Question 2 (3 points in total) "Okun's Law" is an empirical rule-of-thumb describing the quantitative impact of a change in the unemployment rate on short-run aggregate output (see ch. 3.6 in the textbook for more details). Algebraically, this can be expressed as the following linear equation: Y - Y 100 X Y = B(u - u) where the LHS is the output gap - the percentage deviation between an economy's actual GDP and its maximum potential GDP - and the RHS is cyclical unemployment - the difference be- tween an economy's actual unemployment rate and its natural counterpart. The textbook definition claims that S = 2. We want to investigate this relationship for the post- WW2 era, as well as for two sub-samples. In doing so, download the following variables fromthe FRED database and make sure they are all appropriately converted to annual frequency. 8 Real GDP: code GDPCA; Potential real GDP: code GDPPOT; Unemployment rate: code UN- RATE; Natural rate of unemployment: code NROUST. a) Draw a scatter plot of the two variables for the whole sample (1949 - 2019). Put cyclical unemployment on the x-axis and the output gap on the y-axis. Report the OLS regres- sion line equation (line of best fit) by setting the intercept to zero, together with its R2 (coefficient of determination). Compare your findings to the textbook definition. b) Repeat the above analysis for the sub-sample (1949 - 1985) and then for the sub-sample (1986 - 2019). How does the linear coefficient and fit change? What could account for these differences? What does this mean for policymakers