A model of the global economy is, by its very nature, an unwieldy object to work with. There are 40 countries (we want more; that’s coming next) and the economy of each country is described by the economic activity of 35 sectors.
Each sector in each country interacts with each other sector in each other country creating close to two million interactions.
This is great for wowing potential users of the model with the sheer scale and size of thing, but it makes life pretty hard if you want to ask a question like “what effect has a certain change had on… well, everything?”
This is hard because “everything” here encompasses two million numbers some of which will have gone up and others of which will have gone down.
If you don’t put any effort into visualisation, the output of the model looks absolutely horrible:
Needless to say, picking interesting information out of such a mass of numbers involves some careful thought. (For the interested, what you’re seeing here is dollar-valued commodity flows between sectors within the Australian economy, the sectors being numbered 1 to 35.)
The paper I’m writing at the moment asks an even trickier question than “what’s going on?”. I’m trying to work out how our model compares with other, more standard, ways of doing this kind of thing. This means making the same change in two models and comparing the results.
One way to boil down lots of information into a far smaller number of ‘things’ is to rank the numbers you’re analysing. This just means putting the numbers into order then saying which number is biggest, which is second-biggest etc.
So in our case, if we make a change to the global economy, instead of looking at a horrifying table of numbers we can just say “Australia was the country most affected by the change. Netherlands was second, Spain tenth, Bulgaria 39th…” and so on.
The advantage to this approach is that, when comparing the results of two models, you can just compare the ranks of the countries and see if they’re similar. If they are, you might be justified in concluding that the models are doing more-or-less the same thing.
It also allows for some nice visualisation. If we write down all the countries in one column in the order of their rank (most-affected by some change we’ve made, to least-affected) using one model, and make a second column where the countries are ordered according to their rank using the other model, we can quickly see where the differences are, particularly if we draw nice lines between the countries to show how their position has changed.
Here’s the outcome of such an experiment:
The design for this visualisation was inspired by a similar thing in the work of Hidalgo and Hausmann, see here on p4!
It shows the results of reducing demand for Chinese vehicles by $1M on the global economy in 2010. The left-hand column shows the results using a traditional model (for the interested: it’s called a Multi-Region Input-Output model, or MRIO). The most-affected countries are at the top and the least-affected at the bottom. The right-hand column is the same but for our model.
With the exception of Slovakia, the results look pretty good. The ranks are generally pretty similar which is encouraging. We’re currently trying to find out what’s going on with Slovakia, and I’ll post here if we ever find out!
(Note that Taiwan is not in our model, because the UN doesn’t report trade data for it, as it deems it to be a part of China. I won’t be delving into this international controversy here!)
Anyone who’s done any work in the vicinity of network science or, more specifically, seen social scientists attempting network science, will have seen plenty of images such as this:
which add little scientific input, but merely dazzle the reader with the complexity and sheer magnitude of the networks being analysed. At a recent talk in Cambridge I heard the legendary Mark Newman refer to these network spaghetti-servings as “ridiculograms”. I know researchers who have been asked specifically to produce such diagrams to impress the difficulty of their project onto an adoring lay-crowd.
Well, I’m hoping to do a little more with a network visualisation. It’s not because I’m better than the people who made those diagrams (apologies to the researchers in question; I’m not meaning to be rude.) but just because I’ve got a lot of time to dedicate to painfully learning the tools we have available for turning spaghetti into scientific knowledge. (Caution: this pasta metaphor may have overstepped its usefulness.)
The tool of choice for the modern networks visualiser is called Gephi and it really is one of the n wonders of the open-source software world. Which makes me feel guilty about saying that I hate it, but I do. It’s amazing and brilliant but, at least on Windows 64-bit, it’s buggy as hell, and does all sorts of crazy stuff when you’re least expecting it*. Christ knows that if it were up to me to develop all of open-source, the world would be a much, much worse place.
But here’s my friendly guide to untangling that ridiculogram step-by-step, without losing too much sleep in the process:
Here’s how every network visualisation you’ve ever seen has started life. This is what you get when you import your graph into Gephi:
This particular graph happens to be a version of a trade network. Each node is an economic sector in a particular country, and the edges (lines) represent the size of the flow between sectors. The truth is a bit more detailed than that. Actually this graph shows the response of the trade network to a $1M reduction in demand for Chinese vehicles.
