A PROPOSAL AND EVALUATION OF A REGIONAL INPUT-OUTPUT MODELING SYSTEM Dissertation for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY STERLING HENRY STIPE} JR. 1975 ‘LIBRARY Michigan State University This is to certify that the ‘ thesis entitled r. _ ' . A PROPOSAL AND EVALUATION OF '; - ‘ ' A REGIONAL INPUT-OUTPUT 23:25 ' . MODELING SYSTEM presented by Sterling Henry Stipe. Jr. has been accepted towards fulfillment 1 cf, the requirements for Doctoral .degree in Agricultural Economics Date May 21, 1975 0-7639 III III III II III III III III II II IIII II I II II 3 1293 100 2046 ABSTRACT I I I V t}\ :yYR A PROPOSAL AND EVALUATION OF {\ A REGIONAL INPUT-OUTPUT - MODELING SYSTEM BY Sterling Henry Stipe, Jr. The objectives of the study are to: demonstrate a procedure for preparing secondary data models for multicounty planning areas; show how such models can improve the multicounty planner's feel for the linkages of his area economy; develop methods for using the I-0 model to extend river basin analysis to evaluate regional, state and nation- al effects; and to evaluate potential crop and livestock sector output change in the Muskingum River Basin using mechanically derived models. Recent literature specifically related to secondary data reducing procedures for deriving small area models from larger area models was reviewed. Other literature related to anticipated further development and use of I-O systems also was reviewed. Two base model coefficient reducing procedures were compared. One uses the ratio of local processing output available to local pro- cessing output required to reduce the base model coefficients to reflect small area economic structure. The other procedure uses total gross output available to total gross output required as the reducing ratio. The latter was selected for use in the Regional Input—Output Modeling Sterling Henry Stipe, Jr. System (RIOMS) which was developed. The system was programmed to carry out a complex set of computations and displays including the following components: 1. Estimation of local final demand by sector for any sub— state area down to county level beginning with state final demands. Estimation of total gross output by sector based on em- ployment ratios with the base model area. Adjustment of base model direct coefficients to approximate study area economic structure. Computation of base model and study area matrices of direct coefficients and Leontief inverses with and without a households sector. Computation and printing of income multipliers for the study area and the base model area. Computation and printing of direct plus indirect total gross output change resulting from a change in the final demand of a single sector or several sectors. Application of national coefficients for value added and its components to the total gross output change; also esti- mation of man-years of employment change. Estimation of impacts of study area imports on the rest of the state and on the nation. Six study area models, the State of Ohio and five substate study areas, were prepared with RIOMS and their characteristics were compared. It was found that the reducing procedure used in this study Sterling Henry Stipe, Jr. could lead to smaller multipliers for a large area than for a small area contained entirely within the large area. The reason for this inconsistency is due to the addition of relatively more final demand than total gross output in some sectors when the additional area is added. This leads to smaller reducing ratios and smaller coeffi- cients, thus smaller elements in the Leontief inverse. Procedures to strengthen the reducing procedure and eliminate the inconsistency were outlined for further experimentation but were not tested in this study. It was concluded that secondary data procedures hold much pro- mise for aiding in regional secondary impact evaluation on an inter— im basis. Procedures for improving the RIOM System were proposed for further study. Also a proposal was made for a completely different approach for the long run for meeting the needs for county, regional, and national interdependency models. This proposal includes pilot studies to develop consistent data collection procedures through which county planners could build county models that would be addi- tive to larger areas. A PROPOSAL AND EVALUATION OF A REGIONAL INPUT-OUTPUT MODELING SYSTEM By Sterling Henry Stipe, Jr. A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1975 ACKNOWLEDGMENTS I wish to express my appreciation to Professor James T. Bonnen for guiding my program, to Professor Daniel E. Chappelle for guiding the thesis work, and to Professors James D. Shaffer and Milton Steinmueller for serving on the guidance committee and reading the thesis. I especially appreciate the efforts of my wife, Elaine, who typed and edited several drafts of the thesis. Without her help, it would not have been completed. To our children, Valerie, Shannon and Rod, I owe a sincere apology for taking so much time away from fun things for them. I am indebted to many others too numerous to name for typing, programming, encouragement, and suggestions. Professor Wilford L. L'Esperance and Art King of the Ohio State University Economics Department were especially helpful with ideas and as a sounding board. Ralph Fellows, of the NRED staff, provided yeoman's service in program- ming the final version of the system and offered helpful ideas. Ellen Vander Lugt very capably typed the entire final copy of the manuscript. Finally, I wish to thank John Putman, my supervisor, for his understanding, encouragement, and patience and for making the work possible. ii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES Chapter I. INTRODUCTION Input-Output in Policy Analyses Objectives of Study Basic I-O Review Plan of Report II. REVIEW OF SECONDARY DATA METHODS AND RELATED LITERATURE Introduction Base Model Reducing Procedures Schaffer and Chu Location Quotient Methods Pooling Techniques Supply-Demand Pool Technique Modified Supply—Demand Technique An Iterative Procedure Morrison and Smith The RAS Method The Logarithmic Cross-Quotient Modified Cross-Industry Quotient Comparison of Techniques A California Study Boster and Martin Richardson Literature Related to Refinement and Exploitation of I-O Models Leontief and Ford Carter Colorado River Basin I—O Model Polenske Isard Summary iii Page vi viii l6 14 16 l6 l7 l8 18 23 24 26 27 32 33 35 35 36 38 41 43 47 48 50 51 53 S6 57 Chapter Page III. TWO REDUCING MODELS 58 Introduction 58 Sector Aggregation Decisions 59 Assumptions 60 Two Reducing Models 61 Structure and Assumptions of Model I Reducing Procedures 63 Structure and Assumptions of Model II Reducing Procedures 64 Reduced Models Compared 66 Direct Coefficients 67 Direct Plus Indirect Coefficients 73 Output Multipliers 76 Summary 76 IV. A REGIONAL INPUT-OUTPUT MODELING SYSTEM AND DATA PREPARATION 81 Introduction 81 General System Overview 82 Final Demand 83 Personal Consumption 84 Other Nonexport Final Demand 84 Total Gross Outputs 87 Agricultural Total Gross Output 88 Mining Total Gross Output 92 Balancing Study Area Output Against Requirements 93 A Direct Plus Indirect Plus Induced Income Analysis 95 An Impact Analysis 98 Analysis of a Final Demand Change 99 Rest-of—State and National Impacts 100 Project Analysis 100 Summary 103 V. COMPARISON OF SIX SECONDARY DATA INPUT-OUTPUT MODELS 105 Introduction 105 Model Elements Compared 111 Total Gross Output 111 Output Multipliers . 114 Income Multipliers 116 Final Demands 117 Imports to the Study Area 123 Final Demand Changes to be Analyzed 126 Total Gross Output Impacts of a $10 Million Change in Livestock Final Demand 127 Impacts on the Rest of the State 132 U.S. Impacts 138 Value Added and Related Impacts 138 Impacts of a $1 Million Change in Other Agriculture Final Demand 140 Summary 143 iv Chapter Page VI. SUMMARY AND RECOMMENDATIONS 146 Introduction 146 Use of Input-Output in Policy Decisions 147 Output of RIOM System 148 The Reducing Procedures 150 National Consistency of Regional Models 154 Recommendations 155 APPENDICES Appendix A. Sector Aggregation Schemes for the 87 Sector, 1970 U.S. Model and the 27 Sector Study Area Models 160 B. Estimating Procedure for Household Row Transactions and Display of Income Multipliers 173 BIBLIOGRAPHY 173 Table 10. 11. 12. 13. 14. LIST OF TABLES Direct coefficients for the livestock sector both models compared to U.S. coefficients, 9-county study area Direct plus indirect coefficients of the livestock sector for both models compared to U.S. coefficients, 9-county study area Direct plus indirect coefficients for the "other agri- culture" sector for both models compared to U.S. coefficients, 9-county study area Output multipliers for Models I and II compared to the U.S., 9-county study area Population, output, and final demands of the six study areas Total gross output used in the reducing model for each study area Percentage of study area total gross output supplied by each sector Output multipliers for the six study areas compared to the U.S. Number of sectors in each output multiplier rank from highest to lowest Income multipliers, l7-county study area and U.S. Final demands excluding exports The export component of final demand Final demand including exports Imports by industry vi Page 68 74 77 78 108 112 113 115 116 118 120 122 124 125 Table Page 15. Change in total gross output required for the livestock sector of each study area and the U.S. to deliver an additional $10 million to final demand 128 16. Total final demand required of rest-of—scate and rest-of— world as row imports to both final demand an industry by the study area 134 17. Imports to study area industry required for livestock to deliver an additional $10 million to final demand 135 18. The portion of study area import needs met by rest-of- state processing sectors 136 19. Change in rest-of—state total gross output due to imports to study area to meet $10 million increase in study area livestock final demand 137 20. Change in U.S. total gross output required to meet the change in U.S. final demand 139 21. Changes resulting from a $10 million increase in livestock final demand 141 22. Changes resulting from a $1 million increase in "other agriculture" final demand 142 23. Study area reducing ratios 152 A-l. Sector aggregation scheme for the U.S. model 161 A-2. Study area aggregation scheme 162 Ar3. Standard industrial classification codes grouped by census industry, Census of Population, General Social and Eco- nomic Characteristics,gl970 165 B-l. Data for the household row and column of the U.S. transac- tions table 171 B-2. Data for the household row and column of the 7-county transactions table 172 vii Figure LIST OF FIGURES Procedure for estimating study area personal consumption by sector (SAPCi) Procedure for estimating government and capital formation final demand purchases and total final demands exclusive of exports Procedure for computing study area employment by sector for employment to population ratio for the study area Procedure for estimating study area total gross outputs internally and merging with those from other sources Reducing procedure to obtain study area direct coefficients State of Ohio with 19-county Muskingum River study area boundaries delineated State of Ohio Planning Regions and Service Districts viii Page 85 86 89 9O 94 106 107 CHAPTER I INTRODUCTION Public officials, business managers, and community leaders share concerns and responsibilities for the total environment of their com- munities. They face choices among development alternatives which will result in different mixes of monetary and nonmonetary values. They must carefully compare alternative uses for the development funds available to governmental units and/or agencies. Funds invest- ed in one alternative may pay a much higher rate of return, whether measured in dollars or units of environmental quality, than the same funds invested in other alternatives. The President and the Congress make many choices of this na- ture in formulating and approving the annual budget. They must de- cide which agencies are involved in activities returning the greatest value per dollar invested. They must decide which agencies should receive large budget increases and which should be cut. State as well as national leaders are continually making similar choices. County and township level leaders also are charged with the responsi- bility of choosing among alternatives. They may use local taxes or various institutional devices to promote or control development. If decision makers have sufficient information about both the direct and secondary effects of each alternative on income, employment, and environment, their choices will be much easier. Efficient analyti- cal tools are needed for predicting the effects of proposed develop- ment activities. Society's policy makers need to understand the distributional impacts of proposed programs among income groups as well as among in— dustries. They need information about effects both interregionally and among social groups within a region. Bonnen, in a 1969 article prepared for the Joint Economic Committee, stated the need as follows: The distributional impacts of both public and private decision making increasingly are being questioned. Despite our society's equity commitments, many public programs are administered with little attention to their distributional impact. . . . We do not even really understand the process by which distributional ime pacts work their way through society. Without such knowledge we often work at cross purposes, we waste resources, and we fail to attain program objectives. Input-output methods can make a significant contribution towards analyzing policy alternatives and meeting the information needs de- scribed by Bonnen. A national interregional model can reveal geo- graphic distribution of impacts of various public and private expen— ditures. A single region model can indicate some of the economic and ecological linkages between industries. It can aid in tracing the buying and selling reactions that occur between the industry initially affected by some change and those ultimately affected. A recent study by W. Cris Lewis lists four basic purposes of input-output (I-O): 1James T. Bonnen, "The Absence of Knowledge of Distributional Im— pacts: An Obstacle to Effective Public Program Analysis and Decisions," The Analysis and Evaluation of Public Expenditures: The PPB System, Vol. 1. 9lst Congress, First Session, 1969, p. 419. (1) It can provide a detailed description of a national or re- gional economy by quantifying linkages among sectors of the economy and the source and origin of exports and imports; (2) given a set of final demands (exogenous), total output in each industry and requirements for primary factors and resources can be determined; (3) the effects of change in final demands, aris- ing in either the private or public sector, can be traced and predicted in detail; and (4) changes in production technology or relative prices can be incorporated by changing the techni- cal coefficients of production. The I-O technique has been used in many studies by federal, state, and private agencies to analyze economic structure and possi- ble impact of losing or gaining certain types of industry. The tremendous potential of I-O for getting at the answers needed by both public and private decision makers is widely recognized. But time after time in reviewing the literature, one finds reference to the tremendous data requirements of I—O. It has been considered necessary by many users to collect annual sales and payments data from all industries in the study area. From these sales and payments data, a transactions table is formulated showing transactions between the endogenous industries as well as their sales to final demand uses and purchases from outside the study area.2 Many potential users of input-output have rejected it because of limited budgets and study time. This study evaluates the usefulness of a secondary data input- output model of the state and substate areas of Ohio as an aid in 1W. Cris Lewis, Regional Economic Development, The Role of Water (Logan, Utah: Utah State University Foundation, 1971), p. 5. 2For an elementary treatise on the input-output procedure and its uses, see William H. Miernyk, The Elements of Input-Output Analye gig (New York: Random House, 1965). The Bibliography lists other references that would be useful. preparing planning information for water and land development deci— sions. A secondary data model uses existing input-output coefficients of a larger area encompassing the study area. A naive approach which has been resorted to by some researchers is to use the larger area direct coefficients with no adjustment. There have been several studies in recent years, however, which employed various methods to reduce the larger area coefficients to reflect the fact that the smaller area will normally import more of its product needs. Two such methods are compared in this study and one was used to prepare models for several different county groupings in Southeast Ohio. Input-Output In Policy Analyses Guidelines for evaluating proposed water and land development projects have recently been prepared by each federal agency having responsibilities in this area. All agency guidelines are based on the "Principles and Standards for Planning Water and Related Land Re- sources" published by the Water Resources Council in the Federal Register in 1973.1 The guidelines issued by USDA in March, 1974, call for using input-output multipliers: Through the use of multipliers, measurements will be made of indirect effects associated with direct output. . . . Indirect effects are the increased net returns which result from economic activity stimulated by production,utilization, and dis osition of intermediate goods or services by the project plan. 1Water Resources Council, "Principles and Standards for Plan- ning Water and Related Resources," Federal Register, XXXVIII, No. 174, Part III, September 10, 1973. 2U.S., Department of Agriculture, Economic Research Service, Forest Service, Soil Conservation Service, USDA Procedures for Planning Water and Related Land Resources (Washington, D.C.: Gov- ernment Printing Office, March, 1974), p. V-12. In view of the fact that some policy decisions are specifi- cally intended to change the input-output relationships of certain sectors of the economy, how can useful information be obtained from static models? Can a static model be useful even though a water resource development project changes the production function of sev- eral sectors of the economy? These problems were recognized by the authors of the USDA guideline as follows: Transaction tables for input-output studies are short term static records of past economic activity in an area. Therefore, where a project is expected to cause a major change in the pro- duction inputs care must be exercised in using multipliers deve- loped from historical relationships. The development irrigation in a region where the existing agriculture is all or nearly all dryland would result in a situation where the change in techni- cal coefficients would be of sufficient importance to prevent the unrestricted use of agricultural multipliers developed from his- torical information. After the project benefits have been adjusted to conform to the requirements imposed by input-output studies, the indirect benefits are calculated by using the multiplier for the parti- cular sector in which the benefits originate. The service sec- tor is to be used to determine indirect effects of recreation and fish and wildlife purposes. The measurement of national economic development external eco- nomies is thus the adjusted national economic development bene— fits to land and management less the annual cost of the project times the appropriate sector multiplier.1 Some suggestions are made in Chapter IV as to how static models might be adapted to reflect economic structure of a local area econo- my "with project" compared to "without project." Objectives of Study This study demonstrates how a static I-O model can supplement the planner's knowledge and enhance his intuitive judgment about the lIbid., p. v-14-v-15. economy of his area. Use of I-O can help him determine which indus— tries best meet the community's needs in trade-off planning to improve income, employment, and environment. While some industries yield so much pollution relative to income and employment that they are undesirable, others have benefits outweighing their bad effects. The direct impacts of introducing or removing an industry can be evaluat- ed without input-output techniques. But insights into the indirect impacts, which also are important, can be gained by using input-output models. The specific objectives of this study are: 1. To demonstrate a system for deriving I—O models for multi- county planning areas using secondary data. 2. To develop methods for using I-O to extend the impact analysis of river basin plans to evaluate regional, state, and national effects. 3. To evaluate potential crop sector and livestock sector output changes in the Muskingum River Basin using a secon- dary data input—output model. Basic I-O Review The mathematics and assumptions of a static input-output model are reviewed briefly here to facilitate presentation and discussion of the reducing models in Chapter III. Two broad categories of trading develop as an economy evolves: (l) purchases by final users to fulfill immediate needs and desires and (2) purchases of resources by producers from other producers in order to make products for sale to final users (intermediate or internal demands). When speaking of a limited economic area final demand may be characterized as that product removed from the local producing sector for other uses including local consumption, capi- tal formation, government purchases, and exports. That is, final demand is the net product of a particular area's producing sector as a whole. While it never occurs in reality, we can conceive of all con- sumer and producer markets (prices) in an economy being in general equilibrium with each other at a point in time. Then if a disturbance occurs in one market, such as a shift in the demand for wheat, there is a resulting adjustment in the equilibrium price in markets supply- ing inputs for wheat production. Conceptually, a mathematical sys- tem of equations can be designed to describe changes in prices and quantities in each market. Given the supply and demand elasticities for each market, new equilibrium levels of prices and quantities can be predicted. Unfortunately, such a system cannot be made empirical- ly operational due to lack of data and the size of the computing pro- blems. Basing his work on the general equilibrium theory developed by Quesnay and Walras, Wassily Leontief developed an empirically operational input—output model.1 The Leontief model, with certain necessary assumptions, mathematically describes a geographic area's complex patterns of exchange. To use such a model, it must be assumed that the economy can be divided into a number of discrete in— dustries, each of which produces a single homogeneous product. 1Miernyk, The Elements of Input—Output Analysis, p. 4. It must be further assumed that (1) inputs purchased by a sec- tor are a function only of the output of that sector, and (2) for static models, production functions are linear. These two assump- tions rule out any effects from technological or pecuniary externa- lities. If such effects are believed to be important for the situa- tion in which the model is being used, the direct coefficients should be adjusted. It may be necessary to employ some type of ancillary model to estimate adjustments to coefficients. Any one of a variety of models might be appropriate from a simple least squares technique to estimate the reliability of sample data gathered from "best prac— tice" firms to models designed to correct for price changes expected due to large output changes. Still another assumption is necessary if the model is to be used for projections. Due to technology change over time, the econo- mic structure upon which the model is based may not be appropriate for a future time period. Either the assumption of stable techno- logy over the projection period must be made or the technical coeffi- cients must be adjusted. This will be especially important for in— dustries undergoing rapid changes in technology due either to new discoveries or to significant changes in relative prices. For exam- ple, industries which have been heavy users of oil as a source of energy may be shifting to coal due to the increase in oil prices. It may be appropriate to use technical research data to construct future production functions for some industries. Technical coefficients would then be calculated using price relationships expected to exist in the future but with prices adjusted to be compatible with the rest of the model. Given these assumptions, the mathematical system1 can be stated as follows: Let x represent the total value of all transactions in the eco- nomy, both by producers and final users. This value includes double counting. Let xi represent the sum total of all sales by a single industry. Let xij represent the purchases by industry j from indus- try i. Then let yif represent purchases by final user f from process- ing industry i. We put these two categories of transactions into two separate matrices in the transactions table because we want to be able to manipulate them with matrix algebra techniques. The technique employed is based on the assumption that the processing sectors will expand output in a linear fashion in response to an increased re- quirement for goods by the final demand sector. This implies the assumption of linearity for the production functions of every indus- try in the system. The following example shows the two matrices X and Y and their relationship to a third matrix composed of a single column vector called total gross output (xi). Exports are shown as a final use relative to local processing sectors. Products exported may be used by processing sectors outside the study area but are shown in final demand since they are no longer within the region. 