Solow Growth Model

Economic growth has always been a mystery to many of us. It is always difficult to understand and make projections on a country’s economic growth. It is also increasingly difficult to build models and make projections on the growth of an economy. Economic output represents the aggregated activity of billions of people, influenced by forces seen and unseen. Despite the difficulties, economists cannot resist trying.

Forecasters usually rely on two different predictive approaches. 

  1. Theory-based: This one is shaped by how economists believe economies behave.
  2. Data-based: This one is shaped by how economies have behaved in the past. 

I am supposed to teach the chapter “Aggregate Output, Prices, and Economic Growth” to my 2020 Dec CFA Level I students this Friday. The economic growth topics are also part of the CFA Level II and Level III curriculum. Despite years of reading and studying different economies (including Bangladesh), I find it astonishingly difficult to figure out different factors that drive the economy on a year to year basis. Though this is one of my jobs to guesstimate the economic growth and implement asset allocation based on that, if you ask me at what rate the country will grow, my simple answer will be “I don’t know”. 

An irreverent economist, John Kenneth Galbraith, once said, 

 “THE only function of economic forecasting is to make astrology look respectable.”

I am, by nature, a passionate learner on finance and economics, and I always try to understand it by reading a wide range of topics. As a teacher at PFS, I always try to think, understand, and improve the method of teaching so that I can make my students understand the topics better. 

As I was thinking about how I can teach better next Friday, incidentally, I came across an article published on The Economist in Jan 2016. The magazine computed just how far the IMF’s forecasts were off on average over the period 2000–2014.12 For two years from the time of prediction (say, the growth rate in 2014 predicted in 2012), the average forecast error was 2.8 percentage points. That’s somewhat better than if they had chosen a random number between–2 percent and 10 percent every year, but about as bad as just assuming a constant growth rate of 4 percent. 

Let’s revisit the theory first. The simplest of the theoretical bunch is the Solow growth model, named for Robert Solow, a Nobel-prize winning economist. 

Robert Solow developed a model that explained the contribution of labor, capital, and technology (total factor productivity) to economic growth.  The model shows that the economy’s productive capacity and potential GDP increase for two reasons:

  1. accumulation of such inputs as capital, labor, and raw materials used in production, and
  2. discovery and application of new technologies that make the inputs in the production process more productive—that is, able to produce more goods and services for the same amount of input.

Solow’s growth accounting equation shows that the rate of growth of potential output equals growth in technology plus the weighted average growth rate of labor and capital.

Watch the following Video

He also said that if capital grows faster than labor, capital will become less productive, resulting in slower and slower growth. According to his model, there are two major implications  potential GDP:

  1. Long-term sustainable growth cannot rely solely on capital deepening investment that increases the stock of capital relative to labor. This means, increasing the supply of some input(s) relative to other inputs will lead to diminishing returns and cannot be the basis for sustainable growth.
  2. Given the relative scarcity and hence high productivity of capital in developing countries, the growth rates of developing countries should exceed those of developed countries. As a result, there should be a convergence of incomes between developed and developing countries over time.

Source: CFA Curriculum

Coincidentally, I was reading a book named “Good Economics for Hard Times” by Abhijit V. Banerjee and Esther Duflo. Chapter five (The end of Growth?) mentioned another book (The Rise and Fall of American Growth: The U.S. Standard of Living since the Civil War) by Robert J. Gordon where Gordon said, “GROWTH ENDED ON October 16, 1973”.

Gordon has gone out on a limb and predicted economic growth will average a meager 0.8 percent per year over the next twenty-five years.

What happened on October 16, 1973?

On that day, the member countries of OPEC announced an embargo on oil. By the time the embargo was lifted in March 1974, the price of oil had quadrupled. The world economy at this time had become increasingly reliant on oil and was generally facing raw material shortages that were pushing up prices. What followed in the rich countries of the West was a lackluster decade of “stagflation” (economic stagnation accompanied by inflation). 

As I was reading through, I could understand and explain the factors of the economic growth of different economies and it strengthened my understanding of the Solow Growth model.

Below is an excerpt from the book “Good Economics for Hard Times” 


For the thirty-odd years that separated the end of the Second World War from the OPEC crisis, economic growth in Western Europe, the United States, and Canada was faster than it had ever been in history.

Between 1870 and 1929, GDP per person in the United States grew at a then unheard of rate of 1.76 percent per year. In the four years after 1929, GDP per person went down by a catastrophic 20 percent—it is not called the Great Depression for nothing—but it recovered fast enough. The average yearly growth rate from 1929 until 1950 was actually slightly higher than in the previous period. But between 1950 and 1973, the yearly growth rate went up to 2.5 percent.2 There is more difference than there might appear to be between 1.76 percent and 2.5 percent. It would take forty years for GDP per head to double with a growth rate of 1.76 percent, but only twenty-eight years at 2.5 percent.

