Public investment criteria and idle resources: A regional analysis

SO&-LCOU.Plan. Sri. Vol. I, pp. 481-497(1968).PergamonPress.Printedin Great Britain

PUBLIC

INVESTMENT

CRITERIA

A REGIONAL ROBERT

Department

AND IDLE

RESOURCES:

ANALYSIS

HAVEMAN

of Economics, Grinnell College, Grinnell, Iowa 50112 (Received

14 December

PART

1967)

1

IN THE

post-war period, a number of empirical and theoretical analyses recommending improvements in the design and economic evaluation of public investments have been forthcoming. All of these contributions were concerned with both the nature of the “ideal” public investment criterion and the techniques for accurately estimating its constituent parameters and variables.* While all of these efforts recognized the failure of markets to produce adequate market values in evaluating some benefits, generally all accepted market prices in estimating project construction costs.? This position rested on the rationale that given full employment and markets which function as reasonably efficient allocative mechanisms, nominal prices reflect social opportunity costs.: However, even though the full employment assumption was adopted in the work of most analysts, the desirability of adjusting money costs in a severe and widespread depression was indicated by all 0bservers.s * Otto Eckstein, Water Resources Development: the Economies of Project Evaluation. Harvard University Press, Cambridge, Mass. (1958); John V. Krutilla and Otto Eckstein, Multiple Purpose River Development, Strrdies in Applied Economic Analysis. John Hopkins Press, Baltimore, Md. (1958); Roland McKean, ~Jiciency

in Government

Through Systems

Analysis:

With Emphasis on Water Resources

Development.

John Wiley, New York (1958); Jack Hirshleifer, James C. DeHaven and Jerome W. Milliman, Water Supply: Economics, Technology and Policy. University of Chicago Press, Chicago (1960); Arthur Maass, Maynard Hufschmidt, et al., Design of Water Resource Systems. Harvard University Press, Cambridge, Mass. (1962); Allen V. Kneese, The Economics of Regional Water Quality Management. Johns Hopkins Press, Baltimore, Md. (1964); Robert H. Haveman, Water Resource Investment and the Public Interest. Vanderbilt University Press, Nashville (1965); and Robert Dorfman, Measuring Benefits qf Government I!zvestmenrs. The Brookings Institution, Washington, D.C. (1965), to name the principal ones without being exhaustive, and a substantial number of journal articles. t See, for example, Eckstein, op. cit., pp. 29, 32-35; McKean, op. cit., pp. 160-162; Hirshleifer et al. op. cit., pp. 130-131. : Moreover, following Margolis’ classic demonstration that such public works expenditures are poor anti-cyclical measures, it was recognized that even though public investments were initiated in a recession, they may well be completed while the economy operates at full employment. See Julius Margolis, Public Works and Economic Stability, J. PO/it. Econ. 57, 293 (1949). $ Some analysts appear to be somewhat more amenable than others to adjusting observed market prices when faced with significant and (presumably) persistent unemployment. See Maynard Hufschmidt, Julius Margolis, John Krutilla, with Stephen Marglin, Standards and Criteria .for Formulating and Evaluating Federal Water Resource Development, Report of Panel of Consultants to the Bureau of the Budget, Washington, DC. (30 June, 1961), and especially Stephen Marglin in Maass, Hufschmidt et al., op. cit. 481

482

ROBERTHAVEMAN

Although the rationale for this position has varied among economists, essentially the same information is required to correct market costs, irrespective of viewpoint. For any particular investment the direct and indirect industrial and occupational demands imposed on the economy must be estimated and the degree of correspondence of these demands with the pattern of idle labor and capital resources ascertained, In a recent paper, a model of sectoral impacts was developed and employed in estimating the detailed occupational and industrial demands imposed on the economy by several types of public water resource investment. * These detailed sectoral estimates were treated in a national context and provided the basis for adjusting the market cost of the investments under the rather substantial unemployment conditions prevailing in the 1957-64 period. This study employs a multi-regional model and addresses the detailed occupational and industrial demands imposed on the several regions of the nation by water resource investments Iocated in each of the regions. Adjustments of market cost in this case are based on regional employment conditions, PART

