The Web Book of Regional Science  

6 The Frontiers of Input-Output Analysis



The static, open input-output model discussed in preceding chapters is a flexible analytical tool. It can be "opened" or "closed" to varying degrees; the sectors can be highly aggregated or disaggregated, depending upon its purpose; and the model can be applied to local communities, a region, groups of regions, or to a national economy. As it stands, the model is widely used for short-run forecasting, economic planning, and the analysis of economic development.


The spread of input-output analysis has been accompanied by statistical and conceptual refinements. Some of these may be illustrated by comparing the two tables published thus far for the United States. The 50-sector 1947 table, published by the Bureau of Labor Statistics in 1952, was conceptually related to the nation's income and product accounts. But there was a significant statistical discrepancy between the Gross National Product derived from this table and the GNP as measured by the U. S. Department of Commerce. This discrepancy was eliminated in the 86-sector 1958 table, published in 1964 by the Office of Business Economics. The latter table is fully integrated with the national income and product accounts. In addition to interindustry transactions, the 1958 table shows the amounts of income, by type, originating in each of the 86 sectors. These refinements add to the usefulness of the table for market analysis. They will also permit more accurate measurement of the direct and indirect impacts on the economy of major changes in either the public or the private sector.


The relatively short history of input-output economics has been one of continuing research. Much of this research has been centered at the Harvard Economic Research Project.1 Other economists in this country have conducted input-output research on a smaller scale, however, particularly those who have been involved in the construction of regional and interregional input-output systems. As this is written there is a major effort in the United States to construct a model to be used for long-run forecasting purposes. This effort will be discussed briefly in a later section of this chapter. Finally, as noted in the preceding chapter, there has been a great deal of input-output research in other countries, both those which have free-market economies and those which engage in varying degrees of economic planning. In brief, while the usefulness of the static, open input-output model has been amply demonstrated, even the most ardent devotee of this method would not claim that input-output economics is a fully developed branch of econometrics. In this chapter we will review briefly some of the recent advances in input-output research and touch upon some areas still in the early stages of development.


The static, open model discussed in this book is based upon current flows only, and it assumes fixed technical coefficients. From the beginning of input-output analysis some economists have been critical of these limitations. Others have criticized the static model because it does not allow for substitution among the factors of production, and some have questioned the practice of aggregating unlike firms, often producing unlike products, into "industries" or "sectors."2

Some economists who have expressed skepticism about input-output analysis have based their criticism upon departures from conventional economic theory. The assumption of fixed technical coefficients is another way of stating proportionality (or near-proportionality) in the production process. In the jargon of economic theory this is referred to as constant returns to scale.3 It has been argued that while constant returns to scale might be found in some industries, in others we should expect to observe increasing or decreasing returns to scale. The static input-output model assumes constant returns to scale for all sectors, however, and it is this which has disturbed some critics. As Evans and Hoffenberg have pointed out, however, "the question as to proportionality, linearity or nonlinearity is not properly conceptual, but rather a subject for empirical investigation and an appeal to facts. The point is stressed because the assumption of proportionality and the interindustry relations approach have been sometimes discussed as if they were necessarily related; in fact, they are largely independent."4

Few economists have been critical of the input-output technique when it is used for describing the structure of an economy at a given time. What the critics have questioned is the usefulness of input-output as a predictive device. Milton Friedman has stated this point of view as follows: ". . . I want to emphasize at the outset the distinction between the input-output table, regarded as a statistical description of certain features of the economy, and input-output analysis, regarded as a means of predicting the consequences of changes in circumstances."5 But as noted in earlier chapters, input-output techniques have been used for making projections both in the United States and in other countries. How have these projections compared with those made by other methods? Before answering this question a few comments on the general problem of forecasting in a free-market economy are in order.

In unplanned economies all forecasts or projections are subject to a certain margin of error. This is partly because of the built-in uncertainties inherent in free-market economic systems. There are many forces in such economic systems affecting both production and consumer demand. Not all of these forces can be measured statistically. And even where statistical measurements are available they are subject to errors of observation and measurement as well as purely random disturbances. Given uncertainty and the presence of random forces, economic projections can only be approximate. Obviously, if a forecasting technique is to be useful, the margin of error cannot be too wide. But a further point should also be made. Many forecasting techniques are limited to broad aggregates such as gross national product, total personal income, and total employment. The input-output method is used, however, for making highly detailed projections industry by industry and sector by sector.

A limited number of comparisons have been made of input-output projections and those made by other techniques, notably the multiple-regression method which is often used in making highly aggregated projections. In this comparison the input-output method has come off quite well. Perhaps the most comprehensive tests are those which were made by Michio Hatanaka and reported by Chenery and Clark.6 Although Hatanaka's tests were based on comparison of projections made by a static input-output model (one with fixed technical coefficients), they "are the first to reveal a margin of superiority (though an uncertain one) for input-output over multiple regression projections."7 This does not mean, of course, that forecasters using input-output methods can or should rest on their laurels. There is room for improvement in economic forecasting in general. It is significant, however, that input-output projections, which are highly disaggregated, are at least as accurate as those made by other techniques which project only a limited number of variables.

