Shanghai Tower - Building the Skyline

September 24, 2019 by Jason Barr 3 Comments

The Technology of Tall (Part II): The Need for Speed

Jason M. Barr September 24, 2019

Note this is Part II of an on-going series on the evolution of skyscraper technology. The rest of the series can be found here.

The Chicken or the Egg?

What came first: building height or elevator speed? The history of skyscrapers brings us to a kind of chicken-and-egg conundrum. Does the drive to build tall come first and then fast elevators come next? Or do rapid elevators show what’s possible and then developers exploit them to go taller? While I don’t think there’s any way to answer this question, we can look at the history of the elevator to get a sense how this co-dependency has evolved.

We can say for sure that there is a symbiotic relationship between building height and elevator speed, and together they have enabled cities to grow upwards and hold more people and businesses. Ironically, elevator speed history emerges out of a strange paradox. People are willing to spend an hour or more commuting each day—idling in traffic or dawdling on trains—but when they get to a building, they expect to get from the ground floor to their destination in less than two minutes. It’s the quest for convenience, as much as speed, that has driven the technology forward.

The Birth of Vertical Transportation

Modern elevators are products of the Industrial Revolution, and were first installed in factories, mines, and warehouses. By the 1830s, for example, they were in numerous British textile mills. By the 1840s they were used for passengers. Bunker Hill Monument in Boston, erected in 1842, had a steam-powered lift to take visitors to an observation deck. Wealthy people started putting them into their homes in the 1850s. The first commercial elevators seems to have been installed in New York City before the Civil War. The two earliest examples are the 5-story Haughwout Building (1857) in Soho, and the Fifth Avenue Hotel (1859) at Madison Square Park. Over the ensuing decades, inventors and entrepreneurs continued to advance the art and science of elevatoring to make them faster and safer.

The Safety Break?

The conventional story regarding the elevator revolution begins in 1854. In that year, in New York’s Bryant Park, the Exhibition of the Industry of All Nations—housed in a specially-constructed “Crystal Palace”–demonstrated the world’s cutting edge technology. One vendor present was Elisha Otis. He was showcasing his elevator prototype. In front of large crowds, he climbed onto the platform and hoisted it up a story or so. And then–dramatically–cut the rope holding it in place—producing terror that it would crash. And yet, it did not. The elevator hardly moved. His new safety break kicked in and rescued him from injury and obscurity. Since that dramatic display, the story goes, the elevator’s success shot upwards, now that fear of free-falling was gone. This story has been repeated ad infinitum as the pivotal moment for elevators and skyscrapers.

A Drawing of Elisha Otis Demonstrating his Safety Break to the Public in 1854. This drawing is widely circulated as “proof” that, until the public saw Otis’ safety break in action, they were afraid of elevators. However, according to author Andreas Bernard, this drawing was produced in 1978 in celebration of Otis Elevator Company’s 125th anniversary in 1978. It was an imagined recreation of past events and helped fuel the idea that Otis was the keystone in the elevator revolution. Image source: Wikipedia.

Myth Busting

Yet according to Andreas Bernard, author of the 2014 book, Lifted: A Cultural History of the Elevator, the story is not so simple. His search for contemporaneous reporting on this “viral” moment came up short. In fact, he finds, at the time, nary a mention in the press. He argues that for such a seemingly pivotal moment in history, hardly anyone seemed to care. He writes,

In the major American daily newspapers and magazines, the 1854 event showed up only in two marginal locations. In addition to the Scientific American article, a brief report appeared on May 30, 1854, in the New York Daily Tribune, which mentioned the daring of the inventor “who, as he rides up and down the platform occasionally cuts the rope by which it is supported.” No further contemporary traces can be found (just as there were no obituaries of Elisha Otis in 1861). Thus it is no exaggeration to say that the demonstration in the Crystal Palace, that “authentic great moment in architectural history,” went almost completely unnoticed by the public.

The story, evidently, is another case of history being written by the winner. Thanks to the diligence of Otis and his offspring, his company went onto to be one of the largest manufacturers of elevators in the world. In 1911, Elisha’s son Charles set out to “correct the record” about elevator history by writing his version of the events, and which minutely chronicled the display in the Crystal Palace. As Bernard writes,

The influence of … [Charles Otis’] text on the historiography of the elevator is obvious from the fact that after 1911, there was hardly a mention of the elevator’s origins that did not begin by repeating the story of the event in the Crystal Palace.

The First Skyscraper?

As a side note, this story has a familiar ring in regard to the world’s first skyscraper. The conventional wisdom is that it was the Home Insurance Building in 1885, designed by William Le Baron Jenney. But this notion seems to have been the product of Chicagoans winning the battle of historiography. The Home Insurance Building, while novel, could not, by today standards be fully described as a “skyscraper” in that it was not fully iron (or steel) skeletal structure.

At the time, many architects and engineers were developing technologies and methods in parallel. In the years after the first skyscrapers emerged in Chicago and New York, there was a battle within the community to claim the prize of “First Skyscraper.” Jenney argued it was his structure; while New York’s Bradford Lee Gilbert said his Tower Building (1889) was first. Others also offered proof they were the true innovators. In the end, through good marketing, Chicago remains the winner in our minds, but this claim highly debatable and far from conclusive.

