-building portion of the added cost is a relatively small part of the total cost. Once you determine what data are

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. needed to develop the models, and you have collected those data, then the model builder's marginal or additional cost is relatively low. In the interim, however, the data development and the data collection phase will have taken considerable time. If the cost of errors in the use of these projections is relatively low in terms of these decisions, simple models may be providing us with information that is not all that bad. We must judge which of these two costs is closer to reality. If, however, the costs are quite high and we decide it pays to develop more elaborate models, one has to be careful not to fall into a common trap. That trap is that use of a more sophisticated and theoretically elegant model does not ensure that the accuracy of the projections will be significantly improved. A more sophisticated model may assist you in other ways, however, by explaining why you were wrong when your projections are in error. Secondly, it allows you to be a classical two-handed economist, because you can run what are labeled what-if simulations. For example, you can simulate what-if revenues drop by three percent, how will that affect the demand for teachers? Or, if demand increases for other professionals, what impact will that likely have on the supply of teachers? Answers to such simulations can be very useful to policy makers. I am assuming the cost of errors is high and that therefore there is a desire to move to develop more detailed and sophisticated models. I say that because, otherwise, why are we here? Consequently, I will make observations that I think are very pertinent to consider in developing a more elaborate model. First, I am extremely skeptical of what I will label as isolated models. These are models that cover only a small segment of a larger entity. I believe there is considerable interaction within an economy. If I were asked to develop a model for Estonia or for Delaware, I believe it could not be done without taking into consideration everything else that is going on around those jurisdictions. Consequently, in developing better models for projecting teacher supply and demand, I urge that this be done in a broader context, which I will elaborate on in a moment. In addition, we must decide whether these models of teacher supply and demand are designed primarily for short-term or for long-term projections. This is an important distinction because the fundamental nature of how you build these two types of models is different. How to proceed? I would urge that a teacher supply-demand model begin initially with a broad aggregate type model that describes the entire U.S. economy. From that starting point, the model would be disaggregated toward the subject matter of concern, in this case the teaching profession. To do so it certainly would be necessary to consider the educational industry, government revenues sources and uses, and public-private education distinctions—to name just a very few obvious inclusions.

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. There are two factors are important in any model building: national trends and local trends. In order to try to model any phenomenon, you must attempt to capture both the impact of overall national trends and the impact of local trends on this phenomenon. If you do one and not the other, you will likely increase your projection errors. Local trends can mean geography or they can mean more specific detail about the segment of the economy in which you have the greatest interest. After this broad beginning, one can begin to disaggregate toward what you need. If ultimately you are concerned with the teaching profession, you start out overall, but then you begin to disaggregate the model by industry in order to capture other employment opportunities for those educated as teachers, by type of school, by geography and other important factors, which could affect teacher supply and demand. Although disaggregating the model by industry will yield more precision in its estimating equations, there is a concern, however, because you very likely will have more error in the underlying disaggregated data. The disaggregation should not proceed so far that the error in the underlying data overwhelms any additional forecasting power that you have gained by the disaggregation. What other things would I want to see in this model? Well, Steve Barro and Gus Haggstrom both have talked about wages. I think it is very important that wages be in any model that considers supply and demand factors in teaching. According to the Washington Post of March 23, 1991, the average salary of players in the National Basketball Association is $950,000. Does anyone think this conference on teacher supply-demand problems would be held if the average teaching salary was $950,000? If the situation were reversed, maybe the National Research Council would be concerned about the supply and quality of players for the National Basketball Association. So wages are a very important determinant of both the supply and demand of future teachers. Wages are needed not only for teachers but also for other employment opportunities as well. An additional aspect is the revenues that will be available. You cannot use some overall income variable to project the ability to hire teachers, because income is not necessarily a good proxy for the tax revenues of state and local governments or the share of those revenues that will be devoted to education. Furthermore, it can be important to look at nonwage aspects of working conditions—benefits, for example. We reviewed the supply and demand issues in nursing recently and it turned out that, while wages was one of the factors, working conditions may have been as important a determinant of supply problems in nursing as wages. One needs to put all of this into a broader economic context. I think it has been noted a number of times that the supply and demand balance for an occupation in a state in which the unemployment rate is 8 percent is much different than it is in a state in which the unemployment rate is 4

