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Choosing the Right Formula

INITIAL REPORT

Panel on Formula Allocations

Thomas B. Jabine, Thomas A. Louis, and Allen L. Schirm, Editors

Committee on National Statistics

Division of Behavioral and Social Sciences and Education

National Research Council

NATIONAL ACADEMY PRESS
Washington, DC



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Page i Choosing the Right Formula INITIAL REPORT Panel on Formula Allocations Thomas B. Jabine, Thomas A. Louis, and Allen L. Schirm, Editors Committee on National Statistics Division of Behavioral and Social Sciences and Education National Research Council NATIONAL ACADEMY PRESS Washington, DC

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Page ii NATIONAL ACADEMY PRESS 2101 Constitution Avenue, N.W. Washington, DC 20418 NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This study was supported by Contract/Grant No. RN 96131001 between the National Academy of Sciences and the U.S. Department of Education. Support of the work of the Committee on National Statistics is provided by a consortium of federal agencies through a grant from the National Science Foundation (Number SBR-9709489). Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project. International Standard Book Number 0-309-07580-7 Additional copies of this report are available from National Academy Press , 2101 Constitution Avenue, N.W. , Lockbox 285, Washington, DC 20055 . Call (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area). This report is also available online at http://www.nap.edu Printed in the United States of America Copyright 2001 by the National Academy of Sciences . All rights reserved. Suggested citation: National Research Council (2001) Choosing the Right Formula: Initial Report. Panel on Formula Allocations, Thomas B. Jabine, Thomas A. Louis, and Allen L. Schirm, Editors. Committee on National Statistics. Washington, DC: National Academy Press.

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Page iii THE NATIONAL ACADEMIES National Academy of Sciences National Academy of Engineering Institute of Medicine National Research Council The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce M. Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. William A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce M. Alberts and Dr. William A. Wulf are chairman and vice chairman, respectively, of the National Research Council.

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Page iv

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Page v PANEL ON FORMULA ALLOCATIONS THOMAS A. LOUIS (Chair), RAND, Alexandria, Virginia GORDON J. BRACKSTONE, Statistics Canada LINDA GAGE, Demographic Research Unit, California Department of Finance, Sacramento HERMANN HABERMANN, Statistics Division, United Nations, New York ALLEN L. SCHIRM, Mathematica Policy Research, Inc., Washington, DC BRUCE D. SPENCER, Department of Statistics, Northwestern University VIRGINIA de WOLF, Study Director DANELLE DESSAINT, Project Assistant MARISA GERSTEIN, Research Assistant THOMAS B. JABINE, Consultant

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Page vi COMMITTEE ON NATIONAL STATISTICS 2001 JOHN E. ROLPH (Chair), Marshall School of Business, University of Southern California JOSEPH G. ALTONJI, Department of Economics, Northwestern University LAWRENCE D. BROWN, Department of Statistics, University of Pennsylvania, Philadelphia JULIE DAVANZO, RAND, Santa Monica, California ROBERT M. GROVES, Joint Program in Survey Methodology, University of Maryland, College Park HERMANN HABERMANN, Statistics Division, United Nations, New York JOEL HOROWITZ, Department of Economics, The University of Iowa WILLIAM KALSBEEK, Department of Biostatistics, University of North Carolina RODERICK J.A. LITTLE, School of Public Health, University of Michigan THOMAS A. LOUIS, RAND, Alexandria, Virginia DARYL PREGIBON, AT&T Laboratories-Research, Florham Park, New Jersey FRANCISCO J. SAMANIEGO, Division of Statistics, University of California, Davis RICHARD L. SCHMALENSEE, Sloan School of Management, Massachusetts Institute of Technology MATTHEW D. SHAPIRO, Department of Economics, University of Michigan, Ann Arbor ANDREW A. WHITE, Director

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Page vii Dedication We note with sadness and respect the death of Wray Smith on May 19, 2000, less than one month after he played a major role in the April 2000 Workshop on Formulas for Allocating Program Funds that is the primary subject of this report. Wray had a distinguished career as a federal statistician. In 1976-1977, under the auspices of the Federal Committee on Statistical Methodology, he chaired the subcommittee that produced Statistical Policy Working Paper 1: Report on Statistics for Allocation of Funds (U.S. Office of Statistical Policy and Standards, 1978). That report broke new ground in two ways: it served as the prototype for the highly successful continuing series of Statistical Policy Working Papers and it identified the potential for improving the equity and effectiveness of formula allocation processes by paying greater attention to their statistical features. The recommendations in Working Paper 1 have provided this panel with an important starting point for its deliberations. Because of his groundbreaking contributions, Wray was asked to prepare and present an introductory background paper for the April 2000 Workshop (Smith and Parker, 2000), an assignment that he fulfilled with his usual dedication and skill. We dedicate this report to his memory.

