Economic Growth. Spring 2015. Christian Groth

Afterthoughts (follow-ups on lectures). Chronological.

2/2    1. On the arithmetic growth of life expectancy, look here. Notice the slope in Fig. 1: For every ten years, female life expectancy in the record-holding country increases by two and a half year!!

2. Comment to DA, Figure 1.15, p. 18:
In Levine, R., and D. Renelt (1992), A sensitivity analysis of cross-country growth regressions, American Economic Review, vol. 82, 942-963, the authors find that among over 50 different regressors only the share of investment in GDP, other than initial per capita income, is strongly correlated with growth in income per capita.

3. Comment to DA, Ch. 2, p. 28, on the importance of the nonrival character of "ideas" or "technical knowledge":
Let A denote the "level of technical knowledge" and assume the production function Y = F(K, L, A) has CRS w.r.t. K and L and positive marginal productivities w.r.t. K and L. Average labor productivity is y = Y/L= F(K/L,1, A).  We see that the non-rivalry of technical knowledge implies that labor productivity depends on the total stock of knowledge, not on this stock per worker. In contrast, labor productivity depends on capital per worker, not on the total stock of capital. This is because capital is a rival good.

9/2    1. Lawrence Summers has a clear and interesting review of Piketty's Capital in the Twenty-First Century, Harvard University Press, 2014. Apropos our discussion today, on page 94 Summers questions Piketty's assumption of an elasticity of substitution between capital and labor above 1. Response from Piketty concerning the elasticity of factor substitution.

2.    The stuff presented in the lecture about the elasticity of substitution between capital and labor is contained in Short Note 1 (excerpt from Chapter 4 of my lecture notes in macroeconomics; for those interested the whole chapter is here).

16/2    The time-series study I referred to is Attfield and Temple (2010) in LN 1. For data of relevance for skill-biased technical change, see textbook p. 498 ff. and Jones and Romer (2010). See also Ch. 18 and 20 in Handbook of Economic Growth, vol. 1B, 2005, online University Library). Here is Jovanovic and Rousseau's graph of the estimated skill-premium in USA since 1870 (from the same handbook, vol. 1B, p. 1205).

23/2    1. After today's lecture a question was raised concerning "growth accounting". This reminded me that I should probably have emphasized more what is written at the middle of p. 78 in LN 5:

"As a residual it [the Solow residual] may reflect the contribution of many things, some wanted (current technical innovation in a broad sense including organizational improvement), others unwanted (such as varying capacity utilization, omitted inputs, measurement errors, and aggregation bias)."

The point is that year-to-year changes in the Solow residual are not of much interest in a growth context because they may reflect business cycle fluctuations (varying capacity utilization due to short-run fluctuations in aggregate demand, labor hoarding in an economic downturn, etc.). To get something of possible interest from a productivity point of view, we should consider the time path of the Solow residual over at least a decade, preferably several decades. 

2. In today's lecture, concerning "levels accounting", I defined "nabouring countries" wrongly. The "levels accounting", as described in DA, p. 99, does not use the size of Y/L, but the size of the physical-human capital ratio, K/H, in the ranking of the countries.

2/3     On the colonial origins of comparative development: See the empirical criticism by David Albouy, AER, 2012, vol. 102 (6), 3059-3076, and the response by Acemoglu, Johnson, and Robinson, AER, 2012, vol. 102 (6), 3077-3110.

12/3    In the lecture Monday this week, in connection with speed of convergence (SOC) and halflife of the initial distance, I suggested a very imprecise numerical estimate of the halflife, when SOC is 0.08 per year. Based on my (bad) memory, I mentioned a halflife in the neighborhood of 30 years, but that is what you get, when SOC is as small as 0.023. If SOC = 0.08 per year, halflife is 8.6 years.

    Some authors, for instance Barro and Sala-i-Martin (2004), come up with a SOC empirically as well as theoretically close to 0.02, because they choose a value for the capital income share as high as 0.75. This may not be unreasonable if a substantial part of labor income is considered to be a return to human capital. Anyway, the estimates in the empirical literature are more or less uniformly distributed in the interval (0.02, 0.09). For more about these things, including the relevant formulas, see Lecture Note 6, p. 92-93.

19/3     In the lecture Monday this week, in connection with the problem of Optimal Capital Accumulation (DA, Ch. 8.3, LN 8, Section 8.3), we discussed the importance of the inequality

(*)    rho - n > (1-theta)*g, 

when the time horizon in the problem is infinite, cf. p. 116. I said that the intuitive economic meaning of the inequality is that the effective utility discount rate exceeds the maximum sustainable growth rate in "utility". This interpretation of the right-hand side of the inequality (*) may from a mathematical point of view appear strange, since theta can be any positive number. The tricky case is theta > 1 because in this case, the right-hand side of the inequality (*) is negative, and similar for instantaneous utility:

(**)    c^(1-theta)/(1-theta) < 0 for all c > 0, when theta > 1.

Here, a rise in c makes c^(1-theta) smaller. The preference relation we want our utility index to express is that a rise in c is something preferred. This is exactly what the division by 1 - theta in (**) ensures. So growth in utility here means decline in the absolute value of c^(1-theta)/(1-theta), that is, essentially, decline in c^(1-theta) which means growth in c when theta > 1. The maximum sustainable growth rate of c is the exogenous technology growth rate, g. And the maximum rate of decline in c^(1-theta) is therefore (1-theta)*g (use the rule for the growth rate of a power function in continuous time), see my Lecture Notes in Macroeconomics, Ch. 9, p. 377, there is a link to this at the Ec. Growth website under Lectures 9/3-15).

From the mathematical point of view, the issue is treated in my Lecture Notes in Macroeconomics, Ch. 10, p. 422.

9/5    A follow-up on lecture 4/5: ".... a lag in effect of roughly 20 years is found between appearance of research in the academic community and its effect on productivity in the form of knowledge absorbed by an industry." From J.D. Adams, Fundamental stocks of knowledge and productivity growth, J. of Political Economy, vol. 98, no. 4, 673-702, 1990.

10/5    Several of the questions raised in connection with homework, cited in Absalon, are about the relationship between inequality and growth. At the end of this lecture note from 2010 there is a list of references. There is a meticulous empirical study in AER 2000 by Forbes (2000) in the list. Another important reference is Perotti, J. Ec. Growth, 1996, no. 2. Both are available online from the library, of course.