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. percent. When you examine any occupational shortage, you are very unlikely to find shortages if the unemployment rate in the area is 8 or 9 percent. It is only when the unemployment rate drops and other alternative employment opportunities are available that shortages are much more likely to occur. Thus, it is very important to look at the overall economic situation. Of course, I am returning to a point I made earlier about whether the model was to be primarily of a short-term (1–3 years) or long-term (5 or more years) in orientation. From my viewpoint, it is most important to look at other employment possibilities. That clearly is so since some persons educated as teachers can decide to teach or they can decide to go into other fields. Consequently, if you do not know what is happening in these other employment opportunity fields, then it is very hard to know what the supply and demand tradeoff is for teachers. In commenting on Steve Barro's paper, someone noted that they were surprised that the retention rate for mathematicians was different than it was for other scientists. To me, that can be explained by the fact that the alternative employment opportunities for those educated in the other sciences are much greater than are the possibilities for pure mathematicians. Pure mathematicians have a much smaller scope of jobs that are open to them than do natural scientists. So they are more likely to stay on that job. An additional point that I would think important to consider in model development is to take into account the types of pupils that are to be enrolled. Pupils with handicaps have different teacher requirements, as may pupils in rural areas. Size of the school and size of the community may be variables that are extremely important in terms of demand and even the supply of teachers. All these important factors should be built into a more sophisticated model of teacher supply and demand. All of my points are made for consideration in improving models for analyzing teacher supply and demand. Even if these recommendations were followed, one could still not develop a model capable of projecting a numerical shortage or surplus of teachers. Techniques are simply not available to accomplish that and are not likely to be so in the foreseeable future. I would like to close my remarks with one final observation that may only be related indirectly to the question of teacher supply and demand. There is one important trend that is dominant over the last 30 years in the labor market. Almost every professional group has developed a very large paraprofessional or technical group that goes along with the profession. This development of technicians and paraprofessionals exists for the medical, accounting, engineering, and legal professions. It is interesting and ironic that this trend is not true in the education industry—at least not to any degree approaching that found in the other professional groups. This fact may have an important implication for sup-

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. ply and demand balance in teaching. We are at the point in the medical profession, for example, at which physicians and dentists are among the slowest-growing component of the health care delivery industry. It is the technician component that is growing very rapidly. A physician's office 40 years ago was staffed by a nurse and a receptionist. Today that same office may still have 1 or 2 physicians, but very likely will have 4 to 10 trained technicians and clerical assistants. By analogy, if the teaching profession had developed like other professions, a teacher would be responsible for 50 or 75 students. However, each teacher would have several paraprofessionals and clerical assistants in the classroom in order to teach such a large group. I think this may be another important dimension of the supply and demand balance that needs detailed examination.

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. General Discussion The general discussion addressed the following topics: (a) theory underlying TSDQ projection models; (b) the reciprocal relationship of TSDQ modeling and data bases; (c) constraints on accuracy of TSD projections imposed by the quality of data used in projection equations; (d) equilibration mechanisms in teacher supply and demand; (e) problems in modeling the supply of graduates from teacher preparation programs; (f) the appropriateness of applying concepts from economics to modeling teacher supply and demand; and (g) the utility of TSDQ models and of state and national data bases for informing policy issues in education. The following paragraphs summarize each of these topics. Since the Barro paper did not consider theory relevant to TSDQ projection models, a suggestion was made that explication of the theoretical underpinnings of these models would be useful for policy makers who are concerned about teacher supply and demand projections. Although Stephen Barro recognized that such theory was not brought out in the paper, he stated that there is a clear theoretical base for much projection modeling of the teacher force on both the supply side and on the demand side. On the supply side, theoretical strands from human capital theory, labor market search theory, and labor market uncertainty theory pertain to factors that might influence the decisions of individual teachers to enter or to remain in the profession. On the demand side, economic theory of public fiscal behavior is relevant to decisions of state and local government on spending priorities, including the place of education in such priorities. In turn, the demand for teachers is a function of fiscal capacity and the relative price of teachers compared with alternative expenditures.