Input-output researchers are well aware of the limitations of static models, and have continued to work on both the statistical and conceptual problems involved. Some of this work will be discussed in the following sections. While much of recent input-output research makes use of advanced mathematical techniques, which will not be discussed here, the major outlines can be presented in nonmathematical language.

Specialized Coefficients

In the basic input-output model the technical input coefficients are expressed in value terms. They show the amount of inputs (in cents) required from each industry and sector to produce a dollar's worth of the output of a given industry (see Table 2-2). It is possible, however, to calculate other types of coefficients for special purposes. Some of these are measured in value terms. Others, however, are expressed as physical quantities per unit of output.

Labor input coefficients. Leontief has noted that "the technical structure of each industry can be described by a series of technical input coefficients—one for each separate cost element."8 While there might be little occasion to view structural interdependence in terms of each item of cost, the magnitude of labor inputs in many industries suggests that a table of labor input coefficients can be very useful. These coefficients show labor inputs in physical terms (preferably man-hours) per unit of output. The man-hour labor inputs can, of course, be converted to employment. From a table of labor coefficients one can derive the estimated employment effects of any given change in final demand. As with the basic technical coefficients, which are expressed in value terms, labor coefficients show both the direct and indirect effects upon employment of changes in sales to final demand sectors.9

One of the first large-scale applications of input-output in forecasting was by the Bureau of Labor Statistics, which made detailed employment projections to 1950 based upon the 1947 input-output table.10 More recently, detailed employment projections have been made for the state of California based upon a modified input-output model. This study included sectoral employment multipliers and showed the direct, indirect, and induced employment effects of changes in final demand.11

The question of the stability of labor input coefficients is bound to come up when these are used for making employment forecasts. In the short run such coefficients can be quite stable in the absence of major changes in product-mix. It is likely, however, that in the long run labor input coefficients will be less stable than the basic technical coefficients. For example, if capital is substituted for labor, the value of labor inputs is likely to change less than the physical inputs of labor. This is because as capital is substituted for labor the quality of labor inputs will change. Workers with higher skills and more training will be substituted for unskilled and semiskilled workers as a plant uses increasing quantities of capital relative to labor. Because of different pay rates for different grades of labor, the value of labor inputs will decline less than man-hour labor requirements.12

Changes in labor input coefficients will tend to be gradual, and they will also tend to be in the same direction. Hence if such coefficients are to be used in making detailed employment projections they can be adjusted to allow for the effects of technological progress upon labor requirements. In her study of the cotton textile industry, for example, Anne Grosse found that supervisory labor inputs changed little between 1910 and 1936. There were changes in nonsupervisory labor requirements, but these changes followed a fairly stable pattern. This illustrates a case in which labor input coefficients could undoubtedly be projected with a high degree of accuracy if one were interested in using them for making employment projections.13

Water-use coefficients. Economics is concerned with the allocation of scarce resources to competing uses. But scarcity is a matter of degree. Some resources are more abundant than others, and there are significant geographic variations in the relative abundance or scarcity of different resources. Water is an example of a resource that is in relatively short supply in many parts of the world. In the arid and semiarid portions of the United States water must be carefully conserved. As the economic development of these regions continues it is likely that the cost of water will rise. In recent years a number of economists have been concerned with the development of models for optimizing the allocation of this relatively scarce resource. Input-output analysis has played an important part in these studies, which have broad social and economic implications. And an interesting example of an input-output coefficient which is expressed in physical terms is that of the water-use coefficient. Such coefficients have been computed for California by Lofting and McGauhey.14 Following a standard input-output analysis of the California economy, Lofting and McGauhey computed water-use coefficients which are expressed in acre-feet per million dollars of output. The water-use coefficients "aid in tracing out interindustry water requirements which are usually obscured when attention is focused on single industry usage."15 As in the case of other coefficients relating physical inputs to total outputs, water-use coefficients can be used both for structural analysis and for projection purposes. The stability of such coefficients is something which can only be determined empirically. Once patterns of change are established, however, it should be possible to project water-use coefficients with reasonable accuracy. Specialized coefficients, such as labor input and water-use coefficients, will undoubtedly play a growing role in many kinds of regional and national input-output studies in the future.

Capital Coefficients16

The static model is based upon current flows and current outputs. Capital is involved in this system only as part of final demand; that is, current sales to industries purchasing capital goods are recorded, but the latter are lumped together in a single sector called "Gross Private Capital Formation." This section deals with capital coefficients as a stock concept as opposed to the flows involved in the basic transactions table of the static input-output model. In the next section we will introduce the concept of a capital flow coefficient.

