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Unemployment Insurance (UI) is the major social insurance program that protects against lost earnings resulting from involuntary unemployment. Existing literature finds that low-earning unemployed workers experience difficulty accessing UI benefits. The most prominent policy reform designed to increase rates of monetary eligibility, and thus UI receipt, among these unemployed workers is the Alternative Base Period (ABP). In 2009 the American Recovery and Reinvestment Act sought to increase use of the ABP, making ABP adoption a necessary pre-condition for states to receive their share of the $7 billion targeted at UI programs. By June 2012, 40 states and the District of Columbia had adopted the ABP despite the absence of an evaluation of ABP efficacy using nationally representative data. This paper analyzes Current Population Survey data from 1987-2007 to assess the efficacy of the ABP in increasing UI receipt among low-educated unemployed workers. We use a natural-experiment design and logistic regression models to capture the combined behavioral and mechanical effects of the policy change. We find no association between state-level ABP adoption and individual UI receipt for all unemployed workers. However, among part-time unemployed workers with less than a high-school degree, adoption of the ABP is associated with a 3.4 percentage point increase in the probability of UI receipt. (Contains 5 tables, 1 figure and 7 footnotes.)

As Duncomb and Yinger (2001) have stated, "School consolidation represents the most dramatic change in education governance and management in the United States in the twentieth century. Over 100,000 school districts have been eliminated through consolidation since 1938, a drop of almost 90 percent (NCES 1999, Table 90). This longstanding trend continues throughout the country, largely because consolidation is widely regarded as a way for school districts to cut costs" (p. 1). The study described in the present paper applies Duncomb and Yinger's methods to Michigan data, looking as possible to financial consequences of consolidation of school districts at the county level. Research data sets for 10 counties in Michigan are used to estimate cost-saving effects of consolidation, as in the Duncombe and Yinger study. It appears that significant savings can be achieved in consolidating school districts at the county level. The coordination of services also produces cost savings for the districts assuming participation in a county level (ISD) coordination of services. These findings are consistent with other research studies in New York and Indiana. However, consolidation studies conducted in Arizona and New Jersey indicated that the fiscal savings hoped for did not materialize to the extent expected. Overall, consolidation seems to make fiscal sense, particularly in rural and small districts. The coordination of services seems more palatable to Michigan communities and also produces significant reduction in cost of services such as transportation and operation. The results of this study should be of interest to state and local elected officials, to state education agency staff, and to public school administrators. The Future of School Districts Consolidation in Michigan is provided in an addendum. (Contains 1 footnote.) [This study was funded by the Booth Newspapers of Michigan.]

In this paper, we address mathematics education in rural contexts from a critical pedagogical perspective. We imagine our audience to be mathematics educators and rural educators who may not have background knowledge of critical pedagogy. We also confess that we are mathematics educators first, with interests in critical pedagogy and rural education. Thus we do not position ourselves as experts and do not intend to proclaim what rural mathematics educators "should" do. To set up our discussion, in this section we characterize (in broad strokes) critical pedagogy, current reform in mathematics education, and issues in rural education.

This paper explores the application of a mathematical optimization model to the problem of optimal enrollments. The general model, which can be applied to any institution, seeks to enroll the "best" class of students (as defined by the institution) subject to constraints imposed on the institution (e.g., capacity, quality). Topics explored include how the model was applied to actual data and the results of that application. The presentation touches on how well the model mimics "real life," insights that can be gained from the output, the model's limitations, and the modifications that might be warranted to improve performance. (Contains 17 references.) (Author/SLD)

The Progress in International Reading Literacy Study (PIRLS) is a large international comparative study of the reading literacy of young students. The student population for the U.S. 2001 PIRLS (hereafter simply referred to as PIRLS) was the set of all fourth-graders in the United States, corresponding to the grade in which the highest proportion of nine-year-olds are enrolled. The PIRLS school sample consisted of 200 schools (150 public and 50 private) containing a fourth grade, selected with probability proportionate to the school'?s enrollment of fourth-graders. One classroom was sampled from each selected school. PIRLS was conducted in April and May 2001. For the original sample, the unweighted response rate at the school level was 62.5 percent, with 125 out of 200 schools responding. Through the use of replacements, the unweighted response rate was improved to 87 percent, with 174 out of 200 schools responding. However, as the response rate from the original sample was below 85 percent, NCES requested that Westat investigate the potential magnitude of nonresponse bias at the school level. The methodology and results of this investigation are described herein.