The Birth of the Rent Premium

Once vertical transport revealed itself to be practical, however, another revolutionary moment was created. Likely, for the first time in human history, was an inversion in the economic and social value of higher floors. Before that, when climbing was the only way up, the top stories were naturally hard to get to. No one wants to climb more than a few floors; as a result, the highest floors were rented to those with the lowest ability to pay. Offices used them for storage or for their low-level clerks.

Rent Premium in 1900 versus 2019. Left: Rent ($ per room) for walk-up apartment buildings versus floor height in the Lower East Side of Manhattan in 1900. Right: Estimated sales price ($ square foot) versus floor height for luxury condos at 217 West 57th Street. The key takeaway: without elevators the higher floors were worth less to tenants because of the trouble of climbing stairs. Sources: Left: See *Building the Skyline*. Right: See Skynomics Blog post.

In a way, the elevator created treasure in the sky. Because vertical movement was fast and cheap, it generated a rent premium for the higher floors. That is say, the amount of rent paid, per square foot or meter, was higher as one rose up. Today, that premium in New York City is between 0.5 and 1% per floor. In other words, prices on 30^th floor of a skyscraper might rent for up to 20% more per square foot as compared to the same space on the 10^th floor. Developers realized if they could get their building occupants up there, they could reap more profits. And the race for height was on. This rent inversion was first noticed in New York City in 1870, when The Equitable Life Assurance Society built it’s 7-story headquarters near Wall Street, and which included two elevators.

The Value of a View?

How much of this premium is due to views, or increased social status, or more productive workers is still not fully understood; but what is clear is that people in big cities are willing to pay to be high in the sky. It’s also worth noting that this benefit also rests on our particular evolutionary history. Imagine that all humans had an innate fear of heights; that working in high-rise building automatically generated dread and anxiety? If so, the world would look radically different.

Elevator Dilemmas and their Remedies

The earliest elevators were driven by steam or hydraulics. And it was not until widespread use of electricity in the 1880s that efficient speeds were obtainable. Once this barrier was removed, however, a host of new problems arose. Faster speeds allow for taller buildings, which means more people, which generates more congestion and logistical problems in getting people to their final destinations. For example, there’s the problem of waiting times once you push the button in the lobby. Then there’s limits on how many people can fit in one cab. And when it is filled with passengers, it seems to stop on a million floors before you get to yours. Not to mention the fact it’s socially awkward to stand in a cramped box with 15 strangers.

The Pain Index

Keep in mind that, in theory, one can move people faster by creating more elevator shafts and this is certainly necessary for larger or taller buildings. But extra shafts are the bane of developers, since they eat up income-generating space. For the time being, we are going to hold the number of elevators constant and focus more on movement and speed. We will come back to the “shafts problem” in a future post.

The key challenge for efficient mobility is that of minimizing what has been referred to as the Pain Index—the total time to it takes from once you hit the button to when arrive at your final location. Evidently, however, it’s not clear what people hate more—waiting in the lobby for the elevator to arrive, stopping more inside the elevator, or getting into a crowded car.

Traffic Flow and Optimal Stopping

One of the key problems is that of peak usage times. For example, in offices at 8:30am, it seems every employee wants to get into the elevators at the same time. With the old-school call system, when multiple users push the call buttons at the same time, the elevators move to where they were called first. But when many buttons are pushed at the same time the system gets gummed up, increasing waiting time.

Computing technology and software programming has helped mitigate the problem of how to efficiently allocate car space during the day and based on different kinds of traffic patterns. Today, most modern elevator systems employ computer algorithms to minimize travel times, using what is called the Destination Dispatching System (DDS). In real-time, the system analyzes the input data–where the buttons where pushed–and makes a list of who to put in which cars and where the cars are to stop. If with conventional elevators waiting took over a minute, the DDS could reduce that time to half.

Elevator Waiting Times versus Traffic Intensity. The red line is waiting times for the traditional call-button method. The green line is the standard DDS system. The yellow line is a dispatch system created by KONE. Source: De Jong (2008).

Zoning and the Double Decker

For a given set of elevator shafts, the spaces can be used more rationally by the use of zoning and double decking. Zoning is the process of limiting specific elevators to operate only in predefined zones. One elevator can stop for local service, but another one say only goes from the lobby to the higher floors. Zones are normally kept to around 10-20 floors. This reduces the number of stops for the zoned cars and speeds up its return to the lobby. To allow for even higher heights, supertall buildings often have sky lobbies where an express elevator take you there and then you transfer to a separate elevator that operates only up high. For very tall buildings, another way to use the shaft space more efficiently is to have two elevators operate within the same shaft. One way to do this is to have one elevator car sit on top of another, creating the double decker. Odd-floor travelers enter the bottom car, while even-floor travelers enter the top car after walking up a ramp.

