Introduction to Modern Economic Growth where Lj (S) now refers to the total employment of workers with S years of schooling in country j A series for Kj can be constructed from Summers-Heston dataset using investment data and the perpetual invented method In particular, recall that, with exponential depreciation, the stock of physical capital evolves according to Kj (t + 1) = (1 − δ) Kj (t) + Ij (t) , where Ij (t) is the level of investment in country j at time j Let us assume, following Hall and Jones that δ = 0.06 With a complete series for Ij (t), this equation can be used to calculate the stock of physical capital at any point in time However, the Summers-Heston dataset does not contain investment information before the 1960s This equation can still be used by assuming that each country’s investment was growing at the same rate before the sample in order to compute the initial capital stock Using this assumption, Hall and Jones calculate the physical capital stock for each country in the year 1985 We the same here for various years Finally, with the same arguments as before, we choose a value of 2/3 for α Given series for Hj and Kj and a value for α, we can construct “predicted” incomes at a point in time using the following equation 1/3 Yˆj = Kj (AU S Hj )2/3 for each country j, where AUS is the labor-augmenting technology level of the United States, computed so that this equation fits the United States perfectly, i.e., YU S = 1/3 KU S (AUS HU S )2/3 Throughout, time indices are dropped In the Hall and Jones exercise, all values refer to 1985 Once a series for Yˆj has been constructed, it can be compared to the actual output series The gap between the two series represents the contribution of technology Alternatively, we could explicitly back out country-specific technology terms (relative to the United States) as ả3/2 ả1/2 ả KU S HUS Yj Aj = AU S YUS Kj Hj Figures 3.3-3.4 show the results of these exercises for 1980, 1990 and 2000 The following features are noteworthy: 137