DURABLE CONSUMPTION AS A STATUS GOOD: A STUDY OF NEOCLASSICAL CASES



debt n. Of course, the fact that the long-run stock of debt f is independent of the status
parameter
η does not imply a lack of current account dynamics subsequent to an increase
in η. For example, it is straightforward to show, using the solution for f derived in the
appendix, that the current account, depending on the relative intertemporal dynamics of
durable consumption and output, initially improves (resp. deteriorates) before reaching
a time
t = t*, such that f(t*) = 0. Afterwards, i.e., for t > t*, the current deteriorates
(resp. improves) as the stock of debt returns to its initial and steady-state level, f
o = f,
as t
→ ∞.24

4. Conclusions

In this paper we study the dynamic properties of neoclassical, representative agent models
of the consumer-producer in which status depends on relative consumption. Our extension
is to model in closed and open economy contexts relative consumption as a durable good.
Among our major results, we derive the optimizing equilibria of the closed and open
economies, including their dynamic properties, show that they are all of a fourth order, and
establish that the corresponding steady states in all cases possess the saddlepoint property.
Using a particular speci
hcation of relative consumption preferences, we investigate the
implications of changing the importance of status considerations. Among our results, we
hnd: i) an increase in the degree of status preference in the closed economy with endogenous
work e
ffort raises the long-run levels of durable consumption, its corresponding stock,
employment, and physical capital; and ii) an increase in the status preference parameter
a
ffects the stable speeds of adjustment in the special case of fixed employment, depending
on whether it raises or lowers the intertemporal elasticity of substitution. Finally, the
long-run implications of an increase in status considerations in the small open economy
model are generally similar to those in the closed economy.

24The non-monotonic behavior of the current account reflects the fact that it depends on two stable
eigenvalues. Because
n = no in response to a (permanent) increase in the status parameter η, the solution
of n simpli
fies because in (A15b), Q2 = Q1. From the corresponding expression for n, we can show

rι (t*) = 0


,    ,*     ln(θ2θ1)

t = t = θι θ2

22



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