The first thing to do is lay those bad-boys out. I’ve gone for the Yifan Hu layout, because it visually separates clusters.
This then lays the ground-work for the more visually pleasing “Force Atlas 2” layout. Here I’ve gone for “Dissuade Hubs”, “LinLog mode” and “Prevent Overlap” with Scaling=5.0 and Gravity=4.0:
Now let’s colour the nodes by country, to see if the clusters match to countries. It looks like they broadly do (which makes sense because sectors interact most with domestic sectors):
To do this in Gephi, go the the Partition tab at the top right and select Nodes. Click on the refresh button and pick the variable you want to partition by. This will set random colours to each group.
There are rather too many countries showing here, making the colours all a bit similar, and the clusters not all that clear. Let’s wrestle with Gephi filters. (This is hard, boring and severally counterintuitive.) To filter by country, go to Filters > Attributes > Equal and select ‘country’. To filter for just China, you’d simply enter CHN into the pattern box, but our life is a bit more difficult, because we want to filter in a number of countries. To do this we use the regular expression ‘or’ concept, which is a vertical bar: ‘|’. So my pattern looks like ‘CHN|JPN|DEU|USA|KOR|FRA|AUS|ITA|GBR|BRA’. Tick the Use regex box and click OK. Now click Filter and the filter will be applied:
This is starting to look a bit nicer, but we need to resize the nodes to show which are the most important. I usually size by node centrality (basically a measure of how ‘important’ the node is in the network.) To do this, go to the Statistics tab, and click Run next to Eignvector Centrality. This adds the centrality of each node as a property. To set the size of the nodes, go to Ranking at the top-left, and click the red diamond which, for some reason, stands for node size. Select Eigenvector Centrality from the list and click apply:
So this is ok, but the China nodes (in green) are all so much more significant that everything else is basically invisible. The node sizes can be fine-tuned using the Spline… link. I set my spline like this, which gives a some definition to all the big values and allows lots of medium values to come through:
which looks much better.
Now time to label the nodes. An almost invisible button at the bottom-right of the screen is actually an up-arrow behind which hides the labelling dialog. (Note that this is definitely the single-worst piece of UI design I’ve ever seen.) If you’re lucky enough to find this, set node labels on and adjust the size slider until you can see them. If the attribute you want for the label isn’t already selected, click Configure… and change it in there.
We now have:
We’re almost finished with the layout, but let’s space the clusters out a bit, so we can see what’s going on within countries. The ‘Noverlap’ layout isn’t installed by default, but you can install it easily from the Plugins menu. This is really useful for spreading out clusters of nodes. I ran it with a ratio of 2.0 and a margin of 20.0. I then also ran the Expansion layout followed by the Label Adjust layout. This combination of layouts seems to get everything looking peachy:
Now that the layout is complete, we can filter out some of the smaller edges. Edges are great for laying out accurately, but you don’t want to see every one on the finished diagram. To add another filter to the country filter we’ve already go, we need to add it as a subfilter. More crazy counter-intuitiveness. My completed set of filters looked like this:
Note that to set the range, you can double-click on the number and type it in. Saves messing with that stupid slider.
Now that the graph is nicely layed out, and filtered, time to switch to the Preview pane. This pane doesn’t redraw unless you click Refresh after every change. After selecting Nodes > Show Labels and Edges > Rescale weight, the default preview looks like this, already pretty nice:
I’ve changed the font (at least on my system, you have to do this by just typing the name and size into the Font box. I’ve typed “Tahoma 12” here.) and massively up the thickness. This means that the biggest flows are ridiculously thick, but it’s a fair trade-off to get some of the smaller flows to show up too:
For a few final flourishes, export your preview to an SVG, and open it in a vector-graphics editor. (I’m using the free and totally brilliant Inkscape, but feel free to pay a million pounds for Illustrator.) I’ve used the editor to add some country labels, and move a few of the sector labels to make them more readable and less cluttered. I’ve also deleted a few nodes for visual clarity’s sake. Here’s the finished product. Pretty good I reckon, and certainly a world away from the hairball-style ridiculogram we started with:
Here’s a list of Gephi bugs that have had me smashing my completely innocent keyboard in frustration: 1) when you save you work, then close the application, it worryingly asks you if you want to save. (Which makes me feel that something is amiss.) An insanely large number of times, the resulting file is then corrupted somehow and won’t open. 2) Hand-wrought queries you’ve spent ages writing are not saved, so you have to make ’em from scratch every time. Ugh. 3) The export to SVG option often results in a terse little “NullPointerException” error message and no SVG is produced.
