Pick n Pay had to spend a fortune on the Smart Shopper system and has ongoing expenses in terms of rewards and analysis. The curious thing for me is how many loyalty cards incur the system and reward costs for retailers, but without gaining the full benefit of analysis and thus insight into customers.

I don’t get tailored book suggestions from Exclusive Books. They also haven’t tried to entice me back to their stores since I started buying first from Bookfinder.com and then almost exclusively ebooks from Amazon. They’ve basically lost a customer and haven’t done anything about it.

Even my friend’s St Elmos offers sweet deals to customers who haven’t ordered in a while to entice them back. Pick n Pay turned sub R100 pm customers into R350 pm customers (at least while the special was one) by specifically targeting customers that are familiar with Pick n Pay but need a push to become regular, high-spending customers.

I haven’t had a movie card with Ster Kinekor in a while, but I always use the same email address and credit when I purchase tickets online (which I do almost universally). There have been periods of several months where I haven’t gone to the movies, but no attempt from Ster Kinekor to woo me back with free popcorn or a careful movie recommendation.

Retailers are missing a trick to get an edge over their competitors.

I’m continually disappointed that Moneyweb continues to partner with this distraction.

As I’ve done in the past, I’ve analysed very quickly some of the results of the most recent competition. As background to that, the basic rules are:

1. Put up R20,000 of your own money
2. Trade over three months in currencies, commodities single stock futures and some index trackers.
3. Whoever has the most at the end wins a million rand
4. Everyone keeps what is left of their initial “investment”

So let’s be clear, there are no long-term investment learnings here.

The winner did return 165.5% over 3 months, which is not an impressive performance even though it might look like it.  The point is, given the volatility of the investment universe available for the competition and the encouragement towards rampant risk-taking, it’s entirely pedestrian performance.  It’s very likely an individual’s performance will be good given the wide range of possible outcomes.

Let’s look at some other statistics

These are not performance statistics of which to be proud. They are similar to the losses incurred in prior competitions.

So in short, the competition cost the entrants in total just over a million rand. Losing a million rand is a great way to Make a Million.

A MODEL ISN’T REALITY

Any simplified model I can imagine will also therefore not match reality exactly. The closer the model gets to the real world in more scenarios, the better it is.

Not all model parameters are created equal

Part of the approach to getting a model to match reality as closely as possible is calibration. Models will typically have a range of parameters. Some will be well-established and can be set confidently without much debate. Others will have a range of reasonable or possible values based on empirical research or theory. Yet others will be relatively arbitrary or unobservable.

We don’t have to guess these values, even for the unobservable parameters. Through the process of calibration, the outputs of our model can be matched as closely as possible to actual historical values by changing the input parameters. The more certain we are of the parameters a priori the less we vary the parameters to calibrate the model. The parameters with most uncertainty are free to move as much as possible to fit the desired outputs.

During this process, the more structure or relationships that can be specified the better. The danger is that with relatively few data points (typically) and relatively many parameters (again typically) there will be multiple parameter sets that fit the data with possibly only very limited difference in “goodness of fit” for the results. The more information we add to the calibration process (additional raw data, more narrowly constrained parameters based on other research, tighter relationships between parameters) the more likely we are to derive a useful, sensible model that not only fits out calibration data well but also will be useful for predictions of the future or different decisions.

How not to calibrate a model

Scientific American has a naive article outlining “why economic models are always wrong”. I have two major problems with the story:

1. All models are wrong. Some are useful (George Box). “wrongness” isn’t a problem with a model, but lack of usefulness is. The headline demonstrates a starting point poorly informed about the point of economic models.
2. The calibration approach criticised in the article is an extremely poor way to calibrate a model. No serious researcher thinks that is the right way to calibrate a model. So the article merely creates a straw man and then demonstrates how easy it is to knock the argument over.

Calibration and back-testing on separate data sets

The right way to calibrate a model is to separate the data-set into at least two independent subsets. Firstly, the “training set” or portion from which we will calibrate our parameters to get them to match as closely as possible the data. Again, this should make use of all information available and may give rise to several competing models that appear to fit the data similarly well.

The next step is crucial. We back-test the derived models against the second subset of data. This data comes from the same reality (perhaps a different time period) as used to calibrate the model, but the model won’t trivially match the data because none of that data was used to calibrate the model in the first place.

The importance of back-testing

Back-testing is critically important in the model building process, but back-testing against the same data used to calibrate the model is worth than useless (since it takes time and effort and an create a false sense of accuracy or reliability in the model.) Separating the data into two or more subsets is absolutely required, although it has the unfortunate side-effect of reducing the size of the data-set available for calibration.