Cable Height

As buildings get taller, the amount of rope needed to connect the elevator car to the motor becomes longer and longer. This is a problem as conventional ropes, made of steel, can cease to be functional. In very tall buildings, nearly 70% of the elevator’s weight comes from the cable itself and when it gets too long it cannot support its own weight. Companies that manufacture elevator systems are thus in a race to develop new types of ropes that are both stronger and lighter. With conventional ropes the highest that one elevator car can travel is 500 meters (1640 feet; about 140 floors). After that, going taller requires transferring to a new elevator at a sky lobby. The Jeddah Tower is going to install KONE’s “UltraRope,” which has a carbon-fiber core, making it particular light and strong. With this rope, cars can now travel up to 1000 meters (3280 feet), and it pushes possible skyscraper heights upwards (is this the egg for first mile-high tower?).

Human Physiology

Then there’s the problem of the human body, with its delicate carbon-based controllers and pain receptors. To quote James Fortune, a partner at FS2 Consulting, which specializes in elevator designs for supertall towers, “The human body has various internal sensors that are sensitive to external motion forces, noise, and vibrations. These sensors provide constant feedback to the brain and are quite responsive to any “out of the ordinary” elevator vibrations or noises.”

In particular, humans are quite sensitive to the acceleration and deceleration rates, which can cause ear discomfort due to the rapid changes in air pressure. Fortune says that, “However, ear comfort and pressure changes do not usually affect healthy elevator riders unless the descent speeds exceed 10 meters per second (m/s) and vertical travel exceeds 500 meters. For this reason, virtually all the latest supertall high-speed lifts, with “up” travel speeds to 10 to 20.5 m/s, have a maximum “down” speed of 10 m/s. Some cutting edge elevators, such as those installed at One WTC add extra air pressure on the way up to help prevent the annoying ear-popping sensation.

A History of Speed

While it’s fun to focus on the history of speeds, the truth is that the fastest elevators in the world are mostly used for visiting decks and/or to give bragging rights to the developers and companies that install them. For most office buildings, the average maximum speed is about 21 feet per second (5.8 m/s). Nonetheless, as the technology for speed and comfort progresses, it is likely that their benefits will be more widespread. In 1913, the world’s tallest skyscraper, the Woolworth Building, had a maximum speed of 11.6 feet per second (3.6 m/s). In 1931 the Empire State Building, had a maximum speed of 20 feet per second (6.1 m/s). So in in some sense, the top elevator speeds for the typical building haven’t changed all that much. What has changed is that passengers can be much more rapidly moved based on logistical algorithms, zoning, and double deckering. The efficient allocation of occupants is really what allows for buildings to go taller and taller.

The Record Breakers

Be that as it may, the figure below demonstrates the history of maximum elevator speeds over the last century. The left figure shows the speeds (feet per second) for the world’s record-breaking skyscrapers. (Note the Shanghai Tower is also added to the graphs. It did not have record-breaking height but did have record-breaking elevator speed). This figure is clear: maximum elevator speeds have been rising over time. A back-of-the-envelope calculation shows that from the Singer (1908) to the Shanghai (2015), the maximum speed as increased at an average annual rate of 1.78% per year.

The right figure is speed versus the number of stories for the world’s record-breaking buildings. Again, we see a positive relationship. But, while the graph shows elevator speed versus height, we could be equally as justified in showing height versus speed, since we still can’t say which was the chicken and which the egg. All we can say is that the graph shows a strong correlation but says little about causality. Another thing, however, pops out in this graph: the world’s fastest elevators are not in the world’s current record-breaker.

The Burj Khalifa’s elevators can move at a speed of 33 feet per second (10 m/s) and the Jeddah Tower, under construction, is expected to be the same. These are much slower than the Taipei 101 and the Shanghai Tower. In other words, what these findings suggest, again, is that speed, in and of itself, is not paramount. Likely the cost of operating super fast elevators and need to maintain passenger comfort and efficiency of movement currently trump speed.

The Evolution of Maximum Elevators Speeds over the Past Century. Left: Maximum elevator speeds for the world’s tallest buildings versus year of completion. The graph shows that speeds have been steadily increasing since the early 1900s. Right: Elevator speed versus building heights. Notice the world’s fastest elevators are currently in the Shanghai Tower, not the Burj Khalifa. Source: The Skyscraper Center.

The Future of Vertical Transportation

What’s in store for the future? Certainly, we can say that the big five manufactures–Otis, KONE, Thyssenkrupp, Schindler, and Mitsubishi–will continue to invest in R&D to push the elevator envelope, thus encouraging developers to build taller. But what revolutionary technology comes next? Who knows? Likely futuristic buildings will have mag lev elevators with horizontal circulation. In 1957, Frank Lloyd Wright’s design for the one-mile high building called for nuclear powered elevators. But we’ll leave a discussion of these moon-shot technologies for the future, or rather, a future post.

Continue reading. The rest of the series on the technology of tall can be found here.

June 4, 2019 by Jason Barr 7 Comments

The Economics of Skyscraper Height (Part IV): Construction Costs Around the World

Jason M. Barr (@JasonBarrRU) June 4, 2019

Note this is Part IV of a series on the economics of skyscrapers. The rest of the series can be read here.

Rise of the Skylines

As we look around planet Earth, we can’t help but notice that skyscrapers are getting taller. In 2000, for example, the average height of the tallest 100 completed buildings was around 285 meters (935 feet). In 2018, that number was about 385 meters (1263 feet), for an average annual growth rate of 1.8%. What is causing this rise in building height?