Europe had a more checkered history before 1945, partly because of its wars, but after 1945 things really exploded. When Esther was born, late in 1972, France had about four times the GDP per capita than when her mother, Violaine, was born in 1942.3 This was typical of the Western European experience. GDP per capita in Europe increased by 3.8 percent every year between 1950 and 1973.4 It’s not for nothing that the French call the thirty years after the war les Trente Glorieuses (“the Glorious Thirty”).

Economic growth was driven by a rapid expansion in the productivity of labor, or the output produced per hour worked. In the United States worker productivity grew at 2.82 percent per year, which meant it would double every twenty-five years.5 This rise in labor productivity was large enough to more than offset a decline in hours worked per head that was going on at the same time. During the second half of the century, the workweek went down by twenty hours in the US and in Europe. And the postwar baby boom lowered the share of working-age adults in the population 

What made workers more productive?

In part, they were becoming more educated. The average person born in the 1880s studied only up to seventh grade, whereas the average person born in the 1980s had on average two years of college education.6 And they had more and better machines to work with. This was the age in which electricity and the internal combustion engine came to assume their central role.

Making somewhat heroic assumptions, it is possible to guesstimate the contribution of these two factors. Robert Gordon reckons that rising education explains about 14 percent of the increase in labor productivity over the period, and the capital investment that gave workers more and better machines to work with explains a further 19 percent of the increase.

The rest of the observed productivity improvement cannot be explained by changes in things economists can measure. To make ourselves feel better, economists have given it its own name: total factor productivity, or TFP. (The famous growth economist Robert Solow defined TFP to be “a measure of our ignorance.”) Growth in total factor productivity is what is left after we have accounted for everything we can measure. It captures the fact that workers with the same education level working with the same machines and inputs (what economists refer to as capital) produce more output today for each hour they work than they did last year. 

This makes sense. We constantly look for ways to use our existing resources more effectively. This reflects in part technological progress: computer chips become cheaper and faster, so one secretary can now do in a few hours the work a small team used to do; new alloys are invented; new varieties of wheat that grow faster and require less water are introduced. But total factor productivity also increases when we discover new ways to reduce waste or shrink the time either raw materials or workers are forced to stay idle. Innovations in production methods like chain production or lean manufacturing do that, as does, say, the creation of a good rental market for tractors.

What made the few decades before 1970 extraordinary compared to much of history is that total factor productivity increased particularly rapidly. In the United States, TFP growth was four times faster between 1920 and 1970 than between 1890 and 1920.7 In fact, it was this rather than growth in education or capital per worker that gave the later period its special mojo. TFP growth in Europe was even faster than in the United States, especially after the war, partly because Europe adopted innovations already developed in the US.

Rapid growth was not only to be seen in national income statistics. By any measured outcome, quality of life was radically different by 1970 compared to what it was in 1920. The average person in the West ate better, had more heat in the winter and better cooling in the summer, consumed a larger variety of goods, and lived a longer and healthier life.9 With a shorter workweek and earlier retirement, life was no longer quite so dominated by the drudgery of daily labor. Child labor, omnipresent in the nineteenth century, had more or less disappeared in the West. There, at least, children could now enjoy their childhoods.


But in 1973 (or thereabouts) it all stopped. On average, over the next twenty-five years, TFP has grown at only a third of the rate achieved in 1920–1970. What started with an economic crisis with a clear start date, and even a set of foreign powers to blame, became the new normal. The persistence of the slowdown was not immediately apparent. Born and bred during the golden age of economic growth, scholars and policy makers initially believed it was a temporary blip, soon to fix itself. By the time it became clear that slow growth was not just an aberration, the latest hope was that a new industrial revolution, spurred by computing power, was right around the corner. Computing power was increasing at a faster and faster speed, and computers were being introduced everywhere, much as electricity and the combustion engine once were. This would surely translate into a new era of productivity growth that would pull the economy with it. And indeed it finally happened. Starting in 

1995, we saw a few years of high TFP growth (though still significantly less than in the go-go years). It faded quickly, however. Since 2004, TFP growth and GDP growth both in the United States and in Europe seem to be back to the bad days of 1973–1994.11 In the United States, GDP growth did pick up in mid-2018, but TFP growth remains slow. Over the year, TFP grew only at an average of 0.94 percent,12 compared to the 1.89 percent achieved during the 1920–1970 period.

This new slowdown has provoked a lively debate among economists. It seems difficult to reconcile it with everything we hear around us. Silicon Valley keeps telling us we live in a world of constant innovation and disruption: personal computers, smartphones, machine learning. Innovation seems to be everywhere. But how could there be all this innovation without any sign of economic growth?

The debate has revolved around two questions. 

  • First, will sustained fast productivity growth eventually return? 
  • Second, is the measurement of GDP, at best a bit of an exercise in guesswork, somehow missing all the joy and happiness the new economy is bringing us?

…… Robert Gordon reminds us of our longer history. It is the 150 years between 1820 and 1970 that were exceptional, not the period of lower growth that followed. Sustained growth was virtually unknown until the 1820s in the West. Over the period 1500 to 1820, annual GDP per capita in the West went from $780 to $1,240 (in constant dollars), a paltry annual growth rate of 0.14 percent. Between 1820 and 1900, growth was 1.24 percent, nine times more than in the previous three hundred years, but still much less than the 2 percent it would hit after 1900.17 If Gordon is right and we end up with a 0.8 percent growth rate, we would simply be returning to the average growth rate over the very long run (1700–2012).18 This is not the new normal; it is just normal.

Of course, the fact that sustained growth over a long time, the kind we saw over most of the twentieth century, was unprecedented, does not mean it could not happen again. The world is richer and better educated than ever before, the incentives for innovation are at an all-time high, and the list of countries that could lead a new innovation boom is expanding. It could well be the case, as some technology enthusiasts believe, that growth explodes again in the next few years, fueled by a fourth industrial revolution, perhaps powered by intelligent machines capable of teaching themselves to write better legal briefs and make better jokes than humans. But it could also be, as Gordon believes, that electricity and the combustion engine brought about a onetime shift in how much we can produce and consume. It took us some time to reach this new plateau and there was fast growth along the way, but we have no particular reason to expect this episode will repeat itself. Nor, we might add, do we have definitive proof it won’t. Mostly, what is clear is that we don’t know and have no way to find out other than by waiting. 

The year 2004, when TFP growth, after jump-starting in 1995, slowed down again, is when Facebook began to occupy the outsized role it currently plays in our lives. Twitter would join in 2006 and Instagram in 2010. What is common to all these platforms is the fact that they are nominally free, cheap to run, and wildly popular. When, as is now done in GDP calculations, we judge the value of watching videos or updating online profiles by the price people pay, which is often zero, or even by what it costs to set up and operate Facebook, we might grossly underestimate its contribution to well-being. 

….the cost of running Facebook, which is how it is counted in GDP, has very little to do with the well-being (or ill-being) it generates. That the recent slowdown in measured productivity growth coincides with the explosion of social media poses a problem, because it is entirely conceivable that the gap between what gets counted as GDP and what should be counted in well-being widened exactly at this time. Could it be there was real productivity growth, in the sense that true well-being increased, but our GDP statistics are missing this entire story?

…Robert Gordon reckons Facebook is probably responsible for part of the productivity slowdown—too many people are wasting time updating their status at work.


…..In 1956 Robert Solow wrote a paper suggesting growth would eventually slow down.23 His basic point was that as per capita GDP goes up, people save more, and therefore there is more money to invest, and more capital available per worker. This makes capital less productive; if there are now two machines in a factory where there was only one, the same workers will have to operate both at the same time. Of course, a single factory can hire more workers if it gets more machines. But the whole “economy cannot (assuming migration remains unchanged), once its reserve of underused workers is exhausted. Therefore, the extra machines bought with the additional savings will have to be worked with fewer workers. Each new machine and as a consequence each additional unit of capital will contribute less and less to GDP. Growth will slow down. Furthermore, the lower productivity of capital lowers its financial return, which in turn discourages savings. So eventually people will stop saving and growth will slow down.

This logic operates in both directions. Capital-scarce economies grow faster because new investment is highly productive. Rich economies, which are, in general, capital abundant, tend to grow more slowly because new investment is not as productive. One implication of this is that any large imbalance between labor and capital should get corrected. Economies overabundant in labor grow faster, and since incomes grow faster, savings do as well. So these economies accumulate capital faster and become more capital abundant. By the reverse argument, economies with too much capital relative to labor accumulate capital more slowly.

As a result, a sharp divergence between the rates of growth of capital and the labor force is not sustainable over the long haul because if, say, capital grows faster than the labor force, then the economy will have too much capital relative to labor, which will slow down growth. There can be imbalances in the short run (as we are witnessing today in the United States where the share of the GDP paid to the labor force is falling24), but in the long run there is a natural tendency for economies to stay close to a balanced growth path, where labor and capital grow at roughly the same rate, and so does human capital—the part of capital embodied in the skills of the workers, for very much the same reason. Solow argued that GDP (which is after all the product of labor, skills, and capital) would also grow at the same rate as well.