This paper describes a spreadsheet-based faculty flow model developed and implemented at the University of Calgary (Canada) to analyze faculty retirement, turnover, and salary issues. The study examined whether, given expected faculty turnover, the current salary increment system was sustainable in a stable or declining funding environment, and whether further early retirement incentives would be necessary. The model, called the Academic Staff Resource Projection Model, is based on the Markov chain approach to project faculty movement out four years. It was developed using Microsoft's Excel spreadsheet software. Nine alternative policies and assumptions were tested concerning: (1) retirements for ages 55 to 70; (2) resignation rates by years of service; (3) age distribution of newly hired staff; (4) annual attrition of one rank replaced by another rank; (5) overall attrition replacement ratio; (6) adjustments to allow for addition or elimination of academic programs; (7) starting salaries; (8) salary schedule information; and (9) rate of promotion to next rank. Six figures and flow charts illustrate the model and show the spreadsheet file structure and flows. Three appendixes include a policy variables worksheet, a salary schedule, and an age distribution schedule. (Contains 16 references.) (CH)

The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest on forming pairwise available case (PAC) correlation matrices. Developments in statistical theory for missing data show that PAC correlation matrices may not satisfy Wishart distribution assumptions underlying factor analysis, this impacting tests of model fit. A new approach for handling missing data in structural equation modeling advocated by B. Muthen, D. Kaplan, and M. Hollis (1987) is proposed as a possible solution to these problems. The new approach is compared to the standard PAC approach in a Monte Carlo simulation framework. Simulation results show that tests of goodness-of-fit are very sensitive to PAC approaches even when data are MCAR, as is the case for BIB designs. The new approach outperforms the PAC approach for continuous variables and is comparatively much better for dichotomous variables. One table and one figure illustrate the discussion. (SLD)

Any interstate comparison that does not take differences in the cost of education into account will give an incorrect impression of the relative levels at which different states support their schools. The lack of cost-adjusted statistics on state expenditures for elementary and secondary education interferes with policy analysis, resource allocation, and decision making in education. An examination of state cost data indicates that there is substantially more interstate variation in per-pupil spending than in the amounts of the main educational resource--instructional staff--that states provide for each pupil. In fact, the main conceptual and technical problems in constructing a cost-of-education index arise from the labor-intensive nature of education and the types of labor on which schools rely. This report evaluates some ways of constructing cost-of-education indices, focusing on existing approaches rather than proposing new ones. Conceptual advantages of econometric supply-demand modeling approach are noted, as are its practical disadvantages. Improvements in databases should make construction of a model-based cost-of-education index much more feasible in the near future. Chapters are: (1) "Introduction: Cost Differentials and Cost-of-Education Indices"; (2) "Conceptual Foundations of Cost-of-Education Indies": (3) "Alternative Index Construction Methods"; (4) "Demonstration and Assessment of Simple Cost Indices and Proxies"; and (5) "Conclusions: Current Capabilities and Promising Options." (Contains 19 tables and 48 references.) (SLD)