1A general knowledge of I-O on the part of the reader is assumed. This brief review is not sufficient for a full understand- ing of the capabilities and limitations of input-ouput methods. 10 Final User Total Sales Producer Transactions Purchases by i Agri. Manuf. DlStrlb. Local Export (TGO) l 2 3 . - —- '- r '— Agriculture Fill X12 X13 yll y12 xl Manufacturing x21 x22 x23 4- y21 y22 = x2 Distribution x31 x32 x33 y31 y32 x3 This example accounts only for purchases from other sectors within the processing matrix. We could add additional rows at the bottom of the table to account for such things as depreciation charges, taxes, and imports. Also, payments to households for labor, stock dividends, interest, rents, and profits are accounted for in a sin- gle row called "value added." These additional rows are important in building a transactions table from primary data. We will not include them explicitly in this study since we will be estimating transac- tions from secondary source material rather than collecting primary sales data. For convenience in the above example, only the local consump- tion final demand and the export final demand were shown. Other final uses which take goods out of the annual processing stream are govern- ment purchases and capital formation purchases. While capital goods are used in processing, they last more than one accounting period (one year in this study) and, therefore, must be handled outside the pro- cessing sector matrix in a static I-O model. In such a model, the simplifying assumption is made that product sold by an industry to other local industries for expanding capacity is not available to the system. Because it is a static rather than a dynamic model, there is 11 no mechanism which takes account of the increased local production capacity of an industry which has used a portion of its sales dollar to purchase capital goods from other local industries. The static model shows that a portion of an industry's gross sales receipts is set aside to purchase capacity increasing materials but does not take the additional step of showing increased purchases by other local industries or exports from the industry which has increased its capa- city. We can write the static I-O system in mathematical notation as follows: x = x + x + x + yi i = l,...,n i 11 12 i3 1 + in where M II total gross sales or output of the ith sector, K II i1 purchases by sector 1 from the ith sector, = purchases by final use 1 from the ith sector, etc. The most important use for I-O models, historically, is to in- dicate what happens in other sectors of the economy when the output of one sector changes in response to a change in final demand. The I-O model accounts for both direct and indirect linkages among industries. To use I-O for this purpose, the assumption that all production func- tions are linear must be accepted for modeling purposes. We know that they are not likely to be linear, and hence, it must be recognized that the accuracy of the model relative to the real world is affected by this assumption. The necessity for these assumptions is summed up by Chiou-Shuang Yan as follows: 12 Thus, although not totally defensible theoretically, the assumption of constant average cost built into the input—output system may not be too much out of line with the available facts. The impor- tant point is that if we are willing to use the input-output assumptions, we can present the intersectoral technical rela- tions of the entire economy very neatly in a single input-output table. Such tables can be made and used. We cannot make and use such tables unless we make the restrictive assumptions of input- output structure.1 In order to use the input-output system to estimate intersec- toral impacts of a change in output of one sector, several matrix ma- nipulations are useful. The first step is to derive a matrix of direct coefficients. These direct coefficients (often simply referred to as a '8) show the cents worth of purchases by industry j from in- ii dustry i for each dollar of sales by j. A matrix of aij's then shows all the transaction linkages between local industries. The standard notation for the technical coefficient is computed as X.. aij =-;%l i, j = l,...,n J where xij is the sales by sector i to sector j and xj is the total purchases of sector j. By definition xj = x1 for all endogenous sec— tors, i.e., producing sectors in a balanced transactions table. The computation of a for all cells in the processing sector of the trans- ij actions table results in a matrix of a, 's. 11 Let the transactions matrix of xij's be represented by X, the matrix of aij's by A, and the final vector by Y. It can be shown that: X = AX + Y. 1Chiou-Shuang Yan, Introduction to Input-Output Economics (New York: Holt, Rhinehart and Winston, 1969), p. 30. If a =-—$l, then xij = a ,x,. matrix as an example, 311 812 A = aij = 321 822 331 332 I_ It By definition xi = Ea I] And in matrix format x11 x12 X = x21 x22 X31 x32 Then in matrix notation 13 23 33 >4 X Carrying this into a form that facilitates computation: Y = X — AX, thus Y = (I-A)X __l__ ‘1 and X — I-A (I A) Y. We now have a form by which we can determine a new total gross output vector (xi) for any change in final demand (yi) which we wish to evaluate. Each element of the (I-A)-1 shows the total addition to the output of all industries which is required for a single industry 14 to deliver one dollar's worth of goods to final demand. Thus, when a vector of final demand changes is premultiplied by the (I-A)-1 matrix, a vector of total gross output changes is obtained. The matrix mul- tiplication operation sums the total change in output which occurs in each industry to meet the changes in all final demands. This yields a total gross output change vector. The change in employment, water use, pollutants, and any other variable which can be related to an in- dustry's total output can then be estimated byunfltiplyingthe appro- priate coefficient by the change in total gross output. Each column sum of the (I-A)-l (often called the Leontief in- verse) is the output multiplier for that industry. Various other multipliers, including income and employment, can be obtained by appropriate manipulations of the (I-A)-l. Some of these will be dis- cussed later. The capability of input—output techniques to provide useful multipliers is the tantalizing feature which keeps researchers struggling to find ways to overcome limitations. There is a large unexploited potential for using I-O to show how economic and ecologic variables change as a result of private or government expenditures or institutional regulations which affect industry output. The limiting factor is the availability of data at county and multicounty levels where many decisions affecting human well-being must be made. Plan of Report Chapter II contains reviews of some of the literature related to secondary data models and the growing body of consistent I-O data in the United States. 15 Chapter III will compare two reducing procedures, one of which is used in this study to prepare a first approximation input—output model for Ohio and various substate study areas. Chapter IV will present the data and computing routines which may be used to prepare a model and perform analyses for any substate group of counties. Chapter V will present a discussion of six study area models, and Chapter VI is a summary of the study with conclusions about future work needed to improve the system. CHAPTER II REVIEW OF SECONDARY DATA METHODS AND RELATED LITERATURE Introduction Bourque and Cox noted in a 1970 inventory of input-output stu- dies that ". . . I-O tables have become a fundamental block in the social accounting system of the United States and of other coun- tries."1 A large table for the U.S. was prepared by the Bureau of Labor Statistics in 1947 after several small ones had been developed by Leontief for the years 1919, 1929, and 1939. During the 1950's little work was accomplished on input-output in the U.S. but it was progressing rapidly abroad.2 In 1964 the OfficecflEBusiness Economics (now Bureau of Economic Analysis) completed and published an 87 sec— tor model for the year 1958. The most detailed national model is the 370 sector table published by BEA in 1969 for the year 1963. The expansion in industry detail of the 1963 model had been strongly urged by a broad cross section of users who were inter- ested in pinpointing the industrial markets and repercussions of changes in these markets to a greater degree than was possible with 1958 data.3 1Phillip J. Bourque and Millicent Cox, An Inventory of Regional Input-Output Studies in the United States, Occasional Paper No. 22 (Seattle, Wash.: University of Washington, Graduate School of Busi- ness Administration, 1970), p. 2. 21bid., p. 2. 3Ibid., p. 3. l6 17 The most recent national model was published in 1974 for 1967 and con- tains the same 87 sectors used for the 1958 study. "With the publica- tion of these results, the number of comparable benchmark I—O tables is increased to four and the time span covered by these studies is ex- tended to 20 years, covering the period 1947 to 1967."1 The remainder of this chapter is divided into two sections. The section on reducing procedures contains a review of some specific methods reported by several different authors for obtaining small area I-O models from large area models and on efforts to evaluate their validity. The last section is a general review of other relevant literature, touching on two major fields of input-output research: (1) pollution coefficients and (2) studies needed for projecting tech— nology change. Base Model Reducing Procedures The term "reducing," as used in this study, refers to the pro- cess of changing the technical coefficients of a larger area input- output model to reflect the economic structure of a smaller area. The smaller area is normally completely contained within the larger area and, for this reason, is likely to produce less of its local indus— tries' input needs than is the larger area. Objective procedures for making this reduction have been the subject of a number of recent studies. 1U.S., Department of Commerce, Bureau of Economic Analysis, "The Input-Output Structure of the U.S. Economy: 1967," Survey of Current Business, LIV (February, 1974), 24-56. 18 C . Shaffer and Chu Schaffer and Chu, in a 1969 article,1 discussed several procedures for deriving a small area model from a base model. They presented three variations of the location quotient method, three variations of pooling techniques, and an iterative procedure which they, themselves, developed. Location Quotient Methods The first of these methods, the "simple location quotient," com- pares the relative importance of an industry in a region to the rela- tive importance of that industry in the base economy. A location quotient of one (LQi = l) for industry 1 means that the region has its proportionate share of the entire industry 1 production in the base economy judged in terms of total regional production relative to total national production. The simple location quotient for industry i is computed as xi/x LQi = b b i, l,...,n; xi/x where x = total gross output of the ith industry of the region, 1 x = sum of total gross output of all industry in the region, x2 = total gross output of the ith industry in the base economy,2 xb = sum of all industry output in the base economy. Thus, the simple location quotient is the ratio between the percentage of total output supplied by industry 1 in the region and the percen— tage of total output supplied by industry 1 in the nation. 1William A. Schaffer and Kong Chu, "Nonsurvey Techniques for Con- structing Regional Interindustry Models," The Regional Science Associa- tion Papers, XXIII (1969, 83-101. 2The superscript b will denote base model variables throughout this report. 19 Where LQi 3_1, it is assumed that the region is producing more than its local needs and has product available for export. Also, it is assumed that the technical coefficient in the region (ai ) is rea- j sonably well approximated by the national or base model coefficient (an)' The implied assumption is that the regional coefficient is identical to the national coefficient (aij = agj for row i). Then regional interindustry flows for LQi-Z l are X.. .. . 13 13 1 since it was assumed that a = ab . If regional final demand (yi) ij ij has been calculated or estimated by some other procedure, the exports (e1) of industry 1 are assumed to be n t e. = x - 2x . - 2y. i, j = l,...,n 1 i 3'13 flf f=l,...,t; that is to say that exports are assumed to be the residual after re- gional transactions needs (Exij) have been met for all endogenous producing sectors. Where the LQi < 1, local production is assumed to be inadequate to supply local needs; thus, imports are necessary. Each regional co- efficient for row i must be adjusted downward to reflect the fact that relatively more of the product i needed comes through the imports sec— tor at the regional level than at the national level. Theoretically, some coefficients in a purchasing industry which must import to meet local requirements will be lower than the corresponding national (or base) coefficients because a portion of that industry's total gross output comes through its imports sector. The procedure which the loca- tion quotient approach employs to adjust the coefficients downward when LQi < l is 20 b . _ aij - LQi . aij i, j - l, .,n. Then regional gross flows are x = a . x i, j = l,...,n; ij ij j that is, the national purchase transaction per dollar of output is reduced according to the LQi ratio. Imports are m . = a . x. - x.. i, j = l,...,n. The simple location quotient reducing procedure is judged by Schaffer and Chu to be "grossly deficient." Reasons given are that there is no guarantee that a residual for export will exist when LQi > 1, nor that local production is inadequate to supply local needs when LQi < 1. They state that the simple location quotient is likely to give satisfactory results (that is, produce regional coefficients that adequately represent the region's economic structure or interin- dustry linkages) only when the local industry structure closely resem- bles the base model structure. This requirement is seldom met, they feel. Schaffer and Chu credit Charles Tiebout and Charles Leven with two variations on the simple location quotient reducing procedure in- tended to overcome its limitations. These are termed the "purchases- only" location quotient method (by Tiebout) and the "cross-industry" location quotient method (by Leven). Rather than use total gross output of the region (xi) and the nation (x?) in the LQi ratio, Tiebout suggested using only the total output of the inudstries which purchase from industry i. This proce- dure produces either a larger or smaller aij than the simple LQ 21 approach, depending upon the size of the output of the industries which are excluded. The purchases—only location quotient is I . xi/x LQi=;B—/;Tb- i=l,...,n i and -3;_-- x - (xj* + ---) x'b xb - (x?* + ---) , V t b ' where x and x are the total gross outputs of industries purchas— ing from industry 1 and the asterisk shows industries not purchasing. Then I b ij LQi . aij i, j - l,...,n. a By this procedure, the adjusted coefficient is not affected by large outputs of industries which are not directly related to the selling industry. Leven's variation, the "cross—industry quotient," compares the proportion of national output of selling industry 1 in the region to that for purchasing industry j: b xi/xi CIQi. = b i, j = l,...,n. J x./x. J Again, when CIQij 3_l, it is assumed that the regional coeffi— cient is identical to the national coefficient (aij = an) and region- al gross flows are X = a a X is j = 1’ ° an 22 The rationale is, if industry i in the region is producing a larger percentage of the base economy's product i than regional industry j is producing of its product, it is likely that industry j can obtain all the product i it needs within the region. For example, if the per- centage of the nation's steel output produced in Michigan is greater than or equal to the percentage of the nation's auto output produced in Michigan, it is very likely that auto makers in Michigan can pur— chase all the steel they need from Michigan steel makers. When CIQij < l, the regional coefficient is less than the national coefficient and is reduced as _ b . . _ aij CIQij . aij 1, j l,...,n. This has the effect of weighting the national coefficient (a: ) by the 3 ratio of the regional percentage of the national selling industry to the regional percentage of the national purchasing industry to obtain the regional coefficient (a ). This reflects the likelihood that pur- ij chasing industry j cannot obtain all the product i it needs within the region. Returning to the Michigan auto and steel example, CIQi < 1 implies that if auto makers in Michigan produce a larger share of the nation's autos than Michigan steel makers produce of the nation's steel, it is likely that auto makers must import some of their steel. Imports (mij) then are estimated as b . . _ ij — ij . xj) - (aij . xj) 1, j l,...,n. That is, imports are the difference between what the transaction b ij it is estimated to be by using the regional coefficient (aij)° Exports would have been if the national coefficient (a ) maintained and what 23 are then determined as a residual exactly as in the simple location quotient model. PoolingyTechniqges Pooling techniques involve summing "requirements" of all region- al industries for a given product and then using imports and exports to balance total needs against total supplies of that product within the region. Schaffer and Chu note that the "regional commodity balanc- es" procedure outlined by Isard in 1953 served as the forerunner of the "supply-demand pool"1 and "modified supply-demand pool"2 techniques later developed by Moore and Peterson, and Kokat, respectively. In both of these methods, the total regional requirements are computed as suggested by Isard. Individual transactions requirements (iij) for the region are x . = x . a . i, j = l,...,n ‘ Regional final demand (Cif) is the region's share of base economy final demand estimated by individual final demand vectors as follows: = b if. if yif ' b yr [—4. = l,...,n l,...,t C m II where cif is the final demand for i by vector f and t is the number of final demand vectors. The the total regional requirement for pro- duct 1 (ii) is 1Schaffer and Chu "Nonsurvey Techniques for Constructing Region- al Interindustry Models," p. 89. 2Ibid., p. 90. 24 §.=2x +Zc i=1,...,n. Where bi is a surplus commodity balance when it is positive and a de— ficit commodity balance when it is negative. Industry 1 is likely to be exporting product 1 out of the region if b1 is positive and using industries are likely to import product i by b is negative. 1 Supply-Demand Pool Technique This procedure is identical to that shown for commodity balances but goes further. Once a vector of bi's is obtained, the following rules are used to derive regional coefficients, imports, and exports. When b1 > 0 the national coefficient is assumed to be a good approxi- mation of the regional coefficient, i.e., The fact that bi is greater than zero for industry 1 implies that there is a surplus of product i in the region. Therefore, all local needs for product i can be met by local production. Imports are set at zero for this industry. Exports are and final demand is y. = C i = l,...,n 1f if f=l,...,t. 25 That is, when there are exports final demand is assumed to be the re- gional share calculated as —- i = l,...,n . =y. . If If y: - l,...,t. H1 I There is no reason to adjust final demand since the region has a sur- plus of product 1. On the other hand, when b is negative it is assumed that the i deficiency will be met by imports. Final demand is adjusted downward by the same ratio used to adjust the technical coefficients downward. Thus _ b xi . . aij - aij . -_-_- 1, j = l,...,n, x i and 31 i=1 n yif if°- xi f = l,...,t. This procedure assumes that production functions are the same for regional industries as for base economy industries and that the direct coefficients are different due only to lack of sufficient local production to meet local needs. It is further assumed that the pro- cessing sector and the final demand sector share equally the deficien- cy in local production of product 1; therefore, the demand vector must be reduced by the same ratio as used to reduce the direct coefficients. Imports are estimated for both the processing sector and the final demand sector. Imports to the processing industries are 26 and imports to final demand are m. :;i:::::‘.‘, where mij = imports of product i by processing sector j, mif = imports of product i by final demand sector f, cif = region's share of final demand for product i by sector f before the reducing adjustment, region's share of final demand for product i by sector f after the reducing adjustment. Modified Supply-Demand Technique For the case where bi is negative, Schaffer and Chu report a modification developed by Kokat.l Taking final demand as predeter- mined for the deficient sectors, he computes regional flows as fol- lows: s1. _ m., =-——-¥l- . (x. - x ) i, j = l,...,n 1J - 1 i X. "Y. 1 1 and xij= ij-mij i,j=l, .,n or X ‘ Y _- _i____i ._ xij - xij . i - i, j l, .,n. 1 yi This can be restated as 1R. G. Kokat, The Economic Component of a Regional Socio- economic Model, IBM Technical Report 17-210 (IBM, Inc.: Advanced Sys- tems Development Division, December, 1966). 27 MD >< N II x I rH. (.4. 32.. 13 u-MS i.e., the required transaction is reduced by the ratio of the sum of internal demand available to the sum required. An Iterative Procedure Schaffer and Chu present a procedure which they developed using bits and pieces of several other procedures which they reported in their article: The authors have developed a technique embodying several of the above devices but employing an iterative procedure to redistribute local sales allocated initially on the national sales pattern. The Regional Input—Output Table (R-I-O-T) Simulator not only as- sumes that the national production technology applies but also attempts to distribute local production according to both the national sales pattern and local needs. They use national coefficients to compute purchases required to produce the regional total gross output. They distribute regional total gross output (xi) to regional producers according to the nation- al pattern and compare required sales (rij) against distributed sales “13'" Let r be a matrix of required transactions estimated from 13 base model coefficients,.i.e., _ b rij - aij . xi i, j = l,...,n. Let dij be a matrix of regional sales distributed according to base model transactions; therefore, 1Schaffer and Chu, "Nonsurvey Techniques for Constructing Regional Interindustry Models," p. 92. 