Demand changes and real exchange rate dynamics in a finite-horizon model with sectoral adjustment costs.

• Author: Chen, Hung-Ju

1. Introduction

   Although the traditional macroeconomic models tend to explain economic fluctuations by focusing solely on supply shocks, given that equilibrium is determined by both demand and supply it would seem obvious that changes in demand may also have important effects in terms of their contribution to economic oscillations. Changes in demand can easily occur, particularly for those small open economies. For example, small open economies can be easily disturbed by external shocks, such as terms-of-trade shocks through international trade. (1) Another example is the reduction in the mortality rate as a result of higher health investment (both public and private) and better healthcare during the economic development. (2) For export-orientated growth economies in particular, such as those of Hong Kong and Taiwan, changes in either the terms-of-trade or the mortality rate can significantly influence economic performance, impacting the real exchange rate, investment, output, savings, and the current account.

   The phenomenon that life expectancy is steadily lengthening for most developing countries has led to the emergence of a growing number of studies on the impact of population aging. (3) Since an increase in life expectancy will change the expectation of lifetime utility, it will directly affect households' inter-temporal decisions with regard to consumption and savings. However, previous studies tend to analyze the impact of mortality decline in a closed economy or in a small open economy with exogenous and constant factor prices. (4)

   In order to study the impact of mortality rate changes on the economic performance in an open economy, we use the "overlapping generations" model with uncertain lifetime, developed by Yaari (1965) and Blanchard (1985), to examine household savings behavior. Within this model, agents live with a finite lifetime, such that different types of agents simultaneously live in the economy. (5) Furthermore, we extend the Blanchard-type model to a three-good open economy composed of exportable, importable, and non-traded goods to allow us to consider the dynamics of the real exchange rate when demand changes.

   Capital production and accumulation are also incorporated into the framework to facilitate an examination of the investment behavior of firms. We assume that the economy uses both capital and labor to produce exportable goods and non-traded goods while importable goods are imported from abroad. Capital is produced by the non-traded sector, and installation costs are incurred when capital is transported to the exportable sector. (6) As indicated by Morshed and Turnovsky (2004), the inclusion of the sectoral adjustment costs of capital can generate persistent deviations from the long-run equilibrium by the real exchange rate in response to demand changes. (7) Because the real exchange rate is playing a dual role of a non-traded goods price and a capital price, we are able to study the impact of population aging and terms-of-trade shocks on international capital flows in a small open economy with endogenous factor prices.

   There is also a large body of literature concerned with analyzing the impact of temporary and permanent terms-of-trade shocks on economic performance, with economists showing particular interest in the investigation of the consequences of such shocks with regard to the current account. Indeed, the so-called Harberger-Laursen-Metzler (HLM) effect demonstrates that a reduction in current income arising from adverse terms-of-trade shocks lowers both the trade balance and private savings (Harberger 1950; Laursen and Metzler 1950).

   The 1980s witnessed the early stages of the development of a number of economic models with inter-temporal optimization frameworks designed specifically to revisit this issue. Obstfeld (1982a, b, 1983), for example, showed that with infinitely lived households, permanent and temporary terms-of-trade shocks could have diverse effects on the current account. (8) Svensson and Razin (1983) went on to adopt a two-period, two-good (importable and exportable goods) framework to reexamine Obstfeld's propositions and found deterioration in both the current account and savings as a result of a temporary deterioration in the terms-of-trade, but they suggested that this could go either way as a result of a permanent deterioration. (9)

   In most of the prior studies that examine the HLM effect there has been a general tendency for researchers to use two-good open models with a fixed exchange rate regime, and there has been no real consideration of the role of non-traded goods. Although this can clearly simplify the analysis, such an approach essentially ignores the consequences of changes in the real exchange rate brought about by terms-of-trade shocks; however, it is clear that changes in both terms-of-trade and the real exchange rate play a crucial role in the behavior of firms and households.

