Monday, November 23, 2015

Reading list

Saturday, November 7, 2015

Some facts about pyramids

After the story broke a couple days ago, Ben Carson reiterated that he still believes that the ancient Egyptian pyramids were built by the biblical Joseph to store grain. That's a shame, because the truth is so much more fascinating than that.

Carson did not get his belief from the Old Testament. The bible says that Joseph became an adviser to an Egyptian Pharaoh and undertook construction of a large granary to prepare for a predicted famine. It never implies that any of the pyramids had anything to this. Tyler Cowen—himself a non-believer—says we're being unfair about this since the idea the pyramid was a granary is not implausible on it's face; he further notes that the Quran, unlike the bible, makes explicit claims about the pyramids—that the pyramids were made of brick.

What's inside the pyramids?

The Quran is partly right on this particular point. Most of the more than 100 known ancient Egyptian pyramids were built primarily out of sun-baked mud-bricks, often with just an external casing made out of limestone. This is pretty easily verifiable because in most of these sites, the external casing has been decimated over the millenia by earthquakes, erosion, and nearby settlements quarrying the stone, leaving their mud-brick interiors exposed.

The pyramid of Senworset II, built in the 18th century BCE, was the earliest of the large mud-brick pyramids, but came after the era of the giant stone pyramids at Giza.
An untrained eye might mistake most of the surviving mud-brick pyramids for natural formations, because their once-smooth coverings are now gone and their soft interiors have heavily eroded. The much newer Ameny-Qemau pyramid of the Late Middle Kingdom period c. 1790 BCE is barely distinguishable from the surrounding plains.
But not all of the pyramids were mud-brick, and the older, bigger, more famous pyramids were all made of stone, primarily locally-quarried limestone.

Joseph's experience in Egypt is discussed in both the Quran and the bible, and neither make the claim that the pyramids were granaries. That's probably because when the Old Testament was written, they knew better—ancient travelers from all over the Mediterranean and the middle east visited Egypt and saw the Pyramids. Herodotus talked to the locals to try to learn how the pyramids were built and what they were for. But more importantly, in ancient times the entrances to many of the pyramids were well known. The Great Pyramid at Giza in particular was so famous it was considered a must-see site in classical times—leading to its spot on the famous Seven Wonders of the World (it is the only wonder still standing today). Alexander the Great spent a night inside the Great Pyramid at Giza after his conquest of Egypt, and we can tell from the ancient graffiti inside he was by no means the only one. The idea that the pyramids were the biblical granaries originated in Europe in the Middle Ages, when most of the ancient knowledge of the pyramids were lost to western theologians and scholars.

A painting in the ceiling of St. Mark's cathedral in Venice, reflecting the common Medeival lore that Joseph built the egyptian pyramids as granaries.
After the classical period, the entrances to all the pyramids were forgotten and the Great Pyramid was not entered again until 820AD when the Islamic Caliph Al-Mamun blasted a new entrance into it's side after hearing rumors of huge caches of treasures inside. Modern archaeology wouldn't begin exploring the pyramids until the age of Napoleon.

Although Al-Mamun was disappointed in his quest for treasure, his expedition was extremely lucky to find an interior chamber at all—the Great Pyramid is almost solid rock, and Al-Mamun just happened to point his breach in the only direction that would meet up with the internal chambers which occupy only a tiny fraction of the pyramid's volume. Had he entered from any other spot, on any other face of the pyramid, or pointed at any other angle, he would never have found anything but stone. He got luckier than that though: the Great Pyramid is the only pyramid with substantial interior chambers at all—in all other pyramids the chambers were cut into the bedrock beneath the pyramids, which aside from minor passages into the chambers beneath, are entirely solid.

Cross section of the Great Pyramid with the interior chambers to scale. The interior chambers in the Great Pyramid are unique since in all other examples, the burial chambers were in the bedrock below. It is unknown why the unfinished bedrock chamber was abandoned in favor of these interior chambers. The Egyptians did not think of the chambers as we think of buildings—they're built like a side-scrolling video game, along a 2-dimensional slice of the interior with corridors meeting awkwardly on top of each other with no steps or accessibility features of any kind. These chambers were not built to be traversed by the living.
Although the Second Pyramid's chamber is unusually small for the pyramid's unusually large size (it is the second largest, barely shorter than the Great Pyramid), it's orientation is much more typical of a pyramid's chambers which sit below and not, as many people assume, inside the actual interior of the pyramid.
Thus the Egyptian pyramids were actually enormous solid mounds of earthly material that sit over top the site of a Pharaoh's burial. The pyramid structures do not contain anything, so what were they for?