28 x3. d. =X ——b-J_ i, j = l,...,n. X 1 Then subtracting the matrix of required transactions (rij) from the matrix of distributed regional sales (dij)’ they get a "difference" matrix (zij) which contains some positive and some negative cells. The final demand matrix (zyif) is treated the same way; therefore, 213' ij ij zyif = dyif ‘ Cif i — 1,. ,n, f — 1,. ,t, POOLi = sum of all positive zij and zyif, NEEDSi = sum of all negative zij and zyif. When POOLi > (-NEEDSi), there are exportable surpluses. The actual transaction (Xij) is assumed to be equal to the transaction implied by base model coefficients (rij) and final demand receives the exports determined by e = POOLi + NEEDS i, l,...,n. i i When 0 < POOL1_: (—NEEDSi) and zij 3_0, they assume that xij = rij' When zij < 0, they compute = ——i—j- ' ' = xij dij + POOLi . xi 1, j l,...,n. This procedure is iterated until POOLi goes to zero. When POOLi = 0, there is nothing to add to dij' therefore, the iterations cease. The following example is useful in evaluating this procedure. Assume the base model transactions table to be: 29 b b 1 2 3 yi xi 1 6 O 3 l 10 2 2 4 6 3 15 3 2 6 2 4 l4 Payments: 0 5 3 xj Total Outlay: 10 15 14 Steps 1-6 develop the adjusted transactions matrix: (1) Base model direct coefficients: b _ x. .6 0.0 .214 —%1-= agj = .2 .267 .429 xJ 2 .4 .143 (2) Base model distribution of xb: 1 b x .6 0.0 .3 —%i = .133 .267 .4 xi .143 .429 .143 (3) Requirements matrix: 1.8 oQo .856 x a . = - .6 1.068 1.716 ; where x = x i 13 13 .6 1.6 .572 ~ 3 i (4) Regional xi distributed by base model pattern: Y1 x1 b x.. 1.8 0.0 .9 .3 3 -%l . xi = dij = .532 1.068 1.6 + .8 = 4 x .572 1 716 .572 1.072 4 30 (5) Difference matrix of 21 's: j Zzij<0 Xzij 3_0 _ NEEDSi POOLi 0.0 0.0 .044 0.0 .044 zij = dij - rij = —.O68 0.0 —.116 -.184 0.0 -.028 .116 0.0 -.028 .116 (6) The adjusted transactions: Adjusted Ex y e x l __ ij i i i .8 0.0 .856 2.656 .304 .044 3.004 xij = .532 1.068 1.6 3.2 .8 0.0 4.0 .589 1.6 .572 2.761 1.105 .088 3.954 Note in Step 5 in the difference matrix of zij's that sector one had a surplus of .044 above local processing requirements. This is carried as an exportable surplus to the export vector in Step 6. In Step 5 it is revealed that sector two's allocation of output, accord- ing to base model coefficients, was greater than the transactions im— plied by the base model sales distribution pattern. The total row de- ficiency is .184 and is placed in the NEEDS category as a negative. Row three is deficient in the first transactions cell but long in the second; therefore, it has an entry in both categories, NEEDS and POOL. After allocating POOL to the negative cells according to the rules outlined earlier, there is still .044 for export by sector one and .088 for export by sector three. Imports are then estimated by subtracting adjusted transactions (xij) from the requirement (rij) matrix. The rij matrix distributes local sector input purchases as de- termined by base model technical coefficients. The dij matrix distri- butes local sector output according to the base model sales pattern. 1Total xi ending does not balance with beginning xi due to rounding. 31' When zij national sales distribution pattern (dij) was less than the required is negative, it means that the transaction implied by the transaction implied by national coefficients (rij)° If POOLi > 0, some of this surplus is added to cells having dij < rij' POOLi is distributed to the xij as follows: d.. = __:!.J. ' = xij dij + (POOLi . xi ) i, j l,...,n. A cellindicatsdto be deficient because dij < rij receives a share of POOLi, according to the percentage which (11:] is of x . Thus an indus— i try which contributes a large share to local total gross output will receive a proportionate share of the local surplus of product i. This surplus exists because some industries, due to their size locally, require less than their national proportion of the product i being produced in the region. In reality, the purchasing pattern of a region is affected by both the availability of product needs locally and the local technical input requirements. It would seem that the supply-demand pool tech— nique discussed earlier handles very well the adjustment for inade- quate local inputs. Can it be improved by matching production func- tion requirements against the base model sales pattern which is deter- mined by the aggregate input requirements of all sectors in the base model economy? Does the base model sales pattern help in any way to overcome the differences in sector composition that are certain to exist and affect the accuracy of the derived models? It does not seem likely that using base model sales distribution is any better than the simpler commodity balance approach. Forcing the base model pattern of sales on a rural area would only distort 32 the derived transactions pattern by another dimension and would do nothing to improve it beyond using the base model direct coefficients. Morrison and Smith This study evaluates the ability of eight nonsurvey techniques to reproduce an empirically derived model of the City of Peterborough, England.1 Both the national table of England and a primary data model of Peterborough were available for the year 1968. In describing the methods tested, Morrison and Smith state: The methods used divide naturally into three major groups--the quotient approach, the commodity balance approach, and the use of iterative procedures. . . . All the methods operate upon the national input-output matrix and attempt to scale the coeffi- cients down to the regional level. . . . The fundamental assump- tion of all the models is that the national technical relation- ships hold good at the regional level and that the regional trade coefficients differ from the national technical coefficients to the extent that goods and services are imported from other regions. The techniques tested included: 1. Simple location quotient (SLQ). 2. Purchases-only location quotient (POLQ). 3. Cross-industry location quotient (CILQ). 4. Modified cross-industry quotient (CMOD). 5. Logarithmic cross-quotient (RND). 6. Modified logarithmic cross-quotient (RMOD). 1W. I. Morrison and P. Smith, "Nonsurvey Input-Output Tech- niques at the Small Area Level: An Evaluation," Journal of Regional Science, XIV (April, 1974), 1-14. 2Ibid., p. 7. 33 7. Supply-demand pool (SDP). 8. RAS.1 Four of the above techniques, numbers 1, 2, 3, and 7, were discussed in the preceding section on the Schaffer and Chu article. The others will be briefly outlined here before summarizing the Morrison and Smith evaluation results. The RAS Method The RAS method of adjusting coefficients updates an input- output table to a later time period or adjusts national coefficients to a region. It may also be used to adjust for various other sources of variation. It deals primarily with "changes that arise when (l) the relative intersectoral relationship between intermediate demand and final demand changes, and (2) the relative intersectoral relation— ship between intermediate inputs and primary inputs changes."2 These two relationships reflect the degree of absorption and fabrication in the industrial structure. The first relationship works across rows, the second along columns. It is assumed that, given initial changes, the degree of absorption per unit of output and the degree of fabrica- tion per unit of input change proportionally for each row and column. The RAS method does not adjust for price changes; however, these changes can be made independently. 1The letters RAS apparently refer back to the mathematical symr bols used by Stone and Brown when they first reported this technique. See Richard Stone and Alan Brown. "Behavioral and Technical Change in Economic Models." Problems in Economic Development. Edited by E. A. G. Robinson (New York: MacMillan and Company Ltd., 1965), pp. 434- 436. 2Emil Maliza and Daniel L. Bond, "Empirical Tests of the RAS Method of Interindustry Coefficient Adjustment," Journal of Regional Science, XIV (December, 1974), 357. 34 When the RAS method is used for obtaining a regional model from national coefficients, the national table is, in effect, projected to the regional dimension by being made to conform with regional con- straints as to row and column totals. These regional row and column totals are usually prepared by collecting data locally, thus a survey element is usually introduced when using the RAS procedure. In the following quote the symbols u, v, and x are vectors of regional inter- mediate output, intermediate input, and gross output, respectively. The letter i is an identity vector and A is a matrix of input-output coefficients. A prime indicates a transposed matrix, hatted letters denote diagonalized vectors, and subscripts refer to successive esti- mates. Lower case letters refer to vectors and upper case letters refer to matrices. In the first stage of the procedure, the national input-output matrix is treated as a first estimate of the regional table and is combined with the vector of regional gross output to yield an estimated vector of intermediate outputs. Thus: u = A x 1 l The matrix is then adjusted to conform with the row constraint (u): .A -1 A2 — uul Al The matrix A2 is then used to estimate a vector of intermediate inputs: ='A ' v1 1xA2 The matrix is then adjusted to conform with the column constraint (v): A = A vv -1 35 The matrix A is then substituted into (2), and this process is repeated until the matrix converges to a state in which both row and column constraints are fulfilled.1 The Logarithmic Cross—Quotient The logarithmic cross-quotient method is intended to correct for the potential failure of the cross-industry quotient (CIQ) to take account of the size of the region relative to the nation. The loca— tion quotients of selling and purchasing industries are combined in such a way that the properties of the cross-industry quotient are re- tained while the relative sizes of the region and the nation are taken into account. The adjusted quotient is RDij = LQi/log2 (l + LQj) 1, j = l,...,n. Modified Cross—Industry Quotient Morrison and Smith felt that the cross-industry quotient as pre- sented by Schaffer and Chu was potentially misleading in that it im— plies the assumption that every sector can obtain all its requirements of output from its own sector locally. That is, CIQij='i—6; i,j=l,...,n, and CIQij = unity for all i. To correct this, they modified the CIQi approach to use the simple location quotient on cells along the prin— cipal diagonal of the matrix. This modification applies to the logarithmic cross—industry quotient as well as to the simple cross-industry quotient. 1Morrison and Smith "Nonsurvey Input-Output Techniques at the Small Area Level: An Evaluation," pp. 9-10. 36 Comparison of Techniques The authors applied five different measures to the distance between the survey and nonsurvey tables to evaluate the degree of dif- ference. All the tests were applied by columns, by rows, and at the whole matrix level. The five tests included: (1) the mean absolute difference, (2) the mean similarity index, (3) regression, (4) chi- square, and (5) information content. The authors readily concede that the information content and Chi-square comparisons are not ideal due to the fact that they cannot handle a situation in which a . is zero and a* is nonzero (a - ij ij ij - national coefficient and a:j = estimated regional coefficient). They omitted these elements from their calculations of chi-square values and information content. They gave no credence to the actual esti— mated values but used the techniques "only as tentative relative mea- sures."1 In applying the information content test, the survey-based ma- . . 2 trix is con81dered as a forecast of the nonsurvey est1mate. The ad- ditional information contained in the latter is quantified as * * * I (A :A) = zizj aijlog2 (aij/aij) i, j - l,...,n. 1Ibid., p. 5. 2For a more detailed exposition see: S. Czamanski and E. E. Malizia, "Applicability and Limitations in the Use of National Input- Output Tables for Regional Studies," Rggional Science Association Paper, XXIII (1969), 69-70. 37 * where I(A :A) information content, * aij = regional input-output coefficients matrix, a1:] = national input-output coefficients matrix. The lower the information content thus measured, the closer the esti- mate. Another measure, the mean similarity index, was developed by Isard and Romanoff as a modification of the index of relative change. * ///1/2(aij + aij) i, j = l,...,n, had the undesirable characteristic that it ranged from zero to two. The index of relative change, an - aij To remove this feature, they constructed the mean similarity index as * ////(aij + aij) 1, j = l,...,n. Morrison and Smith calculated the index, S * Sij =l- aij -aij ij’ by columns, rows and for each entire matrix. The mean absolute difference, a rather straight forward measure, was calculated for each row, column and whole matrix. This measure, as implied by the name, finds the absolute difference between corres- ponding cells of the survey and nonsurvey coefficients and divides this by the number of cells compared. In the regression analysis comparison, elements of the survey table were treated as the dependent variable and elements of the nonsur- vey table as the independent variable. The advantage of this technique is that more emphasis is placed on the uniformity of relationships throughout a whole column rather than upon the deviations in individual coefficients. 38 They found RAS to be superior by all measures used in their evaluation. They point out that this was to be expected since the transactions were controlled to survey-based intermediate input and output totals. Since these totals are based on survey data, the RAS method is not a purely nonsurvey technique, as are the others. The degree of superiority of RAS appears to be very significant. . . . the size of the mean absolute difference for the best nonsurvey method (SLQ) is almost three times that produced by RAS. The correlation coefficient at the whole matrix level is .501 for the RAS matrix but only .160 for SLQ. A similar re- sult holds for the other three distance measures.1 The simple location quotient appeared to be superior to other nonsurvey techniques by all five tests. Also, the modified cross- industry quotients were superior to the straightforward cross-industry quotients on all tests. The supply-demand pool technique ranked above all other non- survey techniques only in the regression comparison. It was third among the nonsurvey techniques in the mean similarity index test, fifth in the mean absolute difference test, and last in the chi-square and information content tests. The purchases-only location quotient was second of the nonsurvey techniques in three tests and was imme— diately below the simple location quotient in all tests. A California Study One of the most complete studies using secondary data procedures was done for the State of California by Lofting and McGauhey using the 1Morrison and Smith, "Nonsurvey Input-Output Techniques at the Small Area Level: An Evaluation," p. 11. 39 1958 U.S. model as the base model.1 Their purpose was to evaluate water as a factor of production in the California economy. They need- ed an interindustry model to trace the change in direct and indirect consumption of water resulting from various output changes. They first constructed an 81 sector model for California and then aggre- gated it down to 24 to emphasize the water intensive sectors. They developed a mechanical procedure and programmed it for a CDC 6400 computer in Fortran IV computer language. The program reads in the base matrix coefficients, forms the Leontief inverse matrix, and post multiplies this by a column vector of regional gross outputs. From the resulting vector, which is total final demand, regional vectors of household consumption, capital investment, and govern- ment expenditures are subtracted yielding a column vector of commodity exports and imports termed the net external trade balance (Net B) vector. Negative values indicate imports-- positive values, exports. The procedure which appears to be implied in the brief narrative discussion in the Lofting and McGauhey reference is - -1 b y1 = EI-A) ] xi 1 = l,...,n where §i = tentative final demand and x1 = an estimate of regional total gross output. That is, the 1958 national (I-A)-1 times an in- dependent estimate of California total gross output (xi) yields an es- timate of final demand (yi). Final demand (yi) is tentative because it still contains production which is to be imported rather than pro— duced locally. To find the vector containing only imports and exports 1E. M. Lofting and P. H. McGauhey, Economic Evaluation of Water, Part IV: An Input-Output and Linear Programming Analysis of Califor- nia Water Requirements, Water Resources Center Contribution No. 116 (Berkeley, Calif.: University of California, Sanitary Engineering Re- search Laboratory, August, 1968). 21bid., p. 39. 40 (51), other California final demand vectors estimated outside the model had to be subtracted from the tentative final demand. These other vectors included personal consumption, capital formation, and government purchases. The resulting vector contained both positive and negative quantities. The positive quantities were assumed to be exports and were left in total final demand. The negative quantities were assumed to be imports and distributed homogeneously by sector to cells containing transactions in their respective rows. An import row for California could then be formed by summing the distributed quanti- ties column-wise. The Leontief matrix used by Lofting and McGauhey was based on the national coefficients for 1958 with no adjustments.1 Under the procedure used, the residual differences between regional gross out- put and regional demands is treated as imports or exports. And as they point out, any deviation in the national coefficients from the true California coefficients affects the magnitude of imports and exports. They state that "more accurate methods would, of course, be desirable; however, in the California case where the broad cross—checks indicated above could be made on these values, the method seems reasonably sa- tisfactory."2 Lofting and McGauhey anticipated a procedure that is being employ- ed in this study. They were aware that the Harvard Economic Research Project was developing total gross output and final demand vectors, including exports, for all the continental states. They noted that: 1Ibid., p. 36. 2Ibid., p. 36. 41 If such vectors are made available along with a vector of gross outputs, then the 'residual' method of determining exports is of transient importance. It would seem that with firm estimates of final demandsand gross outputs, attention could focus in a mean- ingful way on determining regional interindustry transactions, or coefficients, given the national average as a basis. Boster and Martin Boster and Martin use statistical methods to compare coeffi- cients derived from primary data with those derived by secondary data methods for the State of Arizona.2 The data were collected as a part of the large regional study including the entire Colorado River Basin. The entire primary data study cost $600,000. The secondary data study is referred to as the "Arizona-based study." It was done for $8,000 by one research associate in one and one-half years. While the budgets are not directly comparable, the authors felt that the cost ratio would be at least $20 for the primary study to $1 for the secon- dary study. The Arizona-based study was constructed entirely from secondary sources, while the Colorado-based study collected primary data for the year 1960 for all industries except agriculture and mining. These two sectors were constructed largely from secondary data. The authors aggregated both studies into comparable models of 17 endogenous industrial sectors. They used Wilcoxon's signed—rank 1Ibid., p. 36. 2Ronald S. Boster and William E. Martin, The Value of Primary Versus Secondary Data in Interindustry Analysis: A Study of the Eco— nomics of Economic Models, Arizona Agricultural Experiment Station Journal, Article No. 1900. Presented at the 11th Annual Meeting of the Western Regional Science Association, San Diego, California, Feb- ruary, 1972. 42 test and the sign test for comparisons between matrices and submatri- ces, obtaining similar results in most cases with both tests. Statistical comparisons were made between the entire trade and interdependency matrices, between four submatrices--between columns and between weighted and unweighted output multipliers. They concluded that the two models were not statistically dif- ferent from each other when considered as a whole. When trade coeffi- cients were compared, the null hypothesis of "no difference" was re- jected only once. Rejected was the aggregate coefficient showing agricultural sales to nonagricultural purchasers. They point out that this is paradoxical since the agricultural sectors are based on secon— dary data in both models. In the submatrix where nonagricultural sectors were selling to nonagricultural sectors, the null hypothesis of "no difference" was accepted. This was a direct comparison of primary versus secondary data. When the interdependency matrices were analyzed, only the agri- culture selling to nonagriculture submatrix was statistically similar. The null hypothesis of "no difference" was rejected for the other three submatrices. Six out of 19 columns were statistically different in trade matrix comparisons, but seven out of 17 sectors were dissimi- lar for the interdependency matrix. Little statistical similarity was found between individual pairs of trade coefficients, i.e., correspond— ing coefficients from each model. However, taken as a whole, the trade coefficient matrices were similar using the Wilcoxon test. Multipliers weighted by the relative size of their associated final demands were highly similar. 43 The authors conclude that there is a strong similarity between the two models based on their statistical analysis. They feel that it cannot be argued that the more aggregative components of either model are better than the others. Differences between the models be- come larger, the more disaggregate the coefficients being compared. But, they point out, the question of which coefficient is right still remains. Models developed from secondary data are quite adequate, they believe, for answering many policy questions and can, therefore, free resources to be used on other important matters. Richardson Richardson's book is a well-ordered summary of the state of the art in input-output economics. Richardson handles the subject so well that one gets the feeling he is on top of every phase of it, from con- ventional to secondary data to dynamic models. He seems to have had access to very recent articles on I-0 from all over the world. A rather long quote from his introductory chapter seems warranted at this point to give an overview of how I-O is regarded by different researchers. Input-output economics is a well-established, almost old- fashioned, branch of economics--after all, it has now been with us for forty years. It is true that its regional applications have been more recent--less than twenty years old with a rapid acceleration in the quantity of work in the past few years-—but even so, they can scarcely be treated as a novelty. Despite its simplistic assumptions, input-output analysis has shown a remark- able degree of persistence. Perhaps at the national level there has been some slackening of interest, particularly in countries where short-term econometric forecasting has taken predominance over sectoral planning, but at the regional level, interest is stronger than ever. An important reason for this is that input- output techniques can be implemented empirically in a field where data shortages and under-developed theoretical constructs restrict the scepe for hard empirical research. A strange feature about regional input-output analysis is that attitudes towards its usefulness and validity tend to be very extreme. Every regional economist seems to be either its 44 dauntless champion or its fierce detractor. The aim of this book is to present a more balanced judgment. Whatever the limitations of the input-output approach, the regional economist must give it serious consideration. It provides virtually the sole avenue of escape from partial equilibrium analysis. The other general equi- librium theories available, Walrasian neo-classical price analy- sis and neo-Keynesian interregional macroeconomics, may be a little more satisfying theoretically but they are much more dif— ficult to apply empirically. In particular, interregional trade flows are much easier to measure and make consistent with theory within an input-output framework. Moreover, some versions of interregional input-output models (of which the Leontief-Strout gravity technique is typical) have the added advantage for analy— sis of the space economy that they take distance, in the form of transport costs, explicitly into account as a relevant variable. Another feature of the input-output model is that it is 'neutral' from a policy point of view--a fact that partly explains its appeal to western and communist, industrial and underdeveloped economies alike. At the same time, however, it has become possi- ble in more recent years to extend an input-output model into an optimization technique by converting it into a linear programming model. The advantages go a long way to offset the well-known drawbacks --the restrictive assumptions, the high costs involved in obtain- ing the data required, the practical obstacles in the way of oper- ationalizing the dynamic models needed for long-run regional planning.1 From here we skip to Richardson's Chapter VI--"Data Reduction Methods in Regional Input-Output Analysis"--because of its relevance to this study. He first mentions some reasons why unadjusted national coefficients should not be used as proxies for regional coefficients. "First there is the industry mix problem and the related problem of product mix."2 He points out that industry mix problems can be mini- mized if the base table is disaggregated to very fine industry detail (four to five hundred sectors). "The second major difference between national and regional coef- ficients reflects the fact that regional economies are much more open 1Harry W. Richardson, Input-Output and Regional Economics (Lon- don: Weidenfeld and Nicolson, 1972), p. 2. 