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  • 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

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    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

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  • 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

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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:


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.


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: