Bliss is a $10k Mortgage

There's been a lot of chatter on twitter recently about net government debt being quite small internationally, and at 10%, that is indeed correct.

Judtith Sloan is keen to point out that it's not just the quantity of debt that matters, but the quality.  That is, what that debt has bought, which is also correct (think credit card debt vs a mortgage).  I won't go in to that debate here.

While the debt debate continues, a much more interesting meme has appeared - the comaprison of government debt to an average householders mortgage, and it is that that I would like to dig in to a bit, as it seems to have gained more traction than either of the ideas above.

Here's a typical example of an infographic showing this (courtesy of the ACTU)

 

 

As far as analogies are concerned, its got some real flaws.  Let's dig in to it.

 

1. Net Debt vs Gross Debt

The most obvious thing here is that someone who has a $10,000 mortgage also owns a house. That is, their assets are going to be much larger than their debts, by a significant amount. The government debt is net debt, that is, it is not offset by assets. Perhaps a better analogy would be the fellow on $100k a year with a $10k credit card debt (but see below).

 

On top of that, the government isn't even spending within their income.  A further improvement of the analogy would be the fellow on $100k, with a $10k credit card debt, and spends more than he earns each month.  Even still, I'm not happy with this analogy as the government is not a person.

2. Government Income

GDP is NOT the government income.  It is the estimated total value of goods and services produced by the nation over a year.  The government's income is much less than that, something in the order of 24% of GDP.  A better comparison for our debt, then, would be10% of (24% of GDP), which is closer to 58% of the government's income each year.

 

3. Household Income

There's a bit of a fudge here, too.  Unlike the government, the average household has to pay tax, which reduces the money available to pay back loans, living expenses etc.  It's hard to determine exactly how much tax without knowing the mix of incomes that makes up the $100k, but a single person earning $100k, would pay approximately $26,500 in income tax and Medicare levy, leaving $73,500.

 

A Nice Little Mortgage

Still, a mortgage equal to 58% of $73,500, (about $43,000) would be the envy of most people.  But is even this anolgy reasonable?

 

The underlying assumption in the argument presented by the ACTU (and others) is that mortgages and government debt can actually be compared on a like for like basis.  How well does that assumption stack up?

 

An Average Mortgage

The typical new Aussie household mortgage these days can be anything up to 7 times the (pre-tax) income of a household, historically quite a large mortgage, and can be difficult to manage.  Let's consider a more typical 3.5 times (pre-tax) income.

 

By implying that a mortgage and government debt are comparable, those making the comparison are implying that a net government debt of 3.5 times the government's income of 24% of GDP is quite an acceptable level.

 

Putting this calculation in terms of debt as a % of GDP, we come to 84% of GDP, close to the net public debt of the UK government, and more than that of the US government!

 

So, we know what the ACTU's thoughts are on this, happy to misinform for purely political reasons.

 

What about the thoughts of a senior govenrment minister , who also happens to have a PhD in Economics?  Surely we could trust them to be more honest, yes?

 

 

No.



Don't forget that power-hungry copper

A small debate on Twitter tonight prompted discussions on the relative power consumption of the ALP's FTTH NBN and the Liberal's proposed FTTN model.  My initial thoughts were this was a do-able comparison, but certianly wasn't as simple as some make out.  The most common argument from the FTTH mob is that the local distribution cabinets use a passive splitter technology (PON - passive optical network), and so don't need power, whereas the FTTN cabinets do.  Of course, with FTTH, you still need to convert the optical signal to an electrical signal at the customer's premise, which isn't needed under FTTN.

A big thanks to Tristan (@blondgecko) who posted this link (Baliga, 2011), which is an academic paper comparing the relative power usage of different broadband network topologies

Hungry, Hungry Copper

As you could probably guess, copper is a hungry beast, and the FTTN network topology uses twice the power that FTTH uses.

To put monetary figures on it, in a per person rate, FTTN uses a whole 14W of power compared to only 7W for FTTP.  That might not sound like much, but remember that these systems tend to run 24 hrs a day, 7 days a week etc etc etc.

Do the sums, and the total dollar value of the difference in electricity usage is $12 per household.  Per year.  Certainly doesn't sound like much, but electricity prices have had a habit of increasing at a considerable rate in recent years.

With a 10% increase in power prices a year, over 25 yrs (life of fibre) gives a value of $737 per house in 2013 dollars for the extra power used by a FTTN system over the next 25 years. 