When you go into a career in research, you imagine that you’ll spend all your time thinking, reading and coming to know. In fact, whenever anyone talks to you about your job, it’s clear that that’s exactly what they think you do all day: think, learn, gain wisdom.
My experience of my PhD so far has been pretty different to that imagined paradise of dressing-gown-sporting chin scratching. In actual fact, the general pattern has been something like this:
Have a meeting with a colleague for an hour about how your super-interesting model should work. Bash through the details, make the regrettable but inevitable simplifications, write down some maths.
Write down the maths you discussed 22 months ago, once in Python, and once again in Latex. This is a five-minute job, depending on how thoroughly you completed step 2.
Realise that despite the fact that step 2 is where for all practical purposes all the chin scratching and coming-to-know has taken place, there’s to be no credit given for it whatsoever. The PhD is earned (or otherwise) by the one hour of step 1 you did, and you did that so long ago, that you can’t remember what any of it means anyway.
No, there is nothing gained from those 22 months of toil but the skills you learned in the process.
This is not quite what people have in mind when they talk about learning for its own sake. They’re presumably talking about coming to know a subject for the pure joy, or adding to the sum of human knowledge because that’s a noble aim in itself.
What’s happened to me feels much more like a self-study tutorial in becoming a whizz coder, engineer and software developer. Which is great in itself. But it’s not quite what I signed up for somehow.
I’ve been modelling the interconnected nature of the global economy by simulating a reduction in demand for various sectors in various countries. It’s a very simple little piece of analysis:
What would happen if the demand for a given sector in a given country was reduced by a single US dollar?
In answering this question for every sector in every country in the model, you can get a sense of which sectors have the biggest impact on the global economy. Basically you reduce the demand for each sector by a dollar and watch what happens to the rest of the world.
Unexpectedly, perhaps, this most-important sector is the vehicles sector in China. If demand for vehicles dropped by a single dollar, an unbelievable $98 would be lost in terms of global production. This is a truly astonishing conclusion.
So where does this $98 dollars come from? Well, the interconnectedness of the global economy is behind the magnitude of the number. In short, not only do sectors which feed the Chinese vehicle sector suffer, but all the sectors which feed those sectors and so on through the network that is the global economy. And a hint of how complex the picture is, is given by this image (click for full size):
Each circle is a sector in a certain country. The lines between the sectors represent changes in trade between them due to the $1 reduction in demand for Chinese vehicles. The sectors are sized according to how affected they are by the change. (Note for technical types only: they are sized proportional to their eigenvector centrality.)
It goes to show how interconnected the global economy really is. This small change in China has knock-on effects for the US, Japan, Korea, Germany, Italy, the Netherlands… the list goes on and on.
In the early 1960s two American geography professors, John Nystuen and Michael Dacy, were working on a way to make sense of a huge database of telephone records in Washington state. Clearly the majority of calls were being made either to or from Seattle, the state’s largest city, but they suspected there was more underlying structure to the pattern of calls. They pioneered a simple, but powerful, way of treating the calls going in and out of each urban area in the state as a network, then using this network representation to extract patterns from the data.
An extract from the original 1961 paper shows how simple the idea is, and also how old the typewritten paper looks now!
The data on how many calls were made from one city to another is arranged in a grid. This is exactly the same idea as those tables of distances you get in road atlases. (Look! These things still exist!) You look up your “from city” in the column, and go across to the “to city”. The number you arrive at is the number of calls made from the “from city” to the “to city”. Nystuen and Dacy simply looked at the largest call flows out of each city. Where a city’s largest flow was to a city smaller than itself, that city was deemed to be a node: a kind of ultimate ‘destination’ of calls.
