Sunday, October 13, 2013

Leap years And The Even More Curious Phenomenon Of Non-Leap Years

Autumn has come to Bologna and the past few weeks have been dreary and cold. Today, however, the clouds broke and it was a beautiful, clear, warm-enough day. I took an afternoon break from studying and ran up to my favorite spot in Bologna: Villa Ghigi. My own attempts to capture the view and the ambiance up there have so far been unsuccessful. However, this contributor to wikimedia seemed to do a pretty good job of it. 

View of Bologna from Villa Ghigi

Because of the weather and my battle with a persistent cold over the past couple of weeks, I haven't been running much. Getting out and stretching my legs this afternoon did me a lot of good. Well, maybe. The intellectual result of my run is outlined below. I'll leave it up to the reader to determine the normative value of the outcome which is detailed below.

I've mentioned before that one of my favorite by-products of running is the unpredictable stream of thoughts that go through my head as I settle into an almost meditative state. Today, a particularly lucid stream of thoughts brought me to the question of leap years and how we deal with them. The progression of thoughts that got me to that point are another story entirely, but as I plodded back down the hill, I realized that leap years present a problem. 

The whole idea of celebrating a February 29th every four years comes from our attempt to match the earth's revolutions around the sun to it's axial rotation - i.e. match earth years to earth days. There's no good reason why the earth should rotate on its axis a particular number of times as it revolves around the sun. To make life easy, we typically refer to a year as having 365 days. In fact, it revolves on its axis more like 365.2425 times for every trip around the sun. (I didn't know this as I was running, I just assumed there was a margin of error. Wikipedia told me the exact number when I got back.) Now, if the earth were kind to us, it'd pick a nice even number of days to go around the sun; for example, 365 or, if it were particularly kind, 360 days would make celestial time-keeping very neat and easy. Failing that, it'd be nice if the earth picked an easy fraction of a day to add on or subtract from each year. Granted, 365.2425 rounds up to 365.25 easily enough and so every four years, we add an extra day to even things out. None of us would ever notice a difference over the course of our lifetimes between measuring a year as 365.25 days and the ACTUAL length of 365.2425. But apparently, the Pope Gregory was wise enough to transcend living memory. He wanted a calendar for the ages, and to do that, you need more foresight than a measly lifetime.

Rounding up to .25, adding an extra day every four years and leaving it at that could have DISASTROUS consequences; specifically, the addition of 3/100ths of a day each time we celebrate February 29. The additional .2425 days per year only adds up to .97 days over four years, not a full day. Over the course of many years celebrating February 29, the summer solstice gradually creep up and, instead of happening on June 21, it slips back to June 20. Extrapolate that error over a few thousand years and eventually the summer solstice would be in May. That's just unacceptable. 

So, I came back home and started tooling around on wikipedia. Thank goodness Pope Greg had considered this 3/100ths of a day we were adding every four years and formulated a strategy for correcting it. It turns out that at the turn of each century, the centennial year (e.g. 1700, 1800, 1900, etc.) is NOT counted as a leap year. Even though these years are divisible by four, February 29, 1700, 1800 and 1900 did NOT happen. In 1903, for example, the world had gone without a February 29 for 7 years so that the summer solstice in 1903 didn't happen until more than half way through the 22nd day of June. By comparison, the summer solstice in 1896 (the last leap year) was happening towards the end of the day on June 20th. 

First of all, isn't that wild? There I was, thinking that I knew the calendar that I have spent nearly 30 years interacting with on a near daily basis! Maybe this is all common knowledge, I don't know. Usually I have a chance to talk through blog posts before I write them up but I didn't get a chance to talk through this one. I'm assuming this isn't common knowledge.

There's more.

So, most centennial years omit February 29, but not all of them. As it is, the extra fraction of a day we add each February 29th only adds up to 3/4 of a day each century. So dropping February 29 from centennial years puts us behind a total 1/4 of a day every 100 years. Again, small potatoes, but over the course of thousands of years, that could throw us off by a whole week!

File:Gregoriancalendarleap solstice.svg
I found this on Wikipedia. Search for "Leap Year" and prepare to sacrifice half a day learning about the calendar that measures your life. Don't worry though, you'll make up for the lost 12 hours over the course of the next 100 years.

Thank goodness the Gregorians saved us from this confusion though. The ultimate correction in solving the leap year problem comes by celebrating February 29th on the centennial years that are divisible by 400. This means that the years 1200, 1600 and yes, 2000, celebrated February 29 in order to correct 400 years of ever so slightly shifting the summer solstice later in the year. 

The exciting conclusion to all of this is that the year 2096 will see the earliest summer solstice since 1696; it will actually occur in the MORNING of June 20 (Greenwich Mean Time) opposed to the average of June 21, and the extreme of the afternoon of June 22 witnessed in 1903.

Unfortunately, I probably won't be around in 2096 to experience this once-in-a-quarter-millennium phenomenon, but maybe my kids will? I'll be sure to forward this blog post along to them at some point.