The Demand for Height

First and foremost, skyscraper construction is demand driven. Tall buildings are built to satisfy our need and desire to be together in dense urban areas. The more humans base their economies on services and intangible products, they more they are drawn to cities. The masters of finance, marketing, business services, and high-tech need to cluster together in order to make their products. Also, the great wealth generated by this productivity fuels the growth of the consumer-oriented city, and its concomitant suite of cultural and entertainment-based amenities. The quest for a better life draws people to the same place at the same time. The skyscraper is thus a solution to the problem—it is a machine that converts air to land.

The Supply of Height

But here I want to argue that to really understand skyscraper heights, we need to investigate not only the demand for tall buildings, but also the forces that create their supply. If we want to understand building patterns around the world in places like China or the United Arab Emirates, we need to study the costs of construction in these places. The rise of skylines in Asia is as much as due to the cost side as it is to urbanization and the increasing importance of global cities.

The Economic Theory of Skyscraper Height

But, before we dive more deeply into the costs of building a shiny new skyscraper, we first pause to discuss the economic theory of skyscraper height. The economic height of a structure is the one that makes the most sense in terms of best balancing the demand for height with the costs of providing it. If we did some economic modeling, what pops out is an equation for the optimal building height (based on some simplifying assumptions). Though one can find a more detailed treatment here, the bottom line is that this equation can be given in a simplified form:

Economic Height = (Market Price Per Floor)/(Construction Costs Index Value)

Or for simplicity:

H=P/C.

That is, the economic height is given by the market price per floor, P, relative to a measure of construction costs, C, which includes the prices of materials and labor, and the efficiency of the construction operation.[1] We can observe from the equation that, all else equal, the lower the value of C, the taller a building will be in a given city at a given time.

P

If you want to understand the near-universal pattern of why there are tall buildings in the city center and low-rise building further away, then just look at the nature of the market prices per floor (or per square foot or meter), and you will see they drop off rather steeply as one moves further away from the center. That is to say, within a city, at a given time, we can assume that C is about the same for all builders. It’s P then that measures what building occupants are willing to pay at various locations.

And P can be broken down into, roughly speaking, two parts. Part I is the quality of what’s inside the building (does it have fast elevators, great views, marble floors, etc.?). Part II is the quality of what’s outside the building—its location. This is the key reason why buildings are so tall at the center—the location (or land) value is so high. Wall Street firms need to cluster together to earn greater profits and they pay for the right to do it. Developers respond to the high willingness to pay by going taller. The desire to pay falls rapidly as one moves away from the center. This has been strongly documented around the world and over time.

3D Visualizations of Land Values in Chicago. Each of these graphs shows the relative value of land in the Chicago at different points in time. The peak is in the Loop and falls steeply from there. Source: Ahlfeldt and McMillen (2014).

A Moving Target

Skyscraper height is thus determined by the ratio of the benefits to the costs. If we want to understand height at a given time in a given city, then using the prices at various locations is a decent indicator of about how tall a building should be. But if we want to compare this economic height over time and/or across cities then things get more complicated—both P and C become moving targets.

Compare New York to Shanghai, for example. The average height of the two cities’ completed skyscrapers since 1988 have been similar. But the question we cannot decipher is what are the relative prices to costs? In New York, both prices and costs are higher than in Shanghai; and yet the ratio is about the same. Asking rents in the new 67-story One Vanderbilt tower adjacent to Grand Central Station are up to $160 per square foot ($1,722 per square meter). The 128-story Shanghai Tower, evidently, has asking rents of half that amount (and now you get a sense of the relative costs of building in these two cities that generates the same average heights).

Roaring Twenties

This equation can also help us understand the building boom in New York during the Roaring Twenties. P was rising because of the growing economy, and C was falling due to technological innovations and learning-by-doing. When you put the two things together you can a rapid rise in the heights of buildings.

The Average Heights of Completed Skyscrapers in New York and Shanghai, 1988-2017. Here a skyscraper is a building of at least 150 meters. Source: The Skyscraper Center, CTBUH.

Global Costs

One of the key drivers of costs around the world are wages. An unskilled construction worker in New York, for example, is paid $17.57 per hour. In India, laborers get paid $0.63 dollars per hour. While the same type of workers in China receive about $3.36 dollar per hour. Since labor costs represent a substantial fraction of total costs (in the U.S. they can be as high as half the costs), the less developers must pay for labor, the lower the costs, and thus the more likely they are to build taller.

Consider some examples (in non-inflation adjusted U.S. dollars). One World Trade Center cost nearly $4 billion, as compared to the Shanghai Tower, which cost $2.4 building to construct. On a per-floor basis, that’s nearly double the costs. The Burj Khalifa, is almost 300 meters taller than One World Trade Center, yet the total costs were 61% less! The idea of getting a 163-story building in New York for $1.5 billion is laughable.

Construction Costs for Some Supertall Skyscrapers Around the World. Source: Emporis.