A capital coefficient is defined as "the quantity of capital required per unit of capacity in an industry."17 A table of capital coefficients shows capital requirements per unit of capacity by industry of origin for each industry or group of industries in the input-output system. Like the basic technical coefficients, capital coefficients are expressed as ratios. These show the ratio of units of a given type of capital to the maximum output of an industry. The proportions of different types of capital employed at a given time are determined by engineering considerations. These proportions will, of course, differ between relatively old and relatively new establishments.

Incremental and average capital coefficients. It is important to distinguish between two types of capital coefficients. For a structural analysis average capital coefficients are used. These show the total stock of capital used by any sector distributed among the industries in which this capital originated. They also show the total amount of fixed capital employed per unit of capacity. For a dynamic analysis, however, incremental capital coefficients are required. These coefficients show the ratio of increments in capital to increments in capacity. If engineering techniques remained constant, average and incremental coefficients would be the same. Because of technological change, however, engineering techniques are not constant, and incremental coefficients—based upon data obtained from relatively new plants—will differ from average capital coefficients. The latter are a composite or average of the ratios of capital to capacity in all of the plants in an industry.

Average capital coefficients are based upon the relationship between the existing stock of capital and existing capacity. They represent the capital structure of an economy at a given time. Incremental capital coefficients, however, might be based upon the "best practice" plants in an industry. These are likely to be newer plants using the latest equipment and most advanced engineering techniques available at a given time. Incremental capital coefficients represent the average capital structure of an industry as it is likely to be at some time in the future. Indeed, in some industries it is possible to develop incremental capital coefficients for plants which are still on the drawing board—coefficients based upon engineering estimates of plants not yet in operation. In an industry undergoing rapid technological change, incremental capital coefficients derived from engineering data may be used as the basis for a dynamic input-output analysis. In any case, the major link between a static and a dynamic input-output model is a table of incremental capital coefficients.

Inventory coefficients. One further type of input-output co­efficient will be mentioned before turning to a discussion of dynamic input-output analysis. This is the inventory coefficient, which is defined as "an estimate of the total stocks of an input which must be held in the economy per unit of output."18 The capital coefficients discussed above relate to fixed capital only. Inventory coefficients, by contrast, are a measure of working capital. While the estimation of inventory coefficients is not at all a simple matter, the concept itself is not a complicated one. The definition of inventories for input-output analysis differs markedly from that used in ordinary accounting procedures, however. Inventory coefficients "are based on stock figures which combine for each kind of commodity the stocks of finished goods held for that industry and the stocks of supplies, raw materials, and goods in-process held by the industry."19 That is, finished-goods inventories are associated with the consuming industry rather than the producing industry. This definition is based on the view that "normal" inventories are dependent upon the input requirements of the industry which will eventually use them. Over short periods of time, the "normal" level of inventories is not likely to be affected by technological change. In general, therefore, inventory coefficients are likely to be of the average rather than the incremental variety.

Dynamic Input-Output Analysis

The static input-output model discussed in Chapters 1 through 5 is essentially a finished analytical tool, although there will no doubt continue to be improvements in the statistical implementation of this model. Basically, however, the static model will remain unchanged. As noted in earlier chapters, this model has served and will continue to serve a number of useful purposes. Because it is limited to the flow of current transactions, and because of its fixed technical coefficients, the applicability of the static model is limited to short-run analysis.20

In recent years much of the research on input-output analysis (as opposed to the statistical implementation of static models) has been directed toward the development of dynamic models. As indicated in the preceding section, the nexus between static and dynamic models is a table of incremental capital coefficients. In a completely dynamic system, other changes — such as shifts in consumer tastes —must also be taken into account. For an advanced industrial economy, however, the major requirement for a dynamic input-output system is a complete description of the capital structure of the economy to supplement the flow of current transactions. While the theory of dynamic input-output analysis is in an advanced stage of development, the statistical implementation of existing models has proceeded at a much slower rate.21 The major reason for the lag in empirical work on dynamic input-output analysis is the scarcity of data. It is true that in his impressive work, mentioned above, Robert Grosse has developed capital and inventory coefficients for about 200 industries.22 But as Leontief has noted, "an exhaustive analytical exploitation of the large sets of empirical capital coefficients thus obtained involves extensive computations which will not be completed for some time to come."23

Interesting empirical work on incremental capital coefficients in the tin-can and ball-bearing industries has been conducted by Anne P. Carter, and Per Sevaldson has done extensive research on changing input-output coefficients in the Norwegian cork and woodpulp industries. 24 Meanwhile, Clopper Almon has experimented with a 10-sector dynamic model of the American economy. His model assumes changing flow coefficients, and allows for the substitution of capital for labor. Almon also assumes that consumer demands increase with population growth and changes in the real wage rate. Investment is assumed to increase with out­put, and also as a result of the substitution of capital for labor. This is a "full-employment" model which assumes that the projected final demands will result in sufficient output to fully employ the available labor force which is determined exogenously; that is, the projection of labor supply is independent of the equations in his system. Almon has tested his model by making short-run projections and concludes that it "is possible for the model to reflect the technology of the economy well enough to be of practical value in consistent forecasting or indicative planning."25

Much of the work on dynamic input-output analysis is experimental, and while there have been encouraging results there are as yet no dynamic counterparts of the full-scale static models which have been in use for many years. An operational dynamic model is the goal of much current research, however, and a major cooperative research program currently in progress is expected to make an important contribution toward its realization.