What were they for?

Most of the pyramids are bare; they do not contain direct inscriptions or markings on the structures themselves. But there are a few pyramids that are very talkative.

The burial chambers of the Unas pyramid contain the oldest of the Pyramid Texts dating to 2360BC.
The texts were never meant to be read by the living; to oversimplify just a bit, they are instructions from the priests to the Pharaoh explaining how to navigate his journey from burial in this chamber, through the underworld, to be reborn again as a god. Reading the texts we follow the Pharaohs as they face perilous challenges and recite mystical spells (conveniently listed on the walls, in case our fearless pharaoh forgets!), on which the fate of the living world depends, and witness their triumph over the darkest beasts of the underworld thus fulfilling their part in the never ending cycle of Egyptian mythology.

The pyramid's role, siting high atop all this subteranean strife, is symbolic, representing the earth, conceived of in the Egyptian worldview as a primordial mound that rose out of the watery chaos and gave life to all things.

How did the idea to build pyramids begin?

The pyramid concept emerged quite suddenly, anthropoligically speaking, in Egyptian culture. The first pryamid was conceived of and built—at a shockingly massive scale—out of solid rock during the reign of Djoser in the 27th century BCE.

At 203 feet tall the Step Pyramid of Djoser is about half the height of the Great Pyramid and contains over 11 million cubic feet of stone.
Djoser's monument is exceptional for a variety of reasons. Not only was it one of the top ten largest pyramids the Egyptians ever built, but it was an innovation seemingly out of the blue since no Egyptian before had conceived of a pyramid structure, nor even, for the most part, the concept of building structures out of stone. And it's not just the pyramid: Djoser also deployed this new science of masonry with impressive effect to build his mortuary temple accompanying the pyramid. You may have heard the name Imhotep in pop culture: this is where it originates. Imhotep was Djoser's principle adviser, and probably the architect who invented masonry and the pyramid.

However, Djoser's pyramid was not entirely without precedent. To understand it, and Egyptian burial rites in general, we need to look further back in time. Prior to the 1st dynasty, Egyptians buried their dead in modest pit graves in the desert sands. The dry sands and shallow graves caused their corpses to dry out and thus remain preserved in a naturally mummified state. It also caused bodies to resurface from time to time, and probably the impression of witnessing their degree of preservation shaped much of their future religious beliefs and deep emphasis on preserving their dead and providing funerary goods to sustain their afterlife. It was also a problem for the Egyptians who really did not want these graves, and all the funerary treasures, to resurface later. Beginning around 2900BCE, they started building solid mud-brick boxes, called mastabas across the top of the burial site, and digging the burial chambers deeper, replacing the natural mummification of the shallow sands with artificial processes.

A mastaba
In a stroke of genius, Djoser made two innovations on the mastaba concept: make them out of stone instead of mud-brick, and stack several of them on top of each other. That is why Djoser's pyramid is a step pyramid—he wasn't aiming to build a pyramid shape at all, but rather to build himself a multi-mastaba grave.

Imhotep's idea set off the golden age of pyramid building in Egypt, with most of the largest pyramids built in the subsequent 150 years to a combined volume of more than 317 million cubic feet of solid stone.

Not long after Djoser came up with the concept of masonry architecture and pyramid tombs instead of mastabas, the Pharaoh Sneferu took the idea and really had fun with it, adding his own spin making the sides of the pyramid smooth rather than stepped like Djoser. Sneferu's modifications did not succeed on his first attempt. His first attempt, the Medium pyramid, aimed to take Imhotep's stepped design and make it taller, steeper, and layer a smooth, non-stepped casing on top. Instead, the casing around it collapsed, leaving an awkward, ruined core to this day.

