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Leontief's models are used by the Pentagon, the World Bank, the United Nations, and over 30 countries for budgeting and economic prediction. Numerous other specialized applications of the model have been used in waste disposal management, pollution control, and even world disarmament. Input-output economics. Wassily Leontief. This collection of writings provides the only comprehensive introduction to the input-output model for which Leontief was awarded the Nobel Prize in The structural approach to economics developed by Leontief, and known as input-output analysis, paved the way for the transformation ofeconomics into a truly empirical discipline that could utilize modern data processing technology.

This thoroughly revised second edition includes twenty essays--twelve of which are new to this edition--that reflect the past developments and the present state of the field. Not because of arguments about the appropriate model: all players in the controversy agree that the relationships among trade, technology, and factor prices are indeed very well suited for analysis using the standard competitive trade model. The dispute is, instead, philosophical: it hinges on the question of what thought experiments to perform.

Economists agree that differences among countries drive trade, and that trade acts to diminish some of these differences. Abundant factors tend to be cheaper and thus are used more intensively, and trade tends to lower the price of scarce factors and raise that of abundant ones. Relative cost structures are of critical importance for understanding the structure of the world economy and anticipating changes in it. However, the conventional formalization of the standard assumptions in a mathematical model is arguably far too rigid to replicate the empirical reality at the level of detail of many sectors and many factors for the past, or to be useful for counter-factual scenarios or scenarios about the future.

This is true of a model of even a single economy, let alone the world economy. Looking to the future: the analysis of scenarios The analysis of alternative scenarios as a way of preparing for an uncertain future began in the corporate world and found fertile ground among military planners.

In the s economists began to develop scenarios for model-based analysis — an innovation relative to the standard methods of proving theorems and testing hypotheses. The early scenarios in particular were generally distinguished by assigning high, medium or low values to key variables, such as the growth of the labor force or of productivity. The implications of these assumptions for other variables — such as the growth of GDP or of investment — are then determined using the model. The community of analysts engaged in futures research has developed techniques for elaborating much bolder and more imaginative visions about the future in terms of alternative scenarios.

While they vary in scope, level of detail, and degree of documentation of assumptions, the scenarios involve constructing a story that cuts across disciplinary boundaries. According to Fontela , p. Both futurist and economist, Fontela has called for bridging the gap between the two communities through collaboration in developing scenarios and analyzing them using models of long-term structural change see also Duchin and Hubacek, While Fontela describes what in his opinion are shortcomings of the model and database, he notes that they can be corrected with relative ease.

First, it is comprised of the database that bears on the comparative advantage of all geographic regions: it is the global equivalent of the database used by Leontief in his articles on trade in the s. The data were crude and incomplete, but a much better job could be done today. Second, Leontief developed relatively complex scenarios about the world economy and devised a method for documenting the assumptions to enable an easy comparison of alternatives.

Since the scenarios were formulated in terms of the detailed variables and parameters of the model, each scenario was clearly related to a distinct computation. The outcome was equally detailed, so it was described as a story — not in terms of a few growth rates only.

(1906 - 1999)

What today would be considered a structured approach to developing scenarios see, for example, Rotmans et al. These are challenges that can yield to empirical analysis, but they will require concerted effort and an intellectual division of labor on the part of a new generation of scholars to make substantial headway. As long as I knew him, Wassily Leontief was convinced that it was only a matter of time until this was achieved.

Casas, F. Choi The Leontief Paradox: continued or resolved? Vernon ed. Hubacek Linking social expenditures to household lifestyles, Futures, 35, 61— Hakura, D. The role of technological differences within the EC, Journal of International Economics, 54, — Minhas, American Economic Review, 54, — Bos ed. Minhas, B. Repetto, A.

Anastasi, S. Greeuw, J. Mellors, S. Peters, D. Rothman and N. Rijkens Visions for a sustainable Europe, Futures, 32, — Stern, R. Maskus Determinants of the structure of U. Wolff, E. First, it had an economy to restore — most factories not destroyed by the war were obsolete. This is because most of the then modern equipment in occupied France had been removed to Germany during the war.

Perhaps worst of all, the nation had been dangerously divided, both socially and politically, since some citizens had collaborated with the occupying forces while others had actively resisted those forces. Upon their return home, thousands of Frenchmen — among them soldiers, prisoners and deportees — encountered an exhausted and dejected country. To restore the national economy, the Communists, then a powerful party, sought to apply the Soviet model and advised launching an economic plan.