2Ibid., p. 113. 45 than nations."l He raises the point that a national coefficient for an industry with little or no exports is more nearly a true technical (or production function) coefficient than is a regional industry coefficient, which may be small only because much of the input is imported. The regional coefficient in an I-O table expresses the relationship between local inputs and outputs. Thus he formulates the equation: ar = r + m i = 1 n ij ij ij , J a 9 where aij = the total regional coefficient, rij = the portion provided locally, mij = the portion imported. Two other sources of variation between national and regional coefficients which Richardson believes can be important are (1) dif- ferences in price levels and (2) differences in production functions, aside from the differences due to product mix. Richardson lists four kinds of procedures that can be used to adjust national to regional coefficients: 1. Ad hoc adjustments. 2. Regional weights and aggregation techniques. and m ,. ij ij 4. Estimation of nonlocal requirements and determination of 3. Methods of adjusting aij to separate out r r residually. 13' Ad hoc methods are unsystematic and arbitrary, he thinks. The subjectivity involved makes it difficult to test the accuracy of lIbid. 46 the table in the absence of a survey—based matrix for compari- son. Richardson discusses two studies in which regional weights and aggregation techniques were used. Shenl used regional value added weights to group sectors into a more aggregated regional table. Czamanski and Malizia2 constructed a 1963 table for Washington State derived from the 1958 U.S. table and compared the results with the table based on the 1963 survey. Regional weights used were sales, re- ceipts, value added, and value of shipments. Adjustments were made for domestic imports and for relative price levels between 1958 and 1963. The results were not too encouraging in that comparable coeffi- cients could not be obtained until some of Washington State's major sectors were adjusted by primary survey data (these sectors accounted for 28 percent of regional gross product). Miernyk, in published com- ments ontfimzstudy, concluded that the study showed that short cut meth- ods do not work. Richardson believed this to be too harsh a judgment, stating that there is further scope for refinement of Czamanski's tech- niques as new data becomes available. Furthermore, he believes that some of the other methods yet to be discussed may be more successful. The third category of nonsurvey techniques discussed by Richard- son included the location quotient and commodity balance approaches. 1T. Y. Shen, "An Input-Output Table with Regional Weights," Regional Science Association Papers, VI (1960), 113-119. 2Czamanski and Malizia, "Applicability and Limitations in the Use of National Input-Output Tables for Regional Studies," pp. 65-77. Comments by M. R. Goldman 79—80, and by W. H. Miernyk, 81-82. 47 These procedures have the defect that they normally assume that national and regional technical coefficients are identical (ai. = a?.). However, by dividing the regional technical coeffi— ciedts 1:]into two separate trade components--the local I—O coef— ficients r . and the requirements (by local industries) from out- side the re ion m ,--they produce estimates of the former that are much closer tthhe regional I—O matrix obtained by survey data than they are to national coefficients. On the other hand, they all tend to overestimate intraregional interdependence and to ignore crosshauling. To remedy this imbalance, much more re- fined procedures have to be adopted or alternative approaches to estimating interregional trade flows have to be employed. Richardson concluded his chapter on secondary data I-O models by suggesting that there is a middle way in choice of methods. He calls it a mongrel study in that some coefficients would be estimated by survey methods; e.g., leading sectors in the regional economy, new or rapidly expanding sectors, industries where product mix and indus- try mix problems exist, industries where crosshauling is know to be extensive, and industries where the nonsurvey regional coefficient varies considerably from the national coefficient. Other coefficients may be estimated by secondary data procedures such as the supply demand pool, etc. . . . a mongrel study of this kind might well represent a more effective and balanced compromise between the present extremes of cheap but possibly unreliable nonsurvey methods and prohibitive surveys. It is surely a fruitful line of inquiry for future re- search. Literature Related to Refinement and Exploitation of I-O Models Other fields of study which are important in constructing and using I—O models for impact analyses and projection work include 1Richardson, Input-Output and Regional Economics, p. 116. 2Ibid., p. 118. 48 preparing pollution impact coefficients and projecting models to re- flect the technology that will exist in the future. An article by Leontief and Ford is reviewed in regard to pollution coefficients. Articles by Carter and Udis discuss changing technology and updating or projecting coefficients to reflect probable changes in technology. Another article, by Polenske, describes the Harvard Economic Research Project's multiregional input-output model and the data assembled to implement it. Leontief and Ford Leontief and Ford demonstrate in this article the power of the I-0 techniques in accounting for and displaying pollutants as compo- nents of the total output package of industrial production. Leontief states it quite nicely in his first paragraph: Generation and elimination of various pollutants, in principle at least, lends itself as easily to systematic description and analysis within the framework of a conventional input-output system as production and consumption of all ordinary industrial products and services. Pollutants are by—products of industries already described in detail in a conventional input-output table. Economic activities that would mitigate the environmental dis- ruption that accompanies industrial operations can also be in- corporated into an appropriately expanded input-output system. The authors aggregate the 370 sector U.S. table for 1963 into 90 sectors, preserving detail in the 30 sectors from which most of the atmospheric pollution comes. They present a preliminary report on the dependence of five types of air pollution--particulates, sul— fur oxides, hydro-carbons, carbon monoxide, and nitrogen oxides--on lWassily Leontief and Daniel Ford, "Air Pollution and the Eco- nomic Structure: Empirical Results of Input-Output Computations," Input-Output Techniques, Proceedings of the Fifth International Con- ference on Input-Output Techniques, ed. by A. Brody and A. P. Carter (New York: American Elsevier Publishing Company, 1972), p. 9. 49 the "input-output structure of the American economy and the observed and anticipated future changes in that structure from the year 1958 over the years 1963, 1967 toward 1980."l Pollutant coefficients are based on primary information collect— ed for the year 1967 and adjusted to the appropriate price base for each model year. They point out that computations based on these 1967 coefficients will need to be revised as more accurate estimates become available. With their model they can show the total output of pollutants brought forth by each of 11 different types of final demand: 1. Competitive imports. 2. Personal consumption. 3. Private fixed capital. 4. Inventory change. 5. Net exports. 6. Federal government purchases for defense. 7. Federal government purchases for other. 8. State and local government purchases for education. 9. State and local government purchases for health, welfare, and sanitation. 10. State and local government purchases for safety. 11. State and local government purchases for other. Leontief and Ford also report on a method of estimating price effects of several air pollution control strategies. Although they considered the data they used to be inadequate, they were hopeful that improved data would soon be available. lIbid., p. 11. 50 They close the article on a note which one often finds in the I-0 modeling literature: the models are not the limiting factor in developing interdependency relationships between input and all kinds of outputs but "the real advance of knowledge and of understanding will depend . . . on the progress of systematic fact finding efforts."1 Carter Carter compares the 1947 and 1958 U.S. input-output tables to estimate the importance of various kinds of changing technology. The sectors of the 450—order 1947 model and 80-order 1958 model were stan- dardized and aggregated to form the 73-order table used in her study. She found that there definitely were many structural changes in the 1958 table compared to the 1947 table but that "the two tableaux still retain a striking family resemblance."2 Durable goods and the electrical -electronics group, in particular, embody more change than the rela— tively mature food and textile industries. Across the board, indus- tries use gage services, electric energy, chemicals and synthetics, and lege coal, wood, and metals.3 Carter's analysis serves to make one keenly aware of the come plexity that has been subsumed by the aggregate sectoring of any eco- nomy. This aggregation increases the variety of inputs used by any one sector and reduces the detail of conclusions which can be drawn. 1Ibid, p. 26. 2Anne P. Carter, "Changes in the Structure of the American Eco- nomy, 1947 to 1958 and 1962," Review of Economics and Statistics, IL (May, 1967), 223. 3Energy technology is extremely volatile at present and may be a source of error in secondary data studies where coefficients are based on pre-l974 technology. 51 The more disaggregate the sectoring, the more one could isolate the impacts on individual industries resulting from technological changes that are occurring. Carter described her method of analysis as follows: It is as if we turned first to the 1947 economy, and then to the 1958, asking each to produce the 1962 bill of goods for food and tobacco only, pretending that all other elements of final demand were zero. We listed the resulting industry output levels gener- ated for each year. Then we go back and ask the 1947 and 1958 economies to produce the next final subvector alone, list this second set of industry output levels and so on. The result is a set of ten 73-order total output vectors for each year. Carter noted an across-the—board rise in the importance of gen- eral inputs. Inputs such as energy, services, packaging, printing and publishing, and maintenance construction are needed by almost all industries. This increasing importance of general inputs reflects the important features common to almost all business, e.g., the need to heat plants, maintain buildings, etc. Continuing studies such as this will be needed as a basis for changing the coefficients of secondary data models to reflect alter- native futures being analyzed in regional projections work. Already the energy crisis is very likely to be causing changes in the techno— logical structure of the economy. Another major source of such change is the efforts by government and industry to reduce the output of undesirable pollutants. Colorado River Basin I-O Model This study represents the most significant attempt to use an input-output model to analyze and forecast impacts of water development lCarter, "Changes in the Structure of the American Economy, 1947 to 1958 and 1962," 213. in a river basin. This model was based on primary data collected for the base year 1960. Bernard Udis reported on the use of the model for long-range forecasts for the Colorado River Basin (CRB): We are striving for long-range forecasts for the Colorado River Basin in addition to a model of the region's structural interde- pendence in the base year--l960. It is true, of course, that the quality of any attempt to forecast the future structure of a re- gion's economy through the input—output technique will be no better than the independently determined estimates of final de- mand and the validity of the input coefficients. Nevertheless, we believe that the automatic internal consistency feature of input-output analysis will impose useful limits on the range of our forecasts of final demand, assuming that we have knowledge of factor productivity and of resource contraints within the region . . . . This advantage of input-output technique is especially valuable in our study since one of the major tasks will be to determine the feasibility of alternative growth patterns in the Colorado Basin in terms of anticipated resource availability-- particularly water. Thus, once the water requirements, both quantitative and qualitative, which match alternative demand structures have been ascertained, we should be able to render a judgment on the ability of the region to sustain a particular development path.1 Udis noted that one of the most common criticisms of I-O ana- lysis concerns the assumption of unchanging technical coefficients over time. To overcome this problem, his study group altered both the matrices of direct coefficients and the final demands from the 1960 data base to derive figures for 1980 and 2010. He further stated that the projections were made within the context of ever tightening resource contraints. Specifically: (1) Our initial assumption is that the level of composition of output in our target years is not contrained by limitations on water quantity _or quality except as such influences operated in the base year of 1960. Thus, 1960 levels of salinity and of water lBernard Udis, "Regional Input-Output Analysis as a Tool for Natural Resource Management--The Colorado River Basin Economic Study,” (unpublished paper delivered at an interagency work group meeting of participants hithe Colorado Basin Study, 1970), p. 16—17. 53 availability were assumed to prevail. In the CRB, other pollution parameters appear to be of limited significance. (2) In the next round of projections, the possibility of an explicit water quantity constraint is recognized and a careful accounting is made for water use by sector and in the aggregate. Water quality levels of 1960 are assumed to prevail. Quantity available is limited by river flow and by institutional rules. (3) In the third round, both water quantity and quality are assumed fully operative as potential constraints. Quantity is limited as in case (2) above, and quality is influenced by the uses to which water is subjected upstream. Alternative projections of economic activity for each set of these assumptions were made in order to better evaluate the nature and economic consequences of a water-based contraint on economic activity. This type of model will be extremely useful as better coefficients for water use and various types of pollution are developed, allowing rapid response to policy questions. Polenske The Harvard Economic Research Project completed a massive inter- regional model of the U.S. economy in 1973. This work was begun in 1966 when the Department of Commerce and the Department of Transpor- tation contracted with the Harvard Economic Research Project for a multiregional input-output system for the United States.2 The model was prepared under the direction of Dr. Karen R. Polenske (formerly at Harvard and now at MIT). The entire model, including computer pro- grams and data by state, is now available for 51 producing and lIbid., p. 23. 2Karen R. Polenske, "The Implementation of a Multiregional Input- Output Model for the United States," Input-Output Techniques, Proceed— ings of the Fifth International Conference on Input—Output Techniques, ed. by A. Brody and A. P. Carter (New York: American Elsevier Publishing Company, 1972), pp. 171—189. 54 consuming regions of the U.S.1 Five major sets of multiregional input- output data were compiled for each state: (1) base-year outputs, employment, and payrolls; (2) 1963 interindustry flows; (3) 1963 in- terregional trade flows; (4) base-year final demands; (5) 1970 and 1980 projected final demands. A consistent set of multiregional input— output tables were assembled for each state for 1963, and supplemental historial state final demand estimates have been made for 1947 and 1958. The concept behind this undertaking is that more efficient input- output modeling can be accomplished for various regions if consistent basic data are available. Polenske states: . . . this would eliminate a tremendous duplication of research effort and would therefore reduce the total expenditure of time and funds presently allocated to assembling general sets of re- gional data. More than twenty state input-output tables have been assembled by different research groups in the United States during the past fifteen years. The basic methodology of compiling each set of accounts took time to learn, and additional time was re- quired to make all the estimates internally consistent. If the data had already been available, the analysts could have used their time more profitably to investigate the specific policy issues of their state or to improve and expand these data with supplemental statistics that may be peculiar to their state.2 All data are assembled for 86 industries and 51 regions. At the time Polenske's article was published, the interregional trade flows were available only for 44 regions. In late 1973, however, the trade flow data were published for all 51 regions for commodities that use 1The 51 regions are comprised of the 50 states and the District of Columbia. 2Karen R. Polenske, et al., State Estimates of the Gross Nation— al Product, 1947, 1958, 1963, Vol. I of Multiregional Input-Output Analysis, ed. by Karen R. Polenske (6 vols.; Lexington, Mass.: D. C. Heath and Company, l972--), p. 5. 55 the normal modes of freight transportation and that are included in the regular transportation statistics.1 This excluded construction, service, dummy, and value added industries. There is a 51 x 51 matrix (44 x 44 when the article was written but later disaggregated further) for each of 61 commodities. For example, row number one of the 51 x 51 matrix for industry number one shows the quantity of industry num- ber one product shipped by region one to all 51 regions. The multiregional data developed by Polenske and others is be- ginning to be utilized by other researchers across the nation. If it stands up under the test of wide use by many different researchers, it will provide a much needed point of departure for obtaining con- sistency among input-output models. Trade flows between regions will facilitate studying changes in interstate and interregional impacts resulting from various public expenditures such as for land and water development. The six components of final demand estimated for Ohio provide important data for this study. They are consistent with the 1970 in— terindustry flows published by the Bureau of Labor Statistics and from which are derived the base model coefficients.2 1Karen R. Polenske, Carolyn W. Anderson, and Mary M. Shirley, A Guide for Users of the U.S. Multiregional Input-Output Model, pre- pared for the Office of Systems Analysis and Information, U.S. Depart- ment of Transportation, Updated June, 1973. Available from the Na- tional Technical Information Service (NTIS), Springfield, Virginia. 2Raymond C. Scheppach, Jr., State Projections of the Gross Na— tional Product, l970,y1980, Vol. III of Multiregional Input—Ougput Analysis, ed. by Karen R. Polenske (6 vols.; Lexington, Mass.: D. C. Heath and Company, l972--), p. l. 56 Isard In a recent ground—breaking work Isard conceptually links an eco— nomic system with its related ecologic system. His primary objective was "to make regional planners and other social and environmental analysts, at or close to the decision-making level, aware of the in- tricate interrelationships between the economy and the ecosystem, and between economic development and environmental management."1 He pre- sents an appealing argument for developing the conceptual model to help planners and decision makers go beyond intuition in their thinking about the interrelationships of economic activities and the natural environment. However, at present the data requirements prohibit prac- tical application: Certainly, one would like to be able to put numbers into all the cells of an interrelationship table. Unfortunately, at present this is not possible. There are major data deficiencies; to a considerable extent, research can overcome many of them. There are also conceptual difficulties. However, it should be possible to develop conventions similar to those used in economics and regional science which would enable us to overcome the conceptual difficulties which arise in the attempt to apply input—output methods to the study of the environment. Meanwhile, it is, in fact, quite reasonable to attach numerical values to some of the entries in the table. Isard discusses several traditional economic and regional science techniques for regional analysis. He uses comparative cost analysis to examine several mineral resources of the Continental Shelf and then illustrates how input—output can be used to study the direct and in- direct implications of any development. He examines the capability of the gravity model in estimating the demand for recreational activities lWalter Isard, Ecologic-Economic Analysis for Regional Develop- ment (New York: The Free Press, 1972), p. xv. 2Ibid., p. 57. 57 and explores the use of the "industrial complex" to examine the feasibility of possible recreation complexes. He goes beyond the economic in discussing ecologic principles and subsystems and shows how the food chain, photosynthesis, and the phosphorus cycle can be put into an input-output programming format for interdependence analysis. A huge interrelations table is presented to demonstrate flows among ecologic and economic activities. In a case study of the general Plymouth-Kingston-Duxbury Bay area, the entire model is used to evaluate recreation possibilities. It is important that researchers and planners accept the challenge that Isard has presented in his book. Although the data are not available with which to implement it fully, at least some ecologic- economic interdependencies can be demonstrated. With these demonstra- tions of the model's capabilities, more researchers and funding agencies will get into the pictureanuimake a contribution toward more complete exploitation of the model. Summary This chapter contains short reviews of several articles on secondary data input-output reducing methods. Also reviewed are selected articles and books on subjects relevant to future development of input-output in projections work and in relating industrial output change to environmental change. These are only samples of the literature available in the developing field of input-output. Isard's work, Ecolqgic-Economic Analysis for Regional Develgpment, will be of particular important in stimulating environmental studies with input- output methods. CHAPTER III TWO REDUCING MODELS Introduction The algebra and assumptions of two secondary data reducing pro- cedures are compared in this chapter. The procedures employ mechani— cal routines to adjust technical coefficients of the U.S. model to re- flect the economic structure of a state or substate area. Both methods require that the study area final demands and total gross outputs be developed independently of the base model coefficients. Both reducing models were adapted from a model programmed by Charles Palmer and Ross Layton for reducing Colorado Basin coefficients to one of the subareas within the Colorado Basin.1 They are similar to the modified and unmodified supply-demand pool techniques discus- sed by Schaffer and Chu (see Chapter II). They differ in that final demands are not calculated within the models but taken from other avail- able data. Recently published data2 provided final demands for the State of Ohio for the same 87 sectors used in the U.S. model from which base 1Charles Palmer and Ross Layton, "A User's Guide for Regional Input-Output Analysis," (an "in—house" paper prepared for Natural Re- sources Economics Division, Economic Research Service, USDA, East Lansing, Michigan, 1973). 2Scheppach, State Projections of the Gross National Product, 1970, 1980. 