Statistical Issues in Allocating Funds by Formula

Panel on Formula Allocations

Thomas A. Louis, Thomas B. Jabine, and Marisa A. Gerstein, Editors

Committee on National Statistics

Division of Behavioral and Social Sciences and Education

NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES

THE NATIONAL ACADEMIES PRESS
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Statistical Issues in Allocating Funds by Formula Statistical Issues in Allocating Funds by Formula Panel on Formula Allocations Thomas A. Louis, Thomas B. Jabine, and Marisa A. Gerstein, Editors Committee on National Statistics Division of Behavioral and Social Sciences and Education NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES THE NATIONAL ACADEMIES PRESS Washington, D.C. www.nap.edu

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Statistical Issues in Allocating Funds by Formula THE NATIONAL ACADEMIES PRESS 500 Fifth Street, N.W. Washington, DC 20001 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 supported 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 0-309-08710-4 Library of Congress Catalog Card Number 2002116513 Additional copies of this report are available from the National Academies Press, 500 Fifth Street, N.W., Lockbox 285, Washington, DC 20055; (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area); Internet, http://www.nap.edu Copyright 2003 by the National Academy of Sciences. All rights reserved. Printed in the United States of America Suggested citation: National Research Council (2003). Statistical Issues in Allocating Funds by Formula. Panel on Formula Allocations. Thomas A. Louis, Thomas B. Jabine, and Marisa A. Gerstein, Editors. Committee on National Statistics, Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press.

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Statistical Issues in Allocating Funds by Formula THE NATIONAL ACADEMIES Advisers in the Nation on Science, Engineering and Medicine 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. Wm. 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. Harvey V. Fineberg 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. Wm. A. Wulf are chair and vice chair, respectively, of the National Research Council. www.national-academies.org

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Statistical Issues in Allocating Funds by Formula PANEL ON FORMULA ALLOCATIONS THOMAS A. LOUIS (Chair), Department of Biostatistics, Johns Hopkins University GORDON BRACKSTONE, Statistics Canada, Ottawa, Ontario THOMAS A. DOWNES, Department of Economics, Tufts University 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 (until March 2002) CHRISTOPHER MACKIE, Program Officer THOMAS B. JABINE, Consultant MARISA A. GERSTEIN, Research Assistant MARIA ALEJANDRO, Project Assistant

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Statistical Issues in Allocating Funds by Formula COMMITTEE ON NATIONAL STATISTICS 2002 JOHN E. ROLPH (Chair), Marshall School of Business, University of Southern California JOSEPH G. ALTONJI, Department of Economics, Northwestern University ROBERT BELL, AT&T Research Laboratories, Florham Park, New Jersey LAWRENCE D. BROWN, The Wharton School, University of Pennsylvania ROBERT M. GROVES, Survey Research Center, University of Michigan 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 ARLEEN LEIBOWITZ, School of Public Policy and Social Research, University of California, Los Angeles RODERICK J.A. LITTLE, School of Public Health, University of Michigan, Ann Arbor THOMAS A. LOUIS, Department of Biostatistics, Johns Hopkins University DARYL PREGIBON, AT&T Laboratories-Research, Florham Park, New Jersey NORA CATE SCHAEFFER, Department of Sociology, University of Wisconsin, Madison MATTHEW D. SHAPIRO, Department of Economics, Survey Research Center, University of Michigan, Ann Arbor ANDREW A. WHITE, Director

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Statistical Issues in Allocating Funds by Formula Acknowledgments Many people have contributed their time, expertise, and resources to the panel. The National Center for Education Statistics of the U.S. Department of Education provided financial and program support, and we thank Daniel Kasprzyk for his interest and participation on their behalf. Andrew White, director of the Committee on National Statistics (CNSTAT), developed institutional and financial support for the panel. Many individuals provided important comments and suggestions at panel meetings (see Appendix E). We thank them for their time and insights. We thank the authors of the papers prepared for the panel, which appear in a special issue of the Journal of Official Statistics: Dawn Aldridge, U.S. Department of Agriculture; Paul Sanders Brown, U.S. Department of Education; Jean-Francois Carbonneau, Statistics Canada; John L. Czajka, Mathematica Policy Research, Inc.; Thomas Downes, Tufts University; Thomas B. Jabine, statistical consultant; James A. Kadamus, New York State Education Department; Sean Keenan, Finance Canada; Dan Melnick, Dan Melnick Research; Thomas Pogue, University of Iowa; Allen L. Schirm, Mathematica Policy Research, Inc.; Felizardo B. Suzara, United Nations Statistics Division; Michelle Taylor, Finance Canada; and Alan M. Zaslavsky, Harvard University. We also thank the reviewers of those papers: David Betson, University of Notre Dame; Linda Bilheimer, Robert Wood Johnson Foundation; Hamilton Lankford, Stanford University; David McMillen, House Government Reform Committee; Wayne Riddle, Congressional Research Service; William Seltzer, Fordham University;