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Page ix Acknowledgments Many people contributed their time and expertise to the development of this report of the Panel on Formula Allocations. Financial support was provided by the U.S. Department of Education and Committee on National Statistics. This support made possible the panel and staff work that serves as the basis for this report. Daniel Kasprzyk of the National Center for Education Statistics who served as project officer for the study for the U.S. Department of Education, was most helpful in facilitating the panel's work throughout the project. Contributions of the presenters and discussants at the workshop were informative and invaluable. Many other individuals offered important comments and suggestions at our subsequent meetings as well: Jim Adams, U.S. General Services Administration; Chip Alexander, U.S. Census Bureau; Susan Binder, U.S. Department of Transportation, Federal Highway Administration; Sandy Brown, U.S. Department of Education; Pasquale DeVito, Board on Testing and Assessment; Thomas Downes, Tufts University; Jerry Fastrup, U.S. General Accounting Office; Gregory Frane, U.S. Department of Education; Jerry Keffer, U.S. Census Bureau; Kaeli Knowles, Board on Testing and Assessment; Cindy Long, U.S. Department of Agriculture, Food And Nutrition Service; David McMillen, U.S. House Government Reform and Oversight Committee; Wayne Riddle, Congressional Research Service; Marjorie Siegel, U.S. Department of Housing and Urban Development; William Sonnenberg, National Center for Education Statistics; Max Storrs, U.S. Department of Health and Human Services; Cynthia Taeuber, U.S. Census Bureau; Karen Wheeless, U.S. Cen-

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Page x sus Bureau; and Albert Woodward, Substance Abuse and Mental Health Services Administration. The panel is deeply indebted to Thomas Jabine, whose thoughtful guidance and intellectual contributions permeate this report. I give special thanks to the panel members, who have donated their time and expertise. Staff of the Committee on National Statistics provided key editorial, organizational, and research contributions. Heather Koball served as study director in preparing for the workshop. After the workshop, Andy White developed institutional and financial support for the panel and provided a bridge to Virginia de Wolf, our current study director. She and Danelle Dessaint assisted in organizing and preparing this report, and Marisa Gerstein carried out important research tasks. This report has been reviewed in draft form by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the Report Review Committee of the National Research Council. The purpose of this independent review is to provide candid and critical comments that will assist the institution in making the published report as sound as possible and to ensure that the report meets institutional standards for objectivity, evidence, and responsiveness to the study charge. The review comments and draft manuscript remain confidential to protect the integrity of the deliberative process. We thank the following individuals for their participation in the review of this report: John Czajka, Mathematica Policy Research, Inc., Washington, DC; Thomas Gabe, Domestic Social Policy Division, Congressional Research Service, U.S. Congress; Joel Horowitz, Department of Economics, University of Iowa; and James Wyckoff, Graduate School of Public Affairs, State University of New York at Albany. Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the conclusions or recommendations nor did they see the final draft of the report before its release. The review of this report was overseen by Joel Greenhouse, Department of Statistics, Carnegie Mellon University. Appointed by the National Research Council, he was responsible for making certain that an independent examination of this report was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this report rests entirely with the authoring panel and the institution. Thomas A. Louis, Chair Panel on Formula Allocations

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Page xi Contents Foreword xiii PART I     WORKSHOP REPORT 1     1     Formula Allocation Processes: An Overview 3     2     Case Studies 12     3     Effects on Formula Outputs of Errors in Formula Inputs 37     4     Roundtable and Concluding Sessions 45 PART II     PANEL REPORT 53     5     Themes and Issues 55     6     Anticipated Panel Activities 61 References and Bibliography 70 APPENDIX A     Workshop Agenda and Participants 75 APPENDIX B     Biographical Sketches of Panel Members and Staff 83