58 59 coefficients for this study were obtained. These state final demands were allocated to each county in the state by procedures to be discus- sed in Chapter IV. They are the only nationally consistent data available and are thought to be fairly reliable estimates. For this reason, Model I was designed to avoid changing them. Model II, how- ever, permitted adjusting final demand to show that portion met by local production. Sector Aggregation Decisions The needs of the study and the sector detail of the base model are considerations in deciding on sectors for the study area model. Cost may be a consideration if study funds are limited, since the cost of inverting a matrix rises exponentially with the size of the matrix. Data availability for estimating final demands and total gross outputs are another major consideration. In this study it was desirable to maintain some detail in the agricultural sectors; therefore, the four sectors available in the 87 sector national model were preserved. More detail in agriculture could be achieved by utilizing the sector detail available in the 370 sector 1967 U.S. model, but employment data by county was not available for this level of detail. Coal mining and crude oil production are important in some areas of Ohio; therefore, these two sectors were preserved, and all other mining was included in a single sector. The remainder of the 77 en- dogenous U.S. sectors were aggregated to 20 sectors, as suggested by census employment data. The entire sector aggregation scheme is shown in Appendix A. 60 Assumptions In addition to the standard assumptions necessary to employ sta- tic I-O models, two assumptions are made in order to prepare the study area I-O model from the U.S. technical coefficients. Assumption 1: The technology employed inlproducing project i is the same in the study area as for the United States. This implies that all inputs, including labor, produce with the same degree of ef— ficiency in the study area as in the base model area. It leaves open the possibility that some industries will have to import from outside the study area. The reducing procedure contains a mechanism to adjust the coefficients for imports, i.e., if study area industry 1 is able to supply only half of the total requirements of other endogenous in- dustries for product i, the remainder will be imported. Assumption 2: Sector composition of the study area is similar to U.S. sector composition. Some accuracy in technical coefficients is lost when this assumption is not strictly true. Sectors are come posed as a rule, of firms having similar input requirements. The greater the aggregation, the less troublesome will be a violation of this assumption; but also, the less detailed will be the conclusions which can be drawn about specific industries. With greater aggregation, the sector production function in dollar terms is less likely to dif— fer between the base model and the study area model. There could be technical substitutions without significantly affecting coefficients, due to the higher probability that the substituted input will be pur- chased from the same sector as the original input. These are convenient, simplifying assumptions that let us get on with the model. If time and resources were available, it would be useful 61 to identify efficiency differences between the base model economy and the study area economy and the necessary adjustments. Two Reducinngodels This section presents two alternative procedures for reducing base model coefficients to reflect economic structure of a smaller area. Model I uses the ratio of internal output available to internal output required by sector to reduce the transactions implied by base model coefficients to the amount of output available in the study area after satisfying local final demand. Model II uses the ratio of total gross output available to total gross output required. The Model II proce- dure includes final demand in the reducing ratio whereas Model I uses only internal demand, i.e., demand by the processing sector. Both reducing procedures are sensitive to total gross output and final demand differences between study areas. When additional counties are added to a study area and their final demand is relatively greater than their total gross output, the reducing ratios are lower. This causes smaller direct coefficients, smaller elements in the inverse matrix, and smaller output multipliers. For the same nine-county area, Model I produced significantly lower multipliers than Model II. For example, for the livestock sector, the multiplier produced by Model I was 1.748 compared to 1.976 for Model II. For the crops sector, the multipliers were 1.497 and 1.610, respectively. This is discussed in more detail in Chapters V and VI. In addition to the differences already mentioned, any increases in final demand under Model 11 will be met by both local production and imports. That is, imports will contribute to the increase in final demand in the same proportion as required in the reducing procedure. 62 When available total gross output is less than required, final demand is reduced by the same ratio as used to reduce local transactions. This portion of final demand is assumed to be imported and is added to the imports of the endogenous sectors in estimating imports outside the study area. The following symbol definitions will be used in both Model I and Model 11: x. = study area total gross output of industry 1, y1 = study area final demand for the product of industry i ex- cluding any exports, y1 = study area final demand for the product of industry i includ- ing and exports, yi = study area imports to final demand, ei = study area exports by industry i, mj = study area imports, mij = imports of product i by industry j. The first step in both models is to prepare estimates of total gross outputs (xi) and final demands (yi) exclusive of exports for each sector of the model.1 If the study area sectors to be used are not identical to the base model (the U.S. model in this study), the base model transactions table must be aggregated or disaggregated according- ly. Base model direct coefficients must be available for the same sec— tors to be used in the study area model. 1The estimating procedures are explained in detail in Chapter IV. 63 Structure and Assumptions of Model I Reducing Procedures Given the estimates of study area total gross outputs and final demands without exports, a matrix of required transactions (Eij) can be computed _. _ b . _ (l) xij — xi . aij i, j — l,...,n. The output available to processing sectors after meeting the local final demands is For the sectors where (3) 2x13. 3 Ziij i, j = l,...,n. it is assumed that (4) Xij = xij i, j = l,...,n. The basis for this assumption is essentially the same as Assumption I, discussed earlier in this chapter; that is, that technology employed in producing product i in the study area is the same as in the base model area. The fact that inj 3.221j implies that there is sufficient employment in sector 1 in the study area to meet both the local final demand requirements and the processing sector needs for it. Exports will be (5) ei = inj - inj 1==l,...,n; imports will be 64 (6) mij=0 i,j=l,...,n and the total final demand will be (7) y. = §. + e. i==1,...,n. Structure and Assumptions of Model II Reducing Procedures The same estimates of study area total gross outputs and final demands prepared for Model I are used for Model II. Again, the matrix of required endogenous transactions is computed using base model coef— ficients and total gross output estimates: _ _ b = (1) x13 xjaij i, j l,...,n. Compute total requirements as — n— — (2) xi = §xij + yi i==1,...,n. Compare the total gross output available (xi) with the total gross output required (£1): (A) Ifx _>_§ i it is assumed that sufficient output is produc- 1! ed by sector i locally to meet all processing and local final demand requirements with, possibly, some product exported. In this case, the transactions available are assumed equal to transactions required: (3) xij = xij i==1,...,n. Coefficients for these rows are identical to base model coefficients. Exports are computed as the surplus of available local production over required local production: 65 Total final demand including exports is then (5) y1 = yi + ei 1==l,...,n. (B) If xi < ii, it is assumed that local production is inade- quate to meet both local processing needs and local final demand. Imports are required and are computed later. The local transactions and the local final demand are reduced by the ratio of available to required output: >4 H- (6) x . = I ij ij 1, j = l,...,n. N l i The difference between total processing sector needs and that portion obtained locally, that is, the difference between required transactions and available transactions for a row is computed as n n_ n (7) Zm.. = 2x.. - Xx,, i, j = l,...,n. .1 .1 .1 JJ 1J JJ This is the amount of product i imported by endogenous industries. 1 Compute final demand supplied by local production (yi) as IH?‘ (8) yi=§i. i=l,...,n. XI 1 The difference between final demand obtained from local production and final demand required is assumed to be imported directly to final de- _* mand. This imported portion of local final demand (yi) is computed as1 lThis imported final demand is preserved in the RIOM System and added to the imports of processing sectors in estimating imports out— side the study area. 66 * .. '- (9) yi=yi-yi i-l,...,n. The total amount of product i imported to both final demand and endo- genous industries is * (10) m1 = Emij + yi 1-l,...,n. By reassembling the transactions rows which were changed with those which were unchanged, we obtain a matrix of transactions availa— ble. Subtracting the matrix of transactions available from the matrix of transactions required yields a matrix of imports: (ll) mij = xij - xij i, j = l,...,n. Summing the columns of the imports matrix yields the imports row: (12) mj = Em. j = l,...,n. Model 11 is essentially the same as the supply—demand pool tech- nique discussed by Schaffer and Chu (see Chapter II). It is different only in that final demands are obtained outside the reducing model itself. The procedure presented by Schaffer and Chu calculated final demands directly from national demands in the reducing model. The next section will compare the structural characteristics of the agricultural sectors derived by the two models. Reduced Models Compared The essential difference between Model I and Model 11 is in the reducing ratio itself. The Model I procedure reduces the required transaction by the ratio of local production available after meeting final demands to the total internal product required according to 67 national coefficients. Thus the ratio Ex. is applied to each 11 5‘11 transaction in the row for which total gross output produced locally is inadequate to meet both final demand and local processing require- ments. Model II, on the other hand, uses the ratio of total gross out- put produced by local endogenous industries to total gross output re- quired to meet all processing and final demand needs. Thus, the ratio xi////;i is applied to every transaction in a row which is deficient in local production. Model I results in a smaller reducing ratio because all local final demand needs are assumed to be met from local production with no product imported directly to final demand. In Table 1 the study area livestock direct coefficients1 obtained by both models are compared to the U.S. direct coefficients for the livestock sector. The reducing ratios which were applied to the U.S. coefficients are shown in the fourth and fifth columns underthe heading "Ratio to U.S." The differ- ence between the two ratios is shown in the last column of Table l. The average ratio across all 27 sectors is .626 for Model I and .728 for Model II. Direct Coefficients The direct coefficients of 11 sectors remained identical to the U.S. coefficients in both models since adequate local production was available to meet both processing and final demand requirements (Table l). The livestock sector was unchanged while the other agriculture 1A zero direct coefficient in this table simply indicates that the livestock sector does not purchase directly from that sector. 68 .o .o .o .o .o .o moH>Mmmumm .mm .o .o .o .o .o .o mmmmmmmmho .om ans. ans. .0 «momoo. .o cmmmoo. amazozomnz .mm mom. mam. mew. HmNNHo. mmamoo. wmnomo. moH>memmm .em .o .a .H Hommmo. Hommmo. Hommmo. nMmmm< .q .o .o .o .o .o .o mausoommmm .m mmo. NNN. Nae. moomma. aommma. Nmmomm. ammoA .H H mmmH HH A HH Hovoz H Home: HH Home: H Hmcoz " " .m.D uOuomm oudouommwn " .m.D ou owumm mucmwowwmooo uumuwo " u noun monum mucsoo Issac .mucoaofiwmooo .m.D cu umpmafioo cameos soon MOM Houoom xUOumo>fiH msu pom mucofiowmmooo uoouwa .H mam4 $3,340,000 + ($ -23,444) $3,316,556 Compute the reducing ratio as: = $1,231,000 $3,316,556 x4 RATIO =-:— .371168 x4 The transaction available is — x41 . RATIO - ($1,548,582) . (.371168) >4 l 41 N I 41 $574,784 and the reduced direct coefficient is x41 _ $574,784 = .007212 $79,692,360 Model I (LVSTOCKPRD purchasing from OTHERAGPRD) The data used are: x2 = total gross output available = $31,570,000 §2 = final demand (local only) = $ 4,957,000 n— szj = transactions required = $38,463,000 Compute the transactions available as: ZX23 = x2 ' y2 $31,570,000 - $4,957,000 $26,613,000 72 The reducing ratio is n szj = j = $26,613,000 = RATIO _ $38,463,000 .691912 Ex 2 j j The transaction available is ($19,949,547) . (.691912) >4 II 21 $13,803,331 and the reduced direct coefficient is x21 = $13,803,331 x1 $79,692,360 .173209 Model II (LVSTOCKPRD purchasing fromOTHERAGPRD) The data used are: x2 = total gross output available = $ 31,570 §2 = final demand (local only) = $ 4,957 n— sz. = transactions required = $38,463,000 j J Compute total gross output required as: — n— — x2 = Exzj + y2 J = $38,463,000 + $4,957,000 = $43,420,000 Compute the reducing ratio as: x2 $31 570 000 =_.= L 9 = RATIO ; $43,420,000 .727084 2 73 The transaction available is >4 I 21 — ($19,949,547) . (.727084) $14,504,996 and the reduced direct coefficient is X 21 = $14,504,996 = x1 $79,692,360 '182012 In two sectors, "textile products" and "medical, educational, " the estimated final demand turned out and nonprofit organizations, to be greater than the estimated total gross output. It will be shown in Chapter IV that final demand is likely to be a better estimate than total gross output. Since final demand was considered to be the more reliable estimate, total gross output was arbitrarily set equal to final demand. For these two sectors, the Model I assumption caused local transactions to go to zero. This, of course, caused the direct coefficients and the direct plus indirect coefficients to be zero, implying that these two sectors supplied nothing to local processing sectors (Table 2). Under Model II, the row of textile coefficients in the nine-county study area were 61.6 percent of the U.S. coefficients, a much more acceptable estimate. Direct Plus Indirect Coefficients The preceding section compared the direct coefficients of the study area livestock sector to those of the U.S. livestock sector. This section makes the same type of comparison for the elements of the Leontief inverse. It should be recalled that the Leontief inverse shows the direct plus indirect effect, i.e., the total results of the 74 New. «en. nmmonm.H mummqn.H OHqum.N mMMHAmHHHDS HDHHDO mmo. omq. mmqooo. «mmooo. mmoooo. m0H>mmmumm .NN owe. «mm. memooo. nomooo. wowooo. MMmmmmmmHo .oN mmw. I Noaooo. oooooo. «owmoo. Hhmzoznmnz .nN qu. qu. wwmemo. O©NNHO. quoNH. moH>Mmmmmm .«N How. Hun. Hmwmco. nwmooo. owmwno. Q¢MBHmmmH3 .mN mwn. mmo. cqmmHo. mummHo. «Hmomo. MmzmmmH< .¢ omn. mos. omwooo. omqooo. omHHoo. meomnommmm .m «we. awm. wmmmqu. owmmom. mwommm. ammoH .H HH Home: H Home: . HH Home: H Home: m D . Houomm .m.D ou owumm muamHUHHHmou uooquSH msHm uoouwn mmum hwaum HuaDOUImaHG .mucmHUHH Imoou .m.: ou mounofioo mHmuoa soon you “Ouoom xUOumo>HH osu Ho mucmHoHHHooo noouwmaa msHQ uomufin .N mqmmmmomm .NN own. man. mmaooo. ammooo. oaaooo. mmmmwmmmao .am an“. n amaaoo. oooooo. mmmaoo. amazoznmoz .mm awn. . RAH. “moans. “wanna. aoonH. moH>mmmmmm .am mam. omm. Hamamo. mmaamo. mamaoo. nameHmMmgz .mm cam. Hma. ommaao. mmeHo. ammmmo. mmzMmmm< .a one. mmm. Homooo. wmmooo. maaooo. meosnommmm .m Nam. Ham. ~aw~ao.a oasumo.a Hmnmao.a ammoammmeo .N aHa. mam. maaooa. OHamaH. “Hosea. ammsooem>u .H HH Hapoz H Hope: A HH Hana: H Hope: .m.: A noudam mOHumm mops human zuaooolocfis .musoHonmooo .m.: cu woummaoo mHonoE soon How Houoom :ououHsoHumm posse: was you muaoHoHHHmoo uooufiwafi msHm uomufio .m mqmammomm .HN a.mm a.Hm omm.H moa.H omH.H mmmmmmmmwo .om m.aw m.~m aoa.H Ha~.H aom.H Hmmzoznmnz .mm o.om a.mm aHa.H mom.H a~c.H moH>mHmmmm .am H.oa m.mm HHm.H ~H~.H maa.H nameemmmHz .mm H.aa H.Na mum.H mma.H HH©.H amzMmHH< .a m.mm m.HH amm.H Hoa.H omw.H mHoaaommma .m H.4w a.aH oHo.H Haa.H mam.H nmaoammmHo .N H.mm H.aH HHa.H waH.H wam.~ ammsooem>H .H HH Hdpoz H Hdpoz HH Hana: H Hana: .m.= Houndm .m.D Ho uaoouom mHoHHoHuHsz usmuso noun hnaum hquOUIosH: ..m.D mnu ou mommaaoo HH mam H mHmmoz How mumHHaHuHsa usauso .q mqm<8 79 Model I was considered worthy of analysis because it took the final demand estimates as concrete, requiring them to be satisfied out of local production. This caused lower direct coefficients and, thus, lower direct plus indirect multipliers. It also made two sectors ap— pear to supply nothing to local industry since all their production was required for final demand. Model II permitted some final demand to be met by imports, thus leaving more output available for input to other local industries. The Model II procedure was chosen for developing study area models in the remainder of this study. It was judged more acceptable than Model I primarily because Model I produced very small or zero direct coeffi- cients for some sectors. For sectors in which local final demand was almost as large or even greater than the total gross output estimated for the sector, Model I implied that there was very little of that sec- tor's product available to other endogenous industries. This fault did not exist in the Model II procedure since it permitted some of the local final demand to be imported. That it is reasonable to assume that some product is imported directly to final demand is supported by the Washington State survey-based table.1 About 15 percent of the total final demand for the State of Washington was imported, according to this table. ‘However, the Colorado Basin model2 (also based on survey data 1Philip J. Bourque, et al., The Washington Economy: An Input- Output Study, Business Studies No. 3 (Seattle, Washington: University of Washington, Graduate School of Business Administration; Washington State Department of Commerce and Economic Development, 1967), Appendix Table l, p. 39. 2Water Resources Council, Pacific Southwest Inter-Agency Commit- tee, Economic Work Group, Economic Base and Projections, Appendix IV to Great Basin Region, Comprehensive Framework Study, Preliminary Field Draft (November, 1970), p. 30. 80 but less well-published than the Washington study) shows only about 2 percent imported directly to final demand. Another survey-based model, done in 1965 for the State of New Mexico,1 shows about 24 percent of total final demands being purchased from the imports sector. Neither of the studies quoted provided a breakdown of imports to final demand by type of product. Another reason for believing that some final demand will be im- ported directly is the high level of aggregation used in this study. With a highly disaggregated sectoring scheme, the model would likely show some sectors specializing in products which are consumed largely by final users. But with a highly aggregate scheme, it is unreasonable to imply that the final demand needs for all the products subsumed under a single sector are met by the available local production. A sector's output is, in fact, a mix of products rather than a single homogeneous product. Some of these products are likely to be of the intermediate input type while others may be more toward the final user type. Model I was rejected for further use in this study since it was judged highly probable that a portion of local final demands would be imported from outside the study area. The Model II procedure appears to be the more reasonable of the two. Therefore, it will be used in the analysis to be discussed in Chapter V. 1Bureau of Business Research, "A Preview of the Input-Output Study," New Mexlco Business (Albuquerque, N.M.: University of New Mexico, October, 1965). CHAPTER IV A REGIONAL INPUT-OUTPUT MODELING SYSTEM AND DATA PREPARATION Introduction A generalized procedure for preparing input-output models for the State of Ohio and any substate group of counties is presented in this chapter. The primary purpose of this system is to facilitate rapid response to regional policy questions requiring estimates of direct, indirect, and induced effects of regional sector output changes. The system will generate an approximation of an I-O model for any grouping of counties for which certain basic final demand and total gross out- put data have been assembled. Data inputs can be easily changed to reflect various assumptions about final demand and/or total gross output change. Resulting changes in employment, population, value added, and any other variables which can be functionally related to total gross output can be displayed. Due to the basic nature of projections, assumptions about many variables must be made. Procedures which allow changing assumptions to test various "alternative futures" are desirable in any projections sys- tem. Therefore, a very flexible system was programmed to permit various ways of altering the model including sector composition, final demands, total gross output, and impact coefficients. The model presented udlizes data and prepares study area models for 1970. A U.S. model and final demands by state are available for 81 82 1980. With additional time, the entire system presented in this chap- ter could be updated to prepare study area models for 1980, also. General System Overview Several steps are required in developing and applying the region- al input-output modeling system (RIOMS). The seven steps shown below have been programmed to be executed as a single computerized package: 1. Disaggregation of state personal consumption final demand to any group of counties. 2. Disaggregation of state capital formation, federal govern- ment, and state and local government purchases (final demands) to any group of counties 3. Estimation of total gross output by industry for any group of counties. 4. Adjustment of base model I-O structural data to reflect study area structure. 5. Derivation of income multipliers. 6. Multiplication of a final demand change vector by the Leon- tief inverse and application of selected impact coefficients to the resulting total gross output change vector. 7. Estimation of impacts for the rest of the state by a rest-of- state model. Methods used in the above steps are explained in the remainder of this chapter. Twenty-three subroutines are used in the system as presently programmed. It is likely that this number could be reduced with some gain in system efficiency through additional editing. 83 Final Demands Final demands for six categories of users were published for all states for 87 sectors by the Harvard Economic Research Project1 in 1972. The six categories include: 1. Personal consumption. 2. Gross private capital formation. 3. Net inventory change. 4. Net foreign exports. 5. State and local government purchases. 6. Federal government purchases. The methods used in developing each of these final demands by state are explained in Scheppach. The final demands for the State of Ohio were aggregated to 27 processing sectors for this study. Exports are excluded from the initial estimation of final demand and are calculated as a residual in the reducing procedure. Net inven- tory change is also excluded since it is simply an accounting device to make the base model transactions table balance. In any given year, it may be either positive or negative. It is very small relative to total output and would have very little influence on the estimated fi- nal demand if it were included. The remaining four components of state final demands-—personal consumption, gross private capital formation, state and local government purchases, and federal government purchases --are disaggregated to counties as shown in the following sections. 