The U.S. Economic Growth Studies

For several years the U. S. Department of Labor, in cooperation with a number of other government agencies and various private research organizations, has been working on a series of economic growth studies with the objective of making detailed five- and ten-year projections. The projections are to be based on a series of assumptions about the rate and patterns of growth of the American economy. Various statistical and analytic techniques are being employed in making these studies. But the basis of the long-range projections will be "provided by a study of interindustry sales and purchases in the economy, and the projection of these interindustry relationships over the next decade to reflect anticipated changes in technology and, if possible, relative costs. These interindustry relationships can then be used to convert projections of end-product deliveries to estimates of output requirements from each industry, covering intermediate as well as final products."26

The 1970 projections will be based upon the 1958 national input-output table. The industry output requirements obtained from the projections will be used to estimate the demand for labor on an industry-by-industry basis. Labor supply will be estimated by a series of interrelated projections of population, school enrollment, family formation, and labor force participation rates by age and sex. It is hoped that the resulting employment projections can be presented in considerable occupational detail.

Projections of unit capital requirements will be made to estimate both public and private investment and the accompanying capital stock which will be required by an expanding economy, The effects of anticipated technological change on input requirements will be taken into account. A memorandum issued by the Office of Economic Growth Studies mentions the possibility of using a capital flow matrix to relate total investment demand by purchasing industry to demands on industries producing capital goods.27

The economic growth project is policy oriented. It is hoped that the detailed projections will serve as useful guides to public policy-makers and to private investors. Among specific objectives, the economic growth studies are expected to provide:

a. A framework for developing detailed estimates of employment by occupation.
b. The basis for evaluating the effects of long-range government programs on the economy, including public works, the farm program, defense spending, the space program, and urban renewal.
c. The basis for analyzing, in considerable industrial detail, the economic effects of disarmament.
d. A capability for prompt analysis of current problems which involve complex interindustry relationships such as the impact of foreign trade on employment and the effects of expansion of public works programs.
e. A model for conducting sensitivity analyses to identify those sectors of the economy which are most sensitive to changes from one pattern of growth to another.28

Some phases of the economic growth project are more advanced than others. Given the vast scope of the project and the volume of work that is yet to be completed, however, it is impossible to estimate when the detailed long-range projections will be ready for publication. While spokesmen for the agencies involved are understandably reluctant to discuss the details of the studies before their completion, it is evident that significant progress is being made toward the statistical implementation of a dynamic input-output system for the American economy.

A "Dynamic" Regional Input-Output Model

A completely dynamic input-output system will consist of a table of incremental capital coefficients to supplement the table which records the flow of current transactions. Such a system is far more complicated than the static, open model discussed in this book. While there is evidence that progress is being made on the development of such a model for the national economy, one does not exist at the time this is written. In this section a simple "dynamic" model will be described which does not depend upon capital coefficients. It is an adaptation of a static model which was developed to make long-range regional projections. Conceptually it is quite simple. The model is based on the assumption that at any given time some establishments in an industry are more advanced than others, and that the input patterns of the "best practice" firms in an industry can be used to project the average input patterns of that industry at some time in the future.

The assumption is made that long-run changes in technical coefficients are due to a combination of changes in relative prices and technological progress, and that these changes will be reflected in the technical coefficients of the "best practice" firms during the base period. It is also assumed that the technical coefficients will be affected by changes in interregional trade patterns, and that some of these changes can be anticipated by analysis of long-run trends. The adjustment of technical coefficients on the basis of long-run trends calls for the exercise of some judgment. But an interregional model which fails to take account of changing patterns of regional imports and exports will not be particularly useful for making long-term projections. The method to be described in the following paragraphs is admittedly a bit "rough and ready," but it is the author's conviction and that of his co-workers that it will result in more accurate long-term projections than mechanical reliance upon a static model.

While the example to be discussed is related to an interregional input-output analysis, the method to be described could be applied (if data were available) on a national basis. All figures used in the discussion are purely hypothetical, but the procedure described is one which was used in making a series of long-term regional projections.29

Identifying the "best practice" firms. An industry, however defined, is made up of a collection of firms or establishments. In what follows we assume that the firms comprising an industry produce identical products. While firms are identical on the output side (a simplifying assumption to avoid the aggregation problem) their input patterns are not the same. It is realistic to assume that the firms in an industry will be of different ages. It is also realistic to assume that some of the firms will use older equipment and employ less efficient production processes than others. In brief, the technical coefficients of a static input-output model represents the average input patterns of all of the firms in the industry. There will be, however, a considerable amount of dispersion around this average. The objective of this part of the analysis is to identify a sample of firms which are above average in terms of productivity on the assumption that this sub-sample of firms will be representative of the average firm at some time in the future.

