Archive for the ‘demographics’ Category

Weighted population density

March 15, 2017

A few months ago, as I was lying in bed unable to sleep, I found myself on the Wikipedia page for Bihar, a state in northern India. Now, I’ve never been to India, and if I have the good fortune to travel there at some time in the future, I can’t imagine the first place I will go is Bihar. For me, Bihar is an intellectual construct rather that a real place. Having said that, let me introduce you to (my imagined) Bihar. Bihar lies along the Ganges River, so I’m imagining a mostly flat river valley. It has a population of 103 million, which is enormous. (Locals probably aren’t impressed, because neighboring Uttar Pradesh has twice as many people.) Bihar has a population density of 1,100 people per square kilometer, which is pretty high. In fact, that figure is roughly equal to that of (neighboring) Bangladesh, the densest country in the world other than city-states such as Singapore. But what really woke me up is that the biggest city in Bihar only has 2 million people, and the second largest city only as about half a million people. There are about a dozen cities in the 150,000-400,000 range, and everything else is smaller. Depending on how you define urban, only 5-10 million of those 103 million people in Bihar are urban. That leaves a lot of rural residents. To put it another way, that population density is probably a pretty accurate figure of what you might find. Pick a random square kilometer in Bihar, and you will probably find a mostly rural, agricultural place with 600-1000 people living in it.

Sometimes it is hard to imagine what population density means, and it is easier if we scale it down to more familiar terms. In the USA, we would use a football field; Europeans would use a soccer field, but since this is a Taiwan-centric blog we must use a baseball field. Fair territory in the average major league baseball field is roughly 2.5 acres, or almost exactly 0.01 km2. So all we have to do is take two zeros off all those population density figures and imagine them on a baseball field. If we guess that Bihar’s rural population density is 800 people/km2, then imagine a baseball field with eight residents. They are farmers, so most of the land will be planted in rice and vegetables, and there might be a few chickens or a cow wandering about. Eight people will have one or two houses. Don’t forget to leave a bit of land for communal properties, such as a temple. There will also be one or two small roads or paths cutting through the outfield. I don’t know if they would have irrigation channels, and maybe they have a small fish pond. But imagine baseball field after baseball field, each supporting six to ten people, almost all engaged in some sort of agriculture.

I tried imagining Bihar in Taiwanese terms. Take one Kaohsiung City (minus the mountainous areas), add in a handful of Chiayis (city plus county minus mountains), add 25 copies of Yunlin, and then add 75 more Yunlins without Douliu (the biggest city). It’s still probably too urban, but that’s about as close as we get to dense and rural in Taiwan.

Of course, this post is not about Bihar; my imagined Bihar is just a new angle from which I can think about Taiwan. Taiwan’s official population density is 650 people per square kilometer, which I a bit lower than Bihar. Among non-city states, Taiwan is second only to Bangladesh. However, as you are certainly aware, Taiwan’s population is not distributed evenly. If you randomly choose a square kilometer of land, chances are you will hit a mountain with fewer than 5 people/km2. Throw your dart a few more times, and you’ll hit a place like rural Yunlin, with 200 people/km2. Keep throwing it and you might hit a town center. Then the number will jump to 2000-5000 people/km2. And once in a while, you’ll hit a metro city center, where you might find 50,000 people in your square kilometer. Taiwan and Bihar have similar population densities, but Taiwan’s number is a lie. It tells you almost nothing about how people actually live.

Stop for a second and think about that baseball field again, this time with the population density of a city center. As many as 500 people might live in fair territory. But wait, city centers typically dedicate one third to one half of the land area for roads. There will probably be one high traffic two-lane road cutting straight through the middle of the field with a lot of alleys all over the rest of it. Let’s assume that 40% of fair territory is covered in pavement for roads. A high proportion of road space is occupied by parked cars. 500 people might have 100 cars to park, though perhaps 20 of those will park underground. Then think about businesses. In Taiwan, almost all city centers mix residences and businesses together. Some of the land will be used for banks, noodle shops, beauty parlors, motorcycle repair shops, half a 7-11 and a fourth of a Family Mart, some fraction of an elementary school, a post office, a traditional market, and so on. Let’s just assume that almost no one lives in the infield. After all that, we have to figure out where the 500 people will live. I don’t think we can do this with those gleaming new luxury apartments. Those types of buildings tend occupy quite a bit of space, since they often have courtyards and other green space on the ground level. Besides, since the new units are often bought up by real estate speculators, many of the are empty. There are two viable routes to getting our 500 people. On the one hand, we could put up one of those monstrous behemoths, with 15 floors and eight units on each floor. Most of these 120 units will be full, though the ground floor might be devoted to shops. If we assume an average of three people live in each unit (in reality, the average is probably lower), that gets us to about 330 people. We’ll need one and a half of these monsters, so one will go take up all of right and most of center field, and the other will straddle the left field foul line (and be shared with the neighboring baseball field). One advantage of a huge complex is that it doesn’t require as many roads. There are certainly not lots of little alleys crisscrossing the complex. There should be a fair amount of outfield grass left over. The other possibility is to crisscross the entire outfield with a maze of alleys and fill in the spaces with lots of small buildings. Most people in Taiwan still live in the workhorse of Taiwan city centers, the ramshackle four floor ugly cement block with no elevator and an illegal addition on the fifth floor. These units tend to be about 30 ping, or 900 square feet. Assuming three people per unit and a few vacant units, you will need to to cram about 35 of these five floor buildings into the outfield. I’m guessing you will need three arcs with eight, twelve, and sixteen buildings, respectively. Either way, I think it is safe to say the 500 people living in this baseball field experience everyday life differently than the eight people on the baseball field in Bihar.

