On Growth Theory (Part 1)

In this posting, I pursue my colleagues’ spirit at Café Salemba on spreading economics ideas to general reader. Here, I try to keep the ideas as plain as possible. But putting economics ideas by words is not always simpler than writing by math expressions. However, let’s try.

Some central questions to macroeconomics theory are; why do economic growth rates differ across countries? Why does a country produce more while the others do not? Some countries that were poor grow faster (e.g. East Asian countries) while some countries that were pretty rich in the past grow slower (e.g. Latin America countries). Some seem to end in doom (e.g. Sub Saharan Africa). Why are the economies of some likely to converge to the same pattern (e.g. rich countries and East Asian countries)? How long does one country need to double its output and why does it take so long? Does capital gap explain the differences of growth rates among countries?

Below are some facts

Source: Charles I Jones, Introduction to Economic Growth 2002

Take Zimbabwe as a case. Its average growth rate from 1960-97 is around 0.4 percent. Hence it takes 192 years for Zimbabwe to double its output. It takes only 12 years for South Korea to double its output while the USA needs 50 years to double its output.

Here is a fact of rich countries' economies

Source: Charles I Jones, Introduction to Economic Growth 2002

The graph strongly illustrates that rich countries’ economies converge to the same pattern. Turkey, Mexico and South Korea experience the same thing. Then, another fact is

Source: Charles I Jones, Introduction to Economic Growth 2002

Some countries grow faster but some do not (see African countries). Finally, we also find that growth rates in many countries are persistent.

Source: Angus Maddison: The World Economy. A Millennium Perspective (OECD,2001)

These figures give us good clues. From this posting, we learn that economies grow gradually and stable over period, I mean there is no such “jump” up in economy. Moreover, we also find that growth rates in many countries are persistent. So far, we have four important clues: growth rates are persistent, varied across countries, they converge and grow gradually (relatively stable over periods).

Economists realize that output and factors of production (inputs such as capital and labor) may grow in a different direction. Percent of growth per se does not give us strong information about economic situation as the population also grows. Another problem: this information cannot tell for sure whether the economy of country A produces more output than that of the economy of country B.

Just pick any number, suppose Indonesia economy grows 5 % while Singapore grows 4 %. Looking these numbers and saying that Indonesia produces more than that of Singapore is not sensible. In fact, the Indonesian population increases by 3 % while the Singapore is almost zero. Here, Indonesians enjoy only 2 % additional income while Singaporeans keep 4 %.

As our fact suggests that economies converge, there must be law that both output and inputs (factor productions) move in the same direction. Well, we find the law by such a very simple way. Assuming that the population growth is not influenced by economy (we call it as exogenous since it is an external factor of our economy) and transforming all variables into per capita term make our life simpler. That is the law, "per capita variables"

Now we are ready to framing economy. Just for introduction, let us start from very simple growth model. This model assumes that an economy produces only one good; no government; no technical change; no unemployment; there are only two inputs, namely, capital and labor; saving rates, depreciation and population growth are constant (however after the model is established, we can do such some experiments on what happen if these three are no longer constant).

It is, moreover, common to think of this model as unrealistic. However I cannot agree more to David Romer’s, professor economics of UC Berkeley, suggestion[1].

I try to avoid using too much technical procedures in building our model. Let me begin from the first ‘equation’. An economy consists of capital and labor. Then, the output of economy is divided between investment and consumption. The fraction of output allocated to investment (or simply say saving rate) is assumed constant.

Since capital depreciates, capital stock (or an additional capital) must be equal to the fraction of current output allocated for investment minus the depreciation of existing capital. This is the second equation of our model.

Remember, we need that both output and inputs move in the same direction and we are interested in per capita income rather than unadjusted income. So we transform all variables into per capita terms. Since our model assumes that there is no unemployment, the terms “per capita” means “per labor”. Just for convention, later I’ll use “per labor” concept instead of per capita. But both are the same concept.

The next step is just doing simple exercise. By doing some technical manipulation[2], finally I end up with very important equation, the third equation. Then we call it as capital stock per capita.

The equation above tells that capital stock per labor should be equal to actual investment per labor (sŷ) minus break-even investment ( (n+δ)k ), where n is labor growth and δ is depreciation rate and k is capital per labor.

What is break-even investment? Intuitively, we know that capital is depreciating and population is growing. Therefore, to maintain capital per labor from depreciation and the growth of labor, we need some amount of investment which is exactly equal to (n+δ)k.

Graphically, the third equation can be drawn like this

Suppose our economy stays at K₀/L, then gap BC is the amount of consumption per labor (per capita). DA is the amount of break-even investment and the rest, CD, is the amount of actual investment per labor (per capita).

Would this graph fit with empirical evidences? What does this graph tell us in reality? For a while let these things stay in our mind. I’ll continue to discuss what the graph means and implies, and we’ll find out why, according to our simple model, this statement might be true.

