Useful Resources about the Solow Model

We’ve been updating the blog with a series of short, simple, easy to read essays about the Solow Model. If you’d like to read the entire series, just click here, and read in reverse chronological order.

We haven’t used a single chart, equation, graphic or video, to talk about the Solow mode, and each essay is no longer than around 500 words each. But reading all of them should give you a fairly good idea about the Solow model.

Think of these essays as appetizers, though. They are intended to whet the appetite, not fill you up. However, if your appetite has indeed been whetted, you might want to take a look at these resources to understand more about the Solow model.

Marginal Revolution University (MRU) is an excellent online resource for learning more about economics in general. Started by two professors from George Mason University, Tyler Cowen and Alex Tabarrok, it is a wealth of material, in the form of videos, for understanding both basic and advanced economics. Here is the link for their videos about the Solow Model.

We wouldn’t especially recommend the Wikipedia article about the Solow model, because it isn’t the most intuitive version going around. But if you are comfortable with some math, and know your way around the Solow model well, you could take a look at it.

Any introductory textbook on macroeconomics will also cover the Solow model, because it really is the workhorse model for thinking about the long run growth story for any nation. Dornbusch, Fisher and Startz have a good book out there, but really, take your pick – almost any book will do.

We hope you have enjoyed thinking about the intuition behind the Solow model, and we hope you find the resources put up above useful.

In the next post, we’ll move away from the Solow model, and talk about the most basic model in economics – the supply and demand framework.


Understanding depreciation

Depreciation is a simple word, and a difficult concept.

It simply means wear and tear. If the car you’re driving is about five years old, or maybe more, it isn’t going to be functioning as well as when you first bought it. Maybe the fender is a little bent, and maybe the engine is making noises it really shouldn’t be making. The specifics will be known only to you, the owner, but anybody will be able to predict that things aren’t as great as they were when she was first driven out of the showroom.

That is depreciation.

Now, the reason it is a difficult concept is because of what it implies for an economy, and how to go about accounting for it. Since we’ve been talking about masterclasses by Sachin, let’s continue to use the same example.

Who do you think knows more about the art of batsmanship – you or Sachin? That isn’t an entirely ridiculous question, because the reason behind asking it was this – who is more likely to forget stuff about the art of batsmanship – you or Sachin? Since the Little Master knows more than you ever will about batting, he is more likely to forget some things about it. That is why the very best batsman spend so much time in the nets – not necessarily to learn new things, but to polish stuff they are already very good at.

In other words, what they’re trying to do is reduce the depreciation of their skill sets.And the more you know, the more you have to protect.

It’s the same with countries! The more roads, dams, power plants and airports you have, the more money you have to spend on repairing them. And so, as you increase your capital stock, you have to spend an increasing amount of money every year in keeping that capital stock up and running. And what that means is, you therefore have lesser money to throw at building up new stock.

Put another way, here is what it means: the more you have grown, the more difficult it is for you to grow.

And so, we come to the crux of the Solow model.

Countries that have a low stock of capital, along with a mix of good institutions, are the countries that will grow the most rapidly. But, they can’t grow rapidly forever. As they accumulate more capital, the need to repair it will eat increasingly into the country’s ability to invest more, and growth will slow down. And eventually, all countries settle down into a rate of growth that is just about right for that country.

Economists call this the steady state growth rate – faster than this is unsustainable, and slower than this is not optimal.

Figuring out your long run steady state growth rate, figuring out the best set of institutions for your country, and figuring out how to get there – that’s what long run growth theory is all about.

Why do institutions matter?

Remember the Sachin masterclass example from the previous post?

Well, now imagine that he gives this masterclass to me, and to you. Also assume that I am a middle aged man, slightly portly, and not very good at sports (this would, in fact, be a very good assumption on your part). Furthermore, assume that you are young, lithe, and take to any sport naturally (for your sake, I’m hoping this is a very good assumption on my part!)

Who do you think will learn better in that masterclass? Portly, ungainly me, or lithe, athletic you?

