Summary

Source code (Mathematica)

Refer to the File:Okuns_law_quarterly_differences.svg to see the data set used.

n = Length[unempch];
sol = FindFit[data, \[Alpha] + \[Beta] x, {\[Alpha], \[Beta]}, x]
ts = Quantile[StudentTDistribution[n - 2], 0.975];
\[Alpha]h = \[Alpha] /. sol;
\[Beta]h = \[Beta] /. sol;
xm = Mean[unempch];
sx2 = Mean[(unempch - xm)^2];
s\[Epsilon]2 = 1/(n - 2) Total[(gdpch - \[Alpha]h - \[Beta]h unempch)^2];
s\[Beta] = Sqrt[1/n s\[Epsilon]2/sx2]; 
s\[Alpha] = s\[Beta] Sqrt[sx2 + xm^2];
sp = Sqrt[1/n s\[Epsilon]2 (1 + (x - xm)^2/sx2)];

Show[
  ListPlot[{{{-10, 0}}, {{-10, 0}}, data}, PlotMarkers->{Automatic, Small}, PlotStyle->Hue[0.6]],
  Plot[ \[Alpha]h + \[Beta]h x, {x, -1.1, 1.8}, PlotStyle->{GrayLevel[0], Thick}],
  Plot[ {\[Alpha]h + \[Beta]h x - ts sp, \[Alpha]h + \[Beta]h x + ts sp}, {x, -1.1, 1.8}, 
    Filling -> {1 -> {2}}, PlotStyle -> {Blue, Blue}],
  PlotRange -> {{-1.3, 2}, {-3, 5}},
  Axes -> False,
  Frame -> True,
  FrameLabel -> {"Quarterly change in the unemployment rate (\[CapitalDelta]%)", 
                 "Quarterly change in GDP (\[CapitalDelta]%)"},
  FrameStyle -> Directive[FontFamily -> "Arial"]
]

Licensing

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