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. The reciprocal relationship of TSDQ models and data bases was noted. On one hand, models are useful in furthering the development of data bases. On the other hand, the development of models is constrained by limited availability of data, especially data of sufficient precision and relevance to determine whether the teacher labor market is supply-or demand-constrained. The precision of teacher supply and demand projections, even with good models, is limited by the inaccuracy of estimates for key variables used in projection equations, when the variables themselves have to be projected. Since projections of variables such as teacher attrition rates and enrollment growth in public education are imprecise, so will be projections of teacher supply and demand derived from equations that use these variables. In a world of limited resources, however, projection models will continue to be imperfect. The issue is how to handle this uncertainty. Either sufficient resources will have to be invested to develop projections of adequate precision, or the teacher market will be left to equilibrate on its own in accordance with decisions of individuals in the market based on information available to them at the time. Equilibration mechanisms have been neglected in TSDQ models. In economics, the long-running equilibration mechanism is relative wage rates. While this mechanism is working out in the teacher labor market, shorter-term equilibration occurs through the mechanisms of adjustments in teacher quality requirements and in teacher-pupil ratios. The definition and measurement of teacher quality continues to be a problem. In teaching, a virtually unexplored, but potential equilibrating mechanism is the hiring of a given number of trained teachers versus the hiring of fewer teachers plus paraprofessional assistants. Good TSDQ models will explicate these equilibrating mechanisms and how they function under conditions of disequilibrium. Since much of the entering supply of teachers comes directly from output of teacher preparation programs, difficulty in modeling this source was discussed. It was observed that undergraduate students contemplating teaching as a career can delay making a commitment to this profession much longer than students committing to other professions such as medicine and engineering. In essence, it was hypothesized that the pipeline for newly prepared teachers is much shorter than in many other professions and therefore more difficult to model accurately. Although some doubt was expressed about the validity of this hypothesis, the presumed shortness of the pipeline was viewed as an advantage in that the teacher preparation process, including decisions by individuals to enter it, is very responsive to shifts in demand in the teacher labor market. With increased demand, however, there is the possibility that new supply might quickly overshoot the increase in demand. While the asserted shortness and flexibility of the new teacher pipeline might indeed be valid obser-

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Teacher Supply, Demand, and Quality: Policy Issues, Models, and Data Bases. vations, wide variations in teacher preparation and certification regulations, by state, pose great difficulties in modeling this aspect of teacher supply. This modeling must be done on a state-by-state basis. A question was raised about the utility of applying economic principles of supply and demand to modeling the teacher labor market, since hiring decisions in education typically are made by principals at the school level, and must be responsive to changes in curriculum policy such as increased requirements for mathematics courses. These hiring decisions are strongly affected by school variables such as size. Smaller secondary schools require many teachers who are capable of teaching in more than one field, such as in chemistry and physics, while very large high schools might be able to hire specialized mathematics teachers. Principals consider tradeoffs such as hiring a new teacher in a particular subject matter or reassigning a teacher already on the staff. Similarly, teachers who must instruct in two or more subject areas might be more likely to leave a school for one in which they can concentrate their instruction in their preferred subject. Rather than large-scale supply and demand modeling, it might be more productive to study and model teacher flows at the school level. In the final analysis, the utility of TSDQ projection models depends on the degree to which they inform education policy issues. While there are many problems with models, state and national data independent of models can help clarify a number of policy issues. For example, state and national data can contribute significantly to understanding issues such as the role of minorities in teaching, the quality and preparation of science teachers, and the impact of changes in licensing requirements of teachers. Data can be organized to inform policy debate on such issues, even though such data may not fit well into TSDQ models.