2

The model presented here is a modified form of the Leonteif balanced regional model.? This model estimates the regional impact of a final demand by giving explicit recognition to the fact that the outputs of some industries travel long distances in meeting demands while the outputs of other industries circulate only regionally. It does so by grouping industries by the regional consumption-production balance of their product and employing the geographic pattern of existing industrial capacity to allocate among regions industrial demands imposed at a spatial point. In the model, presented in detail in the Appendix, all industries are divided into two groups-Local and National. Local industries are those whose regional output is equal to (or in balance with) the regional consumption of the commodities which they produce, for fairly narrowly defined regions. Balance in the production and consumption of the products of National industries is achieved only within very large regions, or nationally. It is assumed that Local industries in a region produce a quantity of output equal to the demand imposed in that region. For National industries, a demand imposed at a spatial point is allocated among the regions on the basis of the regional distribution of industry capacity, the position of the industry along the continuum from Local to (completely) National, and a set of synthetic regional preference functions.3 * Robert Haveman and John Krutilla, Unemployment, Excess Capacity, and Benefit-Cost Investment Criteria, Ret>. Icon. Statist., 49,382 and 654 ($967). This study traced each dollar of project expenditure through the chain of transactions until it became a payment to some original contributor to output. The categories of original contribution were defined as (1) employee compensation, (2) net interest, (3) capital consumption a.llowance, (4) corporate profits, (5) indirect business taxes, and (6) proprietor income and rent. Estimates of employee compensation were presented in 156 o~cllpation detail and estimates of the other categories were presented in 80 industry detail. t Wassily Leontief, et al., Studies in the Structure of the American Economy, Chapters 3 and 4. Oxford University Press, New York (1953): Walter Isard and Guy Freutel, Regional and National Product Projections and Their Interrelations, in Long-1paage i?c~omic ~r~~ec~j~~~, Vol. 16. National Bureau of Economic Research, Studies in Income and Wealth, Princeton University Press, Princeton (1954); Wassily Leontief, et af., The Economic Impact-Industrial and RegionaI-of an Arms Cut, Rev. Econ. Stufist. 47, 217 (1965). $ The following procedure is adopted for estimating the demands imposed on National industries: First, on the basis of the National character of these industries, each was placed into one of the categoriesType A, Type B, or Type C. For Type A industries, production and consumption balance only within the entire nation. The outputs of Type B and Type C industries circulate more widety than within a singte Con&wed

at bormm of mm

page

Public Investment Criteria and Idle Resources:

A Regional Analysis

483

In dealing with Type A industries, finaf demands imposed at a spatial point are allocated among regions in proportion to each region’s contribution to the national output of the industry. This relationship is depicted by the function labelled Type A in Fig. 1. For these industries no regional preference is shown. < Local Per cent of industryfinal demand reauired from region in which demand is imoosed

1oc

75

Per cent of national industrycapacity located in region in which demand is imposed FIG. I.

For Type B and Type C industries, a distinct regional preference is shown to the region within which the final demand is imposed. This preference, shown by the Type A and Type B functions in Fig. 1, is based on the proposition that demands imposed at a spatial point on industries with some regional orientation will be satisfied from within the region to a greater extent than is implied by the region’s proportion of the total national output of such industries. The extent of the regional preference within each of the industry types is a function of the proportion of the output of the industry contained in the project region.” For each of these industry types, that demand not so allocated is distributed region but substantial balance is achieved within geographic regions smaller than the entire nation. Type B industries are those lying closer to the Type A extreme of the continuum and Type C industries more closely approximate Local industries. For each category, a synthetic regional preference function was estabtished which defines the relationship between the relative concentration of the industry in a region and the per cent of the regionally imposed final demand for the mdustry’s products which is assumed to be supplied from within the region. They are shown in Fig. 1. * The Type B and Type C functions are clearly jud~ental in character. There is no empirical evidence available to indicate what form they should take or even how many there should be. Nevertheless, these functions do give expficit recognition to the fact that most industries are neither purely local nor purely nationai-that most industries do demonstrate some regional preference in supplying demands imposed at a spatial point. it should be noted that, like the intermediate functions, the extreme functions (Type A and Local) employed by Leontief are also judgmental and incapable of empirical verification. This is true even though the classification of the industries does have an empirical basis.

ROBERTHAVEMAN

451

among the remaining regions on the basis of each region’s contribution to national industry output. For Local industries, regional preference is assumed complete and the entire final project demand for the output of these industries is assigned to the region wherein the project is constructed. The indirect demands on Local industries are, likewise, supplied by industry capacity within the region from which the second, third, etc. round demand arises. With reference to the equations presented in the Appendix, the model proceeds sequentially as follows: Using as basic data the detailed final project demand for material equipment, and supplies, the gross industrial requirements are estimated by accounting for the inter-industry demands imposed by production sectors on each other [equation (l)]. Through equation (2), the gross output of the Type A industries is distributed among the regions on the basis of the geographic distribution of each industry’s capacity. In equations (3), (4), and (5), the final demand of the Type B industries is allocated to the region of final demand imposition by the regional preference function, the remainder of the gross output of these industries is distributed among the regions on the basis of the geographic distribution of each industry’s capacity, and the resulting allocations are aggregated to yield the regional distribution of total Type B industry gross outputs. Equations (6-8) perform the same function for Type C industries. The total demand imposed on a Local industry equals the final demand for the industry’s output imposed in the region of project construction plus the Local industry outputs required by National industry production in each region. These demands are estimated in equations (9) and (IO). In equation (II), the gross outputs of the Local industries are estimated by accounting for Local inter-industry requirements. Equations (12) and (13) translate the gross outputs of all of the industries, regionally distributed, into the regional distribution of off-site labor requirements, by occupation. In equations (14) and (15), the regionally distributed off-site labor costs associated with the occupational demands secured in equation (13) are estimated, adjusted, and then added to the on-site occupational labor costs (which are allocated to the region of final demand imposition) to yield the occupational labor costs for each region. Equation (16) breaks out the non-labor components of value added, by industry. PART