They used this data to produce a simple network diagram of all the calls in the area, boiling a whole table of numbers down to a few simple relationships drawn with arrows between cities:
They went on to extend this idea to include indirect as well as direct flows. For example, if people in Bray, tend to call people in Maidenhead who tend to call people in London, (see this map for an illustration of this made-up example) then London should get some of the ‘credit’ for the Bray to Maidenhead calls too.
I’ve taken this simple idea and applied it to the enormous network of goods and services trade that we’re building here at CASA in London. The results are pretty interesting and make some kind of sense of an otherwise tangled mess of flows within and between countries.
Here’s the UK economy, where the size of the circle is given by the number of ‘in’ connections:
It’s fun to see how metals flows to machinery, which flows to vehicles, vehicle trade and finally to the hospitality industry. It’s exactly this kind of chain of relationships that Nystuen and Dacy were hoping to reveal in their original study. Also the wood/minerals to construction to financial services relationship is interesting. Overall, the UK economy can be seen to be hugely focused around hospitality (bars, hotels, tourism, cafes etc.) and financial services, with all other sectors being subservient to one or other of these two.
Here’s the same picture for the US. You can see that there are many more separate networks, suggesting that the US is less reliant on a small number of sectors. (Don’t be fooled by the small circles for fuel and chemicals: it doesn’t mean these sectors are small, just that few other sectors have these as their nodes.)
Interesting to note here that leather is differently in each of the three examples we’ve seen so far. It’s used in the hospitality industry (chairs?) in the UK, in vehicles in the US and for textiles in China.
Finally, here’s Japan:
What’s also interesting is to look at the connections between sectors worldwide. Here, each country is in a different colour, and it’s clear that most countries exist in their own clusters.
In the whole galaxy of trade that flows between sectors in a country and countries in the world, there are only two clusters of inter-related countries. They are Korea and Indonesia, and Canada, Mexico and the US. By this measure at least, these latter three countries seem to act as a single country in a way that none of the countries in the EU do, for example:
There’s clearly tons to explore here, and this is just using nothing but a simple network analysis from 1961! There will be far more interesting and modern analyses on this blog in the near future, which will be more subtle in helping us pick out clusters between countries and within countries. There may even be something to say on the clusters of trade routes which are most important to global production. All this and more to follow…
Macroeconomics is one of those disciplines where the ideas are simple, but the lingo is complicated.
Paul Krugman, in his New York Times blog, is usually great at communicating the ideas of Macroeconomics in a human-friendly way.
But sometimes the language gets ahead of Krugman—sadly, most obviously when the ideas he’s expressing are important and deep. This post is a perfect example. The ideas are incredibly important for understanding what governments are doing or not doing to manage the financial situation, but without some specialist knowledge, it’s pretty hard to understand.
Here, I’ve written a summary of the stuff you’ll need to know to understand Krugman’s excellent writing, and get a sense of the deep and subtle ideas he’s discussing.
It’s not particularly short: there’ll be plenty of “too long didn’t read”s I suspect, but for those who are keen to understand what on earth is going on with macroeconomics—inflation, interest rates and all that—I think it’ll be worth the while.
Here it is: disclaimer: this is just my own understanding of the situation. Don’t use this summary to actually run an economy, because there’s a chance that parts of it are wrong or oversimplified. If you’re an actual central banker, best get a proper qualification on the subject before fiddling with any knobs or levers.
Rob Levy’s User-Friendly Guide to Macroeconomics
or, how to understand Paul Krugman and his economist pals
A bank traditionally earns a profit by taking the money which savers have deposited with it, called simply deposits, and lending it back out to people who are looking for a loan. These borrowers might be after a mortgage, or after funds to invest in a business venture.
The banks encourage people to deposit their money by offering them interest. In order for the whole thing to make a profit, they charge more interest to the borrowers than they pay to the savers.
A bank has a legal obligation to keep a certain amount of its deposits in ‘cash’, and is free to lend out as much of the rest as they fancy. We’ll call the amount of cash they have to keep a “cash cushion”, because its designed to stop them running out of money if all the depositors suddenly want their savings back at the same time.
The relationship between a central bank and normal banks is exactly the same as between banks and customers: banks stash excess deposits with the central bank and earn an interest rate. Banks even borrow money from the central bank, for which they’re charged an interest rate. It’s this last interest rate which determines how much of a bank’s deposits it want to lend out and how much it wants to cling onto.