There are several ways to measure productivity. One method is to express output in terms of man-hour inputs — the standard measure of labor productivity. It is possible, however, that even among firms producing identical products there will be differences in the ratio of capital to labor inputs. A second measure of productivity often used is one which expresses outputs in terms of combined capital and labor inputs.30 In the study under discussion both measures were used, but primary reliance was placed upon the latter. The labor productivity measures were used largely as a check on the measures of output per unit of capital plus labor inputs.31 After the productivity ratios for each firm had been computed they were expressed in index-number form with the "average" firm in the sample set equal to 100. The firms were then arrayed in terms of productivity class intervals. This is illustrated by Chart 6-1, where 52 hypothetical firms have been arranged in a frequency distribution according to the productivity class intervals to which they belong. The approximate median (halfway point) of the distribution is indicated by the arrow. The productivity class intervals range along the horizontal axis, the number of firms in each class along the vertical axis.

The distribution is not completely symmetrical, but it is close enough for practical purposes. About two-thirds of the sample firms fall within the range of 90 to 130 per cent of "average" productivity.32 The firms represented by bars A and B are clearly marginal firms with productivity ratios well below average. Similarly, the firms in the bars labeled G, H, and I are well above average in productivity. The seven firms represented by bars G and H, set off by the bracket along the bottom axis, represent the "best practice" firms in this sample. When the input coefficients of these seven firms are averaged, the results are considered representative of the "average" technical coefficients of the industry at some future time. If a ten-year projection is to be made we are implicitly assuming that the firms in bars G and H are about "ten years ahead" of their competitors in the industry, or that in another decade their present input patterns will be the average for the industry.

It will be noted that the firm represented by block I was not included in the sample of "best practice" firms although it clearly has the highest productivity ratio of any firm in the sample. This was done deliberately to illustrate a point. In any industry there will be some firms which do not necessarily use the latest and best equipment or the most efficient production methods, but which nevertheless have unusually high rates of productivity. These are often small, family-owned establishments (in industries where such firms exist) and their high rates of productivity may be the result of unusual motivation and above-average effort. They do not necessarily follow the best practices in terms of engineering design and production techniques. Such firms are considered atypical in a statistical sense, and their inclusion among the "best practice" firms would distort the projected technical coefficients for the industry.

Computing the projected technical coefficients. The second step is quite a simple one. In our hypothetical example, the input patterns of the seven "best" firms are averaged. From these averages a new set of direct input coefficients is computed by the method described in Chapter 2. From the table of direct coefficients, a new table of direct and indirect requirements per dollar of final demand is computed (see Table 2-3). The remainder of the analysis is identical to that discussed in Chapter 3. Final demand projections are made independently of the input-output table. The new table of direct and indirect requirements per dollar of final demand is then applied to the final demand projections to obtain a table of interindustry transactions (for all processing sector industries) for the target year. If necessary, the changing input patterns can be extrapolated to obtain both an intermediate and a long-range projection. This process is illustrated by Chart 6-2.

The left-hand bar in Chart 6-2 represents the average input pattern of all firms in the industry during the base year. It includes all interindustry transactions (the processing sectors) as well as inputs from the payments sector. In a regional model the latter are important since they include imports of goods and services as well as payments to government.

The middle bar in Chart 6-2 represents the average input patterns of the sub-sample of seven "best" firms operating during the base year. The distribution of inputs represented by this bar is quite different from that given in the left-hand bar. It is assumed that this will be the average pattern of inputs for all firms in the industry at some future time. Finally, the right-hand bar represents a long-range projection of the input pattern of this industry. It is based on an extrapolation of the changes from the left-hand bar to the middle bar. This is not a mechanical extrapolation, but one which is based in part upon analysis of various long-run trends.

In our hypothetical example we have assumed that raw material inputs (represented by A) remain unchanged throughout the projection period. The sub-sample of "best" firms uses more inputs from industry B than the average firm in the industry, and it is assumed that there will be an even greater use of inputs from this industry in the future. Industry B, we may assume, provides inputs associated with the increasing use of capital. Industry C in the example may be considered to represent the electric-power industry. Since the "best" firms in our sample are more capital-intensive than the average, their power requirements per unit of output are higher. Over time, it is assumed that power-input coefficients will continue to increase. There is relatively little change in inputs from industries D and F in the hypothetical example. These, we may assume, are industries which provide services, and while inputs from them will increase in relative importance the changes are not substantial. There will, of course, be some increase in service inputs (notably financial services) as an industry shifts in the direction of greater capital-intensity. Industry E in the example may be considered one based upon the most advanced technology (data-processing services, for example). The average firm in this industry purchased no services from industry E in the base period, but the "best" firms did. And the average firm is expected to use about the same relative amount at the end of the projection period.