3

Data requirements for implementation of the model are of two basic types: data inputs intrinsic to the model itself and data inputs peculiar to the final expenditure to be analyzed. In the first category are (1) the coefficients describing the inter-industry relationships of the economy (matrix A), (2) the coefficients describing the composition of occupational requirements within each industry (matrix R), (3) the coefficients describing the fraction of a National industry’s output produced in each region (matrix H), and (4) the coefficients relating the components of value added to gross output for each industry (matrix C). In the second category are (1) the detailed final demands for material, equipment, and supply inputs (vector f*) and (2) the on-site employee compensation payments by occupation (vector i,). The input-output coefficients used in the analysis (matrix A) are those estimated in the recent

82-order

input-output

matrix

of the Office

of Business

Economics

of the U.S.

* Morris R. Goldman, Martin L. Marimont, and Beatrice N. Vaccara, The Inter-Industry Structure of the United States, A Report on the 1958 Input-Output Study, Sure. Curr. Business 45, 13 (1965); and National Economics Division Staff, The Transactions Table of the 1958 Input-Output Study and Revised Direct and Total Requirements Data, Suw. Cwr. Business 45, 33 (1965).

Public Investment

Criteria and Idle Resources:

A Regional Analysis

485

Department of Commerce.* The coefficients employed to describe the occupational structure within each industry (matrix B) are those contained in a 1960 occupation-byindustry employment matrix constructed by the Bureau of Labor Statistics of the U.S. Department of Labor. This matrix shows the distribution of total national employment to 137 production sectors and 156 occupations.* The regional distribution coefficients for the National industries (matrix H) were, in large part, calculated from coefficients prepared by the Harvard Economic Research Project.+ Supplementary estimates were calculated directly from published governmental data.: The final data set intrinsic to the model-the ratios of the components of value added to gross outputfor each industry(matrix C)-was secured by placing the 1958 value of the componentsforeach industry as numeratorover thegross industry output. Thesum of these ratios within an industry equals the ratio of value added to gross output for that industry. 9 The data inputs peculiar to the analysis of water resource investment expenditures consist of an exhaustive breakdown of all dollar costs into on-site labor costs by detailed occupation (vector i,) and material, equipment, and supply costs by 4-digit SIC categories (vectorf*). From the latter data a bill of final demand was constructed for each project type by aggregating the SIC breakdown into the 82 industries of the 1958 input-output matrix. In the study, twelve project types were distinguished representing some $326 million of contract cost. /’ In implementing the model, the Local-National segregation used by Leontief et al. in the analysis of defense expenditures was adopted.7 Of the 80 industries whose outputs were * The ratios in the matrix were latter stage although preliminary estimates and have not yet been published. When the employment matrix enters the model, 1958 industry dollar values arc transformed to 1960 industry man-year labor requirements by applying a set of factors prepared by the Bureau of Labor Statistics expressing 1960 industry employment in man-years per 1958 dollar of industry output. While the gross output data from the input-output computation are in 82 industry detail, the occupation-industry matrix contains 137 industrial sectors. Two possibilities existed to secure conformability: the occupation-industry matrix could be aggregated to 82 sectors or the gross output data could be expa.nded to 137 sectors. The latter alternative was chosen. First, the final demand was assigned to the appropriate occupation-industry matrix sector on the basis of the 4-digit SIC classification attached to it. Second, the remainder of the gross output was distributed among the relevant occupation-industry sectors in proportion to the distribution of national employment among these industries. In the model the symbol N defines either the 82 or the 137 sector breakdown, depending on the stage of the analysis. t Leontief, et al., The Economic Impact-Industrial and Regional-of an Arms Cut, op. cit., pp. 233-234. 3 U.S. Department of Commerce, Census of‘ Manu/acturers, 1958. Government Printing Office, Washington, D.C. These data are available from the author. 4 The ratios of total value added to gross output, by industry, were obtained from the 1958 input-output study. See Morris R. Goldman, Martin L. Marimont, and Beatrice N. Vaccara, op, cit. 1958 industry data on employee compensation, capital consumption charges, and corporate profits were obtained from the Office of Business Economics. Similar data on the remaining components of value added were estimated from material in Martin L. Marimont. GNP by Maior Industries. Sure. Curr. Bwinexs 42. 6 (1962). In the component data obtained from both sources, the number of detailed industries is less than the number of industries in the input-output matrix. For those input-output industries which were subindustries of the more grossly defined industries in the value-added-component data, the ratios of the 19% value added component (e.g. employee compensation) to 1958 value added for the entire industry were assigned to each of the sub-industries. In those cases in which the value added components failed to sum to the total industry value added published in the 1958 input-output study, indirect business taxes were estimated as residuals. IIThese data were obtained from the Division of Productivity and Technological Developments of the Bureau of Labor Statistics, the Bureau of Reclamation, and the Corps of Engineers. See U.S. Department of Labor, Bureau of Labor Statistics, Labor and Material Requirements for Civil Works Constructed by the Corps of Engineers, Bulletin No. 1390, March (1964). For estimation procedures used by the agencies in obtaining these data, see Haveman and Krutilla, 0~. cit., p. 358. 7 See Leonteif, ef a/., The Economic Impact-Industrial and Regional-of an Arms Cut, op. cit.