They argued that the USSR owed its wartime success to formal plans. They claimed that, due to the existence of just such an economic plan, the Soviet army had been amply supplied as scheduled with strategic stores. The Communist concept was met with wide approval. So, at the end of the war, the French government had to meet three minimum requirements and do so as soon as possible.

Nationalizing them helped it attain this requirement.

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By doing so, the government was quickly able to transform these industries from a large number of small, obsolete establishments into a single few big one s that could enjoy a public monopoly. Second, the population had to be persuaded that economic growth, rather than stagnancy, should be the rule. Indeed, this — above all — was a vital necessity.

With such aims in view, the French government cautiously promoted a National Development and Equipment Plan. Its target was to achieve rapid growth in the national product. Therefore, public authorities wisely decided to meet with important public and private economic leaders, corporate managers and trade union members alike. In this way, the whole population was able to feel intimately involved in the setting of goals and understand its role in making the Plan a success.


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Thus, the nationalization process and the creation of a National Plan were two different sides of the same policy coin. Nationalizing meant modernizing At the end of the war the necessary modernization of industrial infrastructure seemed rather unlikely. The near-total lack of competition and the deeply rooted torpor of management reinforced stagnation. In general, the industry lacked vitality. It was particularly important since the demand for electricity grew rapidly after the war, at a rate of 7 percent annually.

In order to keep up with this demand increase, electricity production needed to double within ten years. Because the capacity to meet such a production level did not exist, this meant making huge investments.


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  4. Dynamic young men, most of them colleagues from the famous Ecole Polytechnique, were appointed as senior executives. Knowing the expected level of French electricity consumption was particularly useful to the managers, who used the information to build their economic development scenarios on a solid foundation. The French government decided similarly to nationalize other industries with structures that were judged to be outmoded.

    Soon afterwards Gaz de France, i. The various rail companies had already been nationalized in , when on the verge of bankruptcy. The concept seemed to provide a clear advantage to almost everyone involved. Thereby it found itself in a position of allocating and overseeing nearly two-thirds of all industrial investments in France. When it was identifying the nature and volume of this magnitude of investment, the French government was also deciding about the economic future of the country.

    As a matter of fact, experience proved in due course that this reproach was not completely unfounded, as some of these states within the state have on occasion seemed more powerful than the state itself. The spirit of the National Development and Equipment Plan Besides modernization, the French government had to keep in mind its other major post-war objectives: economic growth and national unity. The government took the risk and was rewarded with success.

    In Jean Monnet, a man who a few years later became the main promoter of the European Economic Community, volunteered to establish a national planning system. General De Gaulle, who was then president of the provisional government, agreed to this proposal and supported it thoroughly. In order to restore national unity, Jean Monnet conceived a straightforward policy: to stimulate contact and cooperation among as many French citizens as possible.

    So, not only was the established plan clearly explained and announced to the public, but its various intermediate forms and evolutionary processes were as well.

    Wassily Leontief and the discovery of the input-output approach

    This is because civil servants in charge did their best to give accurate information about the contents of the plan, its scheme and its evolution. At appointed times they even presented brief synopses of the situation. It was also necessary to forecast future needs, especially the likely import levels from the United States, with an emphasis on equipment.

    The United States helped French managers by organizing visits to its state-of-the-art plants. A Committee initially was composed of about twenty members. Each was allowed to create as many subcommittees as deemed necessary. The Committees enjoyed complete autonomy and could consult with any willing public or private expert.

    It was a considerable advantage to the Committees that they were fully independent of public agencies. Their membership was composed of social partners, experts and the administration. Each Committee elected its own president, who was seldom a civil servant and more often from some other walk of life e. Trade unions took on an active role in the Committees, even the one closely connected with the Communist Party, the CGT. Tax incentives were available to induce them to make judicious investments. Only those that followed the recommendations could obtain licenses to import machines that could not be purchased from anywhere but the United States.

    It was of the utmost interest for any employer to be aware of the key elements of the Plan, especially since so many people — his colleagues, civil servants, trade unions, and all sorts of private and public experts — had been so deeply involved in their creation. They played a similar part in the development and implementation of the third Plan. But their weight gradually diminished thereafter. By and by, the Plan lost most of its democratic organization as the private executives and trade unionists progressively shirked active participation in Committee activities.

