The Nobel Series: Leontief & Input-Output model

The Nobel Prize in 1973 was awarded to Wassily Leontief for the development of the input-output method and its application to economic problems. As the Nobel website mentions:

"Professor Leontief is the sole and unchallenged creator of the input-output technique. This important innovation has given to economic sciences an empirically-useful method to highlight the general interdependence in the production system of a society. In particular, the method provides tools for a systematic analysis of the complicated interindustry transactions in an economy."

In this article, we will review the works of Wassily Leontief and see how they continue to be relevant for various economic and public policy problems.

Works of Leontief

Leontief first outlined the input-output technique in the 1930s and his analysis was published in his book in 1941, titled 'The Structure of American Economy, 1919-1929'. Before that, Leontief had published an article, 'Quantitative input-output relations in the economic system of the United States', in the 'Review of Economics and Statistics' in 1936, where he had first laid out the input-output model. As he himself said, this was basically a mathematical tool to understand the structure of the economy. Let us not forget that Keynes 'General Theory' was also published in 1936 and took centre stage, as a result of which Leontief's work did not attract attention at first.

Leontief's idea was quite straightforward. He suggested that an economy is basically divided into sectors and each sector produces a product. Each sector requires input(s) which must come from possibly all of the sectors, including itself. Final demands of products for consumption, investment and exports in the model are treated as exogenous to the model. The purpose of the analysis is then to find out how much production has to be increased in the various sectors of the economy to satisfy a given desired or planned increase in final demand for consumption, investment and exports. The increased production in each sector then has to cover not only the change in final demand but also the derived changes in demand for intermediary products in the various production sectors. Each sector has technical coefficients which define the quantities of intermediary products required to produce a unit of output of that sector. The website of the Nobel Prize has explained the input-output of Leontief, thus:

"One of the most characteristic features of an economic system is the mutual interrelations between the various parts of the system — what is usually called the interdependence within the economic system. Such an interdependence is characteristic also for the conditions in the production sector of an economy. For instance, in order to produce steel we need not only labour but also coal and thousands of other intermediary products, or "inputs", in the production process. But to produce the necessary coal and other inputs we require, in turn, steel and other intermediary products in addition to labour.

This means that if we want to increase the production of steel we must at the same time increase production of coal, which in turn requires increased availability of steel, etc. in an infinite series – and similarly for the thousands of other products which are directly or indirectly involved in the production of steel and coal. This, in itself, rather trivial example illustrates the previously mentioned interdependence within the production system."

The above description of the economy can be reduced to an input-output table, which lists the value of the goods produced by each sector and how much of that output is used by each sector. For example, the following table is derived from the table Leontief created for the American economy in 1947. For ease of explaining, the data has been aggregated into four sectors: agriculture, manufacturing, services and the external sector.

The table shows the inter-sectoral exchange of goods and services in the US for 1947. Thus, in 1947, the manufacturing sector spent USD 163.43 billion for the inputs it needed. Out of this, USD 4.92 billion came from agriculture, USD 61.82 billion came from manufacturing and USD 25.95 billion came from services. In the above matrix, column entries, therefore, represent inputs to a sector, while row entries represent outputs from a given sector. This format, therefore, shows how dependent each sector is on every other sector, both as a customer of outputs from other sectors and as a supplier of inputs.

From the table above, we can derive the consumption matrix of the economy by dividing each column entry by the gross output. This is also the matrix of technical coefficients. We, therefore, have the following table:

From the above table, the equilibrium production levels for each sector can be calculated. These production levels will meet the intermediate demands of the sectors of the economy plus the final demands of each sector.

Later, in 1949, while he was at Harvard, Leontief was one of the first to use a computer model to analyse the input-output method.

Leontief's paradox

Leontief's work also found an application in international trade. He tested the Heckscher-Ohlin theory of international trade using input-output analysis. We may recall that the latter theory argued that a country exports those commodities which are produced by the country's relatively abundant factor. In other words, if a country is capital (labour) abundant, it should export capital-intensive (labour-intensive) products. Leontief tested this theory for post-war US and found that even though the US is a capital abundant country, it still exported labour-intensive commodities.

The paradox was explained by many economists in different ways. Leontief himself argued that American labour is three times more productive than

world labour and other factors such as entrepreneurship and a market-friendly environment explain the paradox. Others pointed out that Leontief disregarded worker's skill and this could be seen as a major explanation if we regard that human capital is the US's relatively abundant factor.

Leontief & public policy

The input-output system has found extensive use in understanding economic policy issues. The input-output matrix is still used around the world in economic planning. It is also popular in forecasting, both in the short and in the long run. It has also been used recently in including the by-products of the production process such as air and water pollution, to understand the environmental impact of production processes.

The model can analyse three types of impact: direct, indirect, and induced, which are basically ways to measure the effect of changes in one sector on other sectors of the economy. The Investopedia website explains this simply as follows:

The direct impact of an economic shock is an initial change in expenditures. For example, building a bridge would require spending on cement, steel, construction equipment, labour and other inputs.

The indirect, or secondary, impact would be due to the suppliers of the inputs hiring workers to meet demand.

The induced, or tertiary, impact would result from the workers of suppliers purchasing more goods and services for personal consumption. This analysis can also be run in reverse, seeing what effects on inputs were likely the cause of observed changes in outputs.

It is therefore clear that an input-output model is a tool that makes it simple to analyse inter-sectoral dependencies in the economy. This is particularly helpful in a more centralised economy, but can also be useful in a market economy. The Nobel website offers two examples of the policy application of Leontief's model. First, the input-output method was used to calculate how the disarmament of the US and rearmament of Korea around the time of the Korean War, would influence the production volume and employment level in the various sectors of the American economy. The other example shows how the model can be used to study the spread effects of change in production costs from one sector to another. For instance, how does a wage hike in one sector impact other sectors?

Finally, an important application of the model is that it helps in forecasting demand and production levels without waiting for the market signals. In other words, the government or firms can use centrally performed input-output studies to anticipate future development without having to wait for the market signals which will appear due to changes in supply and demand in the various markets for commodities and services.

Conclusion

The input-output model was a pathbreaking innovation that certainly helped the centralised economies. But it also provided a useful tool to market economies for forecasting demand, production and investment levels. It also gave us a tool to analyse the dispersal effects of changes in one sector on other sectors. Of course, the pre-requisite of using the model was the availability of basic statistical information. And the model gave a fillip to improved sector-wise data collection across the world. Input-output tables were gradually compiled for most large economies across the world by the 1970s. Applications of the model have been made in economic projections of demand, output, employment, and investment for the individual sectors of entire countries and of smaller economic regions. The model has also been used for the study of technological change and its effect on productivity, development planning and even studying international and interregional economic relationships.

The writer is an IAS officer, working as Principal Resident Commissioner, Government of West Bengal. Views expressed are personal

Views expressed are personal