Yes, it really matters.

A common example of the dangers of bad models fitting data well is with Economic Scenario Generators. These simulate economic scenarios to be used in valuing complex financial securities. If a model is properly calibrated, it will recreate the observable market prices of a wide range of instruments. However, the model could be a black-box neural network, a carefully constructed theoretical model with plausible relationships and constraints, or the proverbial ten thousand (possibly inebriated) monkeys. If all three models are perfectly calibrated to observable market prices, is any of the models inferior to any of the others?

Clearly the answer is yes, but only when it comes to extrapolation. I have far more confidence in the model’s ability to create “market consistent” valuations for instruments that do not have observable prices in the market if I understand how the mechanics of the model make sense on a level other than pure calibration.

Trivial 3 point example

Perfect fit of two models to 3 data points

The example above shows a perfect of a quadratic and cubic model to 3 data points. From this graph, both models appear exactly the same.

However, if we use the model to extrapolate to future time periods, the results are very different. Without additional data to back-test the results on, it’s not possible to tell whether either or any of these models is appropriate, but clearly both can’t be correct.

Extrapolation of the two models shows divergent results

Nevertheless, S&P did downgrade. Why? I don’t think it is primarily to do with a materially increased estimated probability of default. It has more to do with a change in the payoffs in a ‘game’ (as in game theory) S&P is playíng.

Consider the quadrant of options. S&P downgrades or doesn’t and the US defaults or doesn’t. I’ve constructed totally hypothetically, but perhaps plausible scenarios below, for the S&P’s potential assessment of losses under each possibility given their views and external perceptions of them before and after 2008.

Before 2008, the fallout that would come from downgrading the US and the US not defaulting would be significant and cries of “un-American” might be heard again. Even if the US were downgraded, default would still be a blow for S&P since anything above a BBB rating really shouldn’t ever default if there models are “correct”. I’ve thrown in another hypothetical, a 0.01% probability of default – in other words very low, and as you’ll see in the next scenario, not necessarily higher now for S&P to change their view.

Now, either on a traditional minimax (minimizing the maximum cost) or an expected value basis, before 20008 S&P wouldn’t downgrade the US. This is an important calibration, since S&P didn’t downgrade the US.

After 2008, even if we leave the assessed probability of default unchanged, the world is different and therefore we have different costs.  If S&P doesn’t downgrade the US – even if the US doesn’t default, there will be a cost to S&P since might share the view that the US could default now. The dent in credibility since 2008 means that S&P has to try harder to convince the skeptics that they don’t rate risky instruments as AAA. Along with this goes a massive hit if the US does default and S&P hasn’t downgraded the US. The good news is that at least now a downgrade is viewed more with more understanding even if the US doesn’t default (although be sure Obama’s White House is not happy at the moment).

After 2008, even if the assessed probability of default is unchanged, the minimax and expected value rules both suggested a downgrade is the better option for S&P.

Series Id:           LNS11300000
Seasonally Adjusted
Series title:        (Seas) Labor Force Participation Rate
Labor force status:  Civilian labor force participation rate
Type of data:        Percent or rate
Age:                 16 years and over

US Civilian Labour Force Participation Rate

The above graph is possibly the most important number.  How much economic activity are we losing because US citizens simply aren’t working? The unemployment rate is depressed because those discouraged workers who give up searching for work do not count as part of the labour force, thus not factoring into unemployment rate calculations.

The downtick in the unemployment rate looks to be in danger of being reversed, in spite of this “discouraged worker” bias.

Series Id:           LNS14000000
Seasonally Adjusted
Series title:        (Seas) Unemployment Rate
Labor force status:  Unemployment rate
Type of data:        Percent or rate
Age:                 16 years and over

US National Unemployment Rate

It almost looks the following graph shows good news (it doesn’t, keep reading for the punchline.)

Series Id:                       LNS13008756
Seasonally Adjusted
Series title:                    (Seas) Number Unemployed for 5-14 Weeks
Labor force status:              Unemployed
Type of data:                    Number in thousands
Age:                             16 years and over
Duration : unemployed/laid off:  5 to 14 weeks

Unemployed for 5 to 14 weeks

The reason this isn’t good news is that it’s not so much that those unemployed are returning to work, lowering the number of unemployed in this band, but rather there has been an inexorable march towards long-term unemployment.  People are falling out of this band not into employment but into the 15+ weeks and ultimately the 27+ weeks band.

Series Id:                       LNS13008636
Seasonally Adjusted
Series title:                    (Seas) Number Unemployed for 27 Weeks & over
Labor force status:              Unemployed
Type of data:                    Number in thousands
Age:                             16 years and over
Duration : unemployed/laid off:  27 weeks and over

Unemployed for more than 27 weeks

All this translates to an ever-increasing average weeks unemployed.