Similarly, a spanking new airport in Mumbai, and a spanking new airport in Bangui (the capital city of the Central Africa Republic) won’t have the same impact on both cities. I’ve never been to Bangui, and I certainly mean no disrespect, but it would be a safe bet to assume that law and order, level of corruption, ease of transactions are all better in Mumbai than they are in Bangui. Not perfect, not by a long shot, but better.

Institutions, in this context, is the framework in which economics happens. Markets don’t – cannot – exist in a vacuum. They must be protected by courts, who help in mediating disputes. They must be protected by the police, who help in guaranteeing property rights. There must be a state that creates laws for citizens to abide by. When these things function the way they ideally should, markets thrive, capital is rapidly created, and the economy grows fast.

When these things are broken – when corruption, theft and lawlessness are the norm, markets crumble, capital flees and the economy turns moribund.

The key point is, it isn’t enough for Sachin to give you a masterclass. You must have the body conditioning to learn.

Similarly, it isn’t enough for you to have a low stock of capital – your country must also have the right mix of institutions.

But as with most things in life, that is easier said than done. In some ways, it is the classic chicken and egg problem. A country will have quality institutions only once it gets rich, and we’ve just argued that you can’t get rich without having quality institutions. But that is part of what makes thinking about development so tough.

It is fair to say that both institutions and the accumulation of capital proceed hand in hand – when one grows, so does the other, and vice versa.

Are India’s courts, police force, and laws better today than in the 1950’s? Yes. Have we a higher stock of capital today than in the 1950’s? Yes. Does one cause the other, or is it a self-reinforcing process? Probably the latter – but this much is certain: one can’t happen without the other.

So, to sum up our story so far: growth is important, and growth can’t happen without capital. Accumulating capital is hard, but the good news is that if you have hardly any to begin with, you can grow it quite fast. The bad news, institutions really matter.

Next up: depreciation.

Small economies, big economies

Here’s a fun thought experiment.

What if Sachin Tendulkar agreed to give you a one-on-one batting masterclass for an hour? One hour with the Little Master, who will carefully observe your technique, our shots and your overall batting, and then proceed to tell you how he thinks you can become better. It’d be fairly safe to assume that you’ll be a much better batsman at the end of that session, right?

Now, what if Sachin also did a one-one-one masterclass with Virat Kohli? Here’s a batsman who’s at the peak of his game, and who is, in his own right, a very accomplished batsman indeed. Here’s the question: will it be equally safe to assume that Kohli will be a much better batsman at the end of that session?

Hopefully, all of you agree that Kohli was already a very good batsman That masterclass won’t hurt him, but the rate of improvement won’t be all that much, because he was so very good already.

But you? Your rate of improvement will be stratospheric, because you are a novice in batting compared to Kohli.

Similarly, what will be the impact of a spanking new expressway connecting two cities in America? Marginal, because they already have a pretty good network of highways. What will be the impact of a spanking new expressway connecting two cities in India? Much larger, because in all likelihood, this will be the first such road between these cities.

The flow of commerce between these cities will be higher than earlier, the measurement of which will show up as an increase in GDP. This is a central prediction of the Solow model.

Countries with a low level of capital will, other things kept aside, grow faster than countries with a high level of capital. America will not grow at anything in excess of 3% per year, while India will consider it a tragedy if we grow at less than 5% a year.

That doesn’t mean America is somehow worse than India when it comes to economic performance. Of course America will grow slower, because she has seen so much growth already. We, on the other hand, are just about beginning our growth story. Villages in India will see electricity for the first time, and many Indians will travel in a car, on a national highway, for the first time in their lives. These indicators of progress will all be registered in our GDP measurements as growth, and so India will (or at least ought to) grow faster than America in the years to come.

So countries with a low capital stock tend to grow faster. Tend to, unfortunately, isn’t a guarantee of growth. In other words, not all countries with a low capital stock grow rapidly – some don’t.

What holds countries back is institutions – and that’s what we will be looking at next.

Thinking about capital

You’re reading this post, right here and right now, using capital. You’re using some sort of electronic machine – maybe a computer, maybe a phone, maybe a tablet – in order to read these words. I used a laptop to write them.