A Skyscraper Cost Index

To investigate this issue in more detail, I created an index of skyscraper construction costs around the world. The website, Emporis.com, lists the costs of 200 large high-rise buildings. (Details about how I created the index can be found here). It is, admittedly, a first attempt to measure skyscraper construction costs. A more detailed analysis is made difficult by the fact that developers (or their general contractors) generally do not release the cost of construction and so I need to use the limited publicly available data.

But what the exercise shows is that, relative to the U.S., mainland China and the Arabian countries can get skyscrapers for a substantial discount relative to the United States (and even more so compared to New York City).

A Skyscraper Construction Cost Index. Underlying data is from Emporis. Index details are in Barr and Luo (2017).

Costnomics

But an index value doesn’t tell how total costs change with building heights, it only gives a measure of the average costs of construction. To better understand the economics of building height, we need to dive a little deeper. Let’s take the point of view of a developer. Say we own a large lot in an office district in downtown Barropolis. We know (approximately) the average rents we can expect to earn once the building is filled, since we can observe the rents being paid in similar towers. This means that in order to maximize the profit, we need to determine how our total costs change as we go higher, in order to find the sweet spot.

It’s generally believed that average costs per square foot or meter are u-shaped with respect to floor height. For smaller buildings, going taller means that the per floor costs are falling, and then, at some height, they begin to rise. At that point, the costs of providing an additional floor becomes greater. For example, the cost of adding the 51^st floor is more than the cost of adding the 41^st floor. Where that turning point is remains an open question, and, as I will show below, it seems to be different in different cities.

The economic theory of skyscrapers says that the profit maximizing developer keeps adding floors until the revenue of the last floor just equals the cost of providing it. One floor less means leaving money on the table since the revenue from another floor will be greater than the cost. Building one floor above the profit maximizing height means losing money since the cost of the last floor was greater than the revenue is generates.

More Concrete

So why do the costs of adding more and more floors rise after some point? The answer has to do with the nature of building tall. Going taller and taller requires thicker materials, such as concrete or steel, on the lower floors to support the superstructure (as do the internal elements such as plumbing and electricity). Similarly, the cost of the foundation rises as the building gets taller because the it needs to support more weight.

Swaying in the Wind

Next is the additional costs of wind bracing. Tall buildings are constantly being bombarded by the wind. The taller the building, the greater the wind pressure, and the greater the possible sway. Nobody wants to be inside a building that feels like being on a 19^th century whaling boat. Thus, the structure needs to have extra materials to make it more rigid, so any movement is imperceptible to human senses. (The current trick for supertalls is not to make the building perfectly rigid, but rather to use massive pendulums to slow down the swaying to a rate that can’t be detected.)

The Elevator Problem

Then there’s the elevator problem. Going taller means that, as some point, an additional elevator shaft needs to be created and filled with more elevators to move people to the higher floors. The developer must consider whether the lost rentable space and extra costs are less than the extra revenue from going taller. But, in general, taller building require more elevator equipment.

The Evidence

What does the evidence say about the structure of these costs? To look this, I have collected data for recently constructed buildings in New York, Chicago, and Shanghai (details here). The data set contains, for each building, the total cost of the structure and the number of floors; and from this we can look at how the average cost per floor changes as buildings go taller. In this way, we can infer something about the economics of skyscraper height. One caveat though; the sample sizes for each of these cities are very small, and they contain various types of structures, from public housing in Shanghai to supertall offices and luxury apartments. For this analysis, I only present the per floor costs without controlling for these other things. Please consider the findings as preliminary.

Costs in Three Cities

The first fact that pops out of this analysis is that it is much cheaper to build in Shanghai and Chicago than in New York City. The average price per floor for Chicago is about $6.2 million; for Shanghai it’s about $3.7 million per floor. For New York, on average, it costs about $15 million per floor. Or in other words, for a cost of $20 million per floor (on average), you can get a 65-story skyscraper in New York, while in Shanghai you can one that’s 120 stories. In Chicago, at that price, you can get a 100-story structure.

Second, the minimum point for each of these cities is different. The lowest per floor costs in New York about 32 floors. For Chicago, it’s at 55 floors. Shanghai doesn’t seem to have a turning point based on the data—with per floor costs rising at all levels. (Why this is requires further work.)

Skyscraper Costs versus Building Height for New York, Chicago, and Shanghai. Costs are given in millions of 2018USD. Each dot is data for a particular building. The curves are trend lines (polynomial of order 2). Sources: see here.

The Future of Height

It’s clear that the future of height is upward. Though we tend to focus on particular thresholds, like the first one-kilometer or one-mile high tower, these will eventually be achieved as long as two conditions hold. First is continued economic growth, which will bid up the value of central locations in cities around the world. And second is the on-going process of technological innovation which will lower the cost of providing height.

The fact that countries like the U.A.E, Saudi Arabia, and China could enter the skyscraper race in such short order is because they are able to tap into the global skyscraper complex of architects, engineers, banks, and other related institutions. These players rapidly spread information and know-how to newly developed countries that are aiming to grow their cities. The experiences with skyscraper building there then becomes part of the global knowledge base, further increasing the rate of technological change, and lowering the cost of construction. One of the reasons why New York City will never be able to compete anymore for the world’s tallest building (which it invented over a century ago) is because the rapid escalation in construction costs tend to erode any savings from technological improvements.