    There had been a large increase in the production of coal, electricity, steel, building materials, etc. Freight trains as well as passenger trains were running faster and more punctually than ever before. Roads, bridges, harbors, and other civil engineering works that had been destroyed during the war had been repaired. The third Plan, which was to start in , was intended to be a triennial one.

    Stimulated by the Common Market, at the foundation of this Plan was the objective of enabling French industries to contend well against foreign competition. This intricate set of tables was not easy to manage, since it was necessary to 72 Henri Aujac account for the interdependencies of data among the tables. The government tentatively entrusted the SEEF with the task of establishing a preliminary forecast for ; the Plan Committees would make their own as in the previous years.

    It appeared that a good way to improve the aims and means of the French planning process would be to compare the two forecasts for It was thought that the Plan would only be strengthened by the exercise of comparing them and aligning them into something more like a single vision.

    It must be kept in mind that the use of the input-output table in the SEEF forecast had been prescribed only tentatively, to see whether it could be used for establishing long- and medium-term forecasts. A detailed sketch of the economic future desired for had to be drawn up; this situation would be the result of the political program developed prior to by the French government to increase public welfare. The vocabulary available for the design of the survey was that used by the National Accounting System.

    The latest available economic survey, issued in , had gathered statistical data that could be used to produce the National Accounting System. So, two sets of expectations were needed: one covering three years, from to , in order to update the survey data; the other covering the three years of the Plan, from to — the desired forecast. Starting from a hypothetical growth rate, we would discover its probable consequences and modify that initial hypothesis to ameliorate them.

    Thanks to the tables provided by the Accounting System, and — of course — a lot of hard work, we more or less succeeded in analyzing and measuring the consequences of various possible growth rates on the myriad components of the general economic equilibrium. These components were: 1. Household demand. Democratically programming the economic situation for required taking into account the wishes expressed by most Frenchmen in regarding their then current economic situation.

    Since each social group wished to attain the standard of living of the social group ranked immediately above, it was rather easy to forecast the future demand for consumer goods such as refrigerators, washing machines and automobiles. National investment demand. The state wanted weaponry, research especially atomic research , hospitals, schools, bridges, roads, motorways, and other civil engineering works. Public authorities were asked to indicate the probable level of infrastructure and equipment they would require by International exchanges. Civil servants dealing with international commerce attempted to anticipate the evolution of French imports and exports three years in advance.

    Such forecasting was rather uneasy; so experts were trusted. The 74 Henri Aujac French input-output table had about one hundred such commodities, each concerned with an equal number of products and services. Many similar or related products were aggregated and called by a single name: that of the main product of the composite. This composite product was a single commodity in the input-output table.

    Each column displayed the accounts of a sector, including the value of its production, the value of the purchases from various other sectors i. These index cards displayed the framework of either the sales accounts of each sector or the resources-employment accounts for each commodity. Since computers were not yet available at the French Finance Ministry in and the calculations had to be performed by hand, it was essential to avoid being caught in the webs of interdependence and the consequent countless reckonings by iteration see, e.

    But was the French table triangulable? Thus, in case of perfect triangulation, null or low numbers would be located above i. It should be noted that the French table contained no autoconsumption i. Of course, this logic could follow for other sectors if triangulation was possible. Of the largest intermediate demands, only three were located above the diagonal, and they required some lengthy iterative reckoning.

    As a result the number of necessary iterations was considerably reduced, and sequential reckoning could be used for the remaining sectors. With the help of my secretary, I started on it one Monday morning, not knowing how long it would take. Beginning that day, we sort of lived inside a tornado of multiplication, division, subtraction and addition, using lots of pencils and erasers. At noon the following Friday we were met with an incredible surprise: our results, i.

    Nonetheless, it is still worthwhile to investigate the kind of economic structure revealed by input-output table triangulability. The degree to which an economy is triangulable may well be related to its stage of development. Indeed, it depends largely on history. Based on our work, it would seem that a table of a less developed or industrializing economy would probably be easy to triangulate. The economic structure of industrialized countries would tend to be less easy to triangulate since the interdependence of the system would be notably enhanced by the entry of new products with wider usage across the spectrum of industries.