As a political scientist, I’ve been frustrated by population density for decades. We haven’t uncovered a lot of strong patterns relating to urban and rural voters, and I’m convinced that one of the reasons is that we are terrible at measuring population density, which is one of the key components of almost every operationalization of urbanization. To give an example, the population density of Xindian District 新店區 in New Taipei City is 2507 people/km2. That’s not very different from places such as Miaoli City (2373) or Shalu District 沙鹿區 (2257) on the outer edge of the Taichung metro area. Miaoli and Shalu are populated, but I’ll eat my hat if they are anywhere near as urbanized as Xindian. Xindian is part of the core Taipei metro area; that’s a goddamn city! You probably know why these places have similar population densities. Much of Miaoli and Shalu are mostly flat, while most of Xindian is mountainous. Good luck trying to quantify that, though.

What I’ve always wanted to do is look at population density by tsun and li 村里, the unit below townships. (For brevity, I’m going to simply call these “li.”) My big idea is to produce a weighted density, with each li weighted by its population. To illustrate, consider weighting Taoyuan by each district. Taoyuan City officially has a population density of 1760 people/km2, but that figure is pulled down by Fuxing District, which accounts for over a fourth of the total land area. If you weight by where people live, the experience of the 20.2% of the population living in close quarters in Taoyuan District becomes the most important element, not the experience of the 0.5% who live in Fuxing District. I think Taoyuan City’s weighted population density of 5110 people/km2 is a much better reflection of how people actually live than the raw figure of 1760. Of course, I’d like to go a step further and weight by li instead of by district.

District Pop Area density share subtotal
All 2147763 1219.98 1760.5   5110.8
桃園區 434243 34.80 12476.6 0.202 2522.6
中壢區 396453 77.88 5090.5 0.185 939.6
大溪區 94102 105.52 891.8 0.044 39.1
楊梅區 163959 86.55 1894.3 0.076 144.6
蘆竹區 158802 75.71 2097.5 0.074 155.1
大園區 87158 87.39 997.3 0.041 40.5
龜山區 152817 71.93 2124.5 0.071 151.2
八德區 192922 33.69 5726.7 0.090 514.4
龍潭區 120201 75.24 1597.6 0.056 89.4
平鎮區 221587 47.80 4636.2 0.103 478.3
新屋區 48772 84.90 574.5 0.023 13.0
觀音區 65555 87.79 746.7 0.031 22.8
復興區 11192 350.78 31.9 0.005 0.2


Is this a reasonable method? If I were interested in trees or watersheds, it would not be. However, I am interested in how people experience everyday life and how their patterns of living shape political attitudes. From that perspective, it is entirely appropriate to put more emphasis on the heavily populated areas and less emphasis on sparsely populated ones. I also think that a li is a pretty good unit for this. A li is big enough to cover a person’s immediate neighborhood. In comparison, a district is often so big that a many parts of it are irrelevant to a given person’s everyday experience. Philosophically, I think this is a pretty good measure. Mathematically, it has a serious problem. The weighted population density depends heavily on how you cut up a given territory. Cutting Taoyuan into one piece (ie: not cutting it at all) gives a weighted density of 1760. Cutting it into the thirteen pieces defined by districts yields a weighted density of 5110. If I cut it into several hundred smaller pieces, I can get a weighted density of over 10,000. If the government redraws li boundaries, as it sometimes does, the number can go up or down. Unlike district boundaries, li boundaries are commonly redrawn whenever the population grows or shrinks dramatically. Nonetheless, I think this imperfect measure is still an improvement over raw population density. As an analyst, I cannot manipulate the numbers at will; I am limited by the government’s decisions to draw the boundaries in one particular way.