The setting of this interest rate is called ‘monetary policy’ and it’s ‘loose’ monetary policy when the interest rate is low.
When monetary policy is loose, banks are keen to dish loads of their deposits out as mortgages and business loans, because they can borrow for cheap from the central bank to keep their cash cushion at the right level. But if the interest rate is high, the bank will be more tempted to keep hold of its deposits because it doesn’t want to have to borrow to maintain its cash cushion.
When a bank is doing lots of lending, lots of business investment takes place and lots of houses are bought. These things are (usually) good for the economy so the central bank wants to encourage lending.
But there are limits: if the banks are so keen to lend that they’ll offer mortgages and business loans at ridiculously low prices, then people will start buying homes faster than they can be built, or expanding their businesses faster than they can expand their customer base. In this case, inflation sets in: prices rise because businesses have to pass on the cost of all this wasted investment to consumers. It’s this kind of mania for house-buying and business investment that economists refer to as the economy “overheating”.
So, the central bank, via the interest rate it charges to banks, can control how much lending the banks do. It therefore has to set a balance between too much lending (overheating) and not enough (recession); both are bad for the economy. What it really wants to do is set the interest rate to just the right level, such that there is just enough investment in businesses to continue to match a possibly growing demand. This is the so-called ‘natural’ interest rate.
But there are limits to what the central bank can do. If banks have some reason to feel negative about the future, they won’t want to lend money however cheaply they can borrow it from the central bank. In this case, the central banks interest rate could get down to zero (at which point the banks can borrow money ‘for free’) and the banks still won’t take the bait. Once interest rates are at zero, that’s it. The central bank is out of options! This is what Krugman refers to as the ‘zero lower bound’.
Months of blood, sweat and tears (or rather, those all-too modern equivalents coffee, RSI and eye-strain) have been spilled in the last six months. I have an absolutely non-existent ability to concentrate on more than one thing at a time, and the one thing I’ve been thinking, dreaming and going on about non-stop for pretty much all that time reached fruition late last night.
This is the first ever output from what we’re calling a ‘Global Demonstration Model’:
Modelled trade flows and economy shapes for the three countries, based on 2008 input-output data and 2010 trade data
The picture above doesn’t really make much sense yet, in that it’s pretty hard to tell what’s going on and some of the colours are repeated, but it gives you a sense of the sheer magnitude of the model I’ve been building. It shows the economies of India, the UK and the US and the trade flows between them. The economy shapes are from 2008, and the trade flows are from 2010.
There’s a proper paper coming out soon (as if I were an actual academic) but before then, and for the reader who has no interest in reading a literature review, here’s an sketch of the Global Demonstration Model in human-readable terms:
Countries are assumed to trade with one another in fixed proportions; for example, the UK gets around 12% of its agricultural imports from the Netherlands. This percentage then remains fixed when exploring the model. (Since you ask, the 12% is mostly tomatoes, flowers, onions, peppers and cucumbers.)
Each sector is imported in a fixed amount in each country. For example, the US only imports 11% of its total fuel requirements, against the UK’s 45%. These ratios also don’t change.
These assumptions allow us to ‘mess about’ with the world as we see it today, and test how sensitive the global economy is to particular changes, or how the world might have looked if trade patterns had been different.
And this is just the beginning: we’re going to be putting several more social science models around this trade-based core to model the effects of, for example, migration on the global economy.
I’ll be working on the diagram to make it (a) more readable, and (b) more interactive, and we’ll be producing some interesting analysis based on the model pretty soon.
The great thing about having access to the entirety of the UN’s commodity trade database is that you can ask any kind of question you wish of the data.
For example, here’s a network representation of trade flows throughout the entire world in agricultural products in 2010.
A network representation of global trade in agricultural products in 2010. Country size and colour is the exporter-ness of the country (purple = very exporter-y)
Bigger, more purple nodes are the ones with the biggest average export (simply the total export divided by the number of trading partners. Network scientists insist on calling this the ‘Weighted Out-Degree’. Don’t blame me.) When viewed from inside a country’s circle facing towards a particular trading partner exports curve out to the left, meaning, conversely, that imports curve in from the right. The colour of the lines is an average of the colours of the two countries.