    It appeared that the content of both forecasts was a mixture of real planning and mere forecasting. For this group, the so-called forecasts were strictly the Plan targets. A few trade union workers, most of them belonging to the CGT, joined the Committee as well. When needed, the Committee invited consultants. Economic journalists were also invited to attend the meetings. All these people, diverse in origin and training, worked together for many hours. They would ask them for delivery schedules and their needs for specialty steel, glass, plastic and other substitute materials. They wanted to know their demand for workers by occupation and skill.

    Workmen, through their unions, played their part in the main discussions and very often gave sound advice on solid grounds. Consequently, 78 Henri Aujac the forecasts concerning associated activities were also turned into Plan targets. Anyway, their own forecasts did not meet the requirements of being categorized as mandatory Plan targets. Experience proved that, by working together, they would reach a sensible accord. Hence, more frequently than expected, the provisional draft based upon the inputoutput table proved useful.

    In short, the Committees had established the forecasts that became Plan targets. Let us imagine, for instance, national planning in the Soviet mode if the USSR had developed a true input-output table of its own. It alone could have scheduled the target production levels to be attained by each sector and consequently issued production orders to managers of the establishments of the sectors. If by any chance the table were triangulable, a different scenario could take place. This order would be the same as that used in classifying sectors for the triangulation scheme.

    They could perform simple provisional reckoning. Economists and politicians continue to this day to seek normative economic tools that thrive in a decentralized political economy. In our case it was due to the need to forecast technological progress. Soon after the war I had met a Renault engineer who, as a war prisoner, had succeeded in working out the concept of numerically controlled machine tools. As we are all now well aware, he was right. So I suggested that one of the aims of the third Plan should be to develop this new kind of machine. Admittedly, estimating its marketing potential and desired production level for was a rather arbitrary undertaking.

    Since neither the sector nor the product existed in , we had to alter the Leontief table by tabulating in the table a hypothetical value of robot production and the likely production growth rate. Let us, to put it simply, take as the reference year in the development of the third Plan. Fifty years ago, a ton of coke was needed to produce a ton of pig iron. Nowadays, less than half a ton of coke is needed. In this case, input and output are measured in physical units: tons.

    By measuring only the size of the change, one would not get detailed knowledge of the causes of the change. The change might not only be technological but also economic or political. Let us return to the previous example of the steel industry. The various steel products had early on been ranked in lists of items that remained in use. The products and their mix within the industry had not basically changed in nature. Whenever they did change, their name also changed.

    As for statistics, they were continuously updated, calculated annually and quickly released to the public. They took into account tonnages — a physical unit. On the contrary, the input-output table dealt only with values, i. Moreover, the list of products for steel was outmoded, and the products were too aggregate for use by the industry. But, as we are all painfully aware, statistics, even when available, are very often several years old.

    Revising them often destroys a valuable inheritance. For any items where such changes arise, econometricians, for example, can lose the long time series they need to produce forecasts! For instance, the automobile today is very different from an automobile of even ten years ago. It has become a machine packed with electronics regulating speed, fuel consumption, heating, gears, and even self-monitoring systems. Nonetheless, we still call it an automobile.

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    Meanwhile, in economic terms it has changed rather radically. In particular, each of its intermediate inputs in an input-output table has changed in both volume and composition. In fact, technological progress has dictated two forms of dynamism. On the other hand, and at the same time, it has unceasingly created new processes and products, so that new terminology has to be invented to identify them. We found that a sound economic forecast ought to be concerned with characterizing two aspects of an economy. One should forecast productivity change in sectors producing traditional goods using traditional processes.

    The second remains in search of a suitable formal approach. Its function was to match the desired level of demand with corresponding national production activities. The planning approach intended to draw on information supplied by the expert members of the Plan Committees. Nevertheless, it proved impossible with a limited number of exceptions to apply the knowledge obtained to the input-output table Aujac, a. Why was this so? The vocabulary of the French national accounts uses fewer than one hundred terms to describe the whole national production system. Managers of national accounts are able to forecast the type of reality depicted via an input-output table, but the methods at their disposal are rudimentary indeed.

    Our experience clearly demonstrated a collaborative failure between national accounts specialists and industry and business experts. A dictionary should have been established to facilitate translation from one language to the other. Now it seems such a tool will never be created in France. This means the language is likely to be vague in terms of its economic correspondence.