Investments in schooling are often regarded as essential for economic development, implying that such investments have high rates of return in developing countries. This paper examines the accuracy and usefulness of estimates of rates of return to formal schooling based on the standard human capital model of G. Becker and J. Mincer. Focus is on whether failure to account for differences in ability and school quality across a random sample significantly biases estimates of the private return to schooling derived from estimates of wage equations. This is done using an unusually rich data set from Ghana (over 4,700 households), which includes tests of ability and cognitive skills administered to 389 survey respondents. When years of schooling are used to measure the accumulation of human capital, there are virtually no returns to schooling in the private sector. Replacement of years of schooling by reading and mathematical ability does show positive returns to acquired skills, although these rates may be of little use to governments making schooling investment decisions because of the complexity of such decisions. Many government investments in education are designed to raise rates of return to schooling by raising school quality, but decisions by individuals assume that both rates of return and school quality are exogenous. Thirteen tables present data from the analyses. Four appendices provide supplemental data concerning the calculation of rates of return. (SLD)

Given "T" joint observations on "K" variables, it is frequently useful to consider the weighted average or scaled score. L-scaling is introduced as a technique for determining the weights. The technique is so named because of its resemblance to the Leontief matrix of mathematical economics. L-scaling is compared to two widely-used procedures for data reduction, but no attempt is made to survey the voluminous literature on scaling methods. These methods are the first principal component method and the best weight function method. A robust L-scaling technique is described for use when the data matrix is contaminated by outliers. The discussion proceeds in terms of descriptive statistics since the various techniques have sampling properties that are either unknown or intractable. The technique is illustrated with a hypothetical example of 100 observations on three variables drawn from a pseudorandom-number generator. L-scaling is one method a researcher may apply when a sensitivity analysis, which compares the outcomes of several scaling methods, is desired. Four tables illustrate the study. (SLD)

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or other smooth functions.

This paper, one of three related documents, explains a model for school finance in Michigan. First, it analyzes where school districts get their money and how they spend it. Next, it details a financial model that identifies the factors related to staff adequacy levels, estimates the strength of those factors, offers ideas for the components of a policy regarding school funding, and estimates the impact of a possible policy alternative. The paper concludes that the model can be improved in three areas. Salary data can be refined and brought up to date. More factors contributing to staff adequacy levels can be identified. Finally, the model can be observed over time to see if it consistently predicts school district behavior. (Author/LD)

The labor market spillover effects of welfare reform were estimated by using models that pool time-series and cross-section data from the Current Population Survey on the state-year cell means of wages, employment, and other labor market outcomes for various demographic groups. The labor market outcomes in question are dependent variables that are related to control variables and the state's welfare caseload. A key feature of the analysis is that the endogeneity of caseloads is corrected for with a rich set of instrumental variables. State welfare caseloads are treated as endogenous, and 10 instrumental variables reflecting state welfare reform policies are used. The resultant estimates indicate significant spillover effects of welfare policies. Over the short term, welfare reforms reduce the wages of male high school dropouts, the wages of single mothers, and the employment of male high school dropouts. In the long run, more educated groups gain wage boosts because of welfare reform. Tables detailing the following items are appended: (1) logit estimates; (2) first-stage estimated coefficients for the instrumental variables, single mothers group, corresponding to second-stage equation with ln(Wage) dependent variable; (3) 2SLS coefficient estimates; and (4) simulated effects of welfare reform on various labor market outcomes. (Contains 30 references and 11 tables/figures.) (MN)

A model in which nonprice rationing has two effects on the number of medical school applicants in the United States is specified and estimated for the 1951-76 period. The results indicate that low acceptance rates discourage many potential applicants and that a fairly large and constant percentage of rejected applicants can be expected to reapply. Four previous applicant studies are examined. The results also indicate that the rapid growth rates of applicants in recent years can largely be attributed to three factors: growth in women applicants, increases in resident salaries; and induced increases in repeat applicants. Medical school tuition, loan availability, and the attractiveness of science careers do not appear to have been important determinants of applicants over the sample period. (Author/SW)