486

ROBERTHAVEMAN

allocable, 61 were defined as National and 19 as Local. * The further separation of the National industries into Types A, B, and C was based on evidence regarding the extent to which the production and consumption of the outputs of the industries balance within different size regions.? In general, the division of National industries was guided by the rather natural breaks in the empirical continuum of industries from Local to Type A. The number of industries of Types A, B, and C are 4, 25, and 32, respectively. In the analysis, the lo-region breakdown described in Fig. 2 was employed. PART

4

Integrating the primary data inputs into the model yields a detailed breakdown of the industrial and occupational demands imposed on each of the 10 regions by each of 12 water resource project types. In the following tables, several aspects of this breakdown are presented. For comparative purposes, the inter-regional gross output patterns for a final demand of the composition of the Gross National Product are also shown. Table 1 exemplifies the regional breakdown of gross output and total labor demands for a single project type (the Large Multi-purpose Project) and GNP: when the final demand created by each is assumed to be imposed on one region (the Lower Atlantic Region).§ The top section of the table shows the industrial breakdown of gross output requirements as defined by matrix G*, of the model. Of the $1032 gross output generated by the final demand of this project, $300 (29 per cent) is supplied from industry capacity in the Lower Atlantic region, of which nearly two-thirds occurs in the Local Trade, Transportation and Service industries. Recause of the heavy concentration of the durable goods industries in Regions II and III, over 40 per cent of total gross output demands are supplied by these regions. The GNP benchmark data present a significant contrast with the project data. The different pattern of industrial demands of these two bills of goods causes a substantial disparity in regional impacts. While the project favors the durable goods producing regions relative to the region of demand imposition, the GNP vector, with its concentration on Local industry sectors, favors the region in which the bill of goods is demanded. These patterns are still more noticeable when individual industry groupings are analyzed. In the second section of the table, the total occupational impact (both on- and off-site) for both the project and GNP is shown (again assuming that the final bills of goods are imposed on the Lower Atlantic Region). Of the total labor cost $719 for the public project, * Industry 80 in the O.B.E. input-output study is the import sector. Industry I1 is the New Construction industry sector and is treated as a final demand sector in this study. t This evidence is shown in Walter Isard’s Chapter 5 of Leonteif, et al., Studies in the Structure of the American Economy, op. cit. The allocation of the industries into the four categories is available from the author. $ In implementing the GNP vector for benchmark purposes, the final output demand vector used was just sufficient in size to yield a sum of gross outputs equal to that of the Large Multi-purpose project, i.e. $1032. While both final demand vectors generated $1032 in gross industrial output, the sumof final demands of the project vector was $5 14, while the GNP vector summed across industries to $523. The composition of the benchmark vector differs from the composition of the GNP in one significant way. In the benchmark vector, the final demand for the New Construction industry was eliminated. Because it is a New Construction expenditure which is being compared with a more general pattern of final demand, this exclusion was judged appropriate. 5 While Table 1 presents the industrial breakdown in 16 industry detail and the labor cost breakdown in I8 occupation detail for only one project type constructed in only one of the regions, the statistical results of the model are in 82 industry and 156 occupation detail for 12 project types each one of which is assumed constructed sequentially in each of the 10 regions.

Public Investment

Criteria and ldle Resources:

A Regional Analysis

487

488

ROBERT HAVEMAN

73 per cent ($527) was allocated to Region VI of which four-fifths was attributable to on-site labor. As implied in the first part of the table, Regions I1 and III supply the bulk of the off-site labor demands not retained; no other region supplies more than 3 per cent of the total labor demanded by the project. It should be noted that the occupational demands retained in Region VI vary significantly about the 73 per cent figure for total labor costs. Again the GNP data differ markedly from the project data.* Of significance is the fact that the gross output generated by the project generates nearly 20 per cent more labor cost ($303) than does the equivalent gross output generated by GNP ($2.57): the project tends to draw on industries which are more labor intensive than does the GNP. This notwithstandjng, the GNP vector concentrates larger demands on the region of demand imposition (VI) than does the project. Substantial differences in the pattern of occupational demands and the pattern of impacts on other regions between the two vectors are noted. In Table 2, five representative project types and GNP are compared with respect to the industrial and occupational impacts which they have on one of the 10 regions (VI) in which the demand is assumed to be imposed. In each case, the Mining, Transportation, Trade, and Service industries (all Type C or Local) account for over two-thirds of the total gross output retained in the region. For the GNP vector, these sectors account for SO per cent of such retained outputs. While from 24 to 32 per cent of total gross output generated by water project construction is retained in the region, nearly 45 per cent of the GNP gross output is so retained. Of significance in the second part of the table is the wide disparity among project types in the pattern of occupational demands imposed on the region of final demand imposition. While the total labor impact from project const~ction varies from $425 to $525, the highest regional impact on both Craftsmen and Operatives is about three times the lowest. Tables 3 and 4 show the gross outputs and total labor cost allocated to each of the regions both when each is the region of project construction and when project construction is shifted to other regions. These tables focus both on the differences among projects and among regions. Two primary phenomena can be seen from the tables. First, while some of the project types are closely tied to the regional economy in which they are constructed (Pile Dikes, Revetments), others “export” their demands far from the construction site (Powerhouse Construction). For example, the median percentage of gross output retained was $615 for Revetments and $195 for Powerhouse Construction. The geographic concentration of the durable goods industries largely explains this phenomenon. Second, some regions are able to retain a larger proportion of the generated gross output and labor demands than are other regions because of the structure of their productive capacity. This pattern is seen in the last column of both tables. Also shown in the two tables is the variation in the impact on a single region from project construction of various types in other regions. For any given project type in any region, the maximum output and labor impact is typically from 30 to 60 per cent above the minimum. When project type is free to vary, the maximum output and labor demands are typically twice the minimum. * In comparing the structure of occupational demands imposed by the two final demand types, the GNP pattern must be contrasted with the off-site figures in the Lower Atlantic Region column and in the final column. In the computations for the GNP vector, the final demand, gross output, and occupational demand estimated were designed to be comparable with the project final demand, gross output, and, hence, off-site labor demands.

Public Investment

Criteria and Idle Resources: A Regional Analysis PART

489

5

Having identified the pattern of industrial and occupational demands imposed by the various types of public water investments, the question of the correspondence of nominal In a fully employed economy, project contract to opportunity costs can be addressed. costs represent opportunity returns foregone at the margin. With unemployment, however, labor drawn from the idle pool has no comparable opportunity cost.* Similarly, the opportunity rate of return on otherwise idle capital drawn into use by project construction is zero. However, because capital services are largely storeable, depreciation charges are a real cost properly imputed to project construction even when otherwise idle industrial capacity is drawn into use. Accepting the data on the regional, occupational, and industrial breakdown of the value-added components of project construction costs, we shall modify the employee compensation and corporate profits plus net interest val-ues to the extent that the units of labor and capital represented would have been otherwise idle. The capital consumption allowance will be maintained as an estimate of the social cost of capital use even in the presence of unused capacity. The remaining value-added components will be assumed to draw labor and capital in a pattern similar to the pattern traced and will, therefore, be adjusted in the same direction and to the same extent as the sum of the traceable labor and capital costs. In estimating the extent to which any labor and capital demand employs otherwise unused resources, it is assumed that the levels of occupational unemployment and industrial While, for example, an increase in the demand excess capacity are significant variables. for labor at low levels of unemployment will simply shift workers among jobs without reducing unemployment below the frictional minimum, as the rate of unemployment rises so too does the probability that the incremental demand will hire otherwise unemployed labor. In the absence of existing knowledge on the pattern of labor and capital market response, we offer a set of synthetic response functions relating the probability that a given increment in the demand for labor and capital will be drawn from otherwise unemployed resources to the level of occupational unemployment and industrial excess capacity. In Figs. 3a and 3b alternative linear and semi-logarithmic labor response functions are shown. Fig. 4 pictures alternative response functions for capital. In Figs. 3a and 3b, the intercepts on the abcissa (vf) are defined by the national unemployment rate experienced by each occupational group in 1953-the most recent year in which the economy was fully employed. The probability becomes unity at I’ = r,, = 0.25, the rate of unemployment existing at the height of the Great Depression. It is assumed all would agree that increments to the demand for labor are satisfied with no displacement of alternative outputs under the latter set of economic conditions. The response functions pictured in Fig. 4 intercept the abcissa at a very low level of excess capacity and reach unitary probability at a rate of unutilized capacity (Y) of 0.55. This benchmark again refers to conditions at the height of the Great Depression.? Because of the expected behavior of industrial markets, the semi-logarithmic capital response function reflects a greater probability of involving idle capacity at lower levels of unutilized capacity than do the analogous labor response functions. For both labor and capital, the linear functions are * Implicit is the position that involuntary leisure has a zero benefit. t See Donald C. Streever, Capacity Utilization and Business Incestment; pp. 40 and 64. University of Illinois Bureau of Economic and Business Research, Urbana (1960). Full capacity is defined as the preferred operating rate.

ROBERT HAVEMAN

490

Probability of drawing from idle pool

1.c

*7!

A

Professional, technical. and kindred;Managers officialsand proprietors

A

Farmers and farm workersClericaland kindredSales workers>

A Craftsmen,foremen end kindred

k

Operativeand kindred Serviceworkers

I

Unemployment rate Rci.

3a.

- o-

I’

Probability of drawing from idle pool

Rofessiolfal, kindred;Nanagers, and proprietors

5-

Farmersand farm workers Clericaland kindred

LSales

-5O-

workers

Craftsmen,foreman and kindred Operativeand kindred

-2S-

Serviceworkers

0,

0 r

unemployment rate FIG.3b.