Series Id:           LNS13008275
Seasonally Adjusted
Series title:        (Seas) Average Weeks Unemployed
Labor force status:  Unemployed
Type of data:        Number of weeks
Age:                 16 years and over

Average Weeks Unemployed (US)

This is ugly stuff.  Being unemployed for 27 weeks, let alone 40 and beyond starts to have longer term impacts on “employability” and therefore structural unemployment.

He makes a compelling point that the comparison fails.

Egypt’s economic performance has been stable and much better than, say, South Africa’s for example.  Krugman suggests:

Egypt had decent growth — but the gains weren’t trickling down, and youth unemployment was and is a huge problem.

Which sounds rather more like South Africa.  Except with recent data showing unemployment at 9.7% (massively lower than South Africa’s 23.7%) and economic growth above 5% (higher than 3%) and income inequality measured by the Gini Coefficient of 34.4 (compared to South Africa’s 65, which is just about the highest in the world, as in most unequal) Figures from CIA World Factbook

So if you were to back Egypt vs South Africa as most likely to experience violent political upheaval?

This suggests that our official CPI inflation has been understated by approximately 2% over the last ten years. From conversations I’ve had there would appear to be plenty of popular support for this notion.

I’m still not convinced.

The calculation of inflation figures has been closely  watched by economists and asset managers trying to understand what the future holds for monetary policy, earnings growth and returns on inflation-linked bonds. While there have been errors in the calculation, the experts in this area have not been the ones criticising the overall methodology or results (apart from these specific errors).

So why does this 2% differential exist? I have some ideas:

• The components of a Big Mac are not representative of the entire economy. Perhaps (and I haven’t checked) food price and wage inflation (two components I’d guess at being significant inputs into a Big Mag) may have been above average CPI.
• Our currency has had wild swings over the last ten years, dramatically affecting the cost of imported goods and services. This won’t be reflected in the locally made from mostly locally produced ingredients Big Mac.
• Consumer electronics, computers, office equipment etc. have all benefitted from cost reductions over this period.
• The differentials for several other countries are significantly wider, suggesting a high variance between official inflation and Big Mac inflation. In other words, a 2% differential may not be significantly different from a 0% differential.

Argentina, on the other hand, with a 9% differential, is another story.

Census data isn’t the most useful for understanding marriage and divorce patterns and trends. It’s available too infrequently, relies on self-reported status and only shows a snapshot of the population at a point in time without explicitly showing the change from one state to another.

The great thing about the census data is most of it is freely availably from StatsSA so you can slice and dice it and analyse it exactly how you want.

StatsSA also puts out a Marriages and divorces 2008, with the info taken directly from registrations. I don’t have access to the underlying data, but here are some snippets that can be useful to compare and contrast with popular notions in the media.

December is the most popular month to be married

It’s a huge pity StatsSA doesn’t release the raw data, as their analysis is sadly lacking in the focus on reporting absolute numbers with comparing this against a relevant denominator in a ratio. Knowing how many divorces there are for someone who has been married twice before isn’t very helpful unless we understand how many marriages of that type there are in the first place. Knowing how many divorces involved children doesn’t help really unless we know how many marriages at that point in time were in a family with children. This tells us nothing about the relative likelihood of divorcing with or without kids.

I’ve tried to piece together some of this by comparing this transition data with the snapshot data from the census, but I have concerns that inconsistencies between the data sets may be skewing the results enough to limit their usefulness.

I’ve left out civil unions for no reason other than there is too late to analyse reliably.  There were only 80 in 2007, growing significantly to 732 in 2008, but still too few to draw conclusions on.

About Marriage

Unsurprisingly, bride and groom are older when marrying for the second time

1. 80% of bridegrooms are older than their brides when the brides and spinsters of widows. Nearly half of bridegrooms are younger than their brides then the brides are divorcees. Typically around 85% of widowers marry younger women, and this drops to only  just below 80% when the bride is a divorcee. A similar pattern occurs when the bridegroom is a divorcee.
2. The ages of both bride and bridegroom for customary marriages are 2 to 3 years younger than marriages overall.
3. There were approximately 180,000 marriages registered in 2007, when the national census estimated their to be 20.9m unmarried people between the ages of 16 and 80 (a crude assessment of most common marrying ages. Ideally we should look at rate of marriage per age band since this will definitely not be the same across all ages). Given that two people are needed to get married, this gives us 180,000 marriages out of 10.45m pairs (ignoring male:female ratios differences) which is an average marriage rate per year of 1.7%.
4. The number or marriages has been increasing almost every year from 140,000 in 1999 to 186,000 in 2008, which translates to a growth rate of around 3% per annum while our population growth over the same period is estimated by StatsSA to be a little more than 1%. From the graph below you can see a marked jump from 2001 to 2002. The growth rate excluding that jump is more like 0.9%, slightly below the average population growth rate.

