Economic Growth. Spring 2016. Christian Groth

Afterthoughts (follow-ups on lectures). Chronological.

12/2   1. The slides from today's lecture are here.

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!!

3. 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.

4. 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.

27/2  Remark concerning calculations based on the CES production function. Departing from the CES formula (2.35) in Lecture Notes, calculations of marginal productivities and similar are slightly simplified if one starts from the transformation Y^β =A^β[αK^β+(1-α)L^β].

16/3
    LN Ch. 7, p. 119, eq. (7.2):  From the point of view of empirical realism, the parameter inequality "ε ≤ 1" should definitely be added.

19/3    In the first part of yesterday's lecture, where the macro story of the Romer-Jones model was presented (Jones' Section 5.1), I listed the four basic assumptions, numbering them (1), (2), (3), and (4). I have two comments:
    1.  Eq. (2) was written in the general form, Y = C + K_dot + delta*K, not as K_dot = s_K*Y - delta*K where s_K is as in Jones p. 100. Why?
    The reason is that most of the results of Section 5.1 do not depend on a given investment rate (out of manufacturing production). Instead they follow from the assumption of balanced growth and will also hold if the consumption-saving decisions by households are modeled as in a Ramsey model or a Blanchard OLG model or whatever. Indeed, balanced growth implies that the investment rate (out of manufacturing production) is constant. This is because balanced growth  in the present context implies g_Y = g_K = (Y - C)/K - delta = constant = ((Y - C)/Y)*Y/K - delta, and since Y/K is constant in balanced growth, the investment rate, (Y - C)/Y, which we may denote s_K as in Jones, must be constant as well. To determine a specific value for this investment rate, we need a theory of households' consumption-saving decisions. 
    Not until p. 110 do the results depend on a specific value of the investment rate. But the specific formula for the "scale effect on levels" at p. 110 relies on a given value of s_K which is why Jones here speak of a "Solow framework".  
    2. Eq. (4) was written without a duplication externality, that is, with lambda = 1. This is because I find it preferable to first finish the simple case lambda = 1. After that is done one can easily show how some of the results are slightly modified when lambda is less than one.
    Unfortunately, in the finishing of Section 5.1 I forgot to consider lambda less than one. But the modified results are evident from the textbook's (5.5) - (5.7).

1/4    The last step in the national income accounting in the Romer-Jones model of Ch.5.1-2 in the textbook is:

GNI = wL_Y + (r+delta)*K + A*π + L_A = (1 - α)*Y + α^2*Y + (1 - α)*α*Y + w*L_A = Y + w*L_A .

Compare with

GNP = aggregate value added = Y - p*X + p*X + P_A*A_dot = Y + P_A*A_dot = Y + P_A*theta_bar*L_A = Y + w*L_A,

where X = A*x, and the last equality comes from the fact that in an equilibrium with L_A > 0, the value of the MP of labor in R&D must equal the real wage. So GNI = GNP in our closed economy, as it should be. Conclusion: Our accounting is consistent.   

8/4    Follow-up on today's lecture:

1. When considering the profit, π_i, of the monopolist associated with the i'th innovation, to begin with I also subtracted the fixed cost (the opportunity cost of staying in Sector 2) in order to indicate the pure profit. This fixed cost does not affect the choice of the profit maximizing price. In later derivations and formulas concerning π (for instance of (5.30)), it is π in the meaning as gross accounting profit (i.e., the profit ignoring the fixed interest cost) that is considered.

6/5    Follow-up on today's lecture:
As announced in advance, in the exposition of the model of a learning emerging economy (Jones & V., Ch. 6.1-2), rather than using the questionable (6.4), I followed an approach more in line with the life-cycle perspective on human capital described in Lecture Note 9. In the context of the emerging economy the key assumptions are:

a) Average human capital is h = h(u), h'(u) > 0, where u = average number of years in school of the labor force, and where we have ignored that also the level of A while in school may matter for h. (We also ignore that a more adequate approach when studying technology adoption probably is to distinguish between at least two categories of labor, skilled and unskilled labor.)

b) The upper limit, h, of integration in Jones' (6.1) is replaced by h-tilde, which in verbal terms is defined as the current amount of input varieties that the economy is able to use, and which mathematically is defined by h-tilde = (h/eta(A))*A. Here, eta(A) is the level of average human capital required to fully "master" (absorb) the frontier technology level, A, where eta'(A) > 0 but such that eta(A) has an upper limit for A going to infinity. We may think of this upper limit, denoted h_hat, as indicating that a substantial segment of the labor force has a level of education corresponding to a Master of Science degree. We thus imagine that if actual h =  h_hat, then the country is capable of fully absorbing the frontier technology level, A, whatever its current level. Now, for a typical emerging economy we have actual h < eta(A) so that h/eta(A) measures the fraction (less than one) of A that the country is currently able to use. It is this fraction which indicates the "absorption capacity" of the country, not h-tilde - which I am afraid I wrote on the whiteboard. (The textbook essentially assumes in Chapter 6 that eta(A) = A, which seems a little awkward unless one is willing to regard h as an infinitely expansible variable like knowledge, A.)

20/5    In the original course plan (as of 11/2 2016), point IV.B contained a part named "A simple balanced growth framework with human capital and R&D". LN Ch10 and Exercises V.7 and V.8 were referred to. For lack of time, this stuff had to be removed from syllabus. The stuff was meant to be a follow-up on LN Ch9 in order to show, in a transparent way, how the complementarity between human capital and technology can be incorporated in a growth model, building on equation (9.5) and the "life-cycle approach" to human capital (Example 4, say) in LN Ch9.

After the exam.
Among the questions listed in Discussion Forum in Absalon some were about the relationship between inequality and growth. In this lecture note from 2010 there is a list of references (although not quite up to date). Note for instance the meticulous empirical study from AER 2000 by Forbes (2000) in the list. Another very useful paper is Perotti, J. Ec. Growth, 1996, no. 2. Both are available online from the library, of course. Some papers from the more recent blossoming of the issues are listed here.

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