Table 1: Annual per household power cost difference between FTTN and FTTH

Compared to a perhouse cost of approximately $4000, this is a significant extra cost, but this is also not a particularly well-refined model.  While power prices are currently increasing at a high rate, that's no reason to suspect that they will continue doing so for the next 25 years.  Already we are seeing alternative power sources becoming more competitive with fossil fuels, so assuming that after another ten years, the average price increase in power is closer ot the CPI, at 3%, and the total cost difference reduces to a smidge under $500.

One further refinement is to remove the costs of power that the user pays, not the NBN (remembering that we are comparing costs between the two opposing models here).  According to Baliga, at least 65% of the power costs are borne by the final user, which leaves 35% of the $500, or about $175 difference in power costs to NBNco over 25 years.

What does this mean in practical terms?  To get best value for money for the taxpayer, if it is going to cost less than $175 to install fibre from the node to the premise then its a no brainer.  If the copper is still in good nick, and the fibre will cost more than $175 to install, stick with the copper and wear the cost of th extra electricity.

It also means that the government's (and Turnbull's) original FTTN plan, which was going to cost $4.7B, is still quite a bit cheaper than the new and improved FTTP NBN plan, even with power costs factored in.

Where to from here?

If nothing else, I hope this shows that any real economic comparison of the two models is quite complex, and simply yelling that one technology is somehow 'better' than another isn't going to change anybody's mind.

The problem is not the syllabus

The problem is not the syllabus.

In almost 20 years of teaching senior Maths and Physics, I've had plenty of top students go on to unviersity to study Engineering and Medicine, and go on to lead fulfilling, successful careers. Only a handful have decided to become teachers. Each year, I ask the likely candidates why they don't choose teaching, and invariably money is mentioned as the main reason or a significant reason.

Over the last 20 years, I have also noticed a drop in the mathematical ability of my beginning Physics students. The students aren't any less intelligent, so what's happened? We do know there is a huge shortage of maths teachers. In fact, at my school our junior maths classes are currently being taught by PE teachers, English teachers, Home Ec teachers, anyone with a spare in their timetable. These people are all top quality teachers, but not specialists. They can teach the maths, but don't have, nor can enunciate, the broader picture.

We can debate the syllabus all we like, but if students don't have the groundwork for serious Maths and Physics, then all we are doing is bailing out a sinking boat. And if we can't attract the best people to teaching, we're not going to get better results by fiddling with the paperwork.

The problem is not the syllabus.

How to win a Nobel Prize in one easy step

I was highly amused the other day to come across this graph, showing a reasonably strong relationship between per capita consumption of chocolate, and number of Nobel Prizes won by people in that country.





 I'd love to be able to recognise the creator of this graph, but its popped up so many places I'm not sure who's work is actually is.  Still, we can all see from the graph quite clearly that the more chocolate each person in a country consumes, the more Nobel Prizes that country has received over the years.

 

More importantly, how well these two items are related can be measured relatively easily, using something called correlation.  The wonderful person who created this graph has in fact also measured the correlation between chocal consumption and Nobel Prizes being awarded, and you can see it in the top left corner of the graph, where it says r=0.791.

 

Now, there are a large number of ways in which correlation can be calculated, depending on what sort of data you have, but what they all measure fundamentally is how close your data is to a straight line.  If all your points are on a straight line, your correlation or r will be equal to 1.  If all points are spread out randomly, it will be zero (if the line is pointing downwards, the r value will actually be negative, but r=-1 is as good as r=+1).  A value of r=0.791 is pretty reasonable - the two variables are said to be higly correlated.

Now, in no way does this imply causality.  A country could not improve its chances of receiving a Nobel Prize by handing out copious amounts of free chocolate to its school kids or population at large, and expect to start receiving Nobel Prizes left, right and centre.  The set of data above could, in fact, be random.  Or, there could be some other, underlying, relationship.  Perhaps people who receive Nobel Prizes tend to come from welathy countries, countries where people can afford to eat chocolate at will.  Sometimes looking at the outliers can tell you something as useful as looking at the data points in the trend itself.  In this case, what's going wrong in Germany???  All that chocolate eating, and yet its substandard when it comes to Nobel Prizes??  Sweden does alright though, plenty of Nobel Prizes, without all the investment in sweets.

All this thinking about correlation brought to mind a graph that floated around the twitterverse earlier this year, purporting to prove that forcing an economy like Greece to reform and consolidate quickly (ie austerity measures) will only result in a worse result at the end of the day.  Here it is below, again unattributed (but happy to correct if the author lets me know)

Looks pretty convincing, doesn't it.  Nice straight line, lots of points on the line, including, down at the bottom, Greece, trying to consolidate faster than the rest, and getting it more wrong than anyone else (x axis is attempted reduction in spending, y axis is how wrong they got their growth predictions).

