Malthus: Not Wrong But Early

If you have any familiarity with the name Thomas Robert Malthus it is probably based on the following assumption.

Draw the first quadrant of the cartesian plane.

Draw two functions. The first being f(x)=x and the second being f(x)=x^2.

Now look and there’s a point where x=x^2.

That point is where growth in the linear function is surpassed by growth in the geometric function.  As a purely mathematical proposition, it’s easy to see that they intersect where x=1.

But to complicated the matters, we have those functions actually stand in for something, then the linear is the growth in production and the exponential is growth in population. Then you have at that intersection point the place where human population exceeds the productions of technology and then people will solve. (I’ll leave his policy prescriptions for another day). As a thought experiment it seems to work, but it rests on two big assumptions.

The first is that production is linear. Malthus was writing at the early stages of the industrial revolution, but we are children of Moore’s law. Technology has increased at the exponential rate in our lifetimes. Perhaps he was just on the point of the curve where the exponential function looks linear. Though this is a gross over-simplification. Moore’s law is just speed of computer chips and we have to ask what the output of the technological revolution is that makes our lives better.

The other assumption, of course is that population growth is exponential. In current times especially in developed economies, that seems the opposite of true, as western nations are worrying about how to deal with the aging of populations as the later generation are not having babies at the replacement rate for the population and countries are making policy to induce people to have kids.

So, in a way, it looks like on the back of the envelope that the prime conclusion is exactly backwards. Though the world population is growing, the rate of growth is slowing and we are on target to peak. Now that peak is so high that in Malthus’s day it would seem that his population growth projection is correct, output is such that we haven’t met that point of intersection point at a large scale.

But just because we haven’t met it yet doesn’t mean we won’t. Though Malthus takes his inevitable meeting of that point as a reason to keep down the working class, it can be a valuable metaphor for the inheritors of his economic though. The entire economic problem is often defined in some way speaking of finite resources and infinite wants, and that to me is trill true. Though we might not seem to have gotten close to carrying capacity there have been scares with mass famines thwarted by the green revolution and worries about peak oil averted by greater drilling technology. These points can serve as a reminder of the original Malthusian hypothesis as we deplete resources and create chaos on the planet. In a way when we look at the most famous conclusion of Malthus the most important the way to really judge him was not if he was right or wrong. It is better to ask: “Was Malthus too early?”

Why is America Richer than Mexico?

One way to look at the relative wealth of the United States over that of its neighbor Mexico would be to say that the US has a surplus of at least one of the three factors of production. We can say there’s better and more land, more and better trained people, and even that it has more capital stock built up that is also more productive. Another might throw in entrepreneurship but that may be too much like a black box and much harder to quantify. To me, that is one of those ex-post rationalizations you use when you have nothing else to point at. 

But if we want to look at what makes the country to the north richer there are many other factors that we can look at. We have to look not just at one point in time but to the flow of history.

One is to go look at the strength of the institutions like Acemoglu and Robinson speak of. In this framework, the stronger the institutions, like the rule of law in the judiciary, the stronger and wealthier the nation no matter the economic system. So we can point to American fealty to the Constitution over the last 250 years and not matter how flawed the document is, its very constancy has allowed consistency that has not been available in Mexico with its one-time occupation by French forces and having its revolution 100 years ago and then generations of one party rule.

Another way would be to look at the way the flora and fauna of the countries developed. In a theory popularized by Jared Diamond, the layouts of the continent really matter. The US is much broader from shore to shore than Mexico and at the right latitudes that the weather was more like the weather in the vast Eurasian continent. The plants and animals that evolved on the larger continent faced more pressure and competition so what survived there was stronger and more well adapted. Many of the hardy plants and animals that were foreign invaders on the North American shores helped human development and were more suited to the United States. Alternately, there were bacteria that came over too that had negative effects on the population. The cold American winters could shorten the life span of the more deadly tropical diseases that could find their victims in central and southern Mexico.

Geography and history over time had its hands in different aspects. As a British colony, the various colonies could take on the technology of the mother country right at the beginning of the industrial revolution. It didn’t have to lead because industrial capitalism was developing over the Atlantic. Once the revolution was over policy was put in place to protect the young independent country’s producers from foreign competition in infant industry protection – and protecting intellectual property with patents and copyrights while not doing the same for borrowed tech. The early states were split. In the north there were crisscrossing waterways that provided the motive power for the new factories. IN the south there were fertile fields producing tobacco, sorghum, rice, and cotton.

You can’t ignore history if you want to ask why the US is richer than Mexico. You can’t ignore that in 1848, US troops were in Mexico City and expropriating a third of that country’s territories. These lands spread from Texas to California which are now two of the most productive states in the United States. You also can’t ignore the entrepreneurship and inventiveness that led to the cotton gin, but you can’t turn a blind eye to the use that that fertile southern land was put to. We have to reconcile that a lot of the wealth generated in the US for its first third of its existence was through the institution of chattel slavery. On the eve of the civil war, there were more millionaires in Charleston than in New York City.

