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

It is then straightforward to show:

which implies that if γ > 1, (resp. γ < 1), then an increase in η raises (resp. lowers)
σ(c + a) and, thus, the stable speeds of adjustment, consistent with the numerical results
in Tables 1a and 1b.

3. Small Open Economy Equilibrium

In this section of the paper we extend the model and its equilibrium properties to the
small open economy context.¹⁹ While we assume that the preference structures in (2.2)-
(2.5) are the same as in the closed economy specihcation, we alter the model in two
important ways. The Hrst modification of the model is to assume that the small open
economy has an upward-sloping supply function of debt. This specification, which is used
by authors such as Bhandari, Haque, and Turnovsky (1990), Fisher (1995), and Fisher
and Terrell (2000), states that open economies, otherwise satisfying the “small country”
assumption, cannot freely borrow or lend at the prevailing world interest rate r*. Instead,
reflecting the imperfect substitutability of domestic and foreign assets, the interest rate
on domestic assets, denoted by rⁿ(n), rises as the national indebtedness of the country
increases. Letting the variable n denote the stock of international debt, the domestic
interest rate relationship is given as:

rⁿ(n) = r* + α (n),     α' > 0,     oι" > 0,                    (3.1)

where the convex function α (n) can be considered a country-specific “cost” or “risk
premium.”²⁰ The reason why we incorporate (3.1) into our durable consumption model is

¹⁹In the open economy durable consumption goods are traded at a unitary price.

²⁰For convenience, we assume throughout this section of the paper that the small open economy is always
a net debtor, i.e., n > 0, ∀t ≥ 0. An alternative specification of (3.1) would scale the level of indebtedness
by the ability to pay, measured, for example, by the level of output.

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