Natural disasters in a two-sector model of endogenous growth

Abstract

Using an endogenous growth model with physical and human capital accumulation, this paper considers the sustainability of economic growth when the use of a polluting input (e.g., fossil fuels) intensifies the risk of capital destruction through natural disasters. We find that growth is sustainable only if the tax rate on the polluting input increases over time. The long-term rate of economic growth follows an inverted V-shaped curve relative to the growth rate of the environmental tax, and it is maximized by the least aggressive tax policy of those that asymptotically eliminate the use of polluting inputs. Unavailability of insurance can accelerate or decelerate the growth-maximizing speed of the tax increase depending on the relative significance of the risk premium and precautionary savings effects. Welfare is maximized under a milder environmental tax policy, especially when the pollutants accumulate gradually.

Introduction

Natural disasters have a substantial impact on the economy, primarily through the destruction of capital stock. For example, Burton and Hicks (2005) estimated that Hurricane Katrina in August 2005 generated commercial structure damage of $21 billion, commercial equipment damage of $36 billion, and residential structure and content damage of almost $75 billion. These are not negligible values, even relative to the entire U.S. physical capital stock.¹ CRED (2012) reported that the floods in Thailand from August to December 2011 caused US$40 billion in economic damage, which is more than 12% of the nation's GDP. Fig. 1 depicts the time series of the total economic damage caused by natural disasters throughout the world. Although the magnitude of damage caused by Hurricane Katrina may not appear typical, the figure clearly shows a steady and significant upward trend in economic damage arising from natural disasters.

One obvious reason behind this upward trend is the expansion of the world economy. As the world economy expands, it accumulates more capital, which means that it has more to lose from a natural disaster of a given physical intensity. However, this simple account cannot fully explain the overall growing trend in damages. To see this, we plot the ratio of the damage from natural disasters to world GDP in Fig. 2. As shown, this ratio has been increasing since 1960. On this basis, the figure suggests that each unit of installed capital is facing an increasingly higher risk of damage and loss from natural disasters over time. This observation may then have serious implications for the sustainability of economic growth. Also, it is observed from Fig. 1, Fig. 2 that most economic damages are caused by weather-related disasters. Accordingly, if economic activity is to some extent responsible for climate change, and if climate change affects the intensity and frequency of weather-related disasters,² economic growth itself poses a threat to capital accumulation and the sustainability of future growth.

This paper theoretically examines the long-term consequences of the risk of natural disasters on economic growth in a setting where economic activity itself can intensify the risk of natural disasters. We introduce polluting inputs, such as fossil fuels, into an Uzawa–Lucas type endogenous growth model, and assume that the use of polluting inputs raises the probability that capital stocks are destroyed by natural disasters. In the model, we show that as long as the cost of using polluting inputs is constant, economic growth is not sustainable because the risk of natural disasters eventually rises to the point at which agents do not want to invest in capital any further.

Given this result, we introduce a time-varying environmental tax on polluting input, which is shown to have both positive and negative effects on economic growth. On one hand, the faster the environmental tax rate increases, the lower the asymptotic amount of pollution and, therefore, the lower the probability of disasters. This gives households a greater incentive to save, which promotes growth.³ On the other hand, the increased cost of using the polluting input by private firms reduces their (effective) productivity at each point in time, and this has a negative effect on growth. This paper shows that these opposing effects give rise to a non-monotonic relationship between the long-term rate of economic growth and the speed with which the environmental tax increases. We characterize the policy that maximizes the long-term growth rate and examine how it differs from the welfare-maximizing policy. We also examine how the market equilibrium and the optimal policy are affected by the way in which pollutants accumulate and by the extent to which disaster damages can be insured.

The literature on the link between natural disasters and economic growth is relatively new. However, an increasing amount of work investigates both the theoretical and empirical relations between these events. There are mixed empirical results regarding whether natural disasters inhibit or promote growth. Empirical studies that use short-run data tend to find adverse effects of natural disasters on growth. Raddatz (2007) considered a vector autoregressive (VAR) model for low-income countries with various external shocks, including climatic disasters, and his estimates showed that climatic and humanitarian disasters result in declines in real per capita GDP of 2% and 4%, respectively. Using panel data for 109 countries, Noy (2009) found that more significant natural disasters in terms of direct damage to the capital stock lead to more pronounced slowdowns in production. In contrast, using cross-sectional data over a longer period of 1960–90, Skidmore and Toya (2002) found a positive correlation between the frequency of disasters and average growth rates. Although there is no general agreement on the overall effect of natural disasters on growth, the estimation performed by Skidmore and Toya (2002) suggested that the higher frequency of climatic disasters leads to a substitution from physical capital investment toward human capital. Consistent with this finding, our model shows that under appropriate environmental policies, agents accumulate human capital stock much faster than output and physical capital, enabling sustained growth with limited use of the polluting input.

The theoretical literature is still in its infancy.⁴ For instance, Soretz (2007) explicitly introduced the risk of disasters into an AK-type one-sector stochastic endogenous growth model and considered optimal pollution taxation. Hallegatte and Dumas (2009) considered a vintage capital model and showed that under plausible parameter ranges, disasters never promote economic growth through the accelerated replacement of old capital. Lastly, using numerical simulations, Narita et al. (2009) quantitatively calculated the direct economic impact of tropical cyclones. Our analysis complements these studies by considering both human and physical capital accumulation in addition to the polluting input. This is an important extension, not only because the substitution to human capital accumulation in the presence of disaster risk is empirically supported, but also because theoretically it is the key to sustained and desirable growth.⁵ In addition, our methodology can analytically clarify the mutual causality between economic growth and the risk of natural disasters and how this relationship can be altered by environmental tax policy.⁶ Rather than merely considering the optimal tax policy, we consider arbitrary dynamic tax policies and find both welfare-maximizing and growth-maximizing policies.

The rest of the paper is organized as follows. After presenting the baseline model in 2 The baseline model, 3 Market economy shows that in market equilibrium, growth cannot be sustained if the cost of (tax on) the polluting input is constant. We then derive the (asymptotically) balanced growth equilibrium path under a time-varying environmental tax in Section 4. The welfare analysis is in Section 5. Section 6 considers an extension of the model in which pollution accumulates gradually. Section 7 examines the case where the idiosyncratic risks to human capital cannot be insured. Section 8 concludes. Mathematical proofs and derivations are given in Appendix, which is available at the Journal's website.