.In

Public Investment Criteria and Idle Resources:

A Regional Analysis

491

Probability 10 0 of drawing from idle pool

‘n

Rate of unutilized capacity FIG. 4.

assumed to be the minimum boL~llda~ between the rate of ~~nemploymcnt and the probability of drawing factor services from idle pools. Assuming the detailed industry and occupation employment conditions which prevailed in the 10 regions in 1960, what sort of adjustments to nominal contract costs are required? In Table 5, estimates of shadow (opportunity) cost as a per cent of contract cost are shown for 5 representative project types constructed in each of the 10 regions.* While variation in the required cost adjustment exists among project types, the variation in adjustment for a single project type as its geographic location changes is * In adjusting capital costs, national industrial utilization rates were utilized. These rates were the mean of the two least extreme estimates,

by industry, obtained from the Wharton School Econometrics Unit, the National Industrial Conference Board, McGraw-Hill, and Bert G. Hickman for 1960. See Daniel Creamer, Capital Expansion and Capacity in Post-War kfunufucturing, Studies in Business Economics, No. 72. National Industrial Conference Board, New York (1961); U.S. Congress, Joint Economic Committee, on. and Bert G. Hickman, Investmenr Demand and U.S. Growth. The Brookings Institution. Wash, cit.: ington (1965). The NICB, McGraw-Hill and Hickman estimates were adjusted to assure analytical comparability. In adjusting labor costs, the following procedure was followed: First, one state in each region was designated as the site of project construction and all of the on-site Iabor costs were assigned to that state. These states are Massachusetts, Pennsylvania, Indiana, Iowa, Georgia, West Virginia, Kentucky, Texas, Colorado, and California for Regions 1 through X, respectively. The adjustment to on-site labor costs was then based upon the detailed occupationa unemployment rates for the appropriate state. These rates were calculated from U.S. Department of Commerce, U.S. Bureau of the Census, U.S. Census of Population, 1960, Detailed Characteristics, by State. U.S. Government Printing Office, Washington, DC. (1963). Second, off-site labor demands were allocated among the regions according to the regional allocation rules cited. The adjustment to these costs was based on the detailed occupational unemployment rates for each of the regions (calculated from ibid.). The remaining (non-traceable) costs for any project type were adjusted by applying to them the ratio of shadow labor plus capital opportunity costs to money labor plus capital costs of the traceable cost components.

D

492

ROBERTHAVEMAN

substantially more significant. In no case does the range for the latter variation fail to exceed 13 percentage points. The influence of geographic unemployment on required cost adjustment is clearly seen by comparing the cost adjustments and weighted average unemployment rates for projects constructed in the high unemployment Lower Atlantic Region with similar data for project construction in other regions. For every project type, the cost adjustment required for construction in this region is at least 9 percentage points below the median adjustment for all regions. It should also be noted that, of the 50 weighted unemployment rates shown in the table, only 6 are less than or equal to the rate of national unemployment for the relevant period. Moreover, 16 of the 50 cases show rates in excess of 7.0 per cent and one rate (10.4) is twice that of the national unemployment rate. The employment reducing potential of this form of public investment relative to, say, an equivalent increase in demand of the composition of GNP is evident. On the basis of this data we suggest that the opportunity cost of project construction in 1960-and by inference from 1957 to 1964-is between 50 and 90 per cent of nominal cost depending upon project type, the region of construction, and the synthetic response function chosen. Hence, even under our most conservative assumptions concerning the behavior of factor markets, water resource projects bearing an unacceptable benefit-cost ratio of from 0.75 :I to 0.99:1 when evaluated under full employment assumptions are deemed efficient given the pattern of unemployment existing in 1960.

PART

6

In this paper, the regional distribution of occupational and industrial demands imposed on the economy by public water resource investments located in any region was estimated and a basis for adjusting the money costs of project construction in periods or regions of less than full employment was developed. From this discussion, it should not necessarily be concluded that every water resource project which has been rejected because of inadequate benefit-cost ratios should be undertaken when the unemployment rate rises above 4 per cent. The conclusion to be drawn is that there is now an operational model and a computer program by which to re-evaluate projects in terms of their opportunity costs when regional or national unemployment rates Moreover, to avoid biasing public expenditures in the depart from frictional minima. direction of a single program, all public investments (including tax cuts) should be similarly analyzed to determine what, if any, differences exist among them. To be sure, only through substituting social opportunity costs for nominal contract costs in the investment criterion can public decision-makers isolate expenditures which are both intrinsically economic and Through the use of this model, more discriminating substantial employment generators. judgment can be applied to public investment policy in general and especially public investment policy in the chronically depressed, high unemployment, and declining areas of the nation.