This measurement was only a pipe dream until a few weeks ago when I stumbled upon the mother lode. I found a spreadsheet with the population and area of every li in Taiwan. I don’t have any idea who put these data together or why they put them up on the internet. I am simply grateful. There is no date on the spreadsheet, but judging from the population figures, I estimate these data are from some time in 1990. That’s right, I can tell you all about population density 27 years ago. What about today? Finding population data for each li is the easy part. The hard part is finding the area of each li. In many townships the li boundaries have not changed in 27 years, so I can simply copy from the old spreadsheet. However, the places with no changes are places with very little population growth. Nearly every urban district has had an adjustment in li boundaries at some point over the past 27 years. So I started searching online, district by district. Taipei City was the best. In Taipei, every district posts an annual document of official statistics on its website, including the area of each li in the district. Outside of Taipei, it was rare to find such good fortune. Once in a while, I’d find a place like Xizhi, which posted the statistical abstract but left that one critical column in that one critical table completely blank. If I couldn’t find an official document with the area of each li, I tried looking for an official document published by DGBAS stating how the boundaries had been changed. In most cases, the document stated that a certain li had been split off from another li or had been folded into another li. In those cases, I could combine the areas or populations of the two concerned lis. When districts had added lis (most of the changes), I was essentially trying to undo the changes and return to the 1990 boundaries. This could make for some enormous lis. For example, in 1990 Zhongpu Li 中埔里 in Taoyuan District (then Taoyuan City) had a population of 9368. By 2016 it had been split into nine lis with a combined population of 58371. Since I only have the 1990 area, my 2016 spreadsheet collapses them all into one case. After all this, there were still a few places where the li boundaries had changed but I could not find an official record of those changes. For these last few infuriating places (looking at you, Xizhi, you jerkface), I used the eyeball test comparing maps from 1991 to maps from 2015 to see where the new li had come from. I have 2015 maps on my GIS program; the 1991 maps came from the TPGIS system, an invaluable resource put together by my colleague Chi Huang. (Go spend some time on it. It’s fun! The current version is a bit slow, but version 2.0 is coming out soon.) To my sadness, I was never able to find area stats for li in Kinmen or Lienchiang Counties. Those weren’t in the 1990 spreadsheet (probably since they were still under martial law), and there were no stats on their websites. Sorry Kinmen and Matsu, I have to ignore your existence in this post. If all this sounds like a tedious and time-consuming task, well maybe my idea of entertainment is different than yours.


Before I show you township-level maps, let’s look at the city and county level numbers. These are the data for 2016. Density is the regular calculation of population density (population/area). The regular numbers make Taiwan look a lot like Bihar. However, once the numbers are weighted by where people actually live, the picture looks a lot different. The typical person lives in an area with a population density of 14893. This is a decidedly urban society.

The difference in individual cities and counties is striking. Taipei City is ringed by mountains, and once we downweight all those areas, we find the typical person lives in a place with 31000 people/km2, not 10000. The difference in most other places is even more dramatic. New Taipei now looks just as dense as Taipei. Among the six metro areas, only Tainan has a weighted density of less than 10000. Of course, Tainan has a lot of rural agricultural areas – the old Tainan County was significantly bigger than the old Tainan City – so maybe it isn’t surprising that the weighted density for Tainan is a notch lower. From decades ago, I always felt that Nantou was more urban than Miaoli, Chiayi, or Yunlin, but the numbers said it wasn’t. Weighted density says that my gut was right all along. Most people in Nantou live in the downtown areas of the four biggest towns rather than in the vast mountainous areas, so the weighted density is 17.9 times the conventional population density. The smallest difference is in Yunlin, where the weighted density is only 2.93 times the conventional population density. Yunlin is, not surprisingly, mostly flat, rural, and agricultural. Changhua is even flatter, but it has a bigger urban area than Yunlin so its weighted density is inflated a bit more (3.86 times). Flat cities are similar. Hsinchu and Chiayi Cities are mostly flat, and their population is spread out fairly evenly throughout the entire territories. The weighted densities are only 3.04 and 2.18 times the regular densities, respectively. Finally, there is the east coast, where much of the population is concentrated in the Hualien and Taitung urban areas. In Hualien, the weighted density is nearly 50 times higher than the regular density. All in all, weighted population density paints Taiwan in an entirely different light than conventional population density.

