My first letter to you

By Graham

Dear Daniel,

I am your father and this is my first letter to you, my six-year-old son. I’m writing it in a language you can’t read or even speak, on my website which you don’t know exists. It’s a sunny day in Brussels and I’m eating my lunch and thinking of you. You are – most likely – still at school right now, in your classroom which is not far from where I sit and write these words. But you don’t know who I am and certainly you can’t guess how often and how much I think of you.

As I write this, I have no idea whether you will ever read these words. I don’t know if I’ll ever see you again and if so, what you will think of me. Maybe you’ll be afraid of me? Maybe it will be in many years from now and you will hate me for not being a part of your life? Maybe that will never happen, and these words will remain unread by you forever. Maybe (but I doubt it) you will grow up strong and happy and never worry about the fact that you were denied a father, or wonder or care who I was.

The most important thing I want to say right now is that I love you. I miss you terribly, and I have missed you every day since the day, on the 18 January 2012, when you were taken out of my life.

But more than just missing you and loving you, I want what is best for you. If I believed that meant leaving you alone (not writing any letters and not fighting in the courts to see you) that is what I would do. But after everything that has happened over the past five years, I can’t believe that is true. I think you need me in your life, now more than ever. This is why I will keep trying to see you again.

The last time you saw me, you didn’t seem to recognise who I was. You pointed your finger and me and said ‘bad man’, because that is what you had been told to say. I want you to know that I am not a bad man. I am a man (with some bad bits, and some good bits, like all other men in the world), but I have never tried to harm you and I never will.

I’m going off now in a little while in order to attend a meeting with some people who I hope will try to help bring me back into your life. After all the meetings with all the different people, I can’t tell you that I am very hopeful. But doing my best for you means that I have to try everything possible.

Hope to see you soon.

Love,

Dad

 Category: Dear Daniel

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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:

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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