• Bonne vacances d’ete (ma 10ieme lettre a toi)

    Cher Daniel, Bonjour mon cher fils! J’espere que tu profites bien des vacances (il a quand meme fait beau ce dernier temps, bien que un peu frais pour la saison). Moi je dois encore travailler, mais ta soeur Daphne est deja parti en vacances avec ses grand-parents (J’etais un jour a la plage au Pays-Bas,

  • Cher Daniel, ma neuvieme lettre a toi

    Mon cher fils, Tout d’abord un grand bonjour a toi de ma part. Ca fait un bout de temps que je ne t’ai plus ecris, c’est vrai. Malrge, j’ai beaucoup pense a toi ce dernier temps, et surtout avec l’arrivee du coronavirus. Tout est devenu si etrange, avec les rues presque vide. Et en quelques

  • Joyeuses fetes, mon cher fils! (Ma 9ieme lettre)

    Cher Daniel, Ça fait un bout de temps que je n’ai plus écrit, c’est vrai. Malgré, j’ai pensé beaucoup à toi ce dernier temps. Des souvenirs me sont revenus, de l’hiver 2010/2011, juste avant ta naissance. Moi et ta maman ont été très excité de te voir. Il neigeait beaucoup cet hiver-là. Avec une voiture

  • Cher Daniel, ma huitieme lettre a toi

    Cher Daniel, J’ai decide quand meme de t’ecrire en français au lieu de mes lettres habituelles en anglais, car entretemps j’estime que ce sera moins probable que tu apprendra l’anglais dans l’avenir proche. Comme d’habitude je veux te dire a tel point je t’aime. Je pense souvent a toi, bien que ce dernier temps les

  • My seventh letter to you

    Dear Daniel, It has been a while since I’ve written to you, but that is not to say I have stopped thinking about you. Oh, not at all. On the contrary, you are in my thoughts every day. I hope now that the evenings are getting brighter you will have a chance to play outside

  • 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

  • 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

  • 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:

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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