  Pop16 Area Density16 Weighted16
National 2695704 35963.49 650.4 14893.0
Taipei 2695704 268.11 10054.5 31166.2
Kaohsiung 2779371 2947.94 942.8 14939.6
New Taipei 3975564 2022.35 1965.8 31274.2
Taichung 2761424 2227.10 1239.9 11518.2
Tainan 1886033 2194.29 859.5 8179.5
Taoyuan 2148606 1216.35 1766.4 10089.7
Yilan 457538 2115.68 216.3 4019.5
Hsinchu County 547481 1421.44 385.2 4326.3
Miaoli 559189 1817.81 307.6 2940.0
Changhua 1287146 1076.37 1195.8 4620.6
Nantou 505163 4106.50 123.0 2201.8
Yunlin 694873 1291.64 538.0 1577.3
Chiayi County 515320 1901.67 271.0 1378.6
Pingtung 835792 2777.54 300.9 3229.3
Taitung 220802 3510.37 62.9 2343.9
Hualien 330911 4627.38 71.5 3529.9
Penghu 103263 123.08 839.0 5021.2
Keelung City 372100 131.94 2820.2 11369.1
Hsinchu City 437337 104.46 4186.6 12737.7
Chiayi City 269874 70.51 3827.6 8341.2


What does this look like on a map? I thought you’d never ask. Compare a regular population density map with weighted population density. The urban areas suddenly look much larger and much denser, especially in the north.


dense2.pngWeighted population density is always greater than population density. Theoretically, it could be equal, but in practice there is always some inflation. The question is simply how much inflation there will be. If the original area (city, town, county, country) has the same population density everywhere, then the weighted density will not be much greater than the conventional density. If there is a large amount of variance, though, the two numbers might be very different. For example, take the southeastern corner of the Taichung metro area. This is a map of population density by li in three districts: East, Dali, and Taiping. (East is upper left; Dali is lower left; Taiping is on the right.) Years ago, when I used to live in that area, I often wondered why people thought of them so differently. Taiping and Dali didn’t see any less citified than East to me. The official population densities insist that these are differences. East and Dali are cities, though hardly dense ones (8119, 7282, respectively). Taiping is suburb, perhaps maybe not even a part of the urban area (1542). On the map you can see the problem with this. Two-thirds of Taiping’s land is mountainous with fewer than 100 people/km2. The city part, however, is real city. If anything, it looks a bit more dense than neighboring East. Weighed density tells us that these two places are roughly the same. East, which has roughly the same density everywhere, is barely inflated at all (9966). Taiping is inflated significantly, to 10940. Like Taiping, Dali has quite a bit of variance in its density. Unlike Taiping, though, the sparsely populated areas only make up a small part of Dali’s overall territory. Its weighed density (18099) tells us that it is significantly more urbanized than either East or Taiping. Compared to the raw density, the weighted density for Taiping has been inflated 7.09 times; for Dali, 2.49 times; and for East, only 1.23 times.


Remember that I started this with data from 1990? Hey, let’s look at the data from 1990! Here’s a map of each town’s weighted density back then. You might notice that there is an arrow pointing to an orange town in south-central Taiwan. That town is Beigang 北港鎮. I e or less expected to see all the other dense places, but Beigang took me by surprise. If you had told me there would be one fairly dense place between northern Changhua and Chiayi City, I might have guessed Douliu 斗六市, Erlin 二林鎮, Huwei 虎尾鎮, and Xiluo 西螺鎮 before I guessed Beigang. Normal population density doesn’t indicate anything special about Beigang. The conventional population density in 1990 was only 1197, but the weighted density was 12020, an order of magnitude higher. How does that happen? Look at the picture of Beigang (1990 on left; 2016 on right). A whole heaping chunk of the population was jammed into a tiny urban area. That dense little area adds up to almost exactly one square kilometer, and in 1990 it held about 22,000 people. The rest of the town had about 27000 people in 40 square kilometers. Most city cores taper off gradually; Beigang goes from dense city straight to rural countryside with almost no transition. I confess I don’t remember much about the town except for the market right near the spectacular temple. I have no idea if there is some natural barrier that separates the city center from the rest of the town. The discovery that Beigang was a dense (if tiny) city makes me wonder about the birth of the Tangwai in Yunlin. Su Tung-chi 蘇東啟 started from Beigang in the early 1960s, and now it seems possible that he was a product of urban discontent, similar to Kao Yu-shu 高玉樹, Hsu Shih-hsien 許世賢, Huang Hsin-chieh 黃信介, Ho Chun-mu 何春木 and many of the others. (Former Yunlin county magistrate and current legislator Su Chih-fen 蘇治芬 is Su Tung-chi’s daughter. After he was arrested, her mother Su Hung Yueh-chiao 蘇洪月嬌 and elder sister Su Chih-yang 蘇治洋 were elected to the provincial assembly.)



