Bryan Caplan  

Malthus on Stilts: Clark Misinterpets the Malthusian Model

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In the Malthusian economy before 1800 economic policy was turned on its head: vice now was virtue then, and virtue vice. Those scourges of failed modern states - war, violence, disorder, harvest failures, collapsed public infrastructures, bad sanitation - were the friends of mankind before 1800. They reduced population pressures and increased material living standards.

--Gregory Clark, A Farewell to Alms

The Malthusian model is one of the building blocks of Clark's magnum opus. Before I critique Malthus, however, it is necessary to rescue him from Clark. For all its flaws, the Malthusian model simply does not imply Clark's bizarre claims about the wonders of bloodshed and famine.

To get started, let's go over the Malthusian model. Clark neatly reduces it to two inter-related diagrams.
clark.jpg
The first diagram graphs Birth Rates and Death Rates as a function of per-capita income: As per-capita income goes up, Birth Rates rise, and Death Rates fall. In equilibrium, you have a stable population where the Birth Rate equals the Death Rate.

The second diagram graphs Population as a function of per-capita income. This Technology Schedule reflects the key Malthusian assumption that, due to diminishing returns, a bigger population implies lower living standards.

Now where does the conclusion that e.g. harvest failures are good for living standards come from? Clark interprets harvest failures as an upward shift in the Death Rate:
clark2.jpg
So far, so good. When the Death Rate shifts up, population falls and income goes up. The decline continues until the Birth Rate and the Death Rate are equal at the lower-population, higher-income equilibrium.

What's the problem? Quite simply, this isn't how a harvest failure works. Harvest failures don't directly raise the Death Rate. Instead, they kill people by making a given number of people less productive. In a Malthusian framework, the correct way to represent this shock is with a downward shift of the Technology Schedule.
clark3.jpg
Intuitively, this means that, due to the harvest failure, a given number of people now produces less income that it used to. And what is the effect? In the short-run, income plummets from y* to y'. Since the harvest failure doesn't kill people instantly, you initially move along the dotted horizontal line from the initial Technology Schedule to the new Technology Schedule. Eventually, starvation sets in, and you move along the new Technology Schedule back to the old income level, y*.

Thus, the effect of harvest failures in the Malthusian model is to reduce income, which causes starvation, which reduces population, until you eventually get the old level of per-capita income with a new, lower population.

On Clark's misinterpretation of the Malthusian model, negative supply shocks are good. They're "the friends of mankind." On a correct interpretation of the Malthusian model, however, negative supply shocks are bad. Very bad. The only "silver lining" is that some people survive; lower population eventually pulls living standards back up to their initial point. That's hardly a reason to say "Hooray for harvest failures."

For Clark's story to make sense on its own terms, bad stuff would have to directly kill people without affecting the Technology Schedule. If the Angel of Death killed every tenth person, Clark could consistently point to the Angel's beneficial effects on per-capita income. (Though even there, it's probably very bad on balance; ex ante, how many people would trade the extra income for a 10% chance of death?) But very few bad things work this way. Plagues don't just kill people; as Fogel explains, bad health in the pre-modern era also made the living less productive. Wars, similarly, don't just kill people; they also make it harder for people to do their jobs. And so on.

Bottom line: Whatever the merits of the Malthusian model, it doesn't support Clark's strange odes to violence, famine, and filth. In a Malthusian model, these shocks have bad effects that eventually fade out.

P.S. To be fair to Clark, he might argue that some of these shocks shift the Technology Schedule down and directly raise the Death Rate. A plague might do the trick - it kills some outright, and weakens the rest. In the long-run, the survivors will have a higher material level of living. But this hardly makes the plague a "friend of mankind." All it means is that after mass death, the frail, disfigured survivors will get to eat some extra calories beside the graves of their families. With friends like this, mankind doesn't need enemies.


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COMMENTS (11 to date)
tc writes:

That depends on how long the plague or war lasts. After a short, sharp shock, assuming everything else returns to normal, then there will be more land and resources for the survivors - as Clark's data show for Europe after the Black Death.

General Specific writes:

Bryan Caplan wrote: "What's the problem? Quite simply, this isn't how a harvest failure works. Harvest failures don't directly raise the Death Rate. Instead, they kill people by making a given number of people less productive."

I think you are looking at this wrong. The population continues to increase, but resource limitations imply that the productivity per person decreases. A plague is then a shock to the system, reducing the population, and eventually, as you say, the productivity per person goes back to the old value.

The shock to the population, e.g. the plague, solved the problem.

How about a harvest failure? Again, population is increasing. Productivity per person is decreasing because of resource limitations. Productivity does down, down, down, then blam--harvest failure. Large number of people starve to death. Productivity per person eventually goes back to the old value. People have enough to eat.

What Clark is saying seems to make sense to me. A shock to the population (rapid decrease) is a means by which the productivity can return to previous levels, which had dropped under the pressure of resource constraints.

Right?

You would have to look at real data to determine whether either of these scenarios--mine or yours--make sense.

Isegoria writes:

As TC noted, it all depends on how long the war or plague lasts.

A typical war reduces productivity for one season, if that, as pre-modern societies clearly scheduled their wars around the agricultural calendar, but the casualties of such a war are removed from the population of mouths to feed for a whole generation.

