Economic Growth. Spring 2010

Comments on different issues. Chronological.

17/2    A question was raised concerning the interpretation of first-order condition (7.9) in my Chapter 7. Here is a more elaborate explanation.

24/2    We consider the Ramsey model extended with heterogeneity wrt. initial financial assets ownership. All households are assumed to have the preferences. As explained in LN 7, p. 5, unfortunately this extended Ramsey model gives no definite answer as to whether the degree of inequality wrt. ownership of financial assets across the households tends to increase or decrease as the economy converges towards its aggregate steady state.

9/3    A follow-up on two issues in today's lecture:
1) First, the assumption that Rho-n > (1-Theta)*Gamma was named (A2). Unfortunately, the way I derived that (A2) is needed for the utility integral to be bounded, is only valid for Theta < 1. Indeed, the way I defined z on the whiteboard was not convenient. But from that z we can define Z = (1-Theta)*z and consider the integral of Z(t) from t = 0 to t = + infinity. We then find that for that integral to be bounded, (A2) is needed, whether Theta < 1 or Theta >1.
In case Theta = 1, i.e., u(c) = log c, we consider the integral of z = (log c(t))*e^(-(Rho-n)*t) from t = 0 to t = + infinity and use that c(t) = c(0)*e^Gamma*t so that log c(t) = log c(0) + Gamma*t. This integral will be bounded (or "converge" as mathematicians say) as soon as the exponent to t in the exponential function is negative, i.e., as soon as Rho-n > 0. Since (1-Theta)*Gamma = 0 when Theta = 1, the necessity of (A2) is confirmed also in this case.

2)  Concerning Lecture Note 8 a question was raised whether the formula for the market value of the firm on p. 2 took interest costs properly into account. My answer is yes in the sense that the discount factor applied in the formula is based on the interest rate in the market for loans. This is the interest rate (the opportunity cost) at which the owners of the firm could alternatively have placed their financial wealth.
I guess the student's question was motivated by the fact that when writing the firm's problem as it is written on p. 2, it is not specified how the firm is financed. This is legitimate in the present context where problems associated with tax distortions, uncertainty, asymmetric information, and risk of bankruptcy are ignored. Then one can appeal to the Modigliani-Miller Theorem which says that under these conditions, the firm's production and capital investment decision can be separated from its financing decision. Those who are interested, may here read the first part of Appendix A to Chapter 11, which is a text used in another course (Advanced Macroeconomics 2).  

15/3    This is a late additional perspective on Problem 3 in Homework 1, where we considered the difference between a closed-economy-Solow model and what fully integrated international capital markets imply. In the paper "When does domestic saving matter for growth" by Aghion, Comin, and Howitt (NBER Working Papers #12275, May 2006), the authors summarize their theoretical and empirical study this way:

Can a country grow faster by saving more? We address this question both theoretically and empirically. In our model, growth results from innovations that allow local sectors to catch up with the frontier technology. In relatively poor countries, catching up with the frontier requires the involvement of a foreign investor, who is familiar with the frontier technology, together with effort on the part of a local bank, who can directly monitor local projects to which the technology must be adapted. In such a country, local saving matters for innovation, and therefore growth, because it allows the domestic bank to cofinance projects and thus to attract foreign investment. But in countries close to the frontier, local firms are familiar with the frontier technology, and therefore do not need to attract foreign investment to undertake an innovation project, so local saving does not matter for growth. In our empirical exploration we show that lagged savings is significantly associated with productivity growth for poor but not for rich countries. This effect operates entirely through TFP rather than through capital accumulation. Further, we show that savings is significantly associated with higher levels of FDI inflows and equipment imports and that the effect that these have on growth is significantly larger for poor countries than rich.

17/3    In Lecture Note 9 you see that there are different approaches to the calculation of the per capita growth rate under balanced growth in a given theoretical framework. Which approach to use depends on the information you have as a basis for the calculation. In some cases you need information about households' saving behavior, in other cases you don't.
    A second point (after having received some questions): I want to emphasize that it is only in the learning-by-doing models (the sections 1 and 7 of LN 9) that the possibility of Lambda < 0 (the "fishing out" case) should be allowed for. In the learning-by-investing models (the sections 2 - 4 of LN 9) only a non-negative Lambda makes sense.
    A third point: As to terminology, when we talk about just "growth" without a prefix, it should be interpreted as "per capita growth". This is in line with the fact that by "endogenous growth theory" is meant theory about mechanisms generating growth in, say, y = Y/L og c = C/L, not just in Y.

24/3    In the lecture today I claimed that in reduced-form AK models, where policy can affect the long-run growth rate, there often is a trade-off between obtaining higher growth and obtaining higher welfare. As an example, let S.P. in LN 10, p. 9, choose G/Y > 1-Alpha. Then a higher sustainable growth rate, Gamma_SP, is obtained than that in equation (26). Why, then, does S.P. not find such a high G/Y optimal? Because it will cost too much in terms of forgone current utility, since the high initial G and high initial gross capital investment needed to generate such a high growth rate would imply very low initial private consumption. 

26/3    A follow-up concerning Problem 3.a) in Homework 2: In the discussion yesterday I emphasized that the statement does indeed make sense because standard neoclassical growth theory (the Solow model or the Ramsey model as represented in B & S, Ch. 2) implies such a prediction when K/(TL) is initially far below the steady state level, due to the war. This kind of explanation of an initially high, but eventually "back at normal", per capita growth rate is called a transitional dynamics explanation. And in the present case the transitional dynamics are due to the falling marginal productivity of capital as the effective capital intensity increases.
    The catching-up (technology transfer) hypothesis fits well as an additional or alternative explanation. My point was just that this hypothesis is not part of standard neoclassical growth theory (the Solow model or the Ramsey model).

7/4    In the last five minutes of the lecture today, on the basis of my hand-written notes I tried to give a summary on the AK model family (B & S, Chapter 4) at the whiteboard. Like some of you sometimes have difficulties reading my writing on the whiteboard, I could not even read my own hand-written paper notes.
    I wanted to give a list of necessary and sufficient conditions for fully endogenous growth in a one-sector framework. The condition marked by (*) should have been the equation Y=A(.)*K -->A_bar*K, which is clearly a technology condition in addition to the condition that I denoted (**). In words the correct condition (*) says that there are constant returns wrt. producible inputs (for instance K and G), at least asymptotically.

18/5    In investment theory a key notion behind the hypothesis of convex adjustment costs is that "haste is waste". This notion also applies to lecturing. In the lecture 12th of May, as I rushed through the derivation of the break-even utility discount rate based on Arrow's argument (that with risk aversion uncertain losses should be evaluated as being equivalent to a single loss greater than the expected loss), I forgot that the initial consumption level under the "act now" scenario is only 0.99*c0, where c0 is initial consumption in the "business as usual" scenario. This lower initial consumption reflects the investment made from now to reduce global warming and its accompanying economic damages in the future. The derivation is correctly presented in Lecture Note 20, p. 5.

24/5    It was decided that not only § 4 but also § 3 of Kremer (1993) is cursory. The reason is that Kremer's attempt at setting up a complete dynamic model in Section III is not successful. The associated phase diagram in Figure IV of the article fits well the post-Mathusian epoch with permanently rising y. For small p (i.e., small population) we would expect the dynamics to fit the Mathusian epoch with rising population but stationary y. But in the phase diagram, for small p either is y rising forever or temporarily falling and then rising permanently. This is not a satisfactory picture of the Malthusian epoch.