Sneferu's Medium Pyramid. Sneferu's first pyramid project may have actually been started by his precessesor. Due to changes to the original Imhotep design, it's exterior suffered a catastrophic collapse.
Sneferu did not succede on his second attempt either. The resulting pyramid bears the name of it's catastrophe: the Bent Pyramid. Archaeologists suspect that the steepness of the original design caused it to buckle after it reached a certain height, forcing Sneferu to alter the gradient to reduce the weight on the top of the pyramid. Interestingly, Sneferu completed the Bent Pyramid project anyway, perhaps afraid he would not live long enough to complete a third, unadulterated pyramid in the new style.
More successful than Sneferu's first pyramid attempt, the Bent Pyramid still experienced structural failures and had to be reinforced with wooden timbers inside.
But he did. Sneferu's thrid and final pyramid represents the first successful smooth-sided pyramids in egypt, and remains one of the largest, most in-tact pyramids in Egypt today.
Third time's the charm. Sneferu ended his reign with a home-run in the Red Pyramid. A massive first-of-its-kind smooth-sided pyramid.
Combining all three pyramids, Sneferu's prodigious building campaign far exceeded those of any of his successors. But individually, none of his pyramids even come close to matching the size of those built by the next two generations that followed: Khufu and Khafre.

Khufu built the Great Pyramid, the largest and tallest of all the pyramids, and the only one with significant internal chambers. The chambers of the Great Pyramid remain quite mysterious. Like all the other pyramids there's a passageway leading down into the bedrock and ending at a chamber. Except that instead of making that his burial chamber, Khufu evidently left it unfinished and started construction of the so-called "Queen's chamber." Mark Lehrer suggests that the queen's chamber, equipped with an alcove for the ka-statue, was intended for the pharaoh's ka, a kind of symbolic burial that Egyptians practiced in addition to the real one. The King's chamber above it, however, contains the actual sarcophagus that presumably once held the dead king. However, the most mysterious room in the Great Pyramid is the Grand Gallery, a long, hard-to-walk, very tall void leading from the level of the queen's chamber to the king's chamber, with holes along its sides of unknown purpose. Bob Brier and Jean-Pierre Houdin have theorized that the grand gallery was built the way it was to house a counter weight system used to hoist the enormous beams that form the ceilings (there were several layered ceilings separated by "weight-relieving chambers") over the burial chamber.

More interesting than the pyramids themselves are the archeological remains around them. Not far from Khafre's pyramid (background), are the remains of a 5th dynasty Silo Building Complex (foreground) which housed an actual granary and possibly also a bakery used either to feed workers for later pharoahs or to make funerary offerings for some of the tombs. In the plains below (not pictured) extensive remains have been discovered of the nearly industrial-scale rows of bakeries used to feed the workers who built the Great Pyramid.

Khufu's son Khafre built a pyramid nearly as large as the Great Pyramid. It's actually in much better shape, one of the few pyramids in Egypt to still have a significant amount of its original smooth exterior casing. However, it doesn't get nearly as much attention as Khufu's Great Pyramid because it lacks the latter's enigmatic interior chambers, featuring only a simple burial room beneath the pyramid, like all the others.

How do we know who built the pyramids? Every pyramid archeologists have entered has been empty—robbers picked them clean thousands of years ago. Some, like the Unas pyramid, contain deliberate inscriptions attesting to their builder. Khufu is identified on the Great Pyramid only in a marking left on a stone by the workmen, from before the stone was set in place. However, the richest set of information usually comes from the extensive funerary complexes that were built around their associated pyramid.
Khafre's Pyramid complex on the other hand, includes perhaps the most enigmatic monument anyone has ever built: the sphinx, carved from a single outcropping of limestone, with a causeway leading to his pyramid entrance.

And with that, the golden era of pyramid building came to an end. To be sure, succeeding generations had yet to build over a hundred more pyramids (that we know of), but Khafre's successor's pyramid, a bit smaller than the original progenitor built by Djoser, is not on the same scale of Khafre and Khufu's, and the ones that came after that were even smaller.


It's common to interpret the dramatic decline in pyramid size after Khafre as evidence as a general decline in Egyptian prosperity, or a decline in the centralization of the Egyptian state. Both interpretations suffer from bad economics though—in fact Egypt prospered and its economy became increasingly sophisticated. At an anthropological level, one could look at this as a shift in cultural emphasis that elevated the importance of libraries, palaces, and temples while downplaying the importance of pyramid-building. At an economic level though, it all comes down to opportunity costs. Sneferu, Khufu, and Khafre reigned in an era with a relatively unsophisticated economy where interests that might compete with pyramid building, like the sprawling monumental temples of later pharaohs, didn't really exist yet. But as the economy and society became more sophisticated, other enticing uses for all that labor and stone emerged, and later pharaohs pursued them.

Tuesday, November 3, 2015

The difference between economic growth and "economic growth"

Noah Smith has a column on a very common fallacy I see all the time in US politics where people confuse things that increase the level of GDP with things that increase the growth rate of GDP. Smith's column should be required reading for anyone making any claim about "growth."