Acknowledgemenr-The author financial support and to Blair helpful comments on an earlier sions and insights and Robert tational aspects of the study.

is indebted to the Brookings Institution and Resources for the Future for T. Bower, Robert K. Davis, J. Charles Headley and Jack L. Knetsch for draft of this paper. Special thanks are due John Krutilla for helpful discusM. Steinberg for very generous assistance in the programming and compu-

433

The multi-regional model described here contains 2 occupational categories and N industries. Each industry produces a homogeneous output by combining factor inputs with purchased inputs from other industries. The industries are divided into Type A of which there are a, Type B of which there are b, Type C, of which there are c, and Local of which there are d. (a + b + c + d = N). Each of these industries and occupations are present in each of S regions of the country. In the following notational glossary, capital letters (other than Z, S, and N) represent matrices and lower case letters (other than a, b, c, and d) represent vectors or scalars. Matrix and vector dimensions are stated in parenthesis. s-designation

of any one of the S individual

regions.

-column vector (N x 1) of the gross output the fina demand, partitioned into:

level of each industry

required

ga -column

vector (a x 1) of the gross output

level of the Type A industries,

gB --column

vector (b x 1) of the gross output

Level of the Type B industries,

gv -column

vector (c x I) of the gross output

ievet of the Type C industries,

gs --column

vector (d x 1) of the gross output

Ievef of the Local industries.

&-diagonal diagonal. & -diagonal diagonal. .&-diagonal diagonal.

f’=

,f,

matrix matrix matrix

(a x a) with

the vector

(b x b) with the vector (c x c) with

the vector

elements elements elements

by

and

of g, entered

on the principal

of g@ entered

on the principal

of gr entered

on the principal

-column vector {N x 1) of the final demand supplies, by industry, partitioned into :

for materials,

equipment,

and

-column vector (n x 1) of the final demand supplies for Type A industries,

for materials,

equipment,

and

for materials,

equipment,

and

demand

for materials,

equipment,

and

vector (d x 1) of the frnaf demand for Local industries.

for materials,

equipment,

and

fP -column supplies

vector (b x 1) of the final demand for Type B industries,

fY -column vector (c x 1) of the final supplies for Type C industries, and

,fs --column supplies

494 r”p

ROBERT HAVEMAN

-diagonal

matrix (b

‘,h -diagonal

G; =

x

h)

with the vector elements of,& entered on the principal

matrix (c x c) with the vector elements

offY entered on the principal

diagonal. diagonal.

gp” -rectangular matrix (N x S) each column of which shows the gross output s required of each industry in a particular region, partitioned into: g,

OS -rectangular

matrix (a x S) each column of which shows levels of all Type A industries in one particular region,

the gross

output

gi -rectangular matrix (b x S) each column of which shows levels of all Type B industries in one particular region,

the gross

output

g,” -rectangular matrix (c x S) each column of which shows levels of all Type C industries in one particular region, and

the gross

output

ha

gi -rectangular matrix (n x S) each column of which shows the gross output of all Local industries in a particular region.

level

- _ H=

-rectangular describes produced _ _

4

Hy

matrix [(a + b + c) x S] of coefficients each column of which the fraction of the total output of each of the national industries in one of the S regions, partitioned into:

HCI

-rectangular describes industries

matrix (a x S) of coefficients each column of which (Hy8) the fraction of the total national output of each of the Type A produced in one of the S regions,

6

-rectangular describes industries

matrix (b x S) of coefficients each column of which (H& the fraction of the total national output of each of the Type B produced in one of the S regions, and

%

-rectangular describes industries

matrix (c x S) of coefficients the fraction of the total national produced in one of the S regions.

each column of which (Hys) output of each of the Type C

u

-the regional preference function in the form of a scaler applied to the Type B industry regional distribution coefficients of the region wherein the project is constructed.

V

-the regional preference function in the form of a scaler applied to the Type C industry regional distribution coefficients of the region wherein the project is constructed.

ks, -column vector (b x 1) of the final demand of Type B industries allocated region wherein the project is constructed because of regional preference.

to the

k,, -column vector (c x 1) of the final demand of Type C industries allocated region wherein the project is constructed because of regional preference.

to the

/zBs -diagonal ,& -diagonal diagonal.

matrix (h x b) with the vector elements matrix

(c x c) with the vector

of kps entered

elements

on the main diagonal.

of k,, entered

on the principal

Public Investment

Criteria and Idle Resources:

A Regional Analysis

495

Ri -rectangular industries

matrix (b x S) each column of which shows the gross output of Type B not assigned to the project region allocated to one particular region.

R: -rectangular industries

matrix (c x S) each column of which shows the gross output of Type C not assigned to the project region allocated to one particular region.

Ma,---rectangular matrix null vectors.

(h x S) with the .yth column

= kDs and the remaining

columns

MY,--rectangular matrix null vectors.

(c x S) with the k~thcolumn

= k,,

columns

&,-rectangular matrix [cl x (a + b + c)] of input-output from Local to National industries. A,,-square matrix (d x d) of input-output Local industries. L,

coefficients

and the remaining coefficients

describing

describing

flows

flows from Local to

-rectangular matrix (d x S) each column of which shows the final demands imposed on the Local industries of a particular region by the National industries in that region.

