Advanced Macroeconomics
Fall 2014

Follow-ups, comments/corrections on different issues

4/9    In the list of possible supplementary textbooks I have forgotten Ben J. Heijdra: Foundations of Modern Macroeconomics, OUP 2009, http://www.heijdra.org/fomm2.htm. This was unfortunate since that book is an attempt to bridge the gap between bachelor course texts and PhD course texts.
    Regarding short- and medium-run theory I am a fan of Blanchard: Macroeconomics. Although it is clearly a bachelor course text, it is extremely informative and precise.

17/9    Concerning math, here is a recommended manual: K. Sydsæter, A. Strøm and P. Berck, Economists' Mathematical Manual, 4th ed. (or later), Springer Verlag, 2004, or later.
    In today's lecture you probably noticed that when considering equation (6.23), I suddenly had my doubts about what would be the interpretation if the equality sign were replaced by a weak inequality, saying that the left-hand side is larger than or equal to the right-hand side. But there was no reason for that doubt. Indeed, allowing the inequality ">" means allowing for the possibility that a government that initially has positive net debt, after some time begins having positive financial net wealth and accumulates more and more of this. This follows from the fact that strict inequality in (6.21) is equivalent to strict inequality in (6.22).
    After the lecture there was a question about whether to use the nominal interest rate or the real interest when discounting. The answer is that it depends on what is to be discounted, nominal values or real values. Section 8.1.1 of this note (from the course Ec. Growth, Spring 2014) may clarify this.

22/10    Two things after today's lecture:

a) As to p. 484 (in Ch. 12) about how, in the Blanchard OLG model, the rate of return in the long run depends on the parameters, note that the sign of the partial derivatives can simply be found graphically, that is, by curve shifting in a diagram like that on p. 471.

b) As to Ch. 13.1 I had trouble understanding my own text on p. 516. The logic at the middle of that page is correct, but unfortunately not well explained. Here are some additional sentences to make it clear:

The point is that before one writes down the weak inequality at the middle of p. 516 (between (13.6) and (13.7)), one can write:

(*)    H_t + B_t = the RHS of the weak inequality at the middle of p. 516 + the integral on the RHS of (13.6).

The RHS of the weak inequality at the middle of p. 516 (i.e., the first term on the RHS of (*) ) is seen to be given (i.e., independent of the debt B_t and independent of the time profile of the lump-tum tax). Now, if we consider a larger B_t, then the RHS of (13.5) is larger, thus requiring that the integrand in (13.5) "more often" than before is positive. This affects the integral on the RHS of (13.6) positively if and only if beta > 0. Thereby the RHS of (*) is positively affected by the larger B_t if and only if beta > 0. So is then the LHS of (*). This is what was to be shown, namely that a larger B_t affects H_t + B_t positively.

29/10     After today's lecture there was a question about how Tobin's q-theory of investment works in a general equilibrium model of a closed economy. There are som brief remarks about it at p. 586 in Ch. 14. For those interested, here is a reference: Groth and Madsen (2014). The model ends up in three coupled differential equations because, in addition to Tobin's q, sluggish real wage adjustment in the form of a real-wage Phillips curve is assumed. Abel and Blanchard (Econometrica 1983)  introduce Tobin's q into a standard Ramsey framework with perfect competition and price flexibility in all markets. Then the model ends up as a two-dimensional dynamic system.     

17/12    In the break of today's lecture there was a good question about why on p. 1053 and 1085 U_tilde is introduced. I agree it is clumsy and that there is a better way to proceed as described here.