You’ll notice that Beigang doesn’t stick out on the 2016 map. By 2016, its weighted density had plunged to only 7606 due to two trends that I’ll turn to now.

First, let’s turn away from population density momentarily to consider raw population growth. From 1990 to 2016, the overall population grew from 20.5 million to 23.4 million, or just about 15%. This map shows the ratio of 2016 to 1990 population, so anything below 1.15 is below the national average.


All the growing areas – the yellow, orange, and red areas – are in the north and the major urban areas. The rural areas, especially on the east coast and in southern Taiwan, are a sad, sad sea of blue and darker blue. These places have been losing population for the past 25 years, some of them at an alarming rate. There are two exceptions. Many of the majority indigenous townships are holding steady, or at least losing population more slowly than the nearby Han townships. My guess is that this reflects higher birthrates among indigenous people. The other is that single bright orange dot on the west coast, about halfway between Taichung and Tainan. That town is Mailiao 麥寮鄉, home to the huge Formosa Plastics plant. Mailiao has grown 42% while all the nearby towns have shrunk by about 20%. My guess is that an overwhelming majority of my readers have negative attitudes toward huge petrochemical facilities like the one in Mailiao. For you guys, this dot of orange in an ocean of unhappy blue is just something to keep in mind.

I said that there are two trends behind Beigang’s decline. The first is that rural areas, including Beigang, are losing population. The second trend is that city cores are also losing population. The big cities are growing, but this growth is in the ring around the old city core. I like to think of urban growth as a donut. Taichung has the cleanest example. The old city core has lost population, with the densest areas having lost the most. Central District is so tiny that it is hard to see that it is dark blue; its raw population density plunged from 39131 to 21251. East, West, and North Districts are also blue, but they are surrounded by a ring of orange and red. There is a second half ring to the west of slower growth. Then there is a light blue ring around that, and finally a dark blue ring around that one. Metro Taichung is growing, but it is doing so by spreading out rather than by piling more and more people into the city center.


Tainan and Kaohsiung are bounded by the ocean to the west, so they have half donuts rather than full donuts around them. However, the basic pattern is the same.



Northern Taiwan is more complicated. You can see donuts forming around Taipei and Keelung, but they run together a bit. To the west, there is just one huge mess of growth all the way through Taoyuan City to Hsinchu City.


This map of population growth obscures some uneven growth. Consider the difference between Xizhi汐止, just to the east of Taipei City, and Guishan 龜山, on the eastern edge of Taoyuan. Xizhi has doubled in population since 1990, but different areas have grown at different rates. In 1990 (left map) most of the population was concentrated in the old downtown area near the train station. Xizhi has grown everywhere, including in this old downtown area. However, there is basically an entirely new population center in the northwestern border, next to the Donghu area of Neihu (in Taipei City). The city has spread out, but this population center has grown so fast that it is as dense or even denser in 2016 than the old downtown area was in 1990. As a result, the weighted density has grown (from 6471 to 14817) even faster than the raw density (from 1363 to 2772).


Guishan is a different story. In 1990, the population was highly concentrated in the southwest corner, an area adjacent to Taoyuan City (now Taoyuan District). Over the past 25 years, the Taipei metro area has grown out to the edges of New Taipei City. Guishan has gotten some of the overflow. The new growth in Guishan is concentrated on the northern and eastern borders, where Guishan abuts Linkou and Taishan Districts. The new airport MRT line goes through Linkou, which in recent years has been a hot real estate market. Guishan has gotten a bit of the overflow growth from this boom. However, the newer population areas in Guishan are not as dense as the old areas. As a result, even though the overall population has grown by 60%, the weighted density is actually quite a bit lower (from 9024 to 7124). On the map of change in weighted density in northern Taiwan, Guishan is a conspicuous blue patch in a sea of orange.



This leads us to the final and perhaps most surprising result of all. Taiwan has grown by 15% over the past 25 years, and there has been heavy migration from rural areas to the cities. One might expect that this would lead to a more densely populated country. However, because the cities have spread out, with most of the growth coming in the less dense areas, weighted density insists that Taiwan is a less densely populated place today than in 1990. In 1990, the weighted density was 15457 people/km2; in 2016, that figure has fallen to 14893. By this metric, Taipei, New Taipei, Keelung, Chiayi City, Tainan, and Kaohsiung are all less dense than they used to be. The only places with significant increases are Taoyuan, Taichung, and Hsinchu County. There are more people, but the typical person lives in a less concentrated neighborhood. This finding utterly shocked me.