There was a great war, one of the first to kill on an industrial level – and though it remains the worst war in US history, the rest of the world took it as an example and killed more efficiently. But for those both countries were protected in their sovereignty by two vast oceans. Since the last world war the US has developed from the technology boost of the war and the ensuing cold war. Mexico did not invest those resources and the difference. It is hard to pinpoint where they diverged, but you can’t ignore that the US GDP is thirteen times the size of the Mexican economy. If you ran back history, could you run it so that Mexico would develop into the stronger economy? How far back would you go?

Physics Envy and the History of Economics

Looking at the study of economics in comparison to some of the more “hard” sciences it is easy to find points of difference. As economics has moved from a more narrative description of both normative and positive aspect of the political economy to a more math-heavy, quantative discipline, there has been talk of an economist’s physics envy. The problem here is that no matter how much data you have and how strong your model is, the experiments you will be able to run will be limited. And even then they are small scale and depending on your subject group, you might not be able to generalize the results to a whole population. The behavioral revolution led to some interesting insights such as how people are risk averse or have non-transitive preferences, but how does that scale to theories about the macro economy? I’m not aware of a widely used macro model that has a behavioral microfoundation. And that’s the other piece – we’re still debating about what macro model to use. Dynamic, static, multiple equilibria: what are we pulling off the shelf and why? And then even if you design an experiment, you can’t re-run the economy. Time’s arrow is a harsh mistress to the scientist of the economy. There’s much less debate on this in the physics book.

But we also have to think about the physics book we’re opening up. For a couple hundred years, what we knew of physics was purely Newtonian. But as technology advanced in the late 1800s physicist were able to start looking at what the world looked like at micro scales through different kinds of experimentation. This lead to quantum dynamics and then unleashing the power of the atom for good and bad. On the vast scales, Einstein was able to break some Newtonian assumptions and make equations that better described the universe at the vast scale of stars and galaxies. 

What the physics book will do is have that basic Newtonian physics as a model of how everything acts, and for most purposes it will work. You want to figure out how much gunpowder you need and what angle to aim your gun to hit the enemy in the camp three miles away you don’t need to take into the account the quantum effects of the iron atoms in your shell nor the relativistic effects of the moon’s gravity well. It works. And even in a more basic textbook you’ll have simpler models that will hand-wave things like friction to make the math easier and it will mostly work. I think what is missed in criticism of economics is how useful a lot of the models we use can be especially in this small scale Newtonians of the economy – You get something like Al Roth’s market design and it works because it is smaller scale and testable. 

I think learning the history of a science is important because it doesn’t just come across as received wisdom and instead shows that the science was a point of contention. I used to be a chemistry teacher, and the elementary text books show the progression of thought about what the world looked like at an atomic scale. At first it was seen as a small mass of undifferentiated matter, then experiments were run and we found that there were places of greater density creating the “plum pudding” model. Next Rutherford ran the gold foil experiment and saw that the atom as we know it was mostly empty space. He literally aimed a particle beam at gold foil and most of the particles ended up right on the other side of the gold foil.  These experiments were led by theory, of course. At the same time of these scientists others were ordering the existing known elements into groups based on their properties. Carbon acted like silicon so they go together and so on. This led to the development of the periodic table and to me the most impressive thing – they were able to postulate that elements were missing and their properties which lined up once they were discovered. From there you get to the Bohr model of the solar system atom that we’re most familiar with and then the quantum hybridized orbitals which show electrons not as points but as probabilistic clouds. I like this because it also helps reinforce the scientific method – you go to hypothesize and test theories to discover all you can know.

But what wasn’t appealing for me was the sense that Chemistry was at its end point. To go further you had to get into particle physics and even there the standard model is almost complete. The theories about the further constituents of the physical world get into the place where it borders on philosophy borrowing from math. Sure, you can imagine the quarks as made up of nine or eleven dimensional strings and all change from the universe comes from these strings vibrating, but it was at the point where those theories are as of now untestable. That’s why economics is appealing to me. There has been centuries of discovery and description and research roughly paralleling the growth of the other sciences since the enlightenment – but especially at a macro level things are still in contention. One of the things that sticks with me is Greenspan in testimony after the financial crisis hit where he said he had an operating model of the economy that worked pretty well for him for fifty years but he was wrong. If your maestro is wrong, who can be right?

Ultimately though, I do hold out hope that the economy can be better described and the economic problem can be largely solved. I know there’s been a lot of reflection in the discipline in the last decade because the voices who were calling for care in the run up to the bubble were marginalized and not listened to but given derisive nicknames like “Doctor Doom”. Will we get to the point where IT won’t happen again, or will the discipline remain in contention with regards to the dominate models based on fads and influence?