Macroeconomic data are typically collected at a specific observation frequency (e.g. quarters, years). For many questions, the evolution of macroeconomic data over time can be analyzed by considering growth rates. The growth rate between two points in time, t 1 and t
2 , of, e. g., real gross domestic product (GDP) Y, is defined as: g Y,t 1,t 2 = Y t 1Y t 2 −Y t 1. Annual data. For data collected at annual frequency, the annual growth rate is therefore given by: g Y,t−1,t = Y t−1Y t−Y t−1 .Considering now T+1 consecutive years t=0,1,…,T, the average annual growth rate over the period 0 to T can be derived from the following arguments: (i) Starting with the growth rate for year t=1, definition (1) implies: g Y,0,1 = Y 0Y 1 −Y 0 ⇔Y 1 =(1+g Y,0,1 )⋅Y 0
(ii) A similar calculation for the annual growth rate for year t=2 and inserting Y 1 from the first step yields: Y 2=(1+g Y,1,2 )⋅Y 1 =(1+g Y,1,2)⋅(1+gY,0,1 )⋅Y
0Repeated substitution leads to: Y
T =(1+g
Y,T−1,T )⋅…⋅(1+g
Y,1,2 )⋅(1+g
Y,0,1 )⋅Y
0 In the multiple choice part of the exam you will not be required to substantiate your answers by planations.