1Scheppach, State Projections of the Gross National Product, 84 Personal Consumption Since personal consumption makes up 60 to 70 percent of final demand in the U.S. model, it was disaggregated independently of other final demands. Personal consumption from the state data prepared by Scheppach was allocated to study areas as shown in Figure 1. Person- al consumption expenditures for a geographic area are primarily a func- tion of population and income level of the population. Therefore, total income ratios were used in allocating state personal consumption final demand to the study areas. The procedure is SAI SAPCi — SI . spci. 1 - l,...,n. where SAPCi study area personal consumption of sector 1, SAT = study area personal income, 81 = state personal income, SPCi = state personal consumption for industry i. Other Nonexport Final Demand This category includes capital formation, state and local govern- ment purchases, and federal government purchases (Figure 2). All three are added together and treated as a single quantity for purposes of allocating state final demand to study area. This combined portion of final demand was assumed to be directly proportional to total gross output by sector. It was further assumed that the proportion would be the same in any study area as it is for the state. Therefore, the procedure is X SAGC = s s s 1 (C1 + F1 + Gi) " I How H. 85 <: START :> 1" 1970 population byaeity. A ' tors for all counties in state. 2. Base model employment (BE37) by sector for READ 77 sectors. DATA b 3. Base model total gross outputs (xi). 4. Study area model aggregation scheme (SAMAS). Compute emp. by sector for state (SAE?) Compute ratios SAE? d SAEi BEi an BEi' Agg. BE?7 and TGO's _ Study area total gross outputs xb to from (x ) for four agricultural and 1 other three mining sectors (Sectors SAM sectors sources 1-7). Compute 1 3E1 ' x1 - _ _ Merge SAM ‘ TGO's ‘ I Figure 4. Procedure for estimating study area total gross outputs internally and merging with those from other sources 91 agricultural products, (3) forest and fishery products, and (4) agri— cultural, forestry, and fishery services. Ohio produced 2.5 percent of the total U.S. cash sales of live- stock and livestock products in 1970.1 Thus, the state total was 2.5 percent of the U.S. total gross output or 846 million 1958 dollars. This total was distributed to countries proportionately according to each county's percentage of cash receipts from livestock as reported in Ohio Agricultural Statistics.2 Cash receipts reported in Ohio Agricultural Statistics did not adequately reflect the total gross output of the other agricultural product sector. They did not account for the value of output (feed- grains, hay, and pasture) which was fed to livestock on the same farm on which it was produced. To get a reasonable estimate of total gross output for this sector, 1970 agricultural commodity prices were applied to "production harvested" data in Table 8 of the 1969 Census of Agri- culture.3 It was assumed that by using 1970 prices on 1969 production, reasonable proxies for the value of 1970 crop production by county would be obtained. Ohio produced 2.9 percent of the total U.S. cash sales of crops in 1970.4 Applying this percentage to the total gross lU.S. Department of Agriculture, Agricultural Statisticsl_l97l (Washington, D.C.: Government Printing Office, 1971), p. 564. 2Ohio Crop Reporting Service, Ohio Agricultural Statistics, Annual Report (Columbus, Ohio, 1971). 3U.S., Department of Commerce, Bureau of the Census, Census of Agriculture, 1969, Vol. 1, Area Reports, pt. 10, Ohio (Washington, D.C.: Government Printing Office, 1972), Table 8. 4 p. 564. U.S., Department of Agriculture, Agricultural Statistics, 1971, 92 output of the U.S. model, the other agriculture sector yielded an estimate of 862 million 1958 dollars as the total gross output for Ohio. This was distributed to counties according to the distribution determined from the Census of Agriculture data explained above. For the forest and fishery product sector, data were available for the state but nothing could be obtainedlnrcounty except forested acreage. State total gross output from forest products was apportioned to the counties on the basis of forest area in the counties. Forest product sales were only $30,800,000 for the entire state in 1970.1 Ohio's total commercial fish catch from Lake Erie was only 1.1 million dollars in 1965.2 The source did not present the data by county. For this study, it was assumed that the 1.1 million was all from SIC code 091 and was equally divided among all counties bordering on Lake Erie. SIC code 091 included all fisheries except fish hatcher- ies, farms, and preserves. SIC code 098, which includes hatcheries, farms, and preserves, is included in the agricultural, forestry, and fishery services sector. Mining Total Gross Output "Coal mining” and "crude oil and gas production" were considered important enough in Ohio to be separate from "other mining" in the model. Each is included as a separate sector. Coal mining, in par- ticular, provides a large amount of employment in Southeastern Ohio. 1U.S., Department of Agriculture, Forest Service, The Demand and Price Situation for Forest Products: l972-73, by Dwight Hair and Robert B. Phelps, Miscellaneous Publication No. 1239 (Washington, D.C.: Government Printing Office, July, 1973), p. 56. 2U.S., Department of Agriculture, Agricultural Statistics; 1971, p. 564. 93 Its output may be affected in the future by government regulations to reduce adverse effect on the environment, including controls to limit its impact on air quality. Technological advances in this industry, relative to other energy sources, will seriously affect its output in the future. Crude oil and natural gas output may be affected by technological advances, also. It is useful to be able to isolate economic impacts of changes in this industry. Therefore, it is included as a separate sector. Other mining is comprised of stone, sand and gravel, limestone, peat, clays, and gypsum. Total gross outputs of these three mining sectors were estimated from an annual report published by the Ohio Division of Mines for 1970.1 Balancing Study Area Output Against Requirements The base model economic structure is modified to reflect study area structure.2 The procedure shown in Figure 5 is identical to Model II presented in Chapter III. The computer program operates as follows: First, the final demands excluding exports (i.e., required final de— mands) are compared with total gross outputs. On the assumption that the final demands are the better estimates, any total gross output (xi) thio, Department of Industrial Relations, 1970 Division of Mines Report (Columbus, Ohio, 1971). 2Data for the base model were obtained from the Bureau of Labor Statistics. For the assumptions of the base model, see U.S., Department of Labor, Bureau of Labor Statistics, Projections 1970: Interindustry Relationshlps, Potential Demand, Emplgyment. III, Illa-ll t. II I II I M . I I III. II. I.I 94 If yi > xi Set xi = y1 Compute Compute - b = NO Exii -Zaijxi‘ =3; :1. YES Set x. =X. ; Assemb.matrix com hie elj of trans. e = p_{ 3"” available for 1. xi xij yi SA sectors / Compute direct coeff. A ' Exports, Comp. row ComAMmatrix ‘ Imports and {of imports of Im orts trix of m = 2m _P Direct Coef i i ij mij = xij _ xij Figure 5. Reducing procedure to obtain study area direct coefficients. 95 which is less than required final demand (yi) is set equal to final demand (yi). Then a matrix of required transactions (iij) is obtained by multiplying the study area total gross output vector (xi) by the base model matrix of direct coefficients (agj). Summing each row of the requirements matrix, plus the required final demand, yields the total requirement of each sector (E1). If the output available (xi) is greater than the sum of the output required (ii), it is assumed that xij = xij’ and the study area direct coefficient (aij) will be identi- cal to the U.S. coefficient (3:3)’ Then exports are e1 = x5‘ - xi. i = l,...,n. A matrix of transactions available is then obtained by reducing the transactions in each row where xi < ii. The available transactions for these rows are computed as >4 H- =X xij ij i, j = l,...,n. >4 I i A matrix of imports is obtained by subtracting the matrix of available transactions from the matrix of required transactions. Sum- ming each column of the imports matrix yields a row of imports. A Direct Plus Indirect Plus Induced Income Analysis To use the input—output model to estimate income change resulting from final demand change, the table must be closed with respect to households. This means that a row showing purchases by all sectors from the households sector, and a column showing purchases by the house- holds sector from each producing sector, must be placed inside the pro— cessing matrix. Household consumption then is no longer an exogenous 96 use of processing output, but is a part of the processing sector. If a sector increases its sales to final demand, it increases its pur- chases from households (for labor, capital, rent, etc.). These earn— ings by households are spent for additional consumption goods, causing additional output by producers. Thus the income effect from induced spending is captured. To close the transactions table with respect to households re- quires separating a household expenditures column from the final demand vector and separating a corresponding household income row from the pay— ments sector. A new transactions table (Xh) is obtained with this row and column vector included.1 The personal income figures that are needed to show what purchas- ing industries pay to the household sector for labor and other resources owned by households is embedded in the value added component of the U.S. Table. The 1967 U.S. Table, published in 1974,2 provides the best available ratios of value added to total gross output. An initial attempt to estimate the value added component of total gross output and reduce it by a ratio of total personal consumption to total value added was rejected. It was decided that the employee compensation por- tion of value added would give more accurate personal income relation- ships to total gross output. 1Matrices with households included in the processing sector will be identified by addin the superscript h, e.g., the Leontief inverse with households is (I-A )’1 or Rh. 2U.S., Department of Commerce, Bureau of Economic Analysis, "The Input-Output Structure of the U.S. Economy: 1967," 24-56. 97 In the 1967 U.S. input-output model, value added was disaggre— gated into employee compensation, capital compensation, and business taxes. Employee compensation includes wages and salaries primarily. U.S. employee compensation, as a percent of U.S. total gross output, was calculated for each of the 27 industries. This ratio was applied to study area total gross output to obtain a first approximation of payments to households. The adjusting ratio which had to be applied to make the row and column balance was much less drastic when employee compensation was used as the household row than when value added was used. By using employee compensation, an estimate of total income to households was obtained for the seven-county model which was less than total personal consumption by a ratio of .902163. Every element of the initial household row was multiplied by this ratio to make the row total balance with the column total (see Appendix B). In obtaining the households row of study area transactions ma- trices, the imports component of total gross output was subtracted be— fore applying the U.S. employee compensation ratios. Imports do not contribute to local income, but are a leakage instead. After imports were removed from study area total gross output, the procedure was identical to that described for the U.S. Appendix C contains house- holds data derived by these procedures for the U.S. and the seven-county study area.1 1There is a minor error in the procedure as presently programmed. Time and computing funds did not permit revising the program and ob- taining a new set of multipliers. However, a sample table showing Type I and Type II income multipliers, obtained by the procedure as pre- sently programmed, is presented in Appendix C. Correction of the error will change the multipliers by an insignificant amount. The error involves the quantity in the lower right-hand cell of the house- hold transactions matrix. The quantity which households purchase from 98 When households are inside the processing matrix, the direct in- come is simply the household row of technical coefficients from the Ah matrix. The direct plus indirect income for sector 1 is the sum of the products of each household row technical coefficient (from Ah) and the corresponding sector j column element of the Leontief inverse (R) without households. The direct plus indirect (Type I) multiplier for sector 1 is direct plus indirect income divided by the direct income of sector 1. The household row elements of the Leontief inverse con- taining households include all three income effects. The induced ef- fect alone can be calculated by subtracting out the direct plus indirect effect. The Type II multiplier, which accounts for all three income effects, is obtained by dividing the household row element of the Rh matrix by the corresponding household row element of the Ah matrix, i.e., the direct income change. An Impact Analysis The last feature of RIOMS is a subroutine which multiplies final demand changes for which the impact is to be analyzed by the Leontief inverse to obtain a total gross output change vector. Impact coefficients (i.e., changes in certain variables which can be function- ally related to total gross output) can then be applied to the total gross output change vector. These coefficients include man-years of employment,‘ imports, exports, employee compensation, capital compen— sation, and business taxes. All coefficients used in this study were linearly related to total gross output, but, with further study, other households is primarily for domestic services. This can be estimated using ratios from the 1967 U.S. transactions table. The detailed pro- cedure for calculating the multipliers and the table are described in Miernyk. (See Miernyk, The Elements of Input-Output Analysis, pp. 43-49.) 99 functional relationships might be derived which would improve the im- pact estimates.1 Analysis of a Final Demand Change When a final demand change (Ayi) is determined exogenously to the RIOM System, its impact can be estimated as follows: First, the assumption is made that the same portion of the final demand change is supplied by local production as the reducing procedure implied for the study area economy (see Chapter III). The amount of the final demand change to be imported is >4 * i 1 - 1 (l) Ayi - Ayi o g - ’00.,no 1 The change in final demand supplied by local production is ' * (2) Ayi = Ayi — yi 1 = l,...,n. ' The quantity to be supplied by local production (Ayi) is then applied to the study area Leontief inverse to estimate the change in total gross output which each sector must supply. In matrix notation -l (3) AX = (I-A) AY. In order to deliver this change in total gross output, the endo- genous processing industries of the study area must increase their im- ports. It is assumed that they will import the same portion of their increased total gross output as they were importing in the basic model. 1Any other coefficients which can be related to total gross out- put, such as water use, land use, and various types of pollutant out- puts, could easily be included in this analysis if available for the same sectors. 100 n * (4) Ami = Ayi + §Amij i = l,...,n. Imports are summed across the row to preserve product identity. Rest-of—State and National Inpacts The increase in imports to the study area generates production in the rest of the state and in the nation. To estimate these impacts, a rest-of-state model is prepared by the RIOM System. Imports re- quired by the study area, because of its initial change in final de- mand, become a final demand change vector to be applied to the Leontief inverse of the rest-of—state model. The same final demand change vector can be applied to the U.S. Leontief inverse to get national impacts. It was considered impractical for the small study areas analyzed in this study to obtain a rest-of—U.S. model. However, for larger study areas where it is critical to the analysis to isolate "rest-of—nation" impacts, it would be appropriate to obtain a Leontief inverse excluding the study area. Project Analysis The USDA guidelinesl call for utilizing multipliers in a "with" compared to "without" project analysis of the impacts of expenditures for water and land development. For purposes of estimating direct and indirect effects attributable to projects, it will be useful to adjust I-O models for project effects. Such adjustments are particularly relevant, theoretically at least, with respect to agricultural crop production. When the federal government installs a flood control 1U.S., Department of Agriculture, Economic Research Service, Forest Service, Soil Conservation Service, USDA Procedures for Planning Water and Related Land Resources, p. V-12. 101 project which results in a reduced flood risk on cropland, the input— output relationships of crop production are changed. Farmers, aware of the reduced risks, are willing to use more inputs relative to land than previously. They are likely to use more fertilizer per acre be- cause the probability of losing the investment in planting the crop is lower after the project is installed. The LP models currently being used by USDA in river basin plan- ning to estimate costs are restructured to reflect the different tech- nology which may be used after the project is installed. To be per- fectlv compatible with the LP system, the direct coefficients of the I-0 models would need to be adjusted to reflect the technology of each different LP model used. For example, the crop sector may purchase less tractor fuel per unit of output from the supplying sector when yields increase. Depending upon the assumptions about fertilizer use relative to yields, there could be less fertilizer purchased per dollar of total gross output due to different technology. In the case of "no- til" cropping practices, machinery and fuel purchases are replaced, to a large extent, by herbicides and insecticides.1 These types of changes in input use can be reflected in a static input-output system by appropriate changes in the direct coefficients. Since the RIOM System reflects the average technology for the nation, it may be appropriate to change direct coefficients for the study area model to more accurately reflect its "without project" economic structure. 1"No-til" is a term used by agronomists and others to refer to methods of planting row crops, such as corn and soybeans, with minimum disturbance of existing sod or other ground cover. This avoids exposing the surface of the soil to wind or water erosion, thus keeping soil loss to a minimum. This has the environmental advantage of reducing sediment in streams, but the disadvantage that it requires the use of more chemicals. 102 This would require ancillary studies of local area technology compared to average U.S. technology for the sectors most critical to the pro- ject analysis. The same ancillary studies should also reveal appro- priate changes in study area coefficients to reflect "with project" structure. It is conceivable, also, that changes can occur in a small area's economy which would make sector additions or deletions appro- priate. For example, the transformation of a small area from dryland farming to irrigated farming as a result of a project may bring a new sector into the local economy to sell irrigation equipment. Under irrigation, different agricultural products may be produced, requiring new types of inputs. These changes are a radical departure from the economic structure existing before the irrigation project was install- ed. It would be appropriate to alter the historical input-output structure to reflect the additional sectors and outputs due to the project. Such structural changes can be made with the RIOM System by changing the initial estimates of local final demand and total gross outputs upon which the derived structural coefficients are based. By increasing the study area total gross outputs of a growing sector above what the historical data show to be there, we can reflect the potential development expected of that sector in the study area. Thus the study area model derived from the U.S. model will have the expanding sector built into it at the higher level of output. Study area coefficients then reflect interaction of other local sectors with the expanding or growing sector at its projected higher level of out- put rather than at its historical level. 103 There can be no rigid rule on changing model structure. The decision to adjust an input-output model dependscnlthe changes which have occurred since the model was constructed and the anticipated changes to be analyzed. Planners and researchers will develop an in- tuitive feel for appropriate model changes as they work with data and models for their areas. Summary A system for preparing secondary data input—output models for substate areas was presented in this chapter. The system is composed of seven components which prepare estimates of total gross output and final demands, reduce base model coefficients, derive income multi- pliers, estimate value added and its components, and estimate man- years of employment. The system also provides for preparing rest-of- state models for estimating the impacts to a study area. Total gross outputs can be estimated using U.S. productivity per employee ratios for many sectors. For some sectors this is not prac- tical due to lack of adequate detail in study area employment data. Total gross output can be calculated outside the system by other methods for these sectors and read in at the appropriate point in the system. This was done for agriculture and mining in this study since employ- ment detail available from census data at the county level was not suf- ficient for disaggregating them to the desired number of sectors. The coefficient reducing method used in the system is similar to the supply-demand pool and commodity balances techniques described by Schaffer and Chu (see Chapter II). The specific procedure used in this study is described in detail as Model II in Chapter III. The reducing 104 ratio applied to required transactions is total gross output available divided by total gross output required. As will be indicated in Chap- ter VI, however, the reducing procedure may be improved if it is used to prepare individual county transactions tables for aggregation to the desired study area. A multiplier component was developed to prepare Type I and Type II income multipliers. The method used was to move the personal con- sumption final demand vector into the processing sector as the house- hold column and apply U.S. employee compensation ratios to study area total gross output to estimate the household row. The first estimates of the household row were adjusted to obtain elements whose sum would equal the sum of the household column. In addition to the income multiplier analysis, the system prints out estimates of the direct plus indirect total gross output change and applies various impact coefficients to this change. Any variable which can be related to total gross output can be displayed. 11 ll].] I'll-ll III] I I II I 1| I CHAPTER V COMPARISON OF SIX SECONDARY DATA INPUT-OUTPUT MODELS Introduction The regional input-output modeling system (RIOMS) described in Chapter IV is used in this chapter to obtain and compare I-O models for five substate areas and for the State of Ohio. The largest sub- state area is the 19 counties having a significant portion of their economic and geographic area within the hydrologic boundaries of the Muskingum River Basin (Figure 6). The next largest area, the ll: county area, is the same 19 counties less Medina and Summit on the northern edge. These two counties contain large urban areas which may distort the results of impacts which apply mainly to the rural areas of the Basin. Another area is the 9 counties of the State Planning Region 9 (Figure 7). A 7-county area is the smallest area modeled. It is composed of Planning Region 9 less the two counties of Jefferson and Belmont, on the east, which are not in the original 19 Muskingum Basin counties. The 10-county area is the 7-county area plus three counties containing very small populations--Perry, Morgan, and Noble. The 7-county area is entirely contained within the 9-county area, and the l7-county area is completely contained within the l9-county area. Population, total study area output, and final demands are shown in Table 5. When Jefferson and Belmont are added to the 7-county 105 I I. l I]. l‘ I] . .’ It'll. I III. I! 106 I} .0 fi/ ‘ a" \‘f‘ LUCAS I l 3, MI“ 9 ornw {a J00 , A". UVANOOA InuulUl-L smous art 5 ' ' on 0 man gram 0”" s u ca \ INS lam“: HANCOCK ‘” N m. war war unuaoi Huron 1’ ”PD "mt Luv-IAN Aunt Inflow anon ' ' a MA man u A": A an A I n o 2 : m" E N 5~tur ”“0” 0 can: ro~ ‘ “"1 on. I a .34 it: 2 [arm autumn sutmvstv (Luaur MIA u/ MUSKINCU tum“: cu m: g ’ e nun [2 AI In p any 01v 0 a I "t” 1 hcxnnv "0' 3 r4 rt rr: ! How 7 w "INC ran U, n ~33; Hocxm L N CL m 70” m 5 A u N M7 1‘9 . M Mr row ,u army-r uric: § III: -M Cl! ’4 i o z A pal “an Clara '5 '3‘ Q. N ote : 1. Figure6. area. boundaries delineated The 17-county area is the 19-county area has Medina and Summit State of Ohio with 19-caunty Muskingum River study ‘III I 111‘ I . [I I 1‘ 1 ll « ll {I’ll} . ll. 