وضعیت جستجو در اقتصاد کوچک باز

In our modified version of the small open economy Ramsey model, agents have preferences over consumption and status, the latter determined by relative wealth. Contrary to the standard model in which an impatient country asymptotically mortgages all of its capital and labor income, this extension potentially yields interior steady states. This results from the fact that the effective rate of return becomes a function of consumption and net assets. Notably, a permanent increase in government expenditure crowds out long-run consumption more than one-for-one. Similarly, the effects of improvements in productivity on long-run consumption are magnified by relative wealth preferences.

An individual’s utility is usually stated in terms of the absolute levels of economic variables, such as consumption of goods and services, leisure, wealth, etc. This standard specification is intuitively appealing and adequate to study many economic problems. There is evidence, some of which is provided by Easterlin, 1974 and Easterlin, 1995, Clark and Oswald (1996), Oswald (1997), and Frank (1997), to indicate, however, that an individual’s economic well-being depends crucially on his relative position, or status, in society. The idea that individuals are motivated by status considerations is a very old one in economics and can be traced back to thinkers such as Hume (1978) and Veblen (1899). After World War II interest in this idea and its potential policy implications was maintained by authors such as Duesenberry (1949), Scitovsky (1976), Hirsch (1976), Boskin and Sheshinski (1978), Layard (1980), and Frank, 1985a and Frank, 1985b. In the last decade, there are an increasing number of researchers who study the implications of status preference in a dynamic macroeconomic or endogenous growth context. In general, there are two alternative ways in which status is modeled in macroeconomic settings. The approach adopted by Galí (1994), Persson (1995), Harbaugh (1996), Rauscher (1997b), Grossmann (1998), Ljungqvist and Uhlig (2000), and Fisher and Hof (2000) specifies that status derives from relative consumption. In contrast, Corneo and Jeanne, 1997, Corneo and Jeanne, 2001a and Corneo and Jeanne, 2001b, Rauscher (1997a), Futagami and Shibata (1998), Fisher (2001), and Hof and Wirl (2003) consider that status arises from relative wealth. To date, most of the macroeconomic research on status-preference has been restricted to the closed economy, Fisher (2001) and Hof and Wirl (2003) being an exception. Due to the increasing integration of the world economy and the greater role played by international assets in wealth accumulation, we believe additional work needs to be done in analyzing the role played by status-preference in the open economy context. In this paper, we will introduce relative wealth into an otherwise standard small open economy Ramsey model.2 It is well-known that the small open economy Ramsey model—under the assumption of perfect capital mobility—exhibits several problematic features if the domestic rate of time preference differs from the exogenous world interest rate. If, for example, the economy is “relatively patient” in the sense that its rate of time preference is less than the exogenous world interest rate, it then accumulates assets to such an extent that it eventually violates the small open economy assumption. On the other hand, if the domestic rate of time preference exceeds the world interest rate, in other words, if the economy is “relatively impatient”, agents then over time mortgage all their capital and labor income with their consumption converging to zero.3 These counterfactual features of the small open economy Ramsey model have led many authors to restrict their attention to the special case in which the rate of time preference equals the world interest rate. Unless, however, other modifications are incorporated into the model, this condition rules out the possibility of transitional dynamics, since it implies unchanging stocks of physical capital or assets.4 In this paper we will restrict attention to the case in which domestic agents are “impatient” compared to the rest of the world, the case that has attracted more of the interest of the profession. Authors such as Barro and Sala-i-Martin (1995) (hereafter BSM) and Turnovsky (1997) discuss several ways to eliminate the counterfactual results that domestic total wealth and consumption converge to zero.5 The simplest way is to impose an explicit borrowing constraint that prohibits using human wealth as collateral, a constraint that implies that domestic indebtedness cannot exceed the stock of physical capital. Another, though more controversial, approach to generate sensible, long-run equilibria and saddlepath dynamics in the small open economy model is to specify that the representative agent possesses Uzawa (1968)—type preferences in which the subjective rate of time preference depends on the level of consumption or wealth.6 Authors such as Blanchard and Fisher (1989), BSM and Turnovsky (1997) find this formulation intuitively unappealing, however, because a necessary condition in the infinite-horizon context to generate saddlepoint dynamics is to specify that the rate of time preference increases with the level of consumption. Obstfeld (1990), drawing on the work of Epstein (1987), among others, offers a defense of this approach and points out its usefulness in relaxing the more usual assumption of time-additive preferences, which is also restrictive. Two additional, and related, approaches of addressing this issue are either to incorporate costs of holding foreign bonds or to specify an upward-sloping supply curve of debt. Both approaches attempt to model, in a certainty equivalence framework, the macroeconomic implications of imperfect substitutability between domestic and foreign assets. The first approach was taken by Turnovsky (1985), while the second has been adopted in Bhandari et al. (1990). Using these specifications, interior solutions that exhibit the saddlepath property are obtained without imposing equality between the domestic rate of time preference and the world interest rate. It can, however, be argued that it is better to model the implications of international capital market imperfections, which depend, at least in part, on the risk characteristics of domestic and foreign assets, in an explicitly stochastic setting. BSM and Turnovsky (1997) also point out that the potentially counterfactual features of the standard model do not emerge in the usual overlapping generations framework or in its Blanchard (1985) variant in which dynasties that are heterogeneous with respect to age and wealth die off randomly according to a Poisson process.7 Aggregate consumption in this model behaves as if each individual’s time preference rate were positively related to the ratio of own assets to own consumption. This characteristic arises, however, from aggregation and, in contrast to the Uzawa specification, is not due to variations in the subjective discount rates of individuals. Under the assumption that the domestic rate of time preference exceeds the world interest rate, our status preference model will offer an alternative way to generate interior, long-run equilibria with positive consumption and sensible transitional dynamics for consumption and net assets. These properties arise from the specification that the instantaneous utility of agents is a function of own consumption and status, the latter depending on relative wealth. In contrast to the existing literature, we will employ a specification of the status function that does not rule out—by definition—steady states with negative values of nonhuman wealth. In order to concentrate on the influence of status preference, we will abstract from population growth, technological progress, depreciation, installation costs of physical capital, and the heterogeneity of agents. Using an infinite-horizon, perfect-foresight framework, we will derive a symmetric equilibrium in which identical agents make the same choices. Our general formulation of status preference will result in a modified version of the Euler equation. Its crucial feature is that the exogenous world interest rate is replaced by an endogenous, “effective” domestic rate of return that equals the exogenous world interest rate plus the marginal rate of substitution of own assets for consumption in symmetric equilibrium. In addition to incorporating the quest for status, our framework allows agents to possess some degree of debt aversion. Interior steady states are either saddlepoints or unstable nodes. We will show that a necessary condition for the existence of a unique, saddlepoint-stable steady state is that agents are also sufficiently debt averse. Next, we will examine the properties of saddlepoint-stable steady states. Specifically, we will analyze how the effects of (balanced-budget) fiscal policy and improvements in total factor productivity are influenced by status preference. The qualitative results hold irrespective of the degree of debt aversion. We find, for instance, that a rise in government expenditure “crowds out” private consumption by more than one-for-one in steady-state equilibrium. This is due to the long-run decline, attributable to status preference, in net assets, and hence, in net interest income. We argue that this result is more general than that arising in the Uzawa model or in the model with an upward-sloping supply curve of debt discussed above. An analogous result is obtained for an improvement in total factor productivity: the long-run rise in consumption exceeds that of after-tax real wage income due to higher steady-state net interest income. The rest of the paper is organized as follows. The first part of Section 2 describes our general model of status preference and derives the symmetric, intertemporal equilibrium. The main results of this part are summarized in Proposition 1, Proposition 2 and Proposition 3. Proposition 1 analyzes the stability properties of interior steady states. Proposition 2 deals with the relationship between interior steady states and the degree of debt aversion. We close this section with Proposition 3, which analyzes the dynamic evolution of consumption, net assets, and the effective rate of return along a stable arm, corresponding to a saddlepoint-stable steady state. In Section 3 we first investigate how status preference affects the government expenditure and total factor productivity multipliers for the long-run values of private consumption and net assets. In the last part of Section 3, we compare our results with those from some of the competing models discussed above. We close the paper with concluding remarks in Section 4.