Fas -rectangular matrix (d x S) with the .ythcolumn containing the final demands imposed by the project on the Local industries wherein the project is located and the remaining columns null vectors. L;

-rectangular matrix (n x S) each column of which shows the total final demands levied on the Local industries of a particular region due to project construction.

d,

-rectangular matrix (N x S) each column of which requirements for a particular region, by industry.

E

-diagonal diagonal.

matrix

(N x N)

with

man-yr-output

shows the total

ratios

MS-rectangular matrix (2 x S) each column of which requirements for a particular region, by occupation.

entered

shows

man-hr

on

the

the total

labor

principal

man-hr

labor

B

-rectangular matrix (Z x N) each column of which contains labor defining the volume of man-yr occupational requirements per man-year labor requirements for one particular industry.

if

-rectangular matrix (Z x S) each column of which shows the employee compensation generated in each occupational category by the final demand for materials, supplies, and equipment for a particular region.

A

-square matrix industries.

W -diagonal entered

(N x N) of input-output

matrix (Z x Z) with adjusted on the principal diagonal.

coefficients average

annual

of all National wage and

coefficients of industry

and

salary

Local income

matrix (Z x S) with the sth column containing the occupational on-site 12s -rectangular labor cost which is assigned to the region wherein the project is constructed and the remaining columns null vectors. .* matrix (Z x S) each column of which shows the total employee compen1s -rectangular sation generated in each occupational category for a particular region. G* -diagonal principal

matrix (N x N) with the gross output diagonal.

level of each industry

entered

on the

ROBERT HAVEMAN

496

C

-rectangular matrix (N x 5) each column of which contains the ratios of non-labor value added components (respectively, net interest, capital consumption allowance, indirect business taxes, corporate profits, and proprietor and rental income) to gross output, by industry.

D

-rectangular matrix (N x 5) of non-labor final demand, by industry.

value-added

components

generated

by the

The function of this intra-national model is the distribution of the gross industrial and occupational demands generated by project construction among the regions of the country according to the regional preference properties already noted. It will be recalled that gross output by industry sector equals the product of the final demand for materials, equipment, and supplies, by industry, and the inverse of the inter-industry technical coefficient matrix.

g*=(I-&l.f* The gross output regions according the region.

(1)

of the truly National or Type A industries to the proportion of the industry’s national

is distributed among the S output which is supplied by

(2)

g,” = .k * ffct A portion of the final demand of the Type B industries the project is constructed on the basis of the appropriate j- . (I&

is allocated to the region wherein regional preference function.

* 2.4)= k,,

(3)

whens=l,2,...S The non-allocated portion of the gross outputs of Type B industries is distributed the S regions on the basis of Type A regional distribution coefficients. * * (gs - kss) * f& = R;

among

(4)

The regional preference shown to the region wherein the project is constructed is then added to the appropriate regional output vectors obtained in (4) to yield the entire regional distribution of Type B gross outputs. R; + A,& = g;

(5)

The gross outputs of Type C industries are allocated among the S regions through the same allocation procedure shown in equations (3), (4) and (5). The Type C industry preference function (v) is substituted for (u). j; * (E&s * v> = k,,

(6)

(& - ,&s>* H = R,,

(7)

R,

(8)

+ MYs = g.:

The Local industry outputs required in each of the S regions to satisfy the production requirements of the National industry outputs in each region is defined by the product of the National industry gross outputs in each region and the technical coefficients describing flows from Local to National industries.

Public Investment

Criteria and Idle Resources:

A Regional Analysis

497

(9)

The final demand imposed on the Local industries in each region equals the required outputs obtained in equation (9) plus the direct final demand levied by the project on the Local industries in the project region. L, + F,, = L;

(10)

The gross output of the Local industries in each region is the product of the Local industry final demands and the inverse of the Local-to-Local technical coefficient matrix. (I -- A,,)-’

. L; = &

(11)

The total man-year labor requirements for any region required by the final demand for materials, equipment, and supplies, by industry, is obtained by multiplying the regionally distributed gross outputs of each industry by the man-yr-output ratios for each industry. 11, = E . G;

(12)

The occupational breakdown of these labor requirements, by region, is defined by the product of the industry breakdown obtained in (12) and the occupation-by-industry matrix. M,=B.d,

(13)

The adjusted occupational employee compensation generated by the final demand for materials, equipment, and supplies, by region, is the product of the adjusted average annual occupational wage and salary income estimates and the regional man-hr labor requirements, by occupation, derived in (13). I,.s = W.M,

(14)

The total occupational labor income generated by the project, both on- and off-site, by region, is obtained by adding the on-site occupational labor income assigned to the region wherein the project is constructed to the regional distribution of off-site occupational income generated by the final demand for materials, equipment, and supplies. .* _.s . 1s - 11 + 12s (15) Represented in Gi and i& then, is the regional breakdown of both the gross outputs by industry and the total labor costs by occupation. The value of the non-labor valueadded components generated by the final demand for materials, equipment, and supplies by industry are the product of the gross industrial outputs and the appropriate valueadded-component-to-gross-output ratios. D = G*- C

(16)