'lll' II] I {I‘ll WILLIAUS fULrou n N v ( uflCl’ mam @ U u. 71.3[3 3 MIC“!!! Ill-I P'lltl 7 1 NA aura. ® .00..” Note: 1 . 2. Counties. 3. Figure 7. Ch“: I 7‘11 It 107 ("fl The 9-county area. is identical to State Planning Region 9. ' L 1' ~" 6 ' I 0 arm» :‘ A4104 — ‘ .u unuo.‘ ”MWU‘W- nous .- ,‘r t p! v ”Irl'l u 10‘ l 1".” V . 4” mu m. rL—Wo co w on In"! " OLUHDI‘N A 1 an mu 5b ‘ n o u t In I I i 3 3 o osnocroav q M. u. U C 3 E b (lulu: r ., USINNCU .n'.° ' ‘Nk I canny . 8 4r rr I km more»: NFL—.1 . m, “(I63 ‘ JACK! Iv AD I c I 7'0 1.,“ ‘Iv Q The ?-county area is the 9-county area. less Jefferson and Belmont The 10-_county area. is the 7—county area. plus Pen-y, Morgan, and Noble Counties. State of Ohio Planning Regions and Service Districts 108 .muuomxm mmvsaoxm vamamw Hmaam Hmooqm ' Hoo.m qmm.u www.memmm Hoo.¢qaow moa.wmo.oa owno mo mumum He+ oo+ em+ mono >uasoolna Ho>o mmmouoaw unmouom mmw.~ mmn.m mNo.mH~m mmn.~moqa oom.maw.a hu::OUImH oos.~ mos.“ mam.mq~m mam.mwsw oos.-a.a monsoousa Has.~ smm.o Hw~.m~w «ms.oflm~ ooo.mmm suasou-oa Ho+ oo+ No+ mono >uasooln uo>o mummuoofl ucooumm Has.m aam.s mmm.wsHH New.SH~m oom.qos nauseoum onq.m Noo.n 5mm.~Hm wNH.mHom oom.mwm monsoonn mumaaon mumaaoo nulls mumaaon cOfiHHHZ IIIII Hmnasz oufimmo " mufimmo " panama " u " Mom " pom " mHMCHm u unmuso u coaumasmom " mmu< mwauw . . . Houoa . Houoe . mm Hmooq . owH . Hmooq Hmuoa . . . mmoum hvsum xwm onu mo namaow Hmcww mam .usauso .GOHumadmom .m mamsH 109 area, population increases by 62 percent while total gross output in- creases by only 60 percent. When the two counties of Medina and Summit are added to the l7-county area, population increases by 54 percent while total gross output increases by 60 percent. The purpose in using the several areas for comparison is to analyze the results obtained by the purely mechanical secondary data procedure when total gross output and final demand relationships change. For each of the five substate areas, a "rest-of—state" model was obtained composed of all counties in the state other than those in the study area. The study area imports change vector showing changes in both processing sector and final demand imports by row became the final demand change of the rest-of—state model. The change in rest- . of—state total gross output by sectors, due to its exports to the study area, gave an estimate of the rest-of—state direct plus indirect imports. In the following tables an abbreviated sector name is used, in addition to the sector number, as a convenience in reading the table. The full sector names and abbreviations are as follows: Sector Abbreviated Number Sector Name Full Sector Name 1. LVSTOCKPRD Livestock and products 2. OTHERAGPRD Other agricultural products 3. FFPRODUCTS Forestry products 4. AFFSRVICES Agricultural, forestry, and fishery services 5. COALMINING Coal mining 6. OILANDNGAS Crude petroleum and natural gas 10. ll. 12. l3. 14. 15. l6. l7. l8. 19. 20. 21. 22. 23. 24. 25. 26. 27. OTHRMINING CNSTRCTION WOODPRODTS METALPRDTS MCHNXCEPTE ELECTMCHNE TRANSEQUIP OTHRDURGOS FOODPRDTS TXTLEPRDTS PRINTPRDTS CHMCLPRDTS NONDURGOOD TRNSWHSESR COMMUNICAT UTLITSANSR WLERETTRAD FBRSERVICE MDEDNONPFT OTHRPERSER RECSERVICE 110 Other mining Construction Furniture, lumber, and wood products Metal industries Machinery except electrical Electrical machinery, equipment, and supplies Transportation equipment Other durable goods Food and kindred products Textiles and fabricated textile products Printing, publishing and allied products Chemicals and allied products Other nondurable goods Transporation and warehouse service Communications Utilities and sanitary services Wholesale and retail trade Finance, insurance, real estate business, and repair services Medical, educational services, and nonprofit organizations Other personal services Entertainment and recreational services 111 Model Elements Compared Total Gross Output Taken as a whole, the State of Ohio has a balanced economy in that nearly all types of industry are well represented. It has a di— versified agriculture, as well as a broad range of heavy and light industry. However, there are areas including several counties here and there where economic activity is heavily weighted toward specific types of industry. For example, both the 7- and lO-county areas de- pend on livestock for 3.5 percent of their total gross output, while for the state, livestock is only 1.1 percent of total gross output (Tables 6 & 7). The lO-, l7-, and 19-county areas were progressively lower intfluapercentage of total gross output from livestock. However, the absolute output figures increased going from smaller to larger areas. In the crop sector, relationships between the study areas are about the same as in livestock. Livestock and crops make up 2.4 and 2.1 percent of the U.S. total gross output, respectively, while for Ohio the figures are 1.1 percent for both sectors. The location quo- tient for Ohio relative to the U.S. is about .5 for both crOps and livestock. Metal products output is relatively higher in all six areas than in the U.S. by twice the percentage. The 9-county area produces metal products valued at 23.5 percent of its total gross output while for the U.S. it is only 6.6 percent. The other study areas ranged from 12.7 to 17.4 percent. 112 .8338 32 no 2533a 3 33 H ‘ll‘i‘ .mowumu uaoakoaaam hp Hobos .m.D aoum vmumawumm muOu loom nonuo .moOHumoHHnsm mumum msowum> was manuanowuw< mo msmcwo Bonn vmumawumm muouomm am>om umuamm Hoo.¢qaow mN~.~mqu maw.mwmw Nmm.on~ ~0w.oa~m QNH.mHON mqmmmomm .NN mmo.~mw nmm.~mH Nmn.ow onm.o~ Hmn.¢m ooq.m~ MmmMmmmmHo .oN mmH.mmmH me.NHm www.mwa Hom.oq cmm.no 0mm.H< Hmmzoznmnz .mN omn.owmm NMH.~qu «no.0me mom.moa mqm.mmm <¢N.mca moH>mmmmmm .QN mmm.Hmmn omm.moma oma.oaw mNo.mo~ www.mom www.mwa QMmmm¢ .q omn.mm ooa.w mmo.n oo¢.m soa.m mNm.m mHunoommmm .m w~m.wmm mmm.~m Hoa.oa oam.~m mom.am moc.nw ammuA .H mumum " hucsoo ma xucsoo NH muaooo 0H xucnoo m auasoo n u nouomm m mono mvaum Loom you Hobos wcwoopmu as» aw pom: pseudo mmoum Hmuoe .o mqmmmmumm .um mao.a woc.a acN. mca. mmo. Noc. coc. mam. mmmmmmmmeo .om mmc.a cwm.a oom. maa. moo. wmc. eoc. mom. Hmmzoznmaz .mN cmm.a NNc.a cmm. aca. wmo. cnc. ch. mmm. m0a>mmmmmm .cm omn.a co~.a moa. mmo. aum. nmc. omc. New. ncmaemmmaz .mm ano.a mam.a mam. mma. nmm. wmm. amm. omm. MmzMmmm¢ .c ccm.a man.a aom. mca. cmm. mmm. mmm. aow. whomnommmm .m cnm.a mmo.a mwm. coa. one. mac. amm. amm. ammoa .a m: ¢m m: mm one How muoaaaauasa oaooaa .oa mammmmomm .NN nmm.m Nmm.a mm“. mom. mwc. Nea. Nca.a mNe. mmmmmmmmeo .eN moe.m mem.a mme. mew. mmc. oma. mmo.a mum. Hmmzozammz .mN cee.~ amm.a mam. mom. mmc. eea. oma.a oce. mua>mmmmmm .cN nmm.N non.a mme. emN. omc. oea. cca.a nae. QMmmm< .c coc.m cam.~ mme. cmm. cac. mma. wem. mmc. mHoDQommmm .m nm~.m NmN.N mmn. oam. cec. eca. cmo.a aem. nmmu<¢mmwo .N oce.m eme.m mmm. cem. mmc. oma. moo.a Non. ammMUOHm>a .a m: «m m: Mmmomm .mm emn.Noe oem.em cmn.mm mcm.ca nma.a~ ome.~a mmmmMmmmHo .eN mma.mmma mma.~am mem.mma cmm.ec emm.me mmc.oc Hmmzozamnz .mm eme.mmcm nmm.~em amm.m~m Nma.m~a mmo.nma oem.aaa moa>MMmmmm .cN aem.mmem omn.nom mem.amm mmm.mma noc.mma ~mm.maa Q¢MHHmmwa3 .mm oea.cam cmm.nca ec~.om cwm.- eea.cm nen.ma MmzMmmm< .c mcm.ma ~ea.m mmm.a aom. Nan. omc. meosaommmm .m mo~.~ca eae.- www.ma occ.m emm.c emm.m namoa .a oumum " moanou ma u huanoo ma u meadow oa " %uc=oo m ” munnoo n " Houomm monomxm wsaesaoxo meamawe amcam .aa mamMMmomm .mm Noa.moa cme.ma ~m~.ma NNN.m Nmo.m nmm.n mmmMmmmmHo .eN Hmmzoznmnz .mN mua>MMmmmm .cm moe.m mmm.~ QMmmm< .c ecm.a emN.a mam. mHUDoommmm .m ammucmmmao .N mam.mm cme.mm mem.am mam.cm nmmMUOHm>a .a oumum muasou ma huazoo ma muonou oa muasou m mucnoo m uouoom madame amcae mo uaosonaoo uuonxo mna .Na maan 123 up in these two counties to absorb all the output of the food products sector which, together with local processing needs, absorbed all the output of the livestock sector. While exports for the livestock sector and several manufacturing sectors are greater for the 10 than for the 9 counties, the total ex- ports of the 10 is only about 67 percent of the 9. The metal products sector of the 9 accounts for most of this difference since it has ex- ports of $387 million compared to $92 million for the 10 (Table 12). Another item about exports that should be noted is that the model shows no exports by the electrical machinery manufacturing sector for the 9-county area. However, the 7- and the lO-county areas both appear to be exporting electrical machinery. This requires some explanation because the 7 counties are contained within both the 9- and 10-county areas. It appears that the processing and local final demand require- ments of Jefferson and Belmont counties absorb all the local output of electrical machinery, as well as imports. Under a less aggregate sec- toring scheme, it is likely that some types of electrical machinery would be exported from the 9-county area, while others would be import- ed. Total final demands are shown in Table 13. Imports to the Study Area Total imports by sector are shown in Table 14. The column vectors in Table 14 would actually be row vectors in a transactions table. Product identity is not preserved in these sector requirements. In the model, however, total imports by row are obtained to preserve pro— duct identity and permit ratios of total imports of a particular product to total gross output to be calculated. These ratios are later used to estimate imports to the study area when total gross outputs increase 124 mmm.oaacc aae.ocam www.0mom amn.~n~a mmm.moma omm.moaa mamMmomm .mm mmm.oam caN.Naa noo.cn www.mm owa.om nmm.¢~ mmmmmmmmeo .em cme.mcma aoe.cm~ wem.mma acm.mc eam.me eme.mm Hmmzozmmnz .mm mcc.-~c amm.mee amm.m~m emm.en oao.maa mom.ee moa>mmmmmm .cm moc.noem nem.~mm mem.amm em~.mma nao.NoN acm.a~a QMmmm< .c mme.e eem.a mmm.a mc~.~ moo.~ mcm.a msopnommmm .m mmo.ama eaN.Na www.ma mom.~ moe.m mmc.m ommwa .a oumum " mucsoo ma ” mussoo ma huosoo oa zuaaou m huanoo n HOuomm muuoaxo waaeaaoda ecmsme amaam .ma mamm mcoauUMmamuu onu wnauonuunam an emumaaumm kahuna mupana mnu mo Sam canaoo ecu ma amuse commn 12S mNm.amem ae~.Nca amm.emc ma~.moa amm.mma eme.na maMMmomm .mm cmn.m~ Nma.m muo.c ame.a cmN.~ mac.a mmmmwmmmho .eN acN.ac mmm.aa oo~.m ma~.~ meo.c eem.~ Hmazozommz .mm ac~.ch mmc.em aom.mm ean.a ~aa.ca amc.m moa>MMmMmm .cm ooc.aaa oem.am amm.cm cce.ma ema.~a ~co.aa QMmmm< .c occ.a Ncn. cem. mmc. mac. amm. meuaaommmm .m Noa.ec e~c.m omm.m omm.m moa.m cac.~ namea .a mumuw munsoo aa aunsoo ma aucnoo oa aunooo a aucsou n u0uomm mannmsnca an muuoasa .ca mnmca I, .III ’1 I ll! 126 as a result of a change in final demand. Thus it is assumed that the ratio of imports to total gross output remains constant for a parti— cular sector as it expands output. Final Demand Changes to be Analyzed When there is a final demand change, there are likely to be associated forward linkage changes in other sectors, in addition to the backward linkage accounted for in the Leontief inverse. Crop sec- tor output may increase as derived demand from higher livestock sales, or it may increase because technology has lowered the cost of produc- ing crops. The first case is an example of backward linkage, and we only need to increase livestock final demand and the model will show the additional output drawn forth from other sectors. In the second case, livestock farmers are confronted with additional supplies of feed crops; therefore, they may decide to increase production of livestock. Many livestock farmers in the Muskingum area produce their own feed. Such firms are represented in two sectors of the input-output model; thus, the linkage occurs under the same manager on the same farm. The output of the "other agriculture" sector1 is more directly affected by land and water development projects than is livestock. However, in none of the six study areas, which includes the State of Ohio study area, did this sector have exports. Therefore, any change in its output would have to be absorbed by either local processing sec- tors or local final demand. Without a significant increase in local population to raise the local final demand of both livestock and crops, there is only one way to dispose of additional crop output. That is 1The "other agriculture" sector is sometimes referred to as "crops" sector. 127 through sales to local processing sectors whose exports can be increas- ed. Since livestock absorbs so much of crop sector output, it was considered appropriate to assume that livestock exports would increase as a means of utilizing any additional output of the crop sector. It was considered desirable to test the same magnitude of output change on all study areas for comparative purposes. Therefore, the smallest area (the 7 counties) controlled the size oftflwafinal demand changes analyzed. A $10 million increase in livestock final demand was used to compare impact characteristics of the six study area models. A $1 million change in crop sectOr final demand was also analyzed since this is the sector whose output is most directly affected by land development measures. Total Gross Output Impacts of a $10 Million Change in Livestock Final Demand The four smallest study areas had similar total gross output changes because the full $10 million change was applied to their Leon- tief inverses (Table 15). But both the 19-county area and the State were, historically, importing some livestock needs directly to final demand. The $10 million final demand change was reduced, to reflect their historical pattern of imports, by the same ratio used in reduc— ing transactions. For the 19-county area, the ratio was .642, meaning that, according to the secondary data I—O model, the state was produc- ing 64.2 percent of its livestock sector needs and importing the re- mainder to final demand. For the State, the same ratio was .997. Applying the respective ratios to the $10 million change left the 19- county area's processing sector facing a $9.97 million change and the State processing sector facing a $6.42 million change. The total 128 mmcncn.o~ cmaece.o~ ammmem.aa aemomm.om mammmomm .mm cheoo. mammoo. mmcmoo. mmmmoo. mummwmmmeo .eN maaano. Nemomo. mNeaeo. Neeamo. amazozammz .mN mccmae. ocammm. nmmmcm. ammONm. mua>Mmmmmm .cN amamme. maeaON. camcme. oeNNON. QMmmm< .c emmnoo. eemaoo. eacmoo. mneaoo. maosnomamm .m mmmocm.~ naammm.m cmNmmc.~ mmcamm.m ammwa .a meadow ma u auaooo oa " aucsoo a " ausnou a “ uouomm menace amaaw ou aoaaaaa oaw amcoauaeem cm um>aawe Ou .m.D osu can noun aesum noon mo Houoom xo0umo>aa ecu How monasaou usmuno mmoum amuou Ga mwcmno .ma mammMmomm .NN ammmmmmmao . e~ amazozomnz .mm mua>mmmmmm .cN acmeammmaz .mN Mmzcmaaaea .NN ecoazszzoo .am mmmmmzmzme .om nooumsozoz .aa manmmaozmo .wa manmmazamm .ea maceemaaxe .ea meammaoom .ma moom:nmmao .ca maaommzcme .ma mzmozeomnm .aa mammuxzmoz .aa menmmaMmmm< .c meoaaommmm .m namocmmmeo .N ammeooam>a .a uouoom Acmscaucoov .ma mamca 130 gross output change is also shown for the assumption that none of the $10 million change was imported (Table 15). The models imply that the direct plus indirect grand total of the gross output changes from a $10 million livestock final demand change are $20.58 million in the 7-county area, while only $13.09 mil- lion in the entire State as shown in Table 15.1 Since the model is linear, a comparable figure for total gross output, based on a full $10 million final demand increase to state processing sectors, can be obtained by dividing $13.1 million by .642.2 This yields an estimate of $20.38 million as the grand total of the State's total gross output change vector. This is about $200 thousand less than the 7-county change. We would expect the total State impact to be greater than the 7- county impact due to the fact that imports to the study area will be obtained largely from within the State. The explanation for the fact that the 7-county area and other substate areas have greater impacts than the State hinges on the way in which the coefficients are obtained. The lower coefficients for the.1arger area depend on final demand changes relative to total gross output changes. The population increases 1Each column of Table 13 is simply the livestock purchasing col- umn of the Leontief inverse multiplied by 10. When a Leontief inverse is available, the effect of a final demand change for any one sector can be estimated without need of a computer run. If a change in more than one sector is to be analyzed, it becomes more work. Each sector's change is multiplied by each element of its column in the inverse, and the rows of the resulting matrix are summed to get a single column vec- tor showing the aggregate total gross output change for each sector. If detail by sector is not desired, each final demand change can be multiplied by its sector multiplier and summed to get the total output change for the study area. 2This ratio is identical to the reducing ratio calculated for re- ducing the local transactions of a sector which fails to meet local processing and local final demand requirements (see Chapter III). 131 54 percent in going from the l7-county area to the l9-county area. This brings about an additional nonexport livestock final demand re— quirement of $5.86 million (Table 11) and an additional internal live- stock requirement of $42.98 million. This is a total additional live— stock requirement of $48.84 million, while livestock total gross output increases by only $13.01 million (Table 6). Thus, the entire $35 million that the 17 counties were exporting appears to be absorbed by the requirements of Medina and Summit counties. The livestock sector of the l9-county area failed to meet local requirements by a ratio of .9797. Transactions and final demand met by local production could be only 97.97 percent of requirements. The remainder had to be imported. This comparison of models demonstrates a failing of the supply- demand pool and commodity balances reducing procedures, which apparent- ly has not been widely discussed in the literature. A smaller Leontief inverse can be obtained for a large area relative to a small area due to the changing relationship between final demand and total gross output. The impacts derived from two such models can be logically inconsistent. A larger area which completely encompasses a smaller area contains all the impacts resulting from the small area interde- pendencies plus those interdependency impacts picked up in the addi- tional area. The failing mentioned above lies in the fact that the reducing ratio for a sector in any area becomes smaller as final demand becomes greater relative to total gross output. Thus it is possible for a sector of a model derived for a study area to have higher ratio of final demand to total gross output than a smaller study area which is contained within the large study area. When this condition exists 132 for a sector, smaller reducing ratios will be calculated for the larger area. The smaller reducing ratio then applies to the entire study area for purposes of deriving a study area I-O model. It follows that smaller multipliers will be obtained for the larger study area than for the smaller area. Smaller transactions lead to smaller direct coefficients, which lead to smaller elements of the Leontief inverse. The smaller reducing ratio obtained for the larger area then applies to the transactions of the small area, as well as to the transactions of the additional area. The models resulting from these reducing procedures produce re- sults that look reasonable on the surface. The problem is not revealed unless comparisons of small and large areas are made. However, it may be possible to overcome this inconsistency by further experimentation with reducing procedures. A possible line of study to improve the model is suggested in Chapter VI. The U.S. column in Table 15 shows what the result would have been if the "naive model" had been used for all study areas. The naive model simply assumes that national coefficients are suitable for es- timating study area impacts. Total impacts with this model are on the order of $23.5 million compared to $20.38 for the reduced State model. This is a difference of approximately 15 percent. Impacts on the Rest of the State Rest-of—State models for each study area include all counties of the State other than those in the study area. The RIOM System is used to derive a rest-of—State Leontief inverse. A column vector of im- ports to the study area, summed across the row, becomes the change in 133 final demand to be multiplied by this inverse (Table 16). Thus, im- pacts on the rest of the State can be estimated. Note that Tables 16 and 17 have identical column totals but ele- ments in the columns are different. Table 17 shows total import requirements by the purchasing industry. Product identity is not pre— served in these column elements. Table 16 shows the amount by which each local producing industry failed to meet the study area's local processing and final demand needs. These are row totals of imports; therefore, product identity is preserved and the vectors can be used as final demand changes on the rest-of—State models. Total final demand facing the rest-of-State processing sectors (imports by the study area) is reduced by the amount which is assumed to be imported directly to final demand by the rest of the State. For the 9—county area, for example, total final demand for the other agriculture sector is $.91 million (Table 16). But in the rest-of- State basic model, 6.9 percent of the final demand of this sector is being imported directly to final demand. Multiplying $.91 million by 93.1 percent gives $.85 million as the final demand met by rest-of- State industry (Table 18). The other $.06 million is imported from outside the State.1 The impact on total gross output in the rest—of—State (outside the 9-county area) is an increase of $3.08 million (Table 19). This is the result of multiplying the 9-county final demand vector, less im- ports to final demand, by the rest-of—State Leontief inverse. 1This assumption will require some adjustment if the rest-of- State is small relative to the study area; the rest-of-State could be importing from the study area as well as from outside the State. 134 .3ou an muuonaa woaaaom an eo>uommua ma auauamea uoseoumm amcmmm.~ emNcec.a omammc.a nmcmaw.a ammcom.a maMMmomm .nm mammmmmmyo .eN unocoo. wwccoo. aewcoo. maccoo. mccmoo. Hmmzozomnz .mN aoomma. mmnccm. cnmmwm. neoocm. mmamnm. moa>mmmmmm .cN choao. mmcmac. emmmoo. QMmmm< .c eNamoo. maomoo. mHoDQommmm .m menamm.a mamnoa. amemmm. omcmaa. ammowe. ammoa .a auasou aa aucsoo ma aunnoo oa aussou a “ muosou m wouoom mmmum aeoum one an auumseca can menace amcam noon on muuoaaa 30H mm eauoBIHOIumou can oumumIMOIumou eo wouanaow menace amcam amuoe .ea mamuomwun uoa auauamea nonvoumm Nacmma. mmcme.N mmmcec.a amanmc.a mmcmaw.a ommcom.a maMmmumm .NN cmaooo. caNooo. aemooo. mmmooo. Nmmooo. mmmmmmmmyo .eN eoaooo. nmocoo. anomoo. waNcoo. eeacoo. moacoo. Hmmzoznmmz .mN mchao. aoowma. maoamo. ococmo. Newmmo. owemmo. moa>MMmmmm .cN omcoao. choao. ommamo. achco. Nmaamo. mmwaco. Q¢MHHmmma3 .mN mmmmoo. weNaNo. aamaoo. anamoo. mcamoo. eeNcoo. MmzMmmm< .c acaooc. emamoo. mmmooo. eowooo. omwooo. emmooo. mHoDQommmm .m aaamoa. memamm.a maocea. awanem. wmmamm. ammacm. ammua .a mumum auoooo aa auaooo ma aucsoo oa auanoo a zucaoo n acuomm mecmame amaam ou doaaaaa cam amcoauaeem an um>aame ou xUOumm>aa How wmuasamu auumseca moum xenon cu monomaa .ma mamMMmomm .NN mmmmmmmmeo .eN mmwmoo. mmmcoo. moecoo. wmmcoo. eemmoo. Hhmzoznmnz .mm moaeea. mmamam. unmamm. mccmam. Nemamm. moH>mmmmmm .cN ammoao. mammao. mammoo. ammeemmmaz .mN mnmwao. mcmmao. MmzMmmm< .c emwooc. mnmooo. maoaaommmm .m memamm.a mcnaew. NwNemc. aononm. aamcnm. nmmua .a aucsoo aa auaaoo ma auosou oa auasoo a auaaoo n nouomw muouoom wcammoooua mumumleouummu an ace meow: uuoaaa noun aenum mo coauuoa onH .wa mam¢a 137 eemame.m aamNmN.N wNaemm.~ Naamwo.m wanmwm.m mA4HOH cowaoo. nmmaoo. emmaoo. Nunaoo. enmaoo. mUH>MMmumm .nm mmmmoo. mmmaoo. NwNNoo. memmoo. wcmmoo. mmmmmmmmyo .eN mcanoo. mameoo. awONOO. nmcmoo. ecnmoo. Hhmzoznmnz .mN mmowec. ohmmac. mmmcam. emmmmm. emmcam. moa>mmmmmh .cN omemwa. nmwomo. aooeeo. emwwmo. mmaceo. nMmmm< .c oamaoo. manooo. memooo. aamooo. emmoco. wHoDQOMmmm .m o~m0we.a amwaca. canaae. Nacnoo.a ammmON. ammua .a aunsou aa auasou ma auasoo oa aucnoo a aunnou n uouoom ncnaon anaaw xooumo>aa noun ansum ea onnouoca aoaaaaa oam uooa On noun annum ou muuoaaa on one usauno mmouw anuOu ounumIMOIunou ca owanno .aa mamnfi 138 Imports required by rest-of-State industries, as a result of supporting the study area needs, were assumed to come from anywhere outside the rest-of—State area. U.S. Impacts The U.S. Leontief inverse is used in obtaining U.S. impacts in the same way that the study area Leontief inverse is used to obtain study area impacts. The final demand change vector applied to the U.S. Leontief inverse is the column vector of imports to the study area (Table 18). The column vector of imports preserves product iden- tity. The change in total gross output for the U.S., due to a $10 million increase in livestock final demand in the 7-county area, was $2.89 million compared to $2.39 million for the rest-of—State (Table 20). About $.5 million of total gross output change apparently would occur outside the State, according to the 7—county model. Value Added and Related Impacts Coefficients for man-years, value added, and employee compensa- tion, capital compensation, and business taxes were applied to total gross output to derive further impacts. The man-years coefficient is simply an output per employee ratio estimated from U.S. 1970 model data. The remaining coefficients were computed from data contained in the 1967 U.S. model published in the Survey of Current Business.l They were for 87 sectors and were aggregated before obtaining ratios to total gross output. The ratios were used for all study area models. 