The thing is that almost all of the ideas anyone has for "growing the economy" are actually only about static gains: tax cuts result in a one-off, static increase in the level of GDP, not a persistent, dynamic increase in the growth rate in GDP. Deregulation is the same--just a one-time reduction in some dead weight loss. Same for up-zoning. Same for free trade. Hardly any of the traditionally "pro-growth" policies actually increase the growth rate, they just transition us to higher level of GDP with the same growth rate as we have now.

This all rests on a semantic slight-of-hand. Something that increases the level of GDP necessarily increases the measured percentage growth of GDP temporarily, as we transition to the new, higher equilibrium. So technically you could say these policies increased growth. But really the "growth" there is an artifact--the policies merely affected the level, and the measured growth rate will return to what it was before.

Some of these static gains are quite substantial. Easing zoning restrictions, for example, could reduce the cost of our biggest living expense, meaning it would make us all quite a bit wealthier than we are now. But compared to a permanent increase in the growth rate, these gains are minuscule.

I'm reminded of what my international econ prof said about the tension in the room when they estimated the gains from free trade in then newly-formed European Union. Everyone was quietly praying that the result would at least be non-negative. It's not that anyone had any doubt about their theory of the static gains from trade, but they all knew that these effects are easily dwarfed by dynamic effects that would affect growth rates, about which theory is mostly silent. An imperceptibly small negative effect on growth would easily wipe out the static gains from trade many times over. There was a huge sigh of relief when the estimate came out as a small but positive gain from trade.

Friday, October 23, 2015

What's up with those Heritage numbers?

Heritage has a piece arguing that almost all (97 percent) of the increase in insurance coverage in 2014 was just the medicaid expansion, and that there was hardly any expansion of private, non-medicaid coverage due to a large net drop in coverage under employer-sponsored plans (ESI) by 4.5 million. They write
In sum, when it comes to increasing the number of individuals with health insurance coverage, the net effect of the ACA in 2014 was almost entirely a simple expansion of Medicaid.
The implication they're going for, I think, is to suggest that repealing the ACA except for the medicaid expansion would have only very minor effects on coverage levels.

Charles Gaba has already explained that these numbers don't make a whole lot of sense. To be sure, we've known for a while that the medicaid expansion has been among the most effective parts of the ACA in terms of boosting insurance rates. But none of the other data sources can corroborate the extreme disparity in the Heritage numbers.

I was reminded of the on-going RAND health insurance surveys, so I looked up their survey that covers the September 2013-November 2014 period, which should roughly line up with Heritage's numbers. They actually found that almost as many uninsured people gained ESI as signed up for medicaid—7.3 million to 7.5 million respectively. There's plenty of churn though, so counting those who lost ESI, they found a net increase in ESI of 6.6 million, way different than Heritage's -4.5 million. In fact, the gross number of those loosing ESI in the RAND data was just 3.4 million, on the same order as Heritage's net figure. The final sentence in RAND's abstract might as well be a direct rebuttal to Heritage:
These findings suggest that the ACA is expanding coverage through a variety of insurance sources, perhaps because the individual mandate is encouraging people to take up insurance offers that they might otherwise have declined.
Now, the two datasets are looking at slightly different windows—Heritage is looking at, supposedly, January 2014 through December 2014, while the RAND data starts a few months earlier and ends one month sooner. But if what Heritage found is that more than 10 million people lost ESI in December alone—wiping out years worth of gains—they should do a better job writing up their findings!

Heritage and RAND also differ in methods. Heritage took their data from a private consultant, Mark Farrah Associates, who compiled the data from surveys of insurers, while RAND conducted their own survey of households rather than insurers. Methodologically, trying to directly track transitions in a churning market can be error-prone as people will leak through the cracks in your models. So I find it helpful to look at snap-shot pictures like this Gallup survey. Unfortunately, they didn't break out just 2014 for us—to compare to the Heritage data—but their totals for the 2014 and 2015 period don't support Heritage's implication that the ACA is all medicaid and no private insurance: the uninsurance rate dropped 5.5 percentage points, while the proportion covered by medicaid rose only 2.4 percent. Gallup finds that the single biggest contributor to the decline in uninsurance—3.6 percentage points worth—was a large expansion in private insurance not through one's own employer. That sounds like a lot of people signing up for ACA exchange plans, but it's hard to be sure—as I understand their data, the ESI category only counts people covered by their own employer, while those covered by their parent's plan would be in the "self or family member" category along side ACA exchange plans. That's an important caveat because the ACA extended family plans to all under-26-year-olds.