 

Using a spreadsheet like Excel, it's pretty easy to get a basic value for correlation here (doesn't really matter what sort for the moment), using the '=CORREL('x values', 'y values') formula.  To get the values off the graph, I simply read off the axes, to the nearest half value (not particularly precise, but good enough for our purposes.

Using my rough and ready measurements, I calculated a correlation of r=-0.68!  Less than that for Nobel Prizes and chocolate consumption.

Remember I said sometimes it is instructive to look at the outliers in any data set?  I redid the calculations, taking out Greece, and got a new value of r=-0.5.  Borderline low correlation.  Much lower than for Nobel Prizes & Chocolates.

Hmm.  What does this mean for all those economists claiming that austerity is not a good plan?  Not a lot really.  They may well be right.  But this graph doesn't really prove that convincingly.  Nor does it disprove it either, for that matter.  what we can take from this little analysis is that whatever is happening in Greece is somewhat different to what is happening in the other parts of the world, given that it has such a disproportionate effect on the data.  Certainly makes it an interesting place to look at, economically speaking.

For our students, its a nice little study on the importance of looking at data critically.  Graphs can be a great way to communicate information, but they need to be aware both that correlation is not causality, and also of the impact of outliers

Facts, Lies and Statistics

Facts

Facts matter, and most of us will know the phrase Fact Checkers, which came up quite a bit during the recent US presidential election.  But Facts are only part of the story.  The Choice of Facts matter just as much as the facts themselves, and nowhere is this seen more than wherever statistics and data are discussed.  Western mathematics education doesn't serve most people well in this regard, and I could explain to you why, or you could watch this TED lecture by Arthur Benjamin.

The lecture is only 3min long, but for those time-short readers I can summarise by saying: we should teach less algebra, and more statistics at school.  Going to be an engineer?  You need algebra.  The other 99% of the population, you really, really need statistics!
 

You really, really need statistics

Why, I hear you ask?  I'm glad you asked!  Below is an poster of the Incredible Shrinking Doctor, an image commonly used in high school maths classes to explain distortions caused by the misuse of statistics:

The image is linked from this page, which has a great discussion on the ambiguity of data.  Ambiguity?  How?  The image is meant to show the shrinking number of doctors in California between 1964 and 1990.  The reduction in doctors was, in actual fact, approximately half.  But, because the images were shrunk by half in both height and width, it appears as if the number of doctors actually shrunk to a quarter of what they where (the small doctor is about 1/4 the size of the original doctor).  The Facts are right, but they are presented in such a way so that the loss of doctors to family practice is much worse than it actually is. 

 

Statistics

Facts matter.  In fact, Facts matter so much, that some people are willing to choose which Facts they use very carefully to make sure they give the right impression to people who don't know any better (like voters and investors).

Here's an example from a post on twitter today from Stephen Koukoulas (@thekouk), an experienced economist (you can read his Bio here).

Is it a Fact?  Absolutely!  Perfectly correct.  Doesn't look good for the profligate Howard government, does it! As far as I can tell, it comes from here, the 2012 MYEFO documents, table D1 (see screenshot below).

In fact here is the table partially reproduced below (with the relevant data I believe used by @thekouk highlighted).

The 'last 8 Howard Budgets'

Why did he choose the 'last 8 Howard Budgets'?  Is 8 some magic figure, or some standard Economic rule of thumb?  Not as far as I know, but I do know that by choosing the last 8 years, he maximises the point he is trying to make, that the Howard government was a wasteful spender.

Note the first figure in the list - a 10.7 increase in real spending over the previous year.  What happened?  To be honest, I'm not really sure, but I do know that the inclusion of that one, large value significantly biases the average over those 8 years. 

 

The last 7 Howard Budgets

What if 7 was the magical economic rule of thumb?  Then the average increase in spending under the Howard government in its last 7 budgets was less than 2.3% per year, much less than under the current Rudd/Gillard government. So much for the 'profligate' Howard government!

(@thekouk could have used 9 years, and arrived at the figure of 3.6% increase in real spending per annum, still worse than under the current government, but not as usefully 'bad' as using 8 years of data.)

 

Teaching Stats and the Choice of Facts

Don't get me wrong, I follow @thekouk on twitter, and I have learnt quite a bit from doing so.  He has a broad range of experience in both the private and public sector. 

He always uses Facts.

And Facts matter, but our students also need to know that the Choice of Facts also matters. For this reason, Statistics should matter more than algebra when it comes to maths education, and we should always, always question the Choice of Facts that are presented to us, and teach our students to do the same.