• Review of Franz Kafka’s ‘The Trial’

    The Trial by Franz Kafka My rating: 5 of 5 stars When you get used to reading inferior books, even a nibble of a great masterpiece can challenge your digestive system in ways that cause stomach cramps. Franz Kafka is no light read. After a diet of heavily processed modern literature, Franz Kafka’s The Trial

  • Happy Easter Daniel

    Dear Daniel, Yet another Easter is coming around the corner and I find myself thinking, once again, of you. There has, in fact, only ever been one Easter that we have spent together. It was the Easter of 2011. I remember I took you to Mass at Notre Dame au Sablon. In all the years

  • The Social Triangle: A new model for political economy

    Divided we tweet It seems that the public debate is divisive as never before. Left versus right. Social Justice Warriors (whatever they are) versus the alt-right (whatever that is). Admittedly, this impression may simply be a result of our unhealthy addiction to social media, which through its Algorithms of Hate and its cloak of anonymity

  • My sixth letter to you (Happy Birthday)

    Dear Daniel, This is just a brief one to wish you a very happy birthday. You are seven today; a big boy now! I want you to know that although I can’t spend the day with you, I have been thinking about you all day. I miss you more than you can know, and look

  • My Fifth Letter to You (Merry Christmas!)

    Dear Daniel, It’s a few days after Christmas and I’m here at home thinking once again about you. My Christmas has been very merry indeed – with lots of family and friends and games and fun and good food (more about that in a second). But of course, everything is tinged with sadness because you

  • My fourth letter to you

    Dear Daniel, Hi, it’s your dad again. It’s been a number of days since the last hearing in the courts and I have been thinking about you all the time. I heard that you are doing pretty well in school – well that’s good news. I hope your teacher is nice and that you are

  • Aragorn’s Law: Of kings good and powerful

    This post is an attempt to come up with a Law on the fundamental nature of power, which I call ‘Aragorn’s Law’. To begin with, we state three propositions. Proposition One: That Power is about control It’s possible to define the concept of power in a few different ways, but for the most part, when we think of

  • In defence of free speech

    United we chat; divided we shout at each other I promised myself I would not write a post about the Charlottesville riots, the near universal condemnation of Donald Trump’s nuanced position and the taking down of Confederate-era statues. Yet a recent conversation has forced my figurative hand onto the keyboard. I’ll keep my promise nonetheless,

  • My Third Letter to You

    Dear Daniel, Just a quick note to tell you how much I miss you, and that I hope you are having a wonderful summer. The weather has been somewhat mixed, but I hope you have had a chance to get outside and enjoy it, as much as possible. Do you ride a bike yet? I

  • An honest debate on gender equality? Men are dying for it!

    A gap by Any Other Name… The official website for statistics of the European Union is called Eurostat. If you visit their website, and I highly suggest you do, you will find among the many interesting databases one for the Gender Pay Gap, which measures the difference in average gross hourly earnings between men and

As with birth rates, we use data for 4 categories of countries from 1990 to 2015 (100 observations total). We have two explanatory variables, AGE and Y, where AGE is defined as the percentage of the population aged over 65 and Y is per capita GDP.

After eyeballing the scattergrams, we test the following functional form:

d = (minY^a)/Y^a * (1/AGE^g)

Where minY is the constant equal to the smallest value of Y in the series.

Logarithmic transformation gives:

ln(d) = ln(minY^a) – a*ln(Y) – g*ln(AGE)

which we test on the data using OLS. Here are the results:

Adjusted R square: 75.191

Intercept coefficient: 7.37384
t-Stat: 20.4011

Y coefficient: -1.01444
t-Stat: -13.1059

AGE coefficient: 2.0097
t-Stat: 11.5208

The estimated intercept is a good, but not perfect, approximation of ln(minY^a)

Here are the fitted against actual values of the scattergram for death rate against per capita GDP:

fitted-death-rates-against-actual-values

While the results are not as good as with the birth rates calculations, it is nevertheless a good enough fit and the explanatory variables have a strong enough confidence factor to be usable in our estimations.

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We begin by examining the scatter of data for 100 observations of per capita GDP and per capita emissions for 4 categories of countries, over 25 years (1990 – 2015).

The scatter suggests a cubic functional form, so we test:

GHG = a + b*Y + c*Y^2 + d*Y^3

where GHG are per capita emissions of GHG, and Y is per capita GDP.

The results from OLS regression are:

Adjusted R square: 0.980438073

coefficient a: 1090
t-stat a: 3.06

coefficient b: 0.709310153
t-Stat b: 8.241453

coefficient c: -0.0000047025
t-Stat c: -1.01233

coefficient d: -0.000000000105314
t-Stat d: -1.47005

While the t-scores on the squared and cubed terms are low, the number of observations are also limited.

Here is the plot of the fitted against actual values:

fitted-emissions-to-gdp-against-actual-values

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