Nevertheless, for whatever it's worth, Gallup's "covered by own employer" category looks less optimistic than the RAND numbers, with a net decrease of 1.2 percent, which corresponds to a net loss of roughly 1.5 million people. So, that's still way below the Heritage numbers. For reference, the prediction before the ACA went into effect were that coverage in ESI would remain relatively unchanged.

Quick update. I meant to include this remark in the original post but forgot: one might reasonably expect ESI to decline, because the population is aging and in particular large numbers of baby boomers have just become medicare-eligible, and even more will in the coming years. Projections were that the ACA would have little impact on this longer-run trend.

Thursday, October 22, 2015

Fun with Laffer curves

Thomas Sowell strongly implies that there's "mountains of evidence" that a 40 percent income tax rate is on the right tail of the Laffer curve, so that raising the tax to that level would actually result in less revenue.
"This ignores mountains of evidence, going back for generations, showing that raising tax rates does not automatically mean raising tax revenues — and has often actually led to falling tax revenues. A fantasy expressed in numbers is still a fantasy."
He softens the remark in the usual weasle words ("does not automatically mean") but gives away the game by asserting flat out that raising revenues by rasing the tax to 40 percent is "still a fantasy." Sowell claims that the Laffer curve peaks at less than 40 percent. And he's wrong.

I think the idea of 40 percent taxes makes a lot of people nervous because they implicitly think that there's some dangerous threshold at 50 percent, as if that's the threshold at which people will drop out of the labor force. But the reality is that nothing special happens if you tax more than 50 percent. First, it's important to remember that that's a 50 percent marginal rate--most people in this bracket won't pay anywhere near 50 percent of their income because most of their income is in a lower tax bracket. And as for the incentive effects, the poor are actually likely to work more if you tax them at a higher rate because they simply need the money--the wealth effect simply dominates. Now think about the rich. The top income bracket threshold corresponds to roughly $1,000 an hour. Take half of that and they'd still get $500 for an extra hour's worth of work per week--that incentive is still huge. For the rich, the substitution effect does dominate, just as the Laffer curve predicts, but at 50 percent that substitution effect is still pretty strongly weighted towards labor.

That's why, if you actually examine the "mountains of evidence" Sowell refers to, you'll find that economists generally estimate that the peak is somewhere in the 70 percent to 80 percent range. It's hard to know for sure, because it has been a very long time since we had tax rates anywhere near that high, and there are a lot of other taxes and wedges that affect it. But that remains the best estimate we have.

Nevertheless, out of curiosity, let's do the math. Let [$]L[$] be the number of hours per week that you work, which is a decreasing function of the tax rate [$]\tau[$]. You work for an hourly wage [$]w[$] so that [$]wL[$] is your weekly pay. Thus the taxes [$]y[$] you pay is given by [$$]y=\tau wL.[$$] In order for it to be the case that raising taxes reduces the total taxes you pay (and therefore government revenue), the derivative with respect to the tax rate, [$]\frac{\partial y}{\partial \tau}[$] must be negative:[$$]0\gt \frac{\partial y}{\partial \tau} = wL+\tau w \frac{\partial L}{\partial \tau}[$$] which implies that we must have [$$]\frac{\partial L}{\partial \tau}\lt -\frac{L}{\tau}.[$$]

Let's plug in some numbers, shall we? With a 40 hour work week and a 40 percent tax rate, that means for Sowell's claim to apply to our example, [$$]\frac{\partial L}{\partial \tau}> -\frac{40}{0.4}=-100[$$] That in turn means that a 1 percentage point increase in tax must cause you to reduce your weekly hours by at least 1 hour per week. At the median wage of $22 an hour, that's a tax hike of $8.80 per week causing you to reduce your weekly income by $22 per week in exchange for an extra hour of liesure a week.

Whether that sounds reasonable to you is opinion, I supose. But the data does not find many people making that choice.
Sidenote: there are also state and local taxes to consider, as well as other types of taxes. In addition to income tax, sales taxes also have a labor disincentive effect, albeit of different magnitude, so we need to consider those. All told though, the rest of these taxes add up to about 15 percent for a typical city in a typical state, and these tend to be regressive rather than progressive. 55 percent is still way below the peak of the laffer curve.

It's also worth noting that revenue is not necessarily the only way taxes redistribute.