In this paper we studied the implications of modifying the standard version of the small open economy Ramsey model by introducing preferences that depend on status as well as on own consumption. Following the branch of the macroeconomic literature that identifies status with relative wealth, we specified that status depends on the comparison of own and average holdings of net assets. We showed first that this specification can eliminate one counterintuitive property of the standard open economy Ramsey framework: that an impatient economy—in the sense that its pure rate of time preference exceeds the world interest rate—mortgages over time all its physical capital and human wealth. Our economy, in contrast, potentially possesses interior long-run equilibria and sensible saddlepath dynamics for consumption and net assets. This property hinges on the fact that the status motive yields an endogenous domestic effective rate of return that depends on both consumption and net assets. Steady states are either saddlepoints or unstable nodes. A necessary condition for the existence of a unique, saddlepoint-stable long-run equilibrium is that the status motive is accompanied by a sufficiently high degree of internal debt aversion that is embedded in agents’ preferences. We finally analyzed the role of status preference in determining the long-run government expenditure and total factor productivity multipliers. We found that a permanent rise in government expenditure, financed by lump-sum taxes, “crowds out” private consumption by more than one-for-one in the long run. This is due to the fact that in response to this shift in fiscal policy, the private sector dissaves during the transition to the steady state. The resulting loss of net interest income augments the drop in after-tax real wage income due to higher lump-sum taxes and results in the “excessive” crowding out of private consumption. Analogously, a permanent improvement in total factor productivity leads to a long-run increase in private consumption that is greater than the rise in after-tax real wage income. This is caused by the accumulation of net assets during the transition to the steady state that raises long-run net interest income. These results hold (locally) for saddlepoint-stable steady states and do not depend on the degree of debt aversion. Finally, we argued that the relative wealth framework yields more plausible predictions with respect to long-run properties and transitional dynamics than other competing extensions of the small open economy Ramsey model.