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[1] David Romer says “The purpose of a model is not to be realistic. After all, we already possess a model that completely realistic-the world itself. The problem with that “model” is that it is too complicated to understand. A model’s purpose is to provide insights about particular features of the world. If a simplifying assumption causes a model to give incorrect answers to the questions it is being used to address, then the lack of realism may be a defect…if the simplification does not cause the model to provide incorrect answers to the question it is being used to address, however, then the lack of realism is a virtue”. Romer, David. Advanced Macroeconomics 2006

[2] The third equation comes up by differentiating the first equation with respect to time. Then dividing the second equation with capital (K) we find the growth rate of capital stock. Substituting this into the first equation, arranging them, we would find capital stock per capita

Here's a funny comic strip that I would like to share with all of you, it is done by Jorge Cham of the Pile Higher and Deeper fame (phd comics), a famous homourous comic strip depicting graduate student life. In case you cannot read it, just click for larger image. That's all for now, I have to get back writing my paper....isn't procrastination wonderful?:D

A Book on Science

This book is not really a new comer. Yet as I do love physics, I find it really interesting. Part which I like the most is “Evolving Universe..”. It discusses recent advance in physics, such as, String Theory and Loop Quantum Gravity- two theories which seems to compete each other for unifying all of physics. A good quote of Lee Smolin, one of the leaders of Loop Quantum Gravity theorists

“Nature is a unity. This pen is made of atoms and it falls in the earth’s gravitational field. Hence there must be one framework, one law of nature of which these two theories are different aspects. It would be absurd if there were two irreconcilable laws of physics, one for one domain of the world and another for another domain.”

I’m not truly following the debate between String Theory and Quantum Gravity, particularly in technical terms. However, it is likely that fierce competition between them take place. In the last paragraph of his article, Smolin writes

“The good thing about science is that you get these shocks from real world. You can live for a few years in an imaginary world, but in the end the task of science is to explain what we observe. Then you look in the mirror and ask yourself ‘Do I want to be out there in eleven dimensions, playing with beautiful math when the experiments start coming in”

Here, Smolin attacks string theorists who believe that there are eleven dimensions in universe. Smolin's words somehow reminds me to Samuelson’s words arguing to those of Friedman.

Happy Birthday GATT!!

On Tuesday, April 10 2007. GATT or the General Agreement on Tariffs and Trade turns 60 years old. Here's an interesting article written by economist Douglas Irwin commerating the event.

On Growth Theory and Kaldor Facts

Among macroeconomics theories, Growth Theory is one of the most classic fields. Its popularity among economists is like roller-coaster. Once, economists lost appetite scrutinizing the theory. But it revives.

Here are some good suggestions of my prof for those working on economic growth: start from a simple model, then fit your model with Kaldor Facts. If the model is doing well, it is really a good model. The Kaldor facts are (based on the article by Nicholas Kaldor Capital Accumulation and Economic Growth 1961)

1. Output per worker grows at a rate that does not diminish over time.
2. Capital per worker grows over time.
3. The rate of return to capital is constant.
4. The ratio of capital to output is roughly constant.
5. The share of labor and capital in national income are nearly constant.
6. Growth rates differ across countries.

These facts truly portray growth patterns among countries except for many African countries. What has happened is the opposite of first two facts true in Africa. Yet, interestingly, neoclassical growth theory-one of economic growth models predicts that in the long run (hopefully not very long) African countries will enjoy high economic growth and catch those of rich countries. Why ?

The 75th anniversary of Sydney Harbour Bridge…”Our Bridge”

Sydney just celebrated the anniversary of one of its famous icons, Sydney Harbour Bridge. Sydney-siders (the inhabitants of Sydney), if not most, maybe have little idea about when Sydney Harbour Bridge was built and who the man behind was. Knowledge over Australia’s history or even historical dates has been hot-debated issues.

I recall a shameful accident when New South Wales Education Minister, Carmel Tebbutt, once was interviewed by a radio about why Australians should celebrate Australia Day and she accidentally, mixed up between Australia day and Federation day. Australia day is the day when the first Europeans arrived in Australia (some call it as imperialism day) while Federation day is the day when the states joined together to the Commonwealth of Australia.

What happened to Mrs Carmel Tebbutt, perhaps, looks so common for some but for others, it means a degraded spirit of Australian identities and values. Despite rarely do people really know for sure what Australian values are.

Opinions may stand in the opposite way, but Australians seem to know how to break fun and view up. That is when these two groups may stand side-by-side. Finally celebrating the 75th of the Sydney Harbour Bridge is not only about remembering the day when such a mega-structure for the first time was built in Australia but also about making attractions during autumn for Sydney-siders and international tourists. Surely, there were senses of being proud and of belonging as people wore hats dan T-shirt labeled “the 75th of Sydney Harbour Bridge…“Our Bridge”…” and paraded crossing over the bridge.

For people like me who are not part of Australia’s history, at least, enjoyed the latter part. Sitting at a café in the side of the Opera House, drinking a cup of hot coffee and taking pictures of the bridge were really a lot of fun

Colbert on Bill Gates' Altruism and US Foreign Policy

Stephen Colbert told it like it is on the Bill and Melinda Gates Foundation and US foreign policy, i.e. altruism, policies towards developing countries, international politics. Oh, and it's funny too.



I especially like the part where Colbert showed the guy wearing the "Buchanan for President 1992" t-shirt. Here's why the guy wearing the Buchanan t-shirts is so funny.