    This means it will have little real technological content, and that its economic content will become harder and harder to grasp as the forecast period is extended. With this in mind, we used the terminology selected by the industry association. A series of diagrams was drawn, each diagram showing the successive transformations induced by the production process of a particular raw material. We next tried to evaluate these changes by multiplying the physical quantities by the corresponding prices.

    This research soon proved disappointing. The diagrams were indeed rather attractive and allowed the young researchers to deal directly with the real production processes. But it was impossible to identify and quantify the intermediate inputs of the products particularly in the case of services needed to bring about the various changes in the demand for raw materials, for numbers, however necessary, could not be collected easily. In most cases, they were too many and too small.

    More often than not, the corresponding prices were unknown. On the whole, it eventually appeared that this kind of research was inadequate to establish an input-output table that could validly describe the production system and all the production processes at work in a national economy. So we changed our objectives and looked for a method that could allow us to anticipate the eventual appearance on the market of new products and new processes.

    For each of these technologies, it was our job to anticipate both the successive stages of this development and their diffusion into the market. Our research pointed out the nature of the progress that was expected and the likely schedule of the emergence of the new technologies on the market Aujac, As it was rather easy to guess the average life of these older machines from loan information and depreciation schedules, it was possible to guess when the new ones would be purchased. Table 5. It includes a list of the various likely innovations to come and the probable timetable for the technological and economic stages of their development.

    It was obvious from this table that the era characterized by an unceasing improvement of traditional techniques and products, in the years before about , was nearly at an end. Instead, a period of deep technological transformation was afoot. The textile industries, which up to that point maintained a large labor force, would clearly very soon become a set of heavy industries, resting on chemistry and computer science. It was similarly clear that, if the French textile industries could not succeed in making good from this transformation, they would suffer considerable damage.

    So, the systematic synthesis of individual forecasts had the valuable result of permitting the anticipation of imminent technological transformation. Before the publication of that paper, neither corporate managers nor professional associations had been fully aware of the extent of the change to come. Source: Adapted from Aujac b. Within a few years the French economy enjoyed historically strong growth, thanks to an exceptionally high level of investment. More importantly, national unity was restored. Could anyone have anticipated such surprising events about twelve years in advance — say, in ?

    These two factors are sheer luck and outstanding leadership. But, generally, we forecasters do not know how to incorporate such factors. In France, the part played by chance had two sides: the bad luck of a ruined post-war economy with its risks of social disintegration; and the good fortune to nationalize core industries and to undertake national planning.

    The part played by humans was certainly exceptional. It is amazing that two men so different in their opinions and character as General De Gaulle and Jean Monnet were able to work together to restore both the economy and the social unity of France, and to start or actively support the Development Plan. When a technological forecast is made, econometric techniques can only rehash a dead past. A method that can make concrete the practical conditions for mobilizing varied experience must induce its participants to join in a collective, self-educational, forecast-oriented system that will endow them gradually with a common language and modes of reasoning acceptable to all.

    Williams ed. Jantsch, E. Miernyk 1. Dynamics of the input-output system The original edition of The Structure of American Economy, — did not mention economic dynamics Leontief, A fairly complete exposition of dynamic economic theory, in an input-output framework, was presented to the American Economic Association AEA by Leontief in , and later included as chapter D in the enlarged version of The Structure of American Economy, — Leontief, Leontief and several of his associates continued to make major advances in input-output analysis, which were brought together in a major publication see Leontief et al.

    In this volume Leontief described open and closed, static, comparative static, and dynamic models. He also summarized the work he had been doing in the development of spatial models. The basis of any input-output system is a transactions table: a two-way ordering of all interindustry sales and purchases during a given time period usually a year.

    Constructing transactions tables is costly and time-consuming. National tables are assembled by central statistical agencies.

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    All but a handful of regional tables, and only one multiregional table known to this writer, have been derived from national tables. A static model does not include the stock requirements of an economic system. The same is true of comparative static models, which require two or more transactions tables, but which still deal only with sales 90 Leontief and dynamic regional models 91 on current account. For the equations used to construct a dynamic regional model, see Miernyk et al. Details about their calculation and nature are given in a later section dealing with regional input-output.