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Statistical Issues in Allocating Funds by Formula Robert Tannenwald, Federal Reserve Bank of Boston; and Jim Wyckoff, State University of New York, Albany. We have greatly benefited from the contributions of the late Wray Smith, who chaired the federal interagency committee that prepared the 1978 Report on Statistics for Allocation of Funds. He also wrote and presented the keynote paper for the Workshop on Formulas for Allocating Program Funds, held by CNSTAT in April 2000. I want to personally thank panel members, who donated their time and expertise, and give special thanks to Thomas Jabine, consultant to the panel, whose thoughtful guidance, broad and deep knowledge, and good old-fashioned hard work were instrumental in making this report possible. Marisa Gerstein, research assistant, contributed in myriad fashions, organizing, researching, writing, editing, and generally keeping us upbeat. Virginia de Wolf, study director, and Maria Alejandro, project assistant, ensured success for meetings and provided other key organizational contributions. Christopher Mackie, CNSTAT program officer, can and did play all positions and frequently pitched in. 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: Henry J. Aaron, The Brookings Institution; Jerry C. Fastrup, Government Accounting Office; Thomas Gabe, Congressional Research Service; Cynthia Long, Food and Nutrition Services, U.S. Department of Agriculture; Fritz Scheuren, Urban Institute; James Wyckoff, Rockefeller College, University at Albany, SUNY; and Alan M. Zaslavsky, Harvard Medical School. 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 John C. Bailar, Professor Emeritus, University of Chicago, and Joel Greenhouse, Department of Statistics, Carnegie Mellon University. Appointed by the National Research

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Statistical Issues in Allocating Funds by Formula Council, they were 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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Statistical Issues in Allocating Funds by Formula Contents     Preface   xiii     Executive Summary   1     PANEL REPORT     1   Introduction   5 2   Why Provide Aid and Use Aid Formulas?   18 3   Basic Features of Formula Allocation Programs   26 4   Components of Allocation Formulas   35 5   Special Features of Formula Allocations   40 6   Data Sources for Estimating Formula Components   50 7   A State View—California   59 8   International Perspective   71 9   Conclusions and Recommendations   79     References   90     APPENDICES     A   Background Papers   95 B   A Review of Twelve Large Formula Allocation Programs   100 C   Sources of Information   129 D   Handbook on Fund Allocation Formulas and Processes   138 E   Participants in Panel Workshops and Meetings   142 F   Biographical Sketches of Panel Members and Staff   143

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Statistical Issues in Allocating Funds by Formula Preface Each year in the United States statistical formulas are used to allocate large amounts of federal funds to state and local governments in programs designed to meet a wide spectrum of economic and social objectives, such as improving educational outcomes and accessibility to medical care. Many of the programs are designed to equalize the fiscal capacities of the recipient units of government to address identified needs. Furthermore, many states use formulas to distribute aid to local governments. There is a long history of attention to issues associated with allocating funds by formula, though surprisingly little of it has come from statisticians. To reenergize discussion on these matters, the Committee on National Statistics (CNSTAT) convened, in April 2000, a two-day Workshop on Formulas for Allocating Program Funds. Drawing examples from four major U.S. programs, the workshop focused on statistical issues that arise in the development and use of formulas for allocating federal funds to state and local governments. 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 workshop was a direct outgrowth of a previous study by the Panel on Estimates of Poverty for Small Geographic Areas. That panel, established under a 1994 act of Congress, began its work with a specific mission: to evaluate the suitability of the U.S. Census Bureau’s small-area estimates

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Statistical Issues in Allocating Funds by Formula of the number 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 considering that panel’s conclusions, 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. The Panel on Formula Allocations was formed in January 2001 with sponsorship by the National Center for Educational Statistics and also, in part, by the many U.S. federal statistical agencies that support CNSTAT through the National Science Foundation. The panel’s charge was 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, conclusions, and recommendations relating to these issues. Initially, the panel concentrated its efforts on technical and conceptual statistical issues but, as the study progressed, found it essential to embed the statistical issues in a broader political and policy framework. In July 2001 the panel issued Choosing the Right Formula: Initial Report (National Research Council, 2001), which featured the report of the April 2000 workshop, highlighted key issues identified by the panel, and communicated its work plan. In conjunction with its own work, the panel also commissioned a series of papers—some devoted to case studies and others to an examination of the goals of formula allocation programs, the specific roles played by formulas, and the statistical features of allocation formulas and processes. Several of these papers were presented at the panel’s December 2001 meeting, and all of them are assembled as a special issue of the Journal of Official Statistics (September 2002). The journal issue is intended to serve as a companion to this, the panel’s final report, and is a key component of the panel’s work toward fulfilling its charge. I am confident that you will find the panel’s final report interesting and informative. Using allocation formulas to advance legislative aims has become a widely employed policy tool. The panel hopes that this report will be helpful in informing the process in the future when allocation formulae are being crafted in legislation. John E. Rolph, Chair Committee on National Statistics