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Page xiii Foreword Each year, formulas are used to allocate well over $200 billion of federal funds to state and local governments via more than 160 federal programs designed to meet a wide spectrum of economic and social objectives. These programs address societal goals, such as improving educational outcomes and accessibility of medical care, and are designed to equalize fiscal capacity to address identified needs. An early example of such a formula was the Morrill Act of 1862, which allotted to each state 30,000 acres of public land for each of its senators and representatives in Congress. The land was to be sold and the proceeds used to establish one or more institutions of higher learning. Such formulas are developed in the context of a complex political process. Use of a formula, as opposed to arbitrary specification of the amount to be given to each recipient jurisdiction, facilitates informed debate about the allocation process by providing documentation of assumptions and computations. Furthermore, a formula offers legislators an effective way of explaining the allocation process to their constituents. However, as discussed in this report, when funds are allocated according to a formula, there is no guarantee that objectives will be fully met. In particular, properties of data sources and statistical procedures used to produce formula inputs can interact in complex ways with formula features to produce consequences that may not have been anticipated or intended. There is a long history of attention to these matters, but many of the issues identified and recommendations made are still of central importance

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Page xiv and have been only partially addressed. To reenergize attention to these persistent issues, the Committee on National Statistics (CNSTAT) convened a two-day Workshop on Formulas for Allocating Program Funds on April 26-27, 2000. The workshop focused on statistical issues that arise in the development and use of formulas for allocating federal funds to state and local governments in programs with a wide spectrum of objectives. Its agenda included an overview of formula allocation programs and relevant data sources, case studies, presentations on methodology, and a roundtable discussion. Presenters and other workshop participants included formula allocation program managers, economists, statisticians, and demographers from federal and state government agencies, universities, and independent research organizations. The goals of the workshop planners were to issue a report that would make a significant contribution to the field and to lay the groundwork for a subsequent panel study. The workshop was a direct outgrowth of a previous study by the CNSTAT Panel on Estimates of Poverty for Small Geographic Areas. That panel, established under a 1994 act of Congress, began its work with a very specific mission: to evaluate the suitability of the U.S. Census Bureau's small-area estimates of poor school-age children for use in the allocation of funds to counties and school districts under Title I of the Elementary and Secondary Education Act. In carrying out their assignment, panel members came to realize that the properties of data sources and statistical procedures used to produce formula estimates, interacting with formula features such as thresholds and hold-harmless provisions, can produce consequences that may not have been anticipated or intended (See Chapter 3 for specific examples). It also became evident that there is a trade-off between the goals of providing a reasonable amount of stability in funding from one year to the next and redirecting funds to different jurisdictions as true needs change. In one instance, for example, the annual appropriation included a 100 percent hold-harmless provision, ensuring that no recipient would receive less than the year before (For details, see “ Title I of the Elementary and Secondary Education Act” in Chapter 2). However, there was no increase in the total appropriation, with the result that new estimates showing changes in the distribution of program needs across areas had no effect on the allocations. Situations like this can arise not only in the Title I education allocations, but also in the many other formula allocation programs under which large amounts of federal and state funds are distributed to local governments for defined purposes. In considering the panel's conclusions,

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Page xv CNSTAT decided that it was important to explore these issues in a broader context, starting with the workshop and proceeding to a more comprehensive panel study. Following the April 2000 workshop, the Panel on Formula Allocations was formed in fall 2000. The panel's tasks are to refine and follow up on the important issues identified in the workshop, conduct case studies and methodological investigations, obtain input from individuals who design and implement programs using formula allocation, and to develop findings, recommendations, and guidelines relating to these issues. To these ends, a planning meeting was held on December 11-12, 2000; the panel then met on January 11-12, February 15, and April 19-20, 2001, to develop a work plan, review information, and obtain input from individuals involved in developing and administering funds allocation programs. The panel will hold additional meetings during the remainder of 2001 and in 2002. At its first meeting in January 2001, the panel decided to include a summary of the April 2000 workshop in this initial report; the issues identified by workshop participants will be high on the agenda for the panel's work. Part I of this report is the workshop summary. Part II synthesizes the principal themes from the workshop and the panel's initial meetings, highlights the principal issues the panel intends to address, and outlines anticipated panel activities. We invite and encourage feedback on this report and the panel's proposed activities. Please address comments to Virginia de Wolf, study director, at the Committee on National Statistics (2101 Constitution Avenue, N.W., Washington, DC 20418, phone 202-334-3023; fax 202-334-3751; email vdewolf@nas.edu). John E. Rolph, Chair Committee on National Statistics

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