Most interesting to note, are the following features:
The USA is by a huge margin the world’s biggest exporter of agricultural products ($67 billion compared to second-place Brazil’s $29 billion. The biggest products are soya, maize, cotton and wheat.)
China is by a huge margin the world’s biggest importer ($56 billion compared to second-place USA’s $35 billion. Since you ask, it imports soya beans from the US, Brazil and Argentina, cotton from the US and India, and wood from Russia. Now you know.)
Only Canada, Mexico, Ireland, the Netherlands (NLD) and Morocco (MAR) have a visually obvious trade balance. All other countries are either clear net importers or clear net exporters.
Also very interesting—but this ones requires a bit more concentrated looking if you’re not willing to take my word for it—you can definitely see geographic clusters. Look at the star around Japan (JPN); it includes Thailand, Vietnam, Australia, Indonesia and the Philipines. Europe is very clearly at the bottom (note that it’s purely fortuitous that Britain and Ireland have ended up on the Western fringe of Europe, but it’s not chance that they’re together on a fringe.) Israel (ISR) sits at the border of Europe and the Middle East/North Africa (Egypt, Syria, Jordan, and Tunisia are all nearby.)
The products which are categorised as ‘agricultural’ are according to the categorisation used by the World Input-Output Database (WIOD), the subject of at least one blog post here. The trade flow data is from a massive (200+ million rows) database of trade flows which I’ve spent the last hundred and fifty years assembling from the UN’s commodity trade database, COMTRADE. The visualisation is from a piece of open-source software called Gephi with a heavily-tweaked Force Atlas 2 layout.
This is just one of an unimaginable number of interesting analyses and visualisations I’ll be able to do, now that I’ve got my very own copy of UN’s COMTRADE database to play with and ask questions of as I see fit. If you’d like to see any interesting analyses in future blog posts, let me know on Twitter @aid_complexity.
Big data, yeah? It’s great isn’t it? Doesn’t everyone just love to have loads of big data all over the place?
Got 30 million customers in the UK, have you? Each of those customers purchasing thousands of products a year, yeah? Screw it, lets just store ALL that information in a massive database. It’s big data innit? It’s what people do now.
Well I’m sick of it. Regular readers will know that I’m currently in the process of trying to gather trade data from the UN. It’s of the format “we sold this much soap to this country in this year”. Sounds simple, right?
Well it is. But it’s also big. There are around 200 reporting countries, reporting trade with one another, in over 3,000 product categories across fifteen years. This makes the final database somewhere in the region of 150 million rows long. It’s big, and it’s slow, and it’s incredibly painful to deal with.
By way of an example, let me introduce you to a painful problem which has bedevilled me these past few days: due to some kind of wierdness with the import process, some countries’ data ended up with an equals sign at the start of their product codes. So instead of product code “101305” they had “=101305”. I can’t even remember now how this happened, but it’s to do with the fact that the data sets are so large, that they could only be opened in certain pieces of software, one of which has obviously had this wierd side-effect. The affected countries are Japan, Brazil, China, India, Russia and Mexico. So, some nice small countries then. This means that 20 millions pieces of data need an equals sign removing. Sounds easy right?
The process to get rid of those equals signs started yesterday evening, and was still running this lunchtime, a full eighteen hours after it started.
This is not tenable. This is not big data. This is just a big ball-ache.
Similarly to many branches of statistics-gathering, the world’s trade statistics bureaux lack, in their communication style, a certain panache. The writings of such agencies are characterised by a complete absence of zing, lightness-of-touch and joie de vivre. I’ve blogged before about horrific diagrams like that shown here, and how the whole enterprise of gathering information about global trade is inaccessible and unpleasant.
So it gave me an extra tickle, to find a rare example of humour in a working paper from the National Bureau of Economic Research called “World Trade Flows: 1962-2000”.
In the paper, they present a number of databases of world trade flows from a series of years between 1962 and 2000. Blind or indifferent to the fears of the “Millenium Bug“, they use a two-digit code to represent the particular year. Let me recap: it’s a database of World Trade Flows at a given two-digit year we’ll generically call “??”.
The result can be seen here on p48 of the report. Fantastic stuff…