In a tribute to Robert Solow, I4I’s Editor-in-Chief Parikshit Ghosh outlines some of the late Nobel Laureate’s contributions to macroeconomics, and uses examples and metaphors for the economy to explain how the Solow model presents the idea of tapering growth in a mathematical framework. He examines catch-up growth in India in the context of this model, and highlights the need to look beyond the usual suspects to find the path to mass prosperity that remains elusive to many nations.
I first came across Robert Solow’s name in the newspaper, not in a textbook. Shortly after I took up the study of economics as an undergraduate, he won the Nobel Prize. It dawned on me later that two people had laid down much of the conceptual scaffolding and mathematical plumbing for the discipline in the post-war period – Paul Samuelson for microeconomics, and Robert Solow for macroeconomics. They happened to be lifelong colleagues at MIT. Many brilliant economists who have come out of that department were blessed to have stood on the shoulders of not one, but two giants. When Solow passed away on 21 December 2023, he was one year shy of a century. However, his legacy will far surpass his longevity.
Today, even in purchasing power parity (PPP) terms, US GDP per capita is nearly 80 times that of Burundi and roughly 30 times its own figure from 150 years ago (various estimates are summarised here). Sustained economic growth in some parts of the world has transformed how people live. In Europe, life expectancy at birth has almost doubled since the beginning of the twentieth century, infant mortality has been cut down by more than 99%, and the work week has shrunk by probably a third. Ordinary people in a handful of nations have the time and money to travel for vacation, eat fancy meals prepared by others in a restaurant, and catch a play or movie on the weekend. This is a big slice of a lifestyle that once used to be the preserve of aristocrats.
A large part of humanity living outside Europe and North America has seen their aspirations soar, but their hopes often dashed. Mass prosperity is possible, but yet elusive to most nations. Discovering the map of that El Dorado remains one of the most important intellectual and practical pursuits anyone can undertake. It is safe to say that the whole map remains shrouded in mystery, but Solow is the Indiana Jones who found some of its most important fragments. They remain tucked away in two seminal papers – one theoretical and the other empirical (Solow 1956, 1957).
A country grows richer by making its workers more productive, and workers are more productive when they are equipped with more and better tools. A farmer with a tractor and combine harvester can feed many more people than one with sickle and plough; a construction worker operating a crane can move materials faster than one with a wheelbarrow. A nation that saves a larger fraction of its income and invests it in capital goods will obviously grow faster unless it hits some other bottleneck. Before Solow, economists calculated the prevailing capital-output ratio to forecast growth far into the future and set national savings targets to meet policy goals. The ‘fixed-coefficient’ Harrod-Domar model1 which often underpinned five-year plans like India’s, turned out to be too optimistic. It missed a sobering reality – most economic resources, including machinery and equipment, are subject to diminishing returns.
A bank where employees conduct business with paper, pen and physical folders filed away in cabinets will see a jump in productivity when computers start appearing on desks. But as the benefits of modern computing percolates from the branch manager to the tellers to the cleaning staff, the boost is likely to get smaller and smaller. Beyond a point, if the bank keeps purchasing new machines, they will gather dust in a storage room and add nothing of value. Growth, in other words, will fizzle out.
This can be a metaphor for the economy. The Solow model generalises the idea of tapering growth in an elegant mathematical framework. The bad news is that we always seem headed towards a productivity plateau. The good news is that there is hope for laggards. A bank which started its computerisation drive late will meet the early birds on that plateau one day. Similarly, poorer countries should grow faster and eventually catch up with richer countries. India has a relatively high growth potential, being the poorest among the BRICS nations let alone compared to OECD economies. We tend to forget this when we are in self-congratulatory mode – our benchmark should not be today’s mature economies but the early-phase, nearly double-digit growth rates of China and South Korea when they still had low hanging fruit to pick.
Another cautionary note is that the predicted convergence is conditional on making similar choices – a bank which is willing to reinvest profits to replace only one broken computer per year will end up with a smaller stock of computers than a bank which is willing to replace ten. In other words, the miserly bank will come to rest on a lower plateau. The falling rate of private investment in India is indeed a matter of concern (Raghavan 2023).
At any rate, the message that economic growth must vanish like the Cheshire Cat is not to be taken literally. To do so is to miss the punchline of a joke. Britain or America haven’t stopped growing; in fact, their growth rates have held steady for more than a century. The bank, once it is done putting computers on every desk, may seek to train its employees in computing skills, expand the RAM, upgrade the software, reorganise the workflow, build team spirit, strengthen incentives with bonuses and stock options, or even go for full automation of some services using ATMs and internet banking. Hitting a plateau is always a looming danger, but one can keep climbing if one is inventive and resourceful enough. As productivity marches on, however, what will become less visible is not growth, but where it came from. PCs are easy to count, inventorise and put a value on. Managerial innovations are not.