Ever Upwards

The rate and direction of technological change is difficult to measure, but I hope to measure and discuss it in a future post. Suffice it to say, however, that as long as the there’s the desire to go tall, humankind will find a way to get there. The economics of skyscraper height show this to be true.

Continue reading. The rest of the series can be read here.

—

[1] Normally, prices are quoted in dollars per square foot or meters. But for this analysis, I use per floor costs to illustrate the economics. So, for simplicity, assume that each floor in a skyscraper is fixed at 200’ x 100’=20,000 square feet (or about 1858 square meters), which is about the average floor size for a modern high rise in the U.S.

December 17, 2018 by Jason Barr 10 Comments

The Economics of Skyscraper Height (Part I)

Jason M. Barr December 17, 2018

Note this is Part I of a series on the economics of skyscrapers. The rest of the series can be read here.

Clark and Kingston

In 1930, W. C. Clark and J. L. Kingston (CK), an economist and architect, respectively, published a book called, The Skyscraper: A Study in the Economic Height of a Modern Office Buildings. In this work, they act as a hypothetical developer of a Manhattan office skyscraper. Their aim was to determine a height for the structure which maximized the return, given the rents, and the costs of land and construction.

In fined-grained detail, they laid out the various elements of erecting such a building, including floor plans, and the all the different types of costs a builder must pay, from bricks, to elevators, to steel. For their analysis, they chose a large lot across the street from Grand Central Station, in the heart of Manhattan’s midtown business district.

The point of this exercise was to demonstrate that the supertall towers rising in Manhattan during the late 1920s were not “freak” buildings, but rather, were based on reasonable economic foundations.[1] They showed that when one did all of the accounting—comparing the income to the costs—the height that maximized the return was 63 stories. (Ironically, this is not that much different than today. One Vanderbilt, an office building currently under construction across the street from Clark and Kingston’s hypothetical lot, will rise 58 stories.)

**Manhattan Skyscraper Rendering by Architect J. L. Kingston. At 63 stories is was considered the ideal height at the time. Source:**
**The Skyscraper: A Study in the Economic Height of a Modern Office Buildings** **(1930).**

Economic Height

In their book, they present a definition of what they called the Economic Height of the building, based on the writings of the engineer, J. Rowland Bibbins; and one that is still reasonable:

The true economic height of a structure is that height which will secure the maximum ultimate return on total investment (including land) within the reasonable useful life of the structure under appropriate conditions of architectural design, efficiency of layout, light and air, ‘neighborly conduct’, street approaches and utility services. (pps. 8-9)

Economic Height provides a useful guide (though not the only one) for understanding why skyscrapers get built, since this height is determined by the best balance between the revenues and costs. In general, going taller will generate more income, but will also add to the expense. In modern economics terminology, the economic, or profit maximizing, height is one where at the highest floor, the additional or marginal revenue from that floor just equals the marginal or additional cost to providing it. If built one floor higher, the cost of adding the floor will be greater than the revenue and will not be worth it. If less than that height, money is “left on the table,” since adding a floor would produce more income than it would cost to produce it.

It’s worth stressing is that a developer builds this optimal height to earn a profit. People and companies are willing to pay the high prices because of the needs they fulfill and the benefits they provide. Thus, Economic Height is a response to the demand; not the other way around.

Land Values and Building Height

As CK also demonstrate, there is a direct relationship between the cost of acquiring the land and the return on investment from a taller building. We can think of developers as a type of urban farmer; the more it costs to acquire a lot, the more they must intensely develop the land in order to receive enough income to compensate for the high cost of the location. Thus, around the world, we observe taller buildings in places that have higher land values.

Given this notion of Economic Height as a benchmark, we can then say that any building that is taller than this can be considered economically “too tall” in that it is higher than it “ought to be” for pure economic gain; and hence produces lower profits than a shorter building. The difference between the actual and Economic Height is what I call Symbolic Height.

Height in the 21^st Century

Even though Clark and Kingston published their book nearly 90 years ago, the question of whether buildings are economically too tall remains as relevant today as it did during the Roaring Twenties. To look at the Economic Height at one location, Clark and Kingston
(funded by the American Institute of Steel Construction) hired a stable of expert consultants to help them analyze the problem. The ability of someone like myself to determine the Economic Height for even one building must come from publicly available data; and it’s virtually impossible to calculate it for many structures. However, we can make statistical inferences if we collect a large enough data set.

Skyscrapers around the World

For convenience, let’s define a skyscraper as a building that is 150 meters (38 floors, on average) or taller (and just focus on 1960 to 2017). Now imagine that you were a giant and could “harvest” all the world’ skyscrapers and put them into a jumbo pile—like a child might make a pile of sticks of various lengths. Now in our little game, we pick up each skyscraper (stick) and measure its height. Then we place it in one of several bins or buckets. The first bucket will contain buildings that range from 150 to 199 meters. The second contains buildings 200 to 248 and so on. The last bucket ranges from 788 to 836 meters, and which contains the Burj Khalifa at 0.828 km tall.