This volume is an exposition of a mathematical modeling technique for use in the evaluation and solution of complex educational problems at all levels. It explores in detail the application of simple algebraic techniques to such issues as program reduction, fiscal rollbacks, and computer curriculum planning. Part I ("Introduction to the Modeling Formulation") discusses four stages of modeling development related to acceptance of a modeling formulation for decision-making, contextual assessment, planning for modeling development, and the specific design stage. These chapters use specific real-world problems to illustrate the purpose and application of the model. Part II ("Presentation of a Full Formulation"), also composed of four chapters, provides a detailed description of the multiple alternatives framework as a strategy for purchasing computer equipment. The chapters cover conceptualization, development of the framework, format for execution, and approaches to exploring results. Part III ("Example of a Complete Quantitative Solution") is a single chapter focusing on implementation of the model for determining fiscal rollbacks and program terminations during a crisis. Part IV consists of two chapters focusing on current extensions under research and development and a summary touching on related topics. Three appendixes provide a course outline and syllabus for Multiple Alternatives Analysis instruction and an outline for a field project proposal. (TE)

This report provides an extensive discussion of the use of criterion referenced, mathematical modeling procedures to determine which budget reductions minimize reduction in the quality of educational programs. Part I, "Evaluation of Potential Budgeting Roll-backs under Educational Fiscal Crisis," explains the basic design of multiple alternatives analysis and the context for its use. Chapters include (1) philosophical foundation for fiscal modeling, (2) program budgeting for an allocation/deallocation fiscal strategy, (3) traditional modeling via cost analytical design, (4) operations research and the evaluation of feasible alternatives, and (5) simulation modeling within a criterion-impact design. Included also is a background to the field investigation and outline of the technical report. Part II, "Multiple Alternatives Analysis as a Mathematical Decisioning [sic] Model," provides the technical and mathematical details of the analysis, including both construction and validation. Part III, "Field Application of the Rolbak Model," contains an extensive sampling of the use of these procedures in reducing a budget within a local school district, including chapters on (1) construction of the database, (2) initial T-normal transformations, (3) formulation of the rolbak mathematical model, (4) search for regional feasibility as a benchmark, (5) cyclic optimization of the restricted model, (6) cyclic optimization of the relaxed model, and (7) comparison of the restricted and relaxed "decisioning" models. Part IV summarizes the Multiple Alternatives Model and assesses its future. (TE)

This report evaluates alternative approaches to and measures of equity in state school finance plans. It also evaluates the Federal Expenditure Disparity Measure (FEDM). Following an introduction, Part II describes alternative conceptions of equity in education and identifies three components of these conceptions: groups treated, alternative treatments, and criteria for equity. Part III presents numerical models that show how alternative combinations of group, treatment, and criterion can yield different conclusions when applied to a hypothetical school district. In Part IV, the value judgments that underly the alternative conceptions of equity are examined. Since few value judgments are widely held, a number of equity conceptions must be considered valid. Also in Part IV, the value judgments inherent in Per Pupil Expenditure Disparity Measures (PPEDMs) are reviewed and analyzed. In Part V, the theory behind the FEDM and the way the Office of Education applies the FEDM to calculate measures from state data are discussed. In Part VI, recommendations concerning equity measurement in federal regulations and particular procedures used by the Office of Education to measure expenditure disparities are presented. A lengthy appendix considers social welfare theory, social choice theory, equity measures calculations, and the tax price of education. (Author/JM)

A multiparameter, programmable model was developed to examine the interactive influence of certain parameters on the probability of deciding that an examinee had attained a specified degree of mastery. It was applied within the simulated context of performance testing of military trainees. These parameters included: (1) the number of assumed mastery states--master, nonmaster, and perhaps intermediate (likely to soon achieve mastery); (2) the prior distribution of scores from similar examinee groups; and (3) the number of test trials or items administered. The results of several simulations showed that the degree of confidence that a decisionmaker can have about the testee's mastery is markedly affected by the values for the three parameters, and the effects of their combination. Using the Bayesian model, test length and costs could be reduced--as long as the prior information was accurate and valid for the particular group of examinees. Results of the simulation also showed that a test may be too short to be of decision-making value. (Author/GDC)