Solow’s mathematical modelling opened the door to the empirical investigation called growth accounting which he also led from the front. Using the model’s equations and national income data, we can ask: how much of historical growth has been driven by measurable factors like growth of the labour force and investment in productive capital? The part that remains unaccounted for must be driven by intangible factors of technology, institutions, political environment, and suchlike, which are not captured in macroeconomic data. Surprisingly, Solow found that for the USA, a major part of growth (87.5% in his estimate) in the first half of the 20th century has been driven by things that sit inside this black box. To put it more simply: we don’t quite know why America grew to be an economic powerhouse!
It is strange to eulogise work that is Seinfeldian in nature – a discovery about nothing – until we recall the words of Socrates: awareness of ignorance is the beginning of wisdom. It is tempting to ‘explain’ the unexplained part of economic growth by giving it labels that convey a sense of concreteness (such as the Solow residual, or total factor productivity (Hulten 2000) or project our imagination about what lies inside the black box (technical progress). Solow himself is guilty of wishful nomenclature in his 1957 paper. To not recognise it for what it is – a hole in our understanding – would be a disservice to the message: we have to look well beyond the usual suspects if we are to find the whole map of El Dorado.
Subsequent research has managed to shine some light into the darkness. Mankiw, Romer and Weil (1992) showed that human capital (measured in years of schooling) is as important to growth as physical capital, but taken together, they are still subject to the force of convergence. Acemoglu and Robinson’s (2012) tome makes a case for the role of institutions. Endogenous growth theory, which emerged in the 1990s led by Paul Romer (1994), suggested that investments in R&D as well as learning-by-doing may be the engine that has sustained modern growth, beating the force of diminishing returns. Some people would also argue that the secrets of productivity growth can only be unlocked industry by industry and brick by brick – that is, at the microeconomic level. Solow's (1994) take on all these developments is laced with characteristic lucidity and wit – he was one of the best writers in the economics profession, and a frequent contributor to the New York Review of Books.
Finally, it must be said that from the perspective of India, looking at things too much through the lens of Western economies may be misleading. The East Asian miracle could be a more relevant example for us. While Europe had to push the global technology frontier, nations like China, South Korea or Taiwan were in a position to beg, borrow or steal Western technology. As Alwyn Young (1995) showed, their unprecedented growth rates were achieved much more on the back of heavy investments in physical and human capital and a rapidly expanding labour force. We can go a long way if we can do something about our declining female labour force participation and private investment. Growth may disappear in a million years, but in the long run, aren’t we all dead? It will be good if, in a few decades, Sudan can become Sweden.
Anyone who thinks seriously about that is a student of Bob Solow.
- The Harrod–Domar model, developed by Roy Harrod (1939) and Evsey Domar (1946) is a model of economic growth used to explain an economy's growth rate in terms of the level of saving and capital. It suggests that there is no natural reason for an economy to have balanced growth.
- Acemoglu, D and JA Robinson (2012), Why Nations Fail: The Origins of Power, Prosperity and Poverty, Crown Business.
- Domas, Evsey D. (1946), “Capital Expansion, Rate of Growth, and Employment”, Econometrica, 14(2): 137-147.
- Harrod, R. F. (1939), “An Essay in Dynamic Theory”, The Economic Journal, 49(193): 14-33.
- Hulten, CH (2000), ‘Total Factor Productivity: A Short Biography’, NBER Working Paper No. 7471.
- Mankiw, N. Gregory, David Romer and David N. Weil (1992), “A Contribution to the Empirics of Economic Growth”, The Quarterly Journal of Economics, 107(2): 407-437.
- Raghavan, TCA S (2023), ‘Private investment a shrinking slice of India’s GDP pie since 2012. It’s a vote of no confidence’, The Print, 25 April.
- Romer, Paul M. (1994), “The Origins of Endogenous Growth”, Journal of Economic Perspectives, 8(1): 3-22.
- Solow, Robert M. (1956), “A Contribution to the Theory of Economic Growth”, The Quarterly Journal of Economics, 70(1): 65-94.
- Solow, Robert M. (1957), “Technical Change and the Aggregate Production Function”, The Review of Economics and Statistics, 39(3): 312-320.
- Solow, Robert M. (1994), "Perspectives on Growth Theory", Journal of Economic Perspectives, 8(1): 45-54.
- Young, Alwyn (1995), “The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience”, The Quarterly Journal of Economics, 110(3): 641-680.