   Firms will invariably adjust their allocation of capital and labor between sectors based upon the changes in the terms-of-trade or the real exchange rate, while the consumption behavior and savings behavior of households will also be affected, given that, along with the changes in the relative prices of exportable, importable, and non-traded goods, there are corresponding changes in permanent income. (10) It should be noted that there will inevitably be changes not only in the amount of consumer spending but also in the composition of such spending (that is, the amount spent on importable, exportable, and non-traded goods). When terms-of-trade shocks occur, both consumption (savings) and investment behavior have important roles to play in determining the current account. (11)

   The consideration of a model composed of three goods in this study enables us to study the dynamics of the real exchange rate when demand changes. The economic dynamics can be represented by a system containing six first-order differential equations composed of (i) capital used in the exportable sector; (ii) capital used in the non-traded sector; (iii) the real exchange rate; (iv) investment in the exportable sector; (v) consumption; and (vi) foreign asset holdings. Given the complexity of this dynamic system, we then simulate the model to study the effects of terms-of-trade shocks and the mortality rate on economic transition.

   We select 1990 data on Taiwan for use in calibrating the parameter values, essentially because Taiwan is a small open economy that is heavily reliant on international trade. Our computational results show that a steady-state solution does exist and that it is a saddle point. We find that a temporary or permanent appreciation in terms-of-trade will increase foreign asset holdings; that is, we observe the presence of the HLM effect. However, the transitions in the current account differ markedly in terms of their response to temporary and permanent terms-of-trade shocks. The numerical results indicate that a 5% temporary appreciation in terms-of-trade will lead to an immediate sharp increase in both the real exchange rate and consumption, along with a temporary increase in foreign asset holdings. With a permanent 5% appreciation in terms-of-trade, there are corresponding increases of 5% in the real exchange rate and of 5.156% in consumption at the steady state. A temporary reduction in foreign assets holdings is then followed by a 5.228% increase at the steady state. An explanation for foreign asset holdings reacting differently to temporary and permanent terms-of-trade shocks is that permanent shocks induce larger changes in permanent income, which in turn lead to larger changes in consumption and savings behavior.

   The degree of sectoral adjustment costs does not affect the steady-state value; however, it does affect the speed of adjustment in response to terms-of-trade shocks. Furthermore, with an increase in the degree of sectoral adjustment costs, there is a reduction in deviations from the steady-state value by the transitional path of capital within the non-traded sector; this, in turn, affects the wealth of households, and as a result, the dynamic transitions of both consumption and the current account.

   With a permanent 5% increase in the probability of instantaneous death, there is a 12.117% reduction in consumption and a 26.316% reduction in foreign asset holdings at the steady state. (12) There are essentially two effects caused by the increase in the probability of instantaneous death. First of all, this probability raises the effective rate of return on nonhuman wealth, which leads to an increase in households' foreign asset holdings. Secondly, however, since life expectancy is shorter, households will tend to reduce their foreign asset holdings and instead raise their consumption levels. Our simulation results show that at the steady state, the latter effect dominates the former, and, as a result, foreign asset holdings are reduced. However, consumption is also reduced as a direct result of the lower wealth.

   The remainder of this paper is organized as follows: In the next section, we develop a small open economy with sectoral adjustment costs and with finite lifetime. Section 3 carries out the simulation results of the model used to study the impact of changes in demand on economic performance, and section 4 concludes the paper.

2. The Model

   We assume that the economy is composed of identical households with a constant life expectancy and that there is no population growth. Let [beta] represent the constant probability of instantaneous death, and assume that the random variable "time until death" has an exponential distribution; expected lifetime is then equal to the expected value of the random variable, which is 1/[beta]. In other words, 1/[beta] can be thought of as an index of the effective horizon of individuals. As [beta] goes to zero, the horizon becomes infinite, and we have the Ramsey-Cass Koopmans model. At each instant a new cohort of...