It also means that I missed the similarly momentous occasion of celebrating February 29 in 2000. It didn't occur to me at all that that specific leap year was so phenomenal. We were so caught up in the whole millennium and Y2K business and I was still riding the high of my 16th birthday. What a shame.

Finally, in my lifetime I will likely never experience an non-leap year. And I have to say, I'm ok with that. Leap years are confusing enough, celebrating a non-February 29 would just be confounding. 

Sunday, October 6, 2013

Informal Economy

As you may have guessed from the three weeks of silence, classes have started full-time and they are keeping me very busy. I'll give a quick update on academic stuff and then get on to what I've learned about the informal economy since I got here and why that matters in the first place.

SAIS is unique among the graduate programs for international relations in that it requires all students to specialize in economics. This is one of the reasons why I wanted to come here in the first place - to strengthen my economics background. This semester, I'm taking intermediate macroeconomics, corporate finance, weak and failed states and sitting in on a risk management class. Fortunately, I tested out of German, so that covers my language requirement for graduation. Since I still have access to language courses though, I'm taking Italian this semester. Once I get to DC I think I'm going to change to Spanish.

What I really want to talk about in this post though is the informal economy. You'll remember a couple of posts ago I wrote about my interest in the field of threat finance. Very closely related to threat finance and a much more researched field of study is the informal or underground economy. The two are very much linked.

I'm reading a book right now titled "Treasury's War" by Juan Zarate. It's a history of how the Treasury Department has developed a strategy of finding and shutting down terrorist or multi-national criminal financing over the past decade- specifically after 9/11. The thesis of the book is that the US Treasury Department, with its influence over financial institutions around the world, is uniquely positioned to collect financial intelligence on individuals deemed a threat to the US. Before 9/11, the Treasury Department was much more wary of manipulating its power over the global financial networks for political or even domestic security motives. It wanted to maintain neutrality in the markets. 9/11 changed that and the Treasury Department shedded its inhibitions. At first, the mission was relatively easy: terrorist and criminal financiers were easy targets, sending money through conventional networks and keeping their money in major, international banks. For the Treasury Department, it was only a matter of convincing bank presidents and local leaders of the value of shutting down suspect accounts.

However, over the past 12 years, threat finance has become much more sophisticated. Threat financiers have learned to avoid conventional financial vehicles and institutions for moving their money around. This is where informal and underground economies come into play. By definition, these economies are unregulated and decentralized - havens for tax evaders, drug traffickers, terrorist financiers and the like. The Treasury Department's success at shutting criminals and terrorists out of the formal financial sector made their job of maintaining pressure on illegal networks harder. It drove the illicit finances deeper underground where the Treasury Department has less visibility and less influence.

Italy is a great place to study the informal economy. Italy gets a bad reputation these days for its financial capabilities, but don't forget that modern banking was invented in Florence and northern Italy is one of the wealthiest regions of Europe. Italy doesn't lack wealth, it lacks the ability to centralize that wealth. Instead of flowing through regulated, centralized channels, wealth gets squirreled away and hidden out of reach of the central government. The strategies and tactics for doing this are fascinating.

But Italy is also an interesting case in that informal economies are built into the system. A professor of Italian economics came and gave a talk at SAIS a couple of weeks ago and she pointed out that Italy does not have the mega-corporate national giants that Germany and the US have. Italy has no GE, Siemens or Windows. Fiat is perhaps the biggest company in Italy but they are still pretty small in the grand scheme of things. The average Italian company is much more likely to small - around 14 employers. Really small. As a whole, these companies are generally very profitable and very good what they do, mostly being in the high-tech sector making specialty equipment or providing boutique services not found anywhere else. They make up most of Italy's exports.

While these small companies are a blessing to Italy's economy, they are also a curse when it comes to tax collection. It's much harder to police 10,000 small companies than 10 really big companies. Specifically, it's much more expensive to tax a decentralized economy. Each company makes up a very small chunk of the tax base and there aren't any obvious behemoths to keep an extra close eye on to make sure they are paying their taxes. Also, large companies have to keep their reputation in mind. Getting caught not paying your taxes is potentially more harmful to their business than a tiny firm of 20 people making motorcycle brake pads that nobody's heard of.

The decentralized nature of Italy's economy makes for a natural environment of doing things off of the books since it's less likely you'll get caught and if you do get caught, the consequences likely won't hurt your reputation with your customers.

This isn't to say that drug traffickers or terrorists are using tech firms in Bologna to move their money around, but Italy does have a general economic environment that is conducive to concealing the flow of money. It may be a bit easier here to set up a small company and misreport its primary line of business. In a country full of mom and pop shops, adding another to the pile will hardly get noticed.

Possibly contributing to the incentive to misreport business activity here are the multitude of very strict laws and measurements in place to prevent ililicit financial activity from happening. Italy has attacked the underground economy through higher and more taxes along with more bureaucracy. Raising the cost of doing business increases the incentives to do business off the books, so it creates a kind of self-defeating spiral.

As I find time to do more research on this topic, I'll keep updating on what I learn and provide more examples.

Have a good week!