The sector represented by H in Chart 6-2 calls for special comment. This is the household sector, which has been moved into the processing portion of the table for this analysis. Labor inputs in the "best" firms are substantially smaller than those of the average firm in the hypothetical industry. On the basis of long-run trends in productivity, it is assumed that labor requirements per unit of output will continue to decline. Finally, moving outside the processing sector, imports into the region and payments to government show a slight relative increase as we move from the left-hand bar to the right-hand bar.

It should be emphasized that the figures used in this illustration are hypothetical. They are not at all unrealistic, however, since the major change illustrated by our example is a shift in the direction of greater capital-intensity. The "best practice" firms in an industry will be those which move ahead of their competitors in terms of engineering design, capital equipment, and production methods. In an industry characterized by rapid technological change, establishments which do not keep abreast of new developments are likely to fall by the wayside. This is part of the process of economic growth, and while nothing can be said about the future of an individual firm or establishment in an industry the "average" input pattern for the industry will change over time. In some industries the changes are rapid and in others they occur slowly. It is essential, however, that the best possible estimates of future input requirements be made when an input-output model is used for making detailed long-term projections of interindustry transactions.

The simple model sketched in the preceding paragraphs lacks the elegance and rigor of a truly dynamic model. The application of this technique in making input-output projections requires a certain amount of judgment. There is no mechanical method, for example, for selecting a sub-sample of "best practice" firms in each industry. If the industry sample includes enough firms, they can be arranged in a distribution such as that illustrated by Chart 6-1. Then the method of selecting the "best practice" firms is rather mechanical. In some cases (utilities, for example) there are only a few firms, and in these cases a combination of judgment and analysis of long-run trends is required to estimate future input patterns. There is also no assurance that input patterns will shift from the average of all firms in the industry to the average of the "best practice" firms over the period covered by the projections. If complete historical data were available on each firm in the sample it might be possible to determine with greater accuracy the length of time required for such a shift to take place. Finally, the aggregation problem has been "assumed away" in our hypothetical example. And in the application of this technique it remains one of the most vexatious problems to be dealt with.

Because of the assumptions which have been made, it would be the sheerest of coincidences if actual shifts in technical coefficients of the type described in the hypothetical example were to take place over a specified time period. It is necessary to emphasize that what results from the application of this method is a set of projections rather than predictions, and in a free-market economy projections typically have a margin of error. This will certainly be true of input-output projections based upon the relatively crude method discussed above. In the absence of complete data on the capital structure of industries in the regions involved, however, the alternative would have been to make projections based upon fixed technical coefficients. It is reasonable to suppose that long-range interindustry projections based upon changing technical coefficients — even where some judgment was involved in projecting new average input patterns—will come closer to the mark than those based upon the assumption that input patterns are invariant in the long run.


Input-output analysis has come a long way since the basic ideas were introduced by Professor Leontief in 1936. When he began his study of interindustry relations in the United States in 1931, Leontief stated, "the objective prospects of completing it successfully were anything but bright."33 In a little over three decades, however, input-output analysis has become one of the most important branches of econometrics. The static, open model is widely used for regional, interregional, and national economic analysis, in planned and unplanned economies, and by nations in all stages of economic development. Input-output economics will not displace other types of analysis. There is ample room for the division of labor among economists. Some will continue to stress the aggregative analysis which is the heritage of John Maynard Keynes. Others will continue in the tradition of Marshall, Chamberlin, and their successors in stressing the economics of the individual firm. The great advantage of input-output analysis is that it covers the wide range between extreme aggregation and complete disaggregation. Another major advantage of input-output is its stress on interdependence; it is the only branch of economics which shows empirically how "everything depends upon everything else." It has brought to realization, in an operational form, the grand design of general equilibrium theory which had its roots in the work of Francois Quesnay and Leon Walras.

The thing to be stressed about input-output economics is its dynamic nature. The static, open input-output model is operational as it stands 'for a wide variety of purposes. It has won international acceptance as an analytical tool which is an important guide to policy-makers in a great many countries. There are of course many problems still facing input-output analysts. There is, for example, the ever-present data problem. The collection and processing of data for the construction of a transactions table, at either the regional or the national level, is a time-consuming and expensive process. As more and more input-output studies are completed, however, this problem should diminish in importance. This will be true particularly if "data banks" are established where the raw materials behind input coefficients can be stored and made generally available. There are other problems associated with industry classification—part of the aggregation problem— which are particularly acute when comparative input-output studies are being made.34 But there is continued research on these problems, and as more and more countries conform to the United Nations International Standard Industrial Classification these problems can be expected to become less serious. With the advent of high-speed electronic computers, computational problems—much discussed in the early days of input-output analysis —are no longer serious.

