Economic Growth. Spring 2013. Christian Groth
Afterthoughts (follow-ups on lectures). Chronological.
5/2 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!!
Concerning some technical matters, in a couple of footnotes in Lecture Note 2 there is a reference to my Lecture Notes in Macroeconomics, which those who might be interested can find here.
12/2 In today's lecture, when I commented on the elasticity of factor substitution (DA, p. 52, 54), in line with Acemoglu on these pages, I ignored technical progress. If we add Harrod-neutral technical progress to the story, we should replace k in my formulas by k_tilde = K/(AL) and w by w_tilde*A. To stay in Kaldor's world, we now assume that after the industrial revolution, ignoring business cycles, K/L roughly tends to grow at the same rate as A so that k_tilde tends to be roughly constant. Thereby, the labor income share tends to be constant - and so the analysis is in accordance with the full set of Kaldorian stylized facts.19/2 Some of my growth rates in discrete time were written wrongly on the white board. The growth rate of K from the beginning of period t-1 to the beginning of period t should be written (K(t) - K(t-1))/K(t-1), of course, not (K(t) - K(t-1))/K(t).
There are here some corrections/additions to LN 4.27/2 As to the lecture yesterday, at least two things were in need of clarification.
1. I expressed my surprise that in Acemoglu, p. 83, eq. (3.14), there is not only a country index, i, but also a time index, t, on the vector X, representing potential growth determinants. Given the interpretation in LN 5, p. 14, line 3 from below (see errata), X should have no time index, t. In view of what Acemoglu writes at the top of his p. 85, however, eq. (3.14) should be seen as referring to a series of t's as in a panel data analysis.
2. Concerning the importance of the nonrival character of "ideas" or "technical knowledge", let me try again. Suppose Y = F(K, AL) is a CRS production function with positive marginal productivities. Consider (average) labor productivity: y = Y/L= F(K/L, A). We see that the nonrivalry 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.
3. 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.
4. Growth accounting for the very long run.5/3 1. In today's presentation of Kremer's extended model, I used the same notation as in Acemoglu, §4.2, and Exercise III.3. Kremer's notation is somewhat different. More importantly, Kremer has an additional parameter, namely an exponent, psi, on population size in the equation for the time derivative of the stock of ideas. In my presentation I considered the case psi = 1. Kremer estimates that psi may exceed one. If so, the effect is only to fortify the acceleration in knowledge creation.
2. Here is a summary concerning institutions (rules of the game in society and rules about how to change rules of the game): They are of key importance for economic performance because they affect incentives, room to manoeuvre, feeling of justice, social trust, and scope for cooperation and exchange.19/3 1. In today's lecture, when comparing the annual per capita growth rate, g', under MP with that, g, under BAU, I unfortunately wrote g = g' - 0.01 on the whiteboard. Sorry, the right thing is g = g' - 0.001. The other number is much too large.
2. In the last part of the lecture we discussed “Arrow's argument” in the brief article, “Global Climate Change: A Challenge to Policy”, Economists' Voice, June 2007. On page 4 of the article we read that, given the described scenario from the Stern Review, “with this degree of uncertainty, the loss should be equivalent to a certain loss of about 20%.” The calculation behind this number is the following:We look for the certainty-equivalent loss, x, satisfying u((1-x)c) = Eu((1-X)c), where we know that the 5th and 95th percentiles in the loss density distribution are 0.03 and 0.34, respectively, and 0.138 is the mean in the distribution. Moreover, u(c) is CRRA with eta = 2. Assuming Eu((1-X)c) is roughly approximated by 0.5*u((1-0.03)c) + 0.5*u((1-0.34)c), the approximative solution is x = 0.21, that is “about 20%”.
The remaining question is: Is the applied rough approximation valid? That is, is there a symmetric density function such that by splitting the total probability mass into two halfs placed on the 5th and 95th percentiles, respectively, we obtain, in the present context, a reasonable approximation to the expected utility, Eu((1-X)c)?
3/4 In yesterday's lecture on human capital the question was raised why it is useful to have a measure, h, of human capital such that the quality function becomes linear, i.e., such that the quality (or efficiency), q, of the human capital is proportional to the stock of human capital, q = a*h, where a is a positive constant. The main reason is that an expedient variable representing human capital in a model requires that the analyst can decompose the real wage per work hour of a given person multiplicatively into two factors, the real wage per unit of human capital per work hour and the stock of human capital, h. That is, an expedient human capital concept requires that we can write:
I myself do not know any good answer to this and I therefore call for one.
3. The reference in LN 7 to the contributions by John Roemer is somewhat imprecise. Here is a link to one of the relevant papers: Roemer, J., 2011, The ethics of intertemporal distribution in a warming planet, Environmental and Resource Economics, vol. 48, 363-390.
(1) w = wh*a*h = wh*h,
choosing measurement units such that the constant a equals 1. Example: Suppose the production function is Y = F(K, h*L, t). Then, under perfect competition, w = dY/dL = F'2 (K, h*L, t)*h = wh*h.
Now let us introduce an additional factor of potential importance for the real wage, the technology level, A. Suppose the production function is
(2) Y = F(K, E*L) = F(K, A*h*L),
where E = A*h is the efficiency of labor, and L is the number of work hours per year. In this setup we have, under perfect competition,
(3) w = dY/dL = F'2 (K, E*L)*E = wE*E = wE*A*h.
I have a fealing that instead of this correct expression, I wrote w = wh*A*h on the whiteboard which is incorrect. The truth is that with the introduction of the additional factor, the technology level, A, as in (2), (1) remains valid, while we now have an additional multiplicative decomposition,
(4) wh = wE*A.
Work efficiency now is E and not h.
Additional remark. Note that the Harrod-neutrality assumed in (2) is an assumption about how new technical knowledge turns out to manifest itself in a production function. An alternative possibility is that it manifests itself for instance in a Solow-neutral way, i.e., Y = F(A*K, h*L), or some other way. This is an important empirical question. It is different with h because h is embodied in the worker and therefore can not conceptually be separated from the worker. So if someone came and said that the hypothesis Y = F(h*K, L, t) is supported empirically while the hypothesis that Y = F(K, h*L, t) is rejected, we would answer that there must be something wrong with the applied measure of h.