David writes:

A war might only reduce productivity temporarily if it was fought completely Geneva convention style - no looting, pillaging, burning down cities and soldiers eating the livestock. But how many wars have actually worked that way? Especially in Malthusian societies without a surplus to feed soldiers on campaign?

General Specific writes:

Maybe I just don't get it, but it seems to me that production per capita decreases as one approaches malthusian limits. Resource availability (e.g. arable land) plus the state of the art in technology to manipulate these resources (e.g farming techniques) set limits on overall production. Hence, with more people, producitivity decreases.

A war or famine or disease can (a) reduce production per capita further--oops--and (b) reduce population. Eventually, production per capita can rise back up to the pre-malthusian limit levels. So in the end, this can be considered an improvement--of sorts--over the productivity experienced during the runup to malthusian limits.

Technology and resources may set a limit on productivity, and if population outstrips the two, productivity drops until either (a) population drops, (b) more resources are found--like the New World, or Coal--or (c) technology improves (e.g. farming techniques, steam power, etc).

Matt writes:

We are all talking about a sudden, turbulent transition, and Malthusian theory has nothing to say about that. A better theory, say information theory, can give some general trends.

The sudden, and proportional drop in population density across the wealth spectrum has the equivalent effect of raising the noise level across the spectrum.

If the distribution has very long tails on the left, just above poverty, the resulting population distribution will be mish-shapen and the cost of transition is higher. The uncertainty constant buries the left tail.

The right tail suffers from the cost of rearranging production because the number of transactions becomes too small to be smooth over time..

If your population distribution is centered, and fairly broad then raising the noise level may not cause the same level of distortion.

Distortion is a measure of how off-centered and unsmooth the new wealth distribution becomes. The greater the distortion, the more that the binomial approximation breaks down on the tail ends of rht curve, and quantum rearrangement of production becomes apparant.

rvman writes:

All Clark is saying is that stuff that kills people drives up per capita capital stock. After the shock, a small surplus can be created (until the population grows back up to Malthusian Equilibrium), which can be invested in further capital and spent on luxuries (which need skilled labor to create, so motivate investment in human capital). So each bad shock leads to a slightly more capitalized, slightly richer, slightly more skilled society than before. Nothing even particularly scary to the neoclassical model there, other than the Malthusian angle.

I think giving crop failures and plagues 'credit', here is appropriate, at least for survivors. Wars too, until about 1800. Pre-industrial wars were far less destructive to the capital base than more modern affairs. From Napoleon forward, war became a more unmitigated bad.

Jonathan C writes:

I haven't read Clark yet, but from Bryan's discussion this debate over the effects of the black plague and similar population shocks are reminiscent of much older debates. Sure the population collapse was great for the survivors in Western Europe since, as told by North and Thomas and others the higher land to labor ratio raised average incomes and competition for scarce labor between landlords led to the end of serfdoms and higher peasant incomes.
Fine story and makes a lot of sense, until you pause to look at what happened on the other side of the river Elbe, where a similar rise in the land to labor ratio led Russian and East European landlords to collude to find new ways to limit peasant mobility with new forms of draconian serfdom on what had been a comparatively free peasantry. You can well argue that over the long run these new institutions proved very detrimental to the region's long term economic and political development.

In short its not just rising or falling land to labor ratios driven by exogenous envents but also very importantly which groups come out on top in the scramble that follows and how auspicious the property rights arrangements and institutions they seek to uphold are for development.

Don writes:

The strength of Clark's argument on these points is in his hard data, and we get a good summary of these in figure 10.1 on page 194. It would be interesting to see the hard data on the technology schedule (TS, I'm an ecologist not an economist and need some coaching on the TS) pertinent to the history of English population. Perhaps death rate (& birth rate?) covary with the TS, perhaps the age distribution following shocks affects the TS? These time series have lags owing to age distribution in the short run, but age distribution washes out of the the longer time intervals in figure 10.1.

Mat writes:

Ignorant amateur comments follow:

An increase in the mean assets per capita is not the same as an increase in assets for everybody. Intuitively, most of the benefits should go to those who already have most of the capital and can leverage it. Things get worse for primary producers because demand has dropped; things stay roughly the same for secondary producers (30% of your customers are dead but so are 30% of your competitors), improving as the price of raw materials drops.

The angle about increasing luxury spending leading to a more capitalized society and benefiting everyone (or everyone's grandchildren) in the long run sounds rather more solidly grounded, although it also sounds rather trickle-down.

George writes:

Many economists have made the argument that Clark is making, except when referring to the Black Death, not harvest failures.The black death swept through Europe, killing 1/3rd of the population. Ron Findlay argues that this led to the Italian renaissance, by way of a dramatic increase in per capita wealth.

The wages in Italy in 1460 after the Black Death were NOT MATCHED IN REAL TERMS UNTIL 1850.

Bryan-- here's the real question. Is it true or not true that a sudden, population decapitation leads to a long boom of per capita wages? Imagine that 1/2 of the population just disappears. Clark is right that such a phenomenon would increase per capita wealth. He's wrong to call a harvest failure a good proxy for this "vanishing person" phenomenon.

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