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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 develops and estimates a model of college attendance that focuses on the influences of public policy and of economic environment. The Policy instruments examined are tuition, admissions requirements, college locations, breadth of curriculum, draft deferments, and class integration of neighborhoods. The aspects of the economic environment examined are the opportunity cost of the students' study time and the size of the anticipated earnings payoff to college graduates. The first five sections of the paper develop a theory of college attendance and then apply it to the choice and definition of variables and the seletion of functional form for the estimating equation. Section 1 examines the college entrance decision when unlimited borrowing is possible. Section 2 handles a more realistic situation. Section 3 applies this theory to the selection of the college. Section 4 examines how planning for college influences model specification and the selection of variables. Section 5 derives the functional form for estimation and describes how the estimated parameters will be used to test the hypotheses discussed in sections 1 and 2. Section 6 describes the data and section 7 presents the results. Section 8 analyzes the effectiveness of public subsidies of undergraduate education by calculating the subsidy cost of an extra student from each of the 20 ability-by-income strata and discusses the policy implication of the results. (Author/KE)

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)

This paper proposes a model for the process of attaining occupational status and income, where change in attainment is generated by the creation of vacant positions in social structure. The distribution of attainments, or the structure of inequality, is assumed fixed and described by a simple exponential or geometric distribution function, depending on whether attainment levels are assumed discrete or continuous. Persons leaving the labor force create chains of vacancies in this structure that present mobility opportunities for persons entering the labor force. The implications of the model for the attainment process derived from these considerations for status attainment research and stochastic models for job-mobility are discussed. (Author/JM)

In an attempt to bridge the gap between academic understanding and practical business use, the Box-Jenkins technique of time series analysis for forecasting future events is presented with a minimum of mathematical notation. The method is presented in three stages: a discussion of traditional forecasting techniques, focusing on traditional techniques that relate to the Box-Jenkins model; a presentation of the key characteristics of the Box-Jenkins model; and a detailed demonstration of the method's steps. A discussion of the technical requirements needed to use the model, its cost versus that of other forecasting methods, and the potential areas of its application conclude the paper. The mathematical rationale is appended. (Author/DW)

This paper attempts to provide a general equilibrium framework for comparing the merits of alternative methods of raising the income of the employable poor. The strategy is to specify a complete and interacting set of factor markets, parameterize alternative program types in a manner convenient to this specification, and then solve the system of equations that characterize this economy for the comparative static response to the initiation of a small version of each program type. Within the income maintenance category the rankings implicit in impact effect analysis recur when general equilibrium effects are considered. Wage subsidies are more transfer-efficient than the negative income tax, or earning supplements. The size of policy multipliers are, however, quite sensitive to elasticities of substitution in production. The general equilibrium impact of targeted employment and training programs is quite different from the impact effect. Expanding the employment of the skilled lowers the income of the less skilled, especially when elasticities of substitution and occupational choice are low. In general, equilibrium effects of transferring workers from the low to the high skilled work force imply that education and training are by far the most effective means of aiding the low skilled. (Author/AM)

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)

Competitive bidding has recently received considerable attention in the literature of economics and operations research. Unfortunately, the classic formulation of the problem developed by Friedman and still expounded (Stark and Mayer) can lead to an incorrect estimate of the expected profit for a bidder when uncertainty about the cost of fulfilling the contract exists. The purpose of this paper is to point out the deficiency in the formulation and to indicate how it may be corrected. (Author)

Estimating the probability that a proposed bid will win is obviously a central problem in competitive bidding theory. Unfortunately, a method for doing this, which originated with Friedman and which continues to be expounded in the literature, is logically incorrect. This paper points out the deficiency in that formulation. (Author/MLF)

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)

Since research on sex differences in occupational attainment suggests that working men and women attain essentially the same mean level of occupational attainment and do so through quite similar processes, the censoring problem as a potential source of bias in estimating equations for these comparative occupational attainments is investigated. (The censoring problem is defined as a sampling problem in that the sample of working women contains an overrepresentation of successful women, since women who can afford not to work will stay out of the labor force unless they find a job commensurate with their education.) After reviewing and rejecting some alternatives that could correct this problem, a model (developed from an extension of Heckman's set of equations that relate to women's occupational characteristics) is presented for obtaining the structural parameters for the whole female population by accounting for the censoring problem. The censoring problem was found to be minimal and not a reasonable explanation for the apparent similarities between men and women in the process of occupational attainment. It was concluded that before accepting the finding of sexual equality in occupational rewards, the following possibilities should be explored: (1) That the model is misspecified and if certain variables (for example, the status of first job) were included, the process of occupational attainment for the sexes would differ, and (2) that certain dimensions of sexual inequality in occupational rewards are not being tapped by the concept, occupational status. (TA)

Many economists have tried to explain existing wage differentials between men and women. A new approach compares the relative importance of occupational discrimination with that of wage discrimination. This model allows for variation both in occupational distribution and in wages resulting from differences in job qualifications and productivity indicators. It was demonstrated that the usual approach to wage discrimination is a special case of this general model with some restrictive implicit assumptions. A multinomial logit model was used to stimulate the occupational distribution of women that would exist if they faced the same structure of occupational determination as men. Results indicate that there would be more women in managerial and skilled labor jobs and fewer women clerical and service workers. Wages were then estimated as a function of productivity measures for men and women in each occupation so that the components of the wage differential could be calculated. Results indicate that almost the entire differential could be eliminated by ending both forms of discrimination, with occupational discrimination accounting for one-third to one-half of the differential and pure wage discrimination the remainder. (WL)

Neglected issues of simultaneous statistical inference and statistical power in survey research applications of the general linear model are reviewed, and it was found that classical hypothesis testing as it is currently applied, is inadequate for the purposes of social research. The intelligent use of statistical inference demands control over the overall level of Type I error and knowledge of the magnitude of effects one is likely to detect. Techniques are suggested that can be used to routinely incorporate considerations of simultaneous inference and power into statistical analysis of survey data. Several examples of applications of these techniques are presented. (RC)

The Educational Simulation Model (ESM), developed by UNESCO, is designed for use at the national level for long range simulation of educational system fluctuations. The model is a set of equations which describe an educational program and the changes and flows in student enrollment in all the courses of an educational system. Thus the model is restricted to the internal logic of an educational system which is simulated deterministically. Some of the variables employed by the model are population figures for each age and also promotion, repetition, distribution, and leaving rates for each course. The simulation model can be adapted to determine the demand for teachers, the costs, and the cumulative output of any educational system. The model has been employed in several countries, and its implementation on a computer would allow a more objective simulation with more refined results. (WH)

This study investigates how local school districts behave in allocating their budgets among teachers, other professional educators, support personnel, and nonpersonnel inputs. Demands for school inputs are estimated using U.S. Office of Education data on the expenditure and staffing patterns of large (enrollments in excess of 10,000 students) school districts in the 1969-70 school year. In general, results suggest that districts' allocative behavior at the margin is quite different from their average allocative behavior. In particular, relatively small proportions of budget increases (occasioned, perhaps, by reforms in school finance) would be allocated to employing additional teachers. (Author)

A randomization model appropriate for evaluating priority effects in free recall (i.e., whether "new" items are recalled prior to "old" items) is discussed and related to well-known nonparametric significance tests. Since the bases for the measures that have been suggested in the psychological literature may be interpreted either in terms of Wilcoxon's rank sum statistic or through a specific entry in a 2 x 2 contingency table, alternative indices of priority can be adopted directly from classical nonparametric statistics. Finally, the mean and variance formulas for a general correlational statistic are provided that specialize to the moments for the two measures already in common use. (Author)

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)