    What is said there applies, mutatis mutandis, to any dynamic input-output system. These critics seemed unaware, however, that this was far from a critical assumption for the viability of input-output analysis. They also appeared to forget that the assumption of ceteris paribus is central to neoclassical theory. Meanwhile, conventional micro-theorists must continue to examine the effects of a change in economic variables, one at a time, while assuming that everything else remains unchanged.

    This assumption is universally recognized as being at variance with actual economic conditions anywhere. The comparative static model requires a new transactions table for a future period. These, compared with the original set, show the extent of changes in the structure of the economic system under analysis. Input-output tables are typically published only after 92 William H.

    Miernyk a two- or three-year lag, particularly for large, complex economies such as that of the United States. This is an entirely different approach from the one described in the last section. Only two methods will be discussed in any detail here, since they are generally applicable, i. For a more detailed discussion of these methods, including numerical examples, see Miller and Blair , pp. It is designed for more limited use than the others.

    It was suggested by the method used by the Bureau of Labor Statistics to estimate changes in industrial productivity. The elements in A1RAS are meant to be consistent with two vectors — u1 , which represents total intermediate output, and v1 , total intermediate input — of each sector in the target year 1. These were assumed to operate evenly along the columns and rows of the target-year matrix via substitution ri and fabrication s j multipliers see Stone and Brown, , and Bacharach, Two advantages are claimed for the RAS technique.

    First is its computational simplicity, while preserving signs i. This reinforces 94 William H. Miernyk the view that it would be unrealistic, as the RAS method does, to assume uniform change along rows and columns. For illustrations see Miernyk , pp. This is because, following Georgescu-Roegen and — indirectly —Schumpeter , my objection to the RAS method is epistemological rather than mathematical. Economic growth, or — more generally — economic change, is the result of qualitative rather than quantitative factors. And the economic process can only be described dialectically, rather than arithmomorphically, because mathematical models are unable to incorporate qualitative change see Georgescu-Roegen, For a brief, non-technical discussion of dialectics versus analysis, see Miernyk , pp.

    As many of his followers have noted, Georgescu-Roegen was a thinker far ahead of his time. How was he viewed by Leontief? This is not meant to be pejorative. There are circumstances under which the estimates of experts are more reliable than those derived statistically, particularly when qualitative changes are involved. Published input-output tables are expressed in sales and purchases. But Leontief considered these entries to be indexes of physical goods and services.

    That is, he thought in terms of engineering production functions.

    This is also true of the ex ante input-output tables produced at the Battelle Memorial Institute, in Columbus, Ohio see Fisher and Chilton, The stability of dynamic systems 3. Not all purchases on capital account are the result of expansion of capacity. But the chisels used to shape metal parts on the lathe might last only one year. Thus it is useful to distinguish between expansion and replacement capital. For further details, and numerical examples, see Miernyk et al. Say that gross output is known for the year i. The process can be repeated 96 William H.

    Is the dynamic model inherently unstable? Finally, as will be noted presently, economic models can be compared in terms of stability, as well as other characteristics, only if they have common taxonomic origins Miernyk, , pp. There is a further exchange in the same issue of the journal, but it is clear that Leontief and Sargan are talking about two different models; hence their differences are irreconcilable. Leontief and dynamic regional models 3.

    There is no reason, however, why these principles cannot be applied to ideas as well as objects, and there are good reasons why they should be. This is a major taxonomic error, about of the magnitude of making behavioral comparisons between a mouse and a moose because both happen to be mammals.

    Changes in income depend upon changes in the behavior of consumers and investors. The latter is not determined by changes in A; causation goes the other way. For an illustrative example, see Miernyk , pp. Clearly, the Leontief dynamic model is not a more complicated analogue of the simple Harrodian system.

    Thus it should not be expected to contain the same behavioral equations as does the latter. Moreover, the emphasis in input-output analysis is on disaggregation, while conventional growth theory continues to deal in broad aggregates. The Harrodian system, as well as the numerous growth models engendered by it, and the virtually identical model developed independently 98 William H. Miernyk by Domar are lineal descendants of the aggregated Keynesian system.

    The second part, 'Perspectives of Input-Output Economics', includes theoretical and empirical research inspired by Leontief's work and offers a wide-ranging sample of the state of interindustry economics, a field Leontief founded. This is a strong collection likely to appeal to a wide range of professionals in universities, government, industry and international organizations. Subject index. Author index. Part II Perspectives of inputoutput economics.