Which bucket has the most buildings? And what does this suggest? According to the CTBUH, there were 4,162 skyscrapers built between 1960 and 2017. It turns out that the vast majority of tall buildings are less than 200 meters (68.3%). Only 23 are 400 meters or taller. Statistically speaking if you were to randomly pick a skyscraper constructed since 1960, the probability that you would select a building greater than 400 meters is about one-half of one percent. The vast majority of buildings are “regular-talls” (under 50 stories); while the number of “super-talls” is minuscule, in comparison. The super-giants, while most visible from media accounts and their appearances in skylines, only make up a tiny, tiny fraction of the world’s skyscrapers.

Skyscraper Heights Histogram. Each blue bar shows the fraction of skyscrapers (≥150 meters) around the world in that height category (completed between 1960 – 2017). For example, 68% of all skyscrapers are less than 200 meters. The orange line is the fraction in a category or lower. 99% of the world’s skyscrapers are less than 350 meters. Source: **CTBUH**.

The Drivers of Economic Height

The evidence suggests that the bulk of the world’s skyscrapers are consistent with the notion of Economic Height. This is not to say that all skyscrapers reflect the best balance between the costs and benefits, but it is to say that the majority of the world’s skyscrapers have a strong economic rational, in that they are catering to a demand for building height. So what are the key economic drivers of skyscrapers?

Economic Growth

Most important is the process of economic growth and urbanization. The more economic activity there is in a city or region the more central locations become vital because people and business need to cluster near each other to more efficiently produce the goods and services that our modern economies require. The skyscraper shrinks space so that hundreds if not thousands of people can be at the same geographic coordinates at the same time. The tremendous demand to be in the central city creates a kind of “battle for place”—if more people want to be at a central location than can be accommodated, the price of that location rises. As land values rise, so does Economic Height, and skyscrapers rise as a result.

The ability of a country to build skyscrapers is directly related to the size of its economy. Once a country hits a threshold, in terms of its gross domestic product, there is then a very strong relationship between both the number of skyscrapers it has and the height of its tallest building. Arguably the greatest predictor of the height a country’s tallest building is the number of highrise buildings it has; and the greatest predictor of the number of tall buildings is the size of its economy.

Left: Number of Highrise Buildings in a Country versus its Gross Domestic Product ($PPP2011). Right: The Height of a Country’s Tallest Building versus the Number of Highrises. The figures show that there is a strong relationship between national income and number of highrises, and the more highrises the taller is a nation’s tallest building. Note: All variables in natural log form. Sources: GDP, #Highrises, Tallest Building.

The Cost of Construction

Today’s skyscraper technology is the result of a 130-year learning curve. Innovations in design, materials, and engineering, combined with lower labor costs in the developing world, make them attractive investments. While there has been no systematic research on the evolution of (inflation-adjusted) marginal or per-floor costs over the entire 20^th and early 21^st centuries, the evidence we do have suggests that these costs have been declining.

In Manhattan during the early years of skyscraper construction, between 1900 and 1920, I estimate that the marginal or additional cost of adding another floor averaged about 7%; between 1921 and 1931 this cost dropped to about 3%. In other words, in New York City, during the Roaring Twenties it was getting much cheaper to add extra floors. Builders were responding accordingly by adding more floors; this can explain, in part, the building boom of the era.

Costs around the World

Fast forwarding to the 21^st century, it’s instructive to look at a few recent examples. In January 2010, the world’s tallest building, the Burj Kalifa (163 stories) was completed. Its total construction costs was only $1.5 billion, or $9 million per floor. The comparatively expensive 128-floor Shanghai Tower, completed in 2015, cost $2.4 billion, or $18 million per floor. Contrast that with the 2009 58-story Bank of America Tower in Manhattan, which cost $1.76 billion, or $37 million per floor. While a few examples do not prove anything, it does illustrate that Asian countries can pay less to get more, in terms of building height. In New York and other U.S. cities, it seems to be the case that the cost reductions from technological progress are offset by the rising cost of labor and materials. In Asia, rapid economic growth, and intense urbanization, combined with lower building costs and an eagerness to employ innovations in design and construction, are driving building booms in their cities.

Are Megatall Buildings Good or Bad?

But what about the megatall giants like the Burj Khalifa, the Shanghai Tower, or the Taipei 101? They must be wasteful projects, with little economic rational, right? I would argue that the answer is not so clear, and that maybe we should not be so hasty to judge. Stay tuned.

Continue reading. The rest of the series can be read here.

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[1] I would add a few caveats to their conclusion. First, they only analyze one hypothetical building on a very large lot of land in the center of midtown. So their ability to generalize is some what limited. And, second, to the extent that land values and office rents might have been inflated because of over-optimism and an overheated stock market in the late-1920s, means that their resultant height might have been too high.

November 5, 2017 by Jason Barr 3 Comments

Broken Clockism: The “Skyscraper Curse” is Bogus

By Jason M. Barr November 5, 2017

In 1999, an economist named Andrew Lawrence thought he saw a relationship between the business cycle and skyscrapers; he dubbed this the “Skyscraper Index,” and it purports to demonstrate the “Skyscraper Curse,” which is,

an unhealthy correlation between construction of the next world’s tallest building and an impending financial crisis: New York 1930, Chicago 1974; Kuala Lumpur 1997 and Dubai 2010. Yet often the world’s tallest buildings are simply the edifice of a broader skyscraper building boom, reflecting a widespread misallocation of capital and an impending economic correction.