Now, the growth of the effective labor force is determined by past fertility and how much people want to work, both factors that seemed to Solow to be more driven by demography than economics, and therefore more related to a country’s history and culture than to the current state of its economy or economic policy. However, there is also the improvement of TFP—if one worker becomes so productive that he can do the work of two, because of improvements in technology, then the effective labor force would have doubled. Solow assumed such transformations were also unrelated to contemporary economics and policies of the country, in effect placing the growth rate of the effective labor force outside the realm of economics. This is why he called it the “natural rate of growth,” and from his theory, we know that GDP must also grow at the same rate as the effective labor force in the long run; that is, at the natural rate.

A number of implications follow from Solow’s theory. First, growth is likely to slow down after a phase of fast growth that follows a dramatic transformation, once the economy is back on the balanced growth path. This is clearly consistent with what happened to Europe after 1973. After the wartime destructions, capital was scarce and Europe had a lot of catching up to do; by 1973 the era of catch-up growth was over. In the United States, the kind of investment-driven growth Solow had in mind clearly slowed down after the war, but conveniently its place was taken by rapid TFP growth until 1973. Since then, as we already discussed, there has been a slowing trend even in the United States. Interest rates have been falling throughout the West, reflecting, it seems, an abundance of capital, exactly as in the Solow model.


The second implication of Solow’s theory, and perhaps the most striking, is what economists call convergence. Countries scarce in capital and relatively abundant in labor, like most poor countries, will grow faster because they have not yet reached their balanced growth path. They can still grow by improving the balance between their labor and capital. As a result, we would expect the difference in GDP per worker across countries to be reduced over time. All else being the same, poorer countries will catch up with their richer counterparts.

Solow himself was careful to stop well short of promising this. If a country has a lot of labor and very little capital, which is how many poor countries start out, then only a fraction of the labor force will be employable at a wage sufficient to ensure their subsistence (there may be nothing for the others to do), and as a result the country will not benefit much from its labor abundance. Convergence, if it happens at all, may be very slow.

….it is not true that poor countries as a rule grow faster than richer ones. The correlation between GDP per capita in 1960 and subsequent growth is very close to zero.25 How does this square with the fact that after the war Western Europe caught up with the United States? Solow had a possible answer. What his model actually says is that countries that are otherwise identical will head toward each other. This could be why Western Europe and the United States, which are very similar in many ways, converged toward each other. On the other hand, in Solow’s world countries that are naturally thriftier than others and invest more of their output will be richer in the long run. Moreover, for a while, before settling down to grow at the natural rate, initially poor countries that invest more will also grow faster as they converge toward this higher level of GDP per capita.


The third and most radical prediction from Solow’s model is that the growth rate of GDP per head among the relatively rich countries, once the economy reaches balanced growth, may not be very different. Essentially, in Solow’s world these differences must come from differences in TFP growth, and Solow believed that, at least for these rich countries, TFP growth should be more or less the same.

In Solow’s view, as mentioned above, TFP growth just happens—policymakers don’t have very much control over it. 

…..Solow was talking about growth after countries get to their balanced growth path, and while this might have already happened for some of the richer countries, it is probably a long way away for the ones where capital is still scarce. By the time Kenya or India gets to Solow’s balanced growth path, they necessarily would be much richer and be using many or all of the latest technologies. Their current technological backwardness could just be a symptom of their lack of capital.

…..Solow assumed the rate of improvement in TFP was a product of mysterious forces that had nothing to do with the countries, their culture, the nature of the policy regime, and so on. This meant he had very little to say about what we can do about long-run growth once the process of accumulation of capital has run its writ and the return on capital is low enough. Solow’s was what economists call an exogenous growth model, where the word “exogenous,” meaning driven by outside effects or forces, acknowledges our inability to do anything about the long-run growth rate. Growth, in short, is beyond our control.

I think the above excerpts gave us a good idea of economic growth drivers explained by Solow. There is an alternative growth model called  endogenous growth theory. Under endogenous growth theory,   self-sustaining growth emerges as a natural consequence of the model and the economy does not necessarily converge to a steady state rate of growth. Unlike the neoclassical model, there are no diminishing marginal returns to capital for the economy as a whole in the endogenous growth models. So increasing the saving rate permanently increases the rate of economic growth. These models also allow for the possibility of increasing returns to scale.

Thank You for reading. 

Leave a Comment

Your email address will not be published.

Shopping Cart