What happened in 2002 that suddenly made everyone want to get married? World didn't end after all? Or some processing/data error. Maybe you should check that you are actually married if you were married in the last years of the previous millennium.

About Divorce

1. There were about 30,000 divorces in 2007, the same year the national census put the total number of married people as 10.7m. This translates to a divorce rate of just under 0.3% (or 3 divorces per 1000 marriage) per annum. That puts us about the same as the UK. Certainly makes me question the common wisdom that 1 in 2 marriages end in divorce. Using these figures suggests to me less than 1 in 3, maybe as low as 1.5, depending on whether the age of first marriage keeps increasing and what happens to life expectancy.
2. The number of divorces per year has been declining more or less steadily, from 37,000 in 1999 to just under 29,000 in 2008.
3. The StatsSA report doesn’t show number of marriages by population group, but the census shows 2.1m married white citizens and  6.8m married black citizens. The number of divorces is about equal in 2008, having declined from 14,785 in 1999 to 9,481 in 2008 for the white population but having significantly increased from 6,823 in 1999 to 10,110 in 2008 for the black population. Clearly very different population dynamics at work here, or serious problems with at least one of these data sets.

So what is really happening with marriage and divorce in South Africa?

These results confuse me. Yes, there is a slight increase in age at marriage, but divorce seems to becoming less popular and with mixed messages about marriage depending on what the 2001 jump is all about.

Property in one area is a weak substitute for another property in a nearby area, and an awful substitute for property far away.  Supply and demand is determined at least partially independently in each area.

I’m suggesting that in South Africa, we don’t have a single labour market. We have several different labour markets, with fairly independent supply and demand for labour in each, and with each labour in each market being a limited subtitute for labour in neighbourhood markets and with limited portability between markets.

Supply and Demand for Labour (2007 Census data)

Unskilled labour suffers massive unemployment and low wages for the employed

The supply of labour in the unskilled labour market is huge, while the demand for labour in that market is low. Supply is renewed through simple population growth in the absence of good education and skills training. Demand decreases as technology provides more efficient ways of performing the tasks. You can view Chinese competition as either an increase in the supply of cheap labour or a decrease in the demand for South African cheap labour.

Skilled labour has little unemployment and high incomes

The supply of labour in the highly skilled labour market is very limited and the demand very high. Emigration of educated and skilled citizens reduces supply and immigration of skills is limited. Efficiency gains of high technology most help skilled workers to be more productive, increasing the profit from the products and services they offer, thus further increasing demand.

What the table tells us

1. A matric/national certification without university exemption subjects and marks is poor preparation for employment.  18% of the labour force has it and a third of them are unemployed. In 2007, this group represented over a million unemployed South Africans.
2. Worse than completing a dubious-value national certificate is leaving school without one. Nearly half (44%) of those with Standard 9 / Grade 11 and wanting to work are employed.
3. Only 50% of those with Standard 9 / Grade 11 are even part of the labour force. This jumps immediately to 68% for those entering Grade 12 and to 77% for those completing high school without university exemption, suggesting that it’s not only a question of leaving school to live a life of leisure, but more likely a significant proportion of those out of the labour force are discouraged workers, amplifying the real employment problem with this education level. Curiously, the labour force participation rate for those completing Grade 12 and obtaining a university exemption is only 66%.

I’m not for one minute suggesting that if everyone had a masters degree our employment problems would disappear. There are many moving parts. However, any discussion of unemployment or wages by income or race or gender that doesn’t first and foremost consider education is worth ignoring. For that matter, any comparison against other countries that doesn’t at least talk to differences in education levels is also best quietly ignored.

Welcome to structural unemployment

A key feature of structural unemployment is that unemployment isn’t universal. Pockets experience close to full employment and inflationary wages while other groups have high unemployment. South Africa couldn’t be a better example.

Calling a patch a patch

Any economic policy that doesn’t recognise that until education is fixed, we will suffer high and persistent unemployment is dishonest or ignorant. Anything we do in the interim to magically “create jobs” can only hope to be a patch to lift incomes and dignity until education can decrease the supply of unskilled labour and genuinely grow our economy through an economically productive population.

This isn’t the first time car colours have been analysed with some science.