1U.S., Department of Commerce, Bureau of Economic Analysis, "The Input-Output Structure of the U.S. Economy, 1967," 24-56. 139 cammmm.c nmoaan.u chmNm.N eonmon.m ao~aam.~ mammmumm .nm Noomoo. mammoo. emmmoo. commoo. mammoo. mummmmmmeo .em mmmoao. amcmoo. nemmoo. mmamoo. aeaeoo. Hmmzozmmnz .mN aammnm. maccom. Nmemwe. Naanme. ameome. moa>mmmmmm .cm whoama. cmcmao. mmeomo. mmomoa. aaaomo. unmeemmmaz .mN cmmmmo. oeoamo. Nmmmmo. aommco. Ncommo. MmzMmmm< .c emNeoo. mmnmco. nemaoo. emamoo. memaoo. mHoDnommmm .m aaaemm.a ecemao.a ammaon. mmmmma.a Noaean. ammunmmmho .N eenemm. chama. Nmomma. ancocm. amcmma. nmmxooem>a .a aucsoo aa aunsoo ma aucnoo oa auasou a aunsoo n uouoom nonaoe ancae .m.: :a omcnno onu uooa ou nouasaou unnuoo mmouw anuou .m.D ca ownnno .ON mamaa ca owanno noaaaaa oam aanw n uooaeou ou nouoouuoo ouo3 muonnaa noun aesum oan eoe.a Nmu. wcm.c aua.~ mwm.u Nwm.o~ mwameo mumum mmm cmm. mom.a wme. mma.~ cwm.c owameu .m.= oom.a Nee. aew.m cwa.a cmm.e mec.aa mmwamno nauseouau uca mma. eow. mac. occ.a aau.m unease .m.= cma mma. woe. amm. -~.a mu~.N mwcmeo mumumunouumwm aae.a mma. ow~.c mma.~ ama.u ecu.o~ mwameu unasoonua oca eua. man. cmm. mac.a mNm.~ mwameo .m.a cau mcu. mmm. mmc. cka.a emm.~ mmameo monumuno-ummm aae.a mmu. cmm.c auo.~ owa.a uce.o~ mmcmno uncsoo-oa emu mum. one. mme. umw.a wok.m unease .m.= mma emu. mam. acm. cmm.a mmo.m mwamec monumIMouummm ume.a nee. maa.c mmm.a amu.e meu.ma mwameo unasooum ecu mua. ecu. mam. Nec.a Nam.~ mwameo .m.= maa uca. mme. Ncc. ma~.a wwm.~ mwameu monumunouummm aae.a owe. acm.c auo.N mmu.u amm.o~ mwcmeo suasounu unmeasze . - u ..... u - . Amuwaaoa wmaa couaaaze . ..... u I n s n " munow " noan “ coaunmaonaoo " :Oaunmnonaou u nonu< " mownnno one " mnoun annum Inns " moonamsm " anuaano “ ooaoagam " onan> " mo anuoa “ ncnaon ancam xooumo>aa ca omnouona aoaaaaa cam n Eoum wcauasmou nomnnno .aN mam " mo anuoe " @GQEMU HNGHH :ounuanoauwn uonuo: ca omnouoca coaaaas aw n aoum wnauanmou mownnso .NN mamnw 143 a total output change of only $17 million compared to the $20.38 mil- lion by livestock for the State. Summary Model results were compared for the State of Ohio and five sub- state study areas. Two of the smaller areas were completely contain- ed within a larger one, and all were contained within the State of Ohio. One study area was identical to State Planning Region 9, which contains 9 counties. Seven of the 9 counties, all except Jefferson and Belmont, are also inside the Muskingum River watershed boundaries. This 7-county area was the smallest area modeled. A lO-county area was modeled to contrast the addition of three rural, low population counties to the 7-county area. While the 9-county area was the 7-county area plus the more populous and agglomerated counties of Jefferson and Belmont, the 10-county area was comprised of the 7-county area plus the low population counties of Perry, Noble, and Morgan Counties. A l7-county area was completely contained with- in the l9-county area, which comprises the Muskingum River Basin area, recently studied by federal agencies. The two urbanized coun- ties of Medina and Summit were removed from the 19-county area to form the l7-county area. Most of the Muskingum River Basin is fairly rural in nature; therefore, the l7-county model was thought to be a more representative region for analyzing river basin impacts from projects installed in rural areas. The comparison of these models revealed that the secondary data reducing procedure used in this study was insensitive to the degree of interdependency between areas. The procedure used to reduce trans- actions or coefficients from national relationships to approximate 144 study area economic structure fails to give proper weight to agglo- meration interdependencies. This does not refer to economies of scale but to the fact that imports are not properly handled. The problem is reflected in the fact that, for the State, the direct coefficients were reduced for 14 industries; for the 7-county area, only 10 were reduced. For two industries that were reduced in both areas, the State reduction was greater. In several other indus- tries, however, the 7-county reduction was greater. The lower coefficients for larger areas stem from the relation- ship between local production and local requirements. The resulting models imply that a $10 million change in livestock final demand can cause a greater change in total gross output in the 7-county area than in the entire State. This is not consistent with reality. It is logical to expect less leakage through imports for the State than for the 7-county area. Therefore, the impact of a $10 million dollar in- crease in livestock final demand logically should be greater when analyzed with a State model compared to a substate model of only 7 counties. It is believed that procedures can be devised to overcome this failing of the secondary data reducing method used in this study. A procedure for estimating impacts of a study area output change on the rest of the State and on the nation were also presented. Pro- duct identity of imports to the study area were preserved by summing the imports matrix across the row andadding in the imports to final demand. The resulting column vector of row sums of imports became the final demand change vector to be applied to the rest-of—State and the U.S. Leontief inverses. 145 Value added and three components of value added, all of which were calculated by using their U.S. percentages of total gross out— put, were displayed for all final demand changes. Estimates of em- ployment supported by the final demand changes were obtained by apply- ing U.S. output per employee coefficients. Impacts of a $10 million change in livestock final demand and a $1 million final demand change in the "other agriculture" sector were presented. All impact results shown are tentative pending further refinement of the reducing procedure. Possible improvements are suggested in Chapter VI. CHAPTER VI SUMMARY AND RECOMMENDATIONS Introduction This study has produced a regional input-output modeling system which includes an impact analysis component. There is much work yet to be done in refining the reducing procedure to better account for comparative interdependencies among small areas. However, the system is operational and will produce models for various multi-county areas. It will also reveal the rest—of—state and rest-of—U.S. indus- tries most likely to be affected by local final demand changes. Esti- mates of output multipliers as well as Type I and Type II income multipliers can be obtained from the system. The impact on any var- iable which can be related to total gross output changes can also be estimated. The purpose of this study was to investigate the potential use- fulness of secondary data input-output models for small multicounty areas. As reported in the literature review, various tests of secon— dary data models have been made. Many researchers believe them to be adequate for some analyses and to represent tremendous cost savings over primary data models. Although discouraging conclusions have been drawn by other researchers as to their reliability, secondary data procedures do offer a possibility for relating single sector final de- mand changes to all other local sectors. It has been demonstrated 146 147 there is a definite potential for relating local area impacts to the rest of the state and nation. Primary data studies would, of course, be more desirable, but the cost and time involved in collecting data are often prohibitive. Recent publication of nationally consistent final demand and output data by state opens up new possibilities for using secondary data input-output models in interregional studies of comparative ad- vantage.1 This is an especially important field of study for the support of river basin planning and other activities which affect interregional comparative advantage. Use of Input-Output in Policy Decisions Local sponsors of specific river basin projects require evidence that projects are likely to have a net positive economic effect on the local area outweighing negative environmental effects. The water Resources Council requires that river basin plans show an analysis of the impacts of recommended projects on the national economy and on environmental quality.2 For good decisions by either group, the eva- luation of indirect effects is equally as important as the direct effects. Project action in flood control, drainage, and irrigation changes the relative production costs of agriculture among regions through their impact on yields. Changes in agricultural output have important primary and secondary effects which can only be evaluated interregionally by interdependency models. The system presented and lScheppach, State Projections of the Gross National Product, 1970, 1980. 2Water Resources Council, "Principles and Standards for Planning Water and Related Land Resources, "Federal Register, Part III. 148 evaluated (RIOM) can provide I-O models useful in estimating levels of both detrimental and enhancing environmental and monetary effects. While data for implementing the full potential of the system do not exist at present, many agencies have research underway which will contribute to meeting data needs. As suggested in Chapter IV, it may be desirable for policy ana- lyses to adjust coefficients derived by the RIOM System. U.S. aver- age technology is reflected in the initial coefficients derived by adjusting the coefficients to reflect "without project" economic struc- ture and "with project" economic structure. Studies are needed which will develop data and techniques for making such adjustments. Output of RIOM System The RIOM computer program prints out impacts of a final demand change including total gross outputs, exports, imports, value added, employee compensation, capital compensation, and business taxes. The last four elements are based on U.S. relationships obtained from the 1967 U.S. model. The impact tables of the RIOM System can easily be expanded to include a display of pollution impacts. Pollutant coefficients which are available for the same sector aggregations may be applied to total gross output changes in the same way as employee and capital compensa- tion coefficients. The model of Ohio produced both output and income multipliers that appear to be within reason with respect to the U.S. multipliers. For example, the Ohio livestock sector output multiplier was estimated 149 to be 2.04 compared to 2.35 for the U.S. The crop sector output mul- tiplier for Ohio was 1.71 compared to 1.89 for the U.S.1 The total output change required for the State to supply an ad- ditional $10 million worth of livestock products to final demand was estimated by the model to be $20.4 million. The 7-county area, accord- ing to the model, would generate $20.6 million in delivering $10 million worth of livestock to final demand. In addition to estimating total changes for the entire study area economy resulting from final demand changes, the planner can gain additional insight from secondary data models by comparing elements of each column of the Leontief inverse. For example, from the live- stock column of the Leontief inverse of the 7-county area, it may be observed that the coal mining sector will be required to deliver $12,400 to other sectors in support of the $10 million increase in livestock; the wholesale-retail sector would be required to deliver $70,000, etc. The additional value added to the State economy as a result of a $10 million increase in livestock final demand was $7.3 million. This is comprised of $2.2 million of employee compensation, $4.3 mil- lion for capital compensation, and $.75 million for business taxes. The potential employment increase supported by the livestock change is 1,606. Employment is obtained by dividing the change in total gross output by the same output per employee ratios used earlier in the RIOMS to estimate total gross outputs. Impacts presented in Chapter V must be regarded as preliminary. The results of each study area model provide insights into sector 1It should be noted that income multipliers bear a constant relationship to output multipliers. 150 linkages, import needs, and exports; however, some of the study area results are inconsistent with each other. Additional experimentation with reducing procedures should lead to refinements that will bring consistency and better impact estimates. The Reducing Procedures The reducing procedure is the core of the regional input-output modeling system. Neither of the two procedures tested in this study were entirely satisfactory. Model I, which assumed that all local final demand was met by local production, appeared to reduce some coefficients too drastically. It did not allow for any imports direct— ly to final demand but required all imports to go through the process- ing sector. This seemed too severe a limitation on the flow of products to consumers in the area. Model II was structured to allow some local final demand to be imported when there was insufficient output available from local pro- cessing sectors. This left more local output available for local processing needs in Model I and produced larger direct coefficients. Local output multipliers and impacts were larger under Model II. However, there is no completely adequate way to judge accuracy of results other than by the logic of the procedure and reasonableness of the results. No primary data studies are available for comparison for areas covered in this study. Normally, sectors of larger geographic areas are more interde- pendent than in smaller areas because of the existence of a broader range of industrial outputs. Therefore, it is expected that their in— dustrial sectors will have larger multipliers. The reasoning is that 151 less leakage will occur through imports because more inputs are avail- able locally. This neglects the possibility that the larger area may add relatively more final demand requirements than output in some sectors. The additional import requirements may increase by a propor- tionately greater amount than the inputs available within the area. The transactions cell values may increase only slightly, while total gross outlay increases by a greater amount. Total gross outlay is the divisor in computing direct coefficients; therefore, smaller coeffi- cients are obtained for the larger area. When a small study area is enlarged to include additional counties, there is a possibility that more requirements for a particu— lar product will be added than total gross output of that product. If this occurs, the reducing ratio which determines the size of the direct coefficients will be smaller for the large area than for the small area. Thus, smaller multipliers will be obtained for the large area in those sectors in which this occurs. Comparison of reducing ratios for all study areas shows that this occurred in several sectors (Table 23). The possibility also exists that the dollar amount of ab— solute transactions may be lower in the larger area as a result of the smaller reducing ratios. For example, Table 23 shows that the chemi- cal products row (sector 18) reducing ratio was 10 percent lower in the 9-county area than in the 7-county area. The transaction showing livestock purchases from the chemicals sector and the transaction showing other agriculture purchases from the chemicals sector were slightly smaller for the 9 counties than for the 7 counties. All other sector purchases from chemicals were larger for the 9-county area. 152 o.a o.a o.a o.a o.a o.a moa>MMmomm .NN o.a o.a o.a o.a o.a o.a Mmmmmmmmeo .eN meanca. NNmmca. memoca. cemmma. ceNama. mmacma. amazozamnz .mm aommem. omcmem. monamn. Nmaeam. memcae. ammooe. moa>mmmmmm .cm macaaa. aaemma. amnoma. mmamaa. o.a o.a nnmaemmmaz .mN unnamm. cammmm. aaemaa. o.a o.a o.a Mmzmmmm< .c nuamcm. cmmawe. aoemmm. o.a o.a o.a mHoDmommmm .m cmmama. mmaocm. mmmemn. emmccm. enemas. mmmeaw. ammea .a ounum auanoo aa aunsoo ma auanou oa aoanoo a auqsou n uOuoom moaunu wnaoseou noun aesum .MN mamuon auonmam moo .eeo .aauo .ea .mmuo .uuo c u ecu .auummuoe .umusuuaouuec c umo .eeo .ceo .Neo .ueo .cuo m u mouseoua anemmuou m we .ea .mauo .Nmuo .cuo .ea .Nuo .uuo N u nauseoua umuaeusuuuwm guano N awuo .ea .No .ea .mmuo .cuo .ea .mue u nauseoua can uuoeeo>uu u xenon many uom nounwouwwn on “ muonada u muonasz " oanz u .02 monoo oam nmaa " uouoom mm " mannou m auumseoa noaocom doaunwouwmn noun mesum .NI< mamna 163 eemu .ue .eeuee .ueeoueeo moanm muounuonmsnna unooxov om ae mmlom oenuu aanuou non oanmoaonz mN ec ee eu em6u>umm eueuuaee new mouuuuuus Ne eec .eecuuec ueIee eu meouueuueeaaoo um ooa>uon ecucc .Ncuoc ee euueu mesoemues eae aouueuoemaeuu om umuee .eN .ue cmnue .eeIcN .eu cu eeooe oueeuseeo: “meeo eu eeeumee Aeuee no ence mauaeum neeuxme uem omuem mu muoseoue eouuum can mucouameo mu noauumzeca eoaaan em eN Nu eem ecueeuuese .maueauue eu nauseoun oaauxou em .eNNIuNN euIeu uu emueouueme can mmuuexmu eu om cu ou nauseoue emueauu use econ eu em .eeeuuee .ee ceINe .emnee e meoow euemune emeuo cu eem .eemuuem ue .oe .ee e ucoaeuaeo aouumeuoemamuu mu moaaansm non eem .eeenuee melee e .ucmaeuaem .eumaueuma ueuuuuuoum mu aesum mane uom nounwouwwn on " muonaoc " muonaoz " oanz u .02 emeou oum eeeu m Houowe ee m eemamo m enumaeau Aeosauuaooe Nuc muncu 164 .Neue .ee< .uoeeu .muueeo wauueuum nemaaum>oo ".o.n .aouweuemmze oueo «noaumauouonunso anoooom nan anaoom anuoaou .nnmaou onu mo snousm .oouoaaoo mo unoauunaon ..m.D emm on“ afloomH amnuflwwo wflfiufifihm ufiUBGHU>OU u.U.Q efiouwfififimm3v cmm.—H .OZ GfiuwHH—am eUGw—beAOHmBm eflcgmn HNHH Ioouom .auumneaauoucHIIONaa mcoauoofioum .moaunaunum uonna mo snousm .uonna mo unoEuunnoQ ..m.D ”moounom eouasooon ma use wmaa once uouna maoeoa .m.: ca eoununnom no: ma Ace .ozv ucoanoao>oe eon nounomom .uOuoom anaea>anca nono ca uom a .annuw nacu ca noeooo no: moauumnena anaoonm oun we can mm .cm eon moauumanna mason oun mm nwsousu am nuouoon .m.D .eoms oun oooauuna mucoaoaeeooo nan mcoauonmcnuu neocowoeco one uom anaucommo muOuoon onoSu mason meaononnom mm mooa>uon anImm en am annoaunouoou eon uooacanuuounm mm Aaaem .caem unooxov em .Nm .OB mm om mooa>uoo annomuon uonuo em maoaunnaanwuo uaeouacon nan uNee .ee .ce .Ne .oe .ueme .Neeo an emumm emou>ume uncouueusem .umuueoz em u.~ee nemexme ee .ue .eeeu .ceeu .Aeeee .ee cam .uemu .ueme nemexme mu .eeuoe me .ma .ueuoe eNIeN enmeme ummu .muamuseau .muamaue cN aeoum many uom nounwouwwn on " muonenz " muonasz “ oanz " .oz monoo oam mmaa m uouoom mm " msmnou m auunoeca Anoncauaoov NI< mamuom nmouaxo ansaanu eon menouaanm ma umnee .ee .ue meoom «uneaseaoc umeuo cu mm nauseoua eoaaan eon manoaaoso ma we eeuuueeeau eeuuum can waueeuuese .wcueauue Nu mNINN nauseoun oaauxou nounoaunne eon oaauxoe aa om .mueo meoaeoue emueauu can eooe ou eeuee .Ne meooe mueeuee umeuo e um unmanasao Goaunuononnua m em moaannam eon ucoanasvo .auocanona anoauuooam 5 mm anoauuooao unooxo auoaanonz e cmumm .eu emuuueaecu annex e mNIcN nauseoua e003 nan uonasa .ounuanuom c naIma aoauosuumcoo m cuuou mauauz N aOImo .Amano uaooxov no .ao ooauonmam eon umouow .ounuanoauw< a u uoaano wwwoo UHm oano uouoom noncoo uouoom mzmooo nomaa umoaumauouonunnu oaaonoom nan anaoom anuoooo .coaunanmom mo momooo .auumsena mnmnoo an noanouw moeoo coaunoamammnao anauuoaeaa eunnanum .mI< mamnh 166 we .on mooa>uon anoonuon uonuo om mm neaononson oun>aum am enImn .mn mooa>uon uannou can nnocamom mm meINe oocnaae uocuo eon ounumo anou .ooonusona um aeIoe moaooown nanouo nan waaxnnm em am .mmIem .Nm oenuu aanuou uonuo mm mm mnoaunum ooa>uoo nan wcaaanuou oaoano> uouoz cm mm wcaaanuou owaeannouoa anuoaou mm mm moonaa wnaxcaun eon woaunm NN cm nououm auane nan auoxnn .noom am om oenuu oanmoaon3 om ac mooa>uom aunuaanm eon moauaaau: aa mc maoaunoansaaoo ma ncIcc .ac coaunuuoancnuu uonuo ma Nc weannonouns eon ooa>uom woaxosufi ea u uonaso mecca eue mama HOUUOm mDmeU HOUUOm WSwfiUU unencueaoee mI< mumcu '167 .mowoo UHm neaan oece .oeme .oeNe .oeue couumuemuauaem ouueee em am .nem .aa .aa mooa>uom ancoaonoeoun nsoonnaaoooaa eon maauoonawao .anwoa mm Anew unooxov em mdoaunnaonwuo uamouanoo eon mooamaaou .ounmaoz em cm .aNmImNm mooa>uom noueoax eon coaunoneo uonuo em NNmIaNm oun>auaIIoowoaaoo nan maoonom aunenooom .aunuaoaoam mm NNmIaNm uaoscuo>owllmowoaaoo can naoosom aunnooooo .aunuaosoam cm Aeom uaooxov om manuanmo: uaooxo mooa>uom guanom mm eoe eunuuemom mm aeImm mooa>uom anooaunouoou can unoananuuounm am uonaoa mQUOU UHm mama HOUUQW mDmGOU HOUme mfimfimU uemsauuaoUV muc mumcu APPENDIX B ESTIMATING PROCEDURE FOR HOUSEHOLD ROW TRANSACTIONS APPENDIX B Household Row Transactions This section describes the procedure for estimating a household row for the transactions matrix when it is to be closed with respect to households. For the U.S. transactions table, the U.S. employee compensation coefficient (i.e. the ratio of employee compensation to total gross outputl) is applied to U.S. total gross output. The re- sult is an initial approximation of the household row sales to each purchasing sector. The total of this row is then compared to the total of the households column (personal consumption). If they are not iden— tical, the ratio of the column total to the row total is applied to the household row transactions to inflate or deflate them sufficiently to make the row and column total equal. This adjustment ratio for the U.S. was 1.147 (Appendix Table B-l).2 The procedure for deriving the study area household row differs from the U.S. only in that imports are taken out of total gross output by sector before the employee compensation ratios are applied (Appendix Table B-2). The adjustment ratio3 for the 7—county data shown in the 1This is the ratio of employee compensation to total gross output by sector. Data to derive them were obtained from the 1967 U.S. table after aggregating that table to 27 sectors. 2 _ 463.343 _ Ratio - 4037951 - 1.147 3 _ 493.523 _ 170 table was .902163. This factor was multiplied by each element of the initial household row to deflate it to equal total personal consump- tion. . The procedure described above is believed to be acceptable on an interim basis. A special study requiring about one-half man-year would be appropriate to thoroughly investigate the data available from the Bureau of Economic Analysis and adapt it for substate study areas. In addition to the personal income represented by employee compensation, value added as used in the U.S. models contains several other items having personal income content.1 Elrod and LaFerney attempted to sepa- rate these personal income components in a 1970 study.2 Their work would be an aid in a study designed to improve the household row and column data to be used in substate study area models. 1The components of value added intfimzl967 U.S. model include: (1) compensation of employees, (2) proprietor's income, (3) rental income of persons, (4) corporate profits and inventory valuation adjustment, (5) net interest, (6) business transfer payments, (7) indirect busi- ness tax and nontax liability, and (8) capital consumption allowances. Some portion of items 2, 3, and 5 is probably used as personal income (see U.S., Department of Commerce, Bureau of Economic Analysis, "The Input-Output Structure of the U.S. Economy: 1967," p. 25). 2U.S., Department of Agriculture, Economic Research Service, Sector Income and Employment Multipliers: Their Interactions on the National Economy, by Robert H. Elrod and Preston E. LaFerney, Techni- cal Bulletin No. 1421 (Washington, D.C.: Government Printing Office, July, 1970). 171 eueuuoe eeeu e6 eaouuuuze ecm.mec mcm.mec uee.moc mummum< .c uem one eec eeo.m emm. muonaommuu .m eeo.e cce.~ eme.e cee.e~ eeN. aaeecmmmuo .N uoc.e eee.u ecu.c eee.mm emu. ameuooum>u .u nsom " noeaa u nnoaunaaxounn< u nomaa " uooaoaemooo u eaonomsom .m.D " coaunanmnoo " 30m eaonomoom " unauso nmouw “ coaunmnoaaou " uouoom nonmeme< “ ancomuom .m.D u .m.D anauaca u anuOH .m.D u ooaoaaam .m.D u .oannu coauonmonuu .m.D osu mo nasaoo eon Sou eaosoonon one uom nuno .aIm mamMMmumm .NN Nem.e eoe.n eoo.~a cma.a~ eac.a cec.mm ecm. mmmmmmmmao .eN Ncm.m oem.m emN.mm mea.mm eem.~ amm.ac mec. amazozomnz .mu ooc.om mae.mm oem.noa emn.cma amc.m mcm.mca 0mm. moa>MMmmmm .cN mmN.ee mmc.mn mmw.eoa mmc.cna mco.aa emc.mma amc. 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