Advanced Macroeconomics
Fall 2016
Follow-ups and comments on different issues
20/9 At p. 20 in Ch. 2 of Lecture Notes (Ch. 1 - 2) (about a refresher of definitions related to technology) is stated the definition of a neoclassical two-factor production function that I wrote on the whiteboard today in the lecture. Both (a) and point (b) need be satisfied. If we know that an arbitrary production function satisfies (a) and has CRS, then it necessarily satisfies (b) as well and is thus neoclassical. (The proof is in Appendix B to the chapter.
11/10 In the lecture today I
postponed an attempt to clarify why at p. 515 (Ch. 12) the sign of the effect on
k_tilde* of a rise in the retirement rate, lambda, is ambiguous. An explanation
is given at p. 516. See also p. 513.
Concerning Ch. 13, p.
554, Figure 13.2: Today, I drew a similar figure on the whiteboard. I said that
if B_0 > 0, then the C_dot = 0 curve intersects the C axis at a
positive ordinate because the numerator in (13.20) will be positive. I forgot,
however, that the Inada conditions are assumed, whereby the denominator in
(13.20) for K = 0 equals plus infinity. Hence, the Figure 13.2 in the
text is correct.
6/12
The following remark should be deleted:
Still concerning Ch. 13, I was in doubt
whether §13.5 is mandatory or cursory reading. As stated in the
course plan, it is mandatory.
NB! An example of Danish empirics
of relevance for the controversy about Ricardian Equivalence or
Non-equivalence:
C. T. Kreiner, D. D. Lassen and S.
Leth-Petersen (2016), Liquidity
Constraint Tightness and Consumer Responses to Fiscal Stimulus Policy.
Working Paper.
15/11
The question is about Case (d), p. 861-62 in Ch. 22 of Lecture Notes. In brief the question is: Aren’t Fig. 22.9 and Fig.
22.10 inconsistent?
Answer: Yes, unfortunately they are. The problem is that Fig. 22.10 contains a misleading
feature. It looks as if R immediately after t_0
must equal the new steady-state value. The truth is that we
generally only know that R immediately after t_0 must be higher than the old
steady-state value but lower than the R immediately after t_0 in Fig. 22.7 (Case
(c): unanticipated policy shift).
Concerning Case (d), Fig. 22.9 shows a possible
position of the economy immediately after t_0, namely at the point A. Let the
associated R be denoted R_A. This value happens to be
lower than the new steady-state value and
far lower than R_A in Fig. 22.7 (Case (c)). This is an example where
the time interval (t_0, t_1) is relatively
long and so there is a long time until monetary policy is tightened
and the upward jump in r takes place. Hence, to be consistent with Fig. 22.9,
Fig. 22.10 should show R immediately after t_0 to be
lower than the new steady-state value which it doesn’t.
If instead the time interval (t_0, t_1) is short, the
situation is close to Case (c), where the time interval is nil. The upward jump
in r takes place soon after t_0 and so the weighted average of the expected
future short-term interest rates will be high as seen from immediately after
t_0. Thereby R will immediately after t_0 be high and close to its value in Fig.
22.7, i.e., higher than the new
steady-state value.
18/11 In for instance Ch. 14 and 15.2 it is convenient to
use "implicit differentiation" while in larger equation systems, e.g. Ch. 22,
using "differentials" and "total differentiation" is convenient. If you are not
familiar with these mathematical techniques, Section 2 of this
note
may be useful.
Addition:
21/11: More details
in Sydsæter
and Hammond, Essential Mathematics for
Economic Analysis, 3rd edition, 2008 (online from
the library), pp. 207, 217, 412-13,
417-19, 436.
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