Would it have been possible for me to write these words without any machine whatsoever? No computer, no paper, no pen, no nothing. In theory, yes. I could have used my foot to etch some words in the sand. But not only would that have been tedious and impractical, it would also have required you to be there in order to read it. But with my laptop, and its internet connection, I could put this post up on the internet, and anybody could read it, including you. So I could produce something of value (and you could consume it) much more easily because of the presence of capital.

And in general, that holds true for almost everything. Most goods and services are far easier to produce, and turn out to be of far better quality, when produced with the aid of machines. This is true of something as simple as haircuts (scissors), or classes (computers and projectors), and something as complicated as a rocket launch. Machines (that is, capital) help us grow faster.

So a growth in the amount of capital we possess (what economists refer to as capital stock) is almost a prerequisite for economic growth. Now, if this is true, we can make a series of predictions. I have outlined them below.

One, countries that have a low level of capital stock will be poor, and countries that have a high level of capital stock will be rich. Also, countries that are in the process of adding to their capital stock will be growing more rapidly than others.

Are these claims true? Nothing is ever completely true in economics. It is, after all, a social science, and you’ll always have a bit of error. But most economists would agree with the claims made above.

And without getting into the data and the charts, it is possible to see that the claim makes sense. Which country, do you think, has more roads, airports, seaports and power plants – India or the United States of America (USA)? Which country is richer?

Has China added, in the last three decades, an enormous number of airports, seaports and power plants (besides much else)? Has China grown rapidly?

Long story short, if we want India to grow rapidly, we have to add to India’s capital stock. We have to, in the years to come, build more roads, more dams, more solar farms – more everything, really. This will raise, to use a bit of jargon, our productivity. That is to say, it will raise our ability to produce more goods and services in the future – and that is what we mean by growth.

And this is the first intuition behind a model that we will be fleshing out now. The model is called the Solow model, and the intuition is painfully obvious in hindsight: adding to the capital stock helps a nation grow.

Thinking About Long Term Growth

We now know what GDP is, and why it is important to measure growth using GDP. We know what statistical adjustments are made over time so that growth is made truly comparable. We also know the difference between long term and short term growth.

Armed with the answers to all of these questions, we now ask the million dollar question:

What makes a nation grow over time?

That is, if we are to transform India into a developed nation by increasing her growth rate in a sustained, sustainable fashion, then what, specifically, needs to happen? Well, lots of things, is the easy answer. And a true answer, too.

Here’s a better question. What are the things without which this growth story absolutely can not happen?  What are the indispensable factors?

Answering this question takes us into the realm of growth, or development economics. Nomenclature aside, it is the area that lies at the heart of all economic policy-making. What we are looking for is the framework, the core, around which everything else can be built, added and embellished. Just as a truly great dish looks good and tastes better with more accompaniments, but can’t really work without the core ingredients – similarly, our growth story needs some core ingredients, around which we’ll add more stuff later.

And our core ingredients are labor, and capital. Turns out, India’s growth story cannot happen, without first possessing (and growing) capital and labor.

What is capital, and what is labor?

Capital is machinery. You’re almost certainly reading this post on an electronic device, and that device is your capital. The ladle with which a dosa-wala flips a dosa is capital. The pushcart that a chaiwala uses as his makeshift shop is capital. An assembly line in a Tesla factory is capital.

And the effort that I put in to type out this article is labor. The hands that use the ladle to flip the dosa is labor, as is the chaiwala himself and the worker on the factory floor of that Tesla factory. That is all labor.

And any production, anywhere in the world, of any good at all, can only be done with some combination of labor and capital. In order to produce something – anything – you need capital and labor.

The more you produce, the more you grow. The faster you produce, the faster you grow. And so in order to grow more, and grow fast, you need more capital, and you need more labor. So any story about the long term growth prospects of a nation need to start from capital, and labor.

Economists call these the factors of production, and without them, our story can’t start. But with them, we encounter another question: how do you get capital and labor to grow?