Alternative mathematical models for scoring and decision making with criterion referenced tests are described, especially as they concern appropriate test length and methods of establishing statistically valid cutting scores. Several of these approaches are reviewed and compared on formal-analytic and empirical grounds: (1) Block's approach to setting mastery standards, involving student performance and academic requirements; (2) Crehan's classification, comparing scores of students who have and who have not completed training; (3) the probabilistic models of Macready, Dayton, and Emrick, which assume an equal proportion of masters and nonmasters; (4) the binomial distribution model, which allows for partial acquisition of proficiency; (5) the Bayesian model, which considers prior experience; (6) Rasch's one-parameter logistic model, which yields person-free test calibrations and item-free person measurements; and (7) the regression approach of classical test theory, which enables the estimation of true scores to be made from observed scores. Examples of these approaches are given, as well as their advantages, disadvantages, and ambiguities. (GDC)

A psychometric model called Saltus, which represents the qualitative aspects of hierarchical development in a form applicable to additive measurement, was applied. Both Piaget's theory of cognitive development and Gagne's theory of learning hierarchies were used to establish the common features of hierarchical development: (1) gappiness--the logical construction of the hierarchy which occurs when there is no state between adjacent stages; and (2) rigidity--learning behavior, exhibited by a fixed sequence of progression through stages. Saltus assumes a theory with gappiness expressed through items or tasks, and estimates the rigidity of data, thus testing the hypothesized gappiness. Four experiments tested the Saltus model in elementary school Australian children and with subjects aged 3, 4, 5, 8, 12, and 21 years. Three Piagetian tasks of rule assessment involving proportionality (balance scale, projection of shadows, and a probability task) gave clear evidence of rigidity in the step from the pre-operational stage to the concrete operational stage. The next step, to the formal operational stage, did not show rigidity, although gappiness was evident. The hypothesized existence of a gap to split the concrete operational stage was not supported. The Gagnean data on a subtraction task showed strong rigidity. (Author/GDC)

The stability of Rasch test item difficulty parameters was investigated under varying conditions. Data were taken from a mathematics achievement test administered to over 2,000 Australian students. The experiments included: (1) relative stability of the Rasch, traditional, and z-item difficulty parameters using different sample sizes and designs; (2) effect of different sample types and sizes on the Rasch item fit estimator; (3) effects, on the item fit parameter and the Rasch item difficulty parameter, of removing some less appropriate items from the test; and (4) an examination of Wright's statement that the standard error of the item difficulty parameter is a good estimator of its variance, and that it has an inverse square root relationship to the sample size. Results showed that Rasch and z-item difficulty parameters were similar. Item fit increased as sample size increased. The removal of poorly fitting items improved fit values for the entire test, but worsened them for the remaining items. The Rasch standard error parameter was an appropriate measure of the true error of estimation as calculated from the square root of the sampling variance of the item difficulty index. (Implications for test calibration are concluded, and detailed item analyses are appended.) (GDC)

This report details the data requirements and procedures used to develop new school bus routes for Six Mile Elementary School in South Carolina. The project examined the current routes of the school and applied computer based techniques to develop new routes given the existing bus stops. Bus routes were developed so that distance and travel time were minimized. Before the routes could be generated, the map of Six Mile had to be modeled as a network, requiring numerous modifications to fit the heuristics used by the computer program. Using Floyd's Algorithm, the shortest path between every pair of bus stops was computed. The bus stops were clustered into routes, considering the number of children allowed on a bus. A model was developed which estimated the travel time based on a description of the route, and was validated by an actual bus ride through the route. The new routes were evaluated by comparing the time and distance of the old and new routes. The appendix contains a complete description of the seven new routes that were developed, including a listing of all stops and turns the buses must make and the roads the buses are to travel on. Contains numerous tables and figures and 16 references. (KS)