# Nobel Perspectives

## Wassily Leontief: Input-Output Models

An old economics professor always would start his principles classes by telling his students a trite story about some average person living in NYC: The person got up every morning at 7:00, drank several cups of coffee to wake up, drove to work, labored for eight hours, drove home, and so on. The professor would then tell his students that if they wanted to make the story more interesting, then they should consider the fact that there are millions of people in NYC, along with over 100 million people in the United States, who do roughly the same things every day. He then asked them the question: How is it that an economic system knows how to produce just enough coffee to wake everyone up, just enough gas to get people back and forth to work, and so on? The students would later discover that the answer lies in understanding how a market-oriented, capitalistic system works.

The professor would go on to explain that the study of economics focuses on explaining how complex systems function by developing models. Economist Fritz Machlup defined models such as Keynes General Equilibrium Model and Solow Growth Theory as abstractions of complex phenomenon. However, Russian economist Wassily Leontief (1906–1999) believed it was impossible to understand an economy by studying it in abstraction. In the 1930s, Leontief developed the Input-Output Model: a general model of production based on economic interdependence. He later expanded the theory by generating the first empirical input-output model.

Leontief’s Input-Output Model is a matrix based framework that explains the outputs of one industry as inputs to other industries and final demand. There are three major input-output matrices which are transactions, direct, and direct/indirect (Table 1). The transaction table is broken into three components: processing or intermediate sectors, the payment sector (wages, rents, interest, profits, depreciation, taxes, and savings), and final demand sectors (consumption, capital investments, government, and net exports). The direct table shows the amount of sector inputs needed to produce $1.00 of a sector’s output. For example, the 2015 U.S. input-output model shows that to produce $1.00 of manufacturing goods, the manufacturing sector buys $0.045 from itself, $0.056 from the mining sector, $0.075 of professional services, $0.158 for labor employment, and spends $0.014 in taxes. In the direct matrix, each row shows the sales of that sector to other sectors. The direct/indirect table, in turn, shows the total output requirements needed to meet final sector demands. For example, in order to produce say $1.00 of construction goods, the table factors in both the direct and indirect input requirements needed by each sector to generate the $1.00 of output. Thus, the product of multiplying the matrix by each sector’s final demand equals the total output of each individual sector. The direct-indirect matrix is particularly useful in conducting impact assessments. For instance, using the 2015 U.S. input-output model, a $1.00 increase in construction demand would lead to a $0.398 increase in manufacturing output, a $1.004 increase in construction sector output, and a $0.122 increase in professional services; which means a $1.00 increase in construction results in a total increase in aggregate output of $1.485. Economists have also used the direct/indirect matrix to forecast sector outputs based on expected demand in each sector and to study the impact of policy changes.

Today, there are input-output models disaggregated into as many as 300 subsectors, regional and state models, and country models.

These models have proved to be crucial in understanding the economies of the world and how they are interconnected through global supply chains. Leontief himself used his model to test the Heckscher–Ohlin theory. This classic theory held that capital abundant countries like the United States gain by exporting relatively more capital-intensive commodities and importing more labor-intensive goods. However, Leontief, in examining the input-output structure of the U.S. economy found just the opposite — Leontief Paradox.

Input-output models also provide the framework for many of today’s supply-chain models. One of the most sophisticated of these models is Bloomberg’s supply chain platform. The platform provides a comprehensive supply chain breakdown for thousands of publicly traded companies. For example, Bloomberg’s supply chain platform for Apple Inc. shows that Apple has 343 suppliers and 166 customers. Apple pays 49.67% of their cost of goods sold to Hon Hai Precision, 14.09% to the Pegatron Corporation, and 10.23% to Quanta Computer. Among Apple’s customer, 3.80% of its revenue comes from sales to AT&T, 2.46% from Best Buy, and 2.17% from China Mobil (Table 2).

In 1996, a graduate student at Stanford University developed an algorithm that ranked the popularity of pages appearing on the worldwide web. The algorithm is known as the “Page Rank Algorithm” and the author is Larry Page, co-founder of Google. Interestingly, the algorithm uses a methodology similar to the one used by Leontief to develop his input-output model.

Leontief taught four doctoral students, who were awarded the Nobel Prize in Economic Sciences: Paul Samuelson 1970, Robert Solow 1987, Vernon L. Smith 2002, Thomas Schelling 2005. Wassily Leontief was himself awarded the Nobel Prize in Economic Sciences in 1973 for his work on the Input-Output model—a model that goes far in helping us understand how an economic system knows how to produce just enough coffee to wake everyone up, just enough gas to get people back and forth to work, and so on.

(Sources.)