Bratislava in the Rain

The seamless blending of a McCafe into Soviet-era blocks of substandard housing
Is not enough to snuff it out;
Nor the hard bucket seats of a Monday evening tram that blinks feebly at the death of
summer
Cannot contain it;
Nor even as the light is further lost in mist and drizzle and encroaching night,
Can the gaudy glare of sex shops and casinos obscure its finer nature;
No, not even Bratislava in the rain has the power to drown out the Flame of Human
Joy
Which bursts to life a million ways a second.
Here, in the bright blue eyes of a woman, early sixties,
Who meets by chance her niece, just back from Vienna.
There, as a determined foot of six years and as many inches
Plants itself with purpose upon the puddles,
Transforming broken footpaths into a water theme park.
And once again, as the tram rattles off behind me,
In the fingers of young lovers parting for the night,
Which etch in condensation a symbol of their breathless love
upon the glass.

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.

×

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

×