It has proven a very seductive idea, and the media and public have glommed onto it as some kind of infallible truth. But the idea that the construction of the world’s tallest building is a harbinger of economic doom is specious.

It is an example of what I call Rorschach Economics: people see a relationship because they want to. It is easy for the eye to produce patterns that don’t exist, despite the fact that they come from random chance. (In this nice coin tossing simulation example, you can see that “patterns” are really naturally occurring randomness.)

Economic downturns, panics, and/or crises happen very frequently, much more frequently than record-breaking skyscrapers. By my count, there have been at least 28 panics, crises, or severe downturns in the last 125 years, over twice as many as record-breaking buildings. So it’s quite easy to find a crisis and pair it with a tall building, proving the adage that even a broken clock is right twice a day.

The Purported Skyscraper Curse. Source: here.

The “Skyscraper Index” is not even an index, which is a set of measurements that represents the average value of something, such as the Consumer Price Index, which measures the cost of living, or the Dow Jones Industrial Index, which measures the value of 30 large-company stocks. The “Skyscraper Index,” on the other hand, is simply a montage that shows pictures of the world’s tallest buildings over a time line with some “nearby” financial crises.^[1]

The point of generating real indexes is that you can then use them to perform statistical tests to avoid conclusions based on “truthiness.” This just what I, along with my co-authors, did. We performed two kinds of analyses. First, as a very simple test of the “Skyscraper Index” hypothesis, we found both the announcement and completion dates of the world’s record-breaking buildings, and looked to see where they fell within the business cycle. We used the U.S. business cycle—which is based mostly on changes in Gross Domestic Product (GDP)—because of its importance for the world economy, and because, until relatively recently, all the record breakers were in the U.S.

Table 1 lists all of the record-breaking buildings completed since 1890, the dates that the developers first publicly announced their decisions, and the timing within the business cycle. While it is true that 10 of them were announced during an upswing in the cycle, the range of months between the announcement and cycle peak is tremendous, varying from zero to 45 months.

Data sources are given in Barr, J. Mizrach, B., and Mundra, K. (2014). “Skyscraper Height and the Business Cycle: Separating Myth from Reality.” *Applied Economic*s, 47(2), 148-160.

Looking at the opening dates of the buildings shows a similar story. Table 2 provides the date of opening of each building (i.e., either the official opening or the date that the building received its first tenants), the closest peak, and subsequent trough.

First, we can see that only half were completed during the downward phase of the cycle, and furthermore, there is no pattern between when the building is opened for business and when the trough occurs. The range is from one to 54 months. In short, there is no way to predict the business cycle, based on either when a record-breaker is announced or when it is completed.

In a second exercise, we collected data on the tallest building completed each year in the U.S., Canada, mainland China, and Hong Kong, and their respective annual GDP values. Using the statistical technique of vector error correction modeling, we attempted to predict changes in GDP from the heights of completed skyscrapers. The bottom line: you can’t do it. For decades, economists have searched for the holy grail of forecasting that predicts the end of economic bubbles. Alas, skyscraper height is not it.

Yet despite the fact that there is no real evidence, it has not stopped writers from reporting on the relationship, and even making up new relationships along the way. The Skyscraper Index was originally a story about the newest world’s tallest building, but now has morphed to apply to any very tall building. The strategy is to say, “here’s a new supertall; a crisis must be on the way.” Or, writers go out and find a crisis that conveniently pairs with a new building.

Here are a few examples:

The Lotte Tower: Two journalists on Bloomberg.com, in March 2017, claim that the Lotte Tower, a 123-story skyscraper completed is Seoul in 2017, has cursed South Korea. The authors proceed to itemize a series of political and economic problems that thus “proves” a connection, including the corruption scandal of Park Geun-hye, Korea’s former President. So now, the “curse” extends to political crises. Good to know.

The Shanghai Tower: In this January 2016 Washington Post Wonk Blog, the author suggests that the recent official opening of the Shanghai Tower (128 floors) “caused” the Shanghai stock market to go down on the same day. Then she proceeds to discuss how the skyscraper is likely to unleash an economic plague upon China. Best I can tell, China is still humming along; its 2016 GDP growth rate was 6.7%, more than double that of the U.S.

The Jeddah Tower: In 2020, the new world’s tallest building is slated to open in Saudi Arabia with the soaring height of one kilometer (3,281 feet). The author of this 2015 PBS.org blog is already predicting gloom and doom for the kingdom five years before completion. Apparently, he is an expert on spotting financial bubbles before they burst. So much so he is already predicting the next bubble (and crash) before it even starts. Now that’s foresight!

So note to journalists, bloggers, and would-be clairvoyants: the “Skyscraper Index” is NOT an index, the “Skyscraper Curse” is bogus, and skyscraper heights cannot predict the future. That is all. ♦

^[1] In the interest of scientific replicability, I, too, have created a “New Skyscraper Index,” which shows an eerie relationship between skyscraper heights and maritime disasters.