 Input-output analysis has had and continues to have its critics. This is not at all unusual. Indeed, it would be unfortunate if the situation were otherwise. The advancement of knowledge is accelerated by constructive, scientific criticism. Weaknesses in any system of thought can be better attacked if they are pinpointed by detailed critical analysis. This is true not only of input-output analysis but of any scientific endeavor, whether in the physical or the social sciences.

 There are continuing efforts to improve on static, open input-output models and on the analytical tools, such as sectoral multipliers, derived from them. But the main thrust of input-output research in recent years has been in the direction of dynamic analysis. This is the area where the greatest amount of work remains to be done, and where the truly challenging problems lie. Significant progress has been made in identifying the data needs, and elegant dynamic models have been developed. The rapid progress of the past three decades should continue unabated. Since the frontiers of knowledge are being pushed back at an accelerated rate in all disciplines, major advances in dynamic input-output analysis are to be expected. The policy implications of operational models of this kind for a world in which economic interrelationships are becoming increasingly complex are sufficiently obvious to require no further comment.



ALMON, CLOPPER, "Consistent Forecasting in a Dynamic Multi-Sector Model," The Review of Economics and Statistics, LXV (May 1963), 148-62.

________________, "Numerical Solution of a Modified Leontief Dynamic System for Consistent Forecasting or Indicative Planning," Econometrica, XXXI (October 1963), 665-78.

________________, "Progress Toward a Consistent Forecast of the American Economy in 1970," paper presented at the Conference on National Economic Planning, University of Pittsburgh, March 24-25, 1964 (mimeographed).

BAUMOL, WILLIAM J., "Input-Output Analysis," Economic Theory and Operations Analysis (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1961), pp. 299-310.

CARTER, ANNE P., "Incremental Flow Coefficients for a Dynamic Input-Output Model with Changing Technology," in Tibor Barna (ed.), Structural Interdependence and Economic Development, Proceedings of an International Conference on Input-Output Techniques, Geneva, September 1961 (New York: St. Martin's Press, 1963), pp. 276-302.

CHENERY, HOLLIS B. and PAUL G. CLARK, Interindustry Economics (New York: John Wiley & Sons, Inc., 1959), pp. 71-80, 157-78.

GROSSE, ROBERT N., "Structure of Capital," in Studies in the Structure of the American Economy (New York: Oxford University Press, 1953), pp. 185-242.

LEONTIEF,'WASSILY, "Dynamic Analysis," Studies in the Structure of the American Economy (New York: Oxford University Press, 1953), pp. 53-90.

________________, "Structural Change," Studies in the Structure. of the American Economy (New York: Oxford University Press, 1953), pp. 17-52.

SEVALDSON, PER, "Changes in Input-Output Coefficients," in Tibor Barna (ed.). Structural Interdependence and Economic Development (New York: St. Martin's Press, 1963), pp. 303-28.

SHISHIDO, SHUNTARO, "Problems in the International Standardization of Interindustry Tables," Journal of the American Statistical Association, LIX (March 1964), 256-72.

STONE, RICHARD, Input-Output and National Accounts (Paris: Organization for European Economic Co-operation, September 1960), pp. 63-72, 1 17-28.



1 For the most recent, detailed progress report on this research see Wassily Leontief, et al., Studies in the Structure of the American Economy (New York: Oxford University Press, 1953).

2 For a critical discussion which at the same time recognizes the major contribution of input-output analysis, see Robert Dorfman, "The Nature and Significance of Input-Output," The Review of Economics and Statistics, XXXV1 (May 1954), 121-33. See also Input-Output Analysis: An Appraisal, Studies in Income and Wealth, Vol. 18, National Bureau of Economic Research (Princeton: Princeton University Press, 1955). For a critical review of regional and interregional input-output studies see Charles M. Tiebout, "Regional and Interregional Input-Output Models: An Appraisal," The Southern Economic Journal, XXIV (October 1957), 140-47.

 3 1f the proportional change in output is greater than the change in all inputs, we have increasing returns to scale; if output changes in smaller proportions than all inputs we have decreasing returns to scale.

4 W. Duane Evans and Marvin Hoffenberg, "The Interindustry Relations Study for 1947," The Review of Economics and Statistics, XXXIV (May 1952), 100.

5 lnput-Output Analysis: An Appraisal, p. 170.

6 Hollis B. Chenery and Paul C. Clark, Interindustry Economics (New York: John Wiley & Sons, 1959), pp. 173-76. For further discussion of other tests see also pp. 157-73
and 176-78.

7 Ibid., p. 175. 

Wassily W. Leontief, The Structure of American Economy, 1919-1939(New York: Oxford University Press, 1951), p. 144.

9 For further discussion of labor input coefficients, and their use in projecting employment, see ibid., pp. 144-52. 

10 Full Employment Patterns, 1950, U. S. Department of Labor, Bureau of Labor Statistics, Serial No. R. 1868 (Washington: U.S. Government Printing Office, 1947); see especially pp. 29-38.

11 W. Lee Hansen, R. Thayne Robson, and Charles M. Tiebout, Markets for California Products (Sacramento, Calif.: California Economic Development Agency, 1961); see also W. Lee Hansen and Charles M. Tiebout, "An Intersectoral Flows Analysis of the California Economy," The Review of Economics and Statistics, XLV (November 1963), 409-18.

 12 The relative shift of capital inputs, in value and physical terms, is less easy to determine. The initial cost of installing "higher quality" capital, per unit of output, may or may not go up since this depends upon the rate of interest, and the latter is not a simple function of the quality of capital. There is probably a closer relationship between the operating cost of capital per unit of output and capital inputs in physical units. If power inputs are used to approximate physical capital inputs, it is possible that capital inputs in value terms will be more stable than the physical capital inputs. The number of kilowatt-hours per unit of output will go up as the quantity of capital is increased, but because of step rates the incremental cost of power will go down. Thus the ratio of output to kilowatt-hour inputs will change more than the ratio of output to the cost of power inputs. For a discussion of the use of power input coefficients to approximate physical inputs of capital see Anne P. Grosse, "The Technological Structure of the Cotton Textile Industry," in Leontief, et al., Studies in the Structure of the American Economy, pp. 400-1.

 13 Anne P. Grosse, loc. cit., pp. 392-400: see especially Table 8, p. 393.

14 E. M. lofting and P. H. McGauhey, Economic Evaluation of Water, Part III, An Interindustry Analysis of the California Water Economy, Contribution No. 67, Water Resources Center (Berkeley: University of California, January 1963). 

15 Ibid., p. 62. See pp. 68-72 for the method of calculating these coefficients.

 16 This section draws heavily upon Robert N. Grosse, "The Structure of Capital," Leontief, et al., op cit., pp. 185-242, and upon Chenery and Clark, op. cit., pp. 149-53. 

Grosse, op. cit., p. 185.

18 Robert N. Grosse, op. cit., p. 205. 

p. 206. 

does not refer to any specific time period. In the case of a slowly growing economy in which the underlying technical relationships are changing at a slow rate, the static model can be used to make projections extending over several years. For input-output purposes short-run might be considered any period during which the difference between average and incremental capital coefficients
is negligible. 

21 See Wassily Leontief, "Dynamic Analysis," Studies in the Structure of the American Economy, pp. 53-90. See also Chenery and Clark, op. cit., pp. 71-79: Richard Stone, Input-Output and National Accounts, OEEC (June 1961), pp. 117-30: Anne P. Carter, "Incremental Flow Coefficients for a Dynamic Input-Output Model with Changing Technology," in Tibor Barna (ed.), Structural Interdependence and Economic Development (New York: St. Martin's Press, 1963), pp. 277-302; Per Sevaldson, "Changes in Input-Output Coefficients," idem, pp. 303-28; Clopper Almon, "Consistent Forecasting in a Dynamic Multi Sector Model," The Review of Economics and Statistics, XLV (May 1963), 148-62; and Almon, "Numerical Solution of a Modified Leontief Dynamic System for Consistent Forecasting or Indicative Planning," Econometrica, XXXI (October 1963), 665-78.

 22 Op. cit., pp. 209-42. 

Studies in the Structure of the American Economy, p. 12. 

Op. cit., pp. 288-98, 311-27.

Clopper Almon, "Numerical Solution of a Modified Leontief Dynamic System for Consistent Forecasting or Indicative Planning," p. 676. See also, Almon, "Consistent Forecasting in a Dynamic Multi-Sector Model."

26 Economic Growth Studies, U. S. Department of Labor, Bureau of Labor Statistics, Division of Economic Growth Studies (March 1963). 

27 Research Program of Economic Growth Studies, Bureau of Labor Statistics, Office of Economic Growth Studies, August 1962 (mimeographed), p. 13.

 28 Ibid., p. 1.

29 The technique employed was suggested by Professor Leontief. It has been used by the author and his associates in the Colorado River Basin Study to make long-term interindustry projections for each of the sub-basins in the Colorado River Basin. 

See for example Solomon Fabricant, Basic Facts on Productivity Change (New York: National Bureau of Economic Research, Inc. [Occasional Paper 63], 1959), pp. 3-13. 

31 Complete data on capital inputs were not available, but depreciation allowances in the base year were obtained in the surveys. These figures were used to estimate the "combined capital and labor" inputs.

32 In a normal distribution this would about equal the mean plus and minus one standard deviation.

33 Tibor Barna, "Introduction," Structural Interdependence and Economic Development, p. 1. 

See for example Shuntaro Shishido, "Problems in the International Standardization of Interindustry Tables," Journal of the American Statistical Association, LIX (March 1964), 256-72.





Regional Research Institute, West Virginia University