The impact of oil prices on an oil-importing developing economy

Journal of Development Economics 94 (2011) 18–29

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Journal of Development Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d eve c

The impact of oil prices on an oil-importing developing economy Stefan F. Schubert a, Stephen J. Turnovsky b,⁎ a b

Free University of Bozen-Bolzano, I-39100 Bolzano, Italy University of Washington, Seattle, WA 98105, United States

a r t i c l e

i n f o

Article history: Received 6 January 2009 Received in revised form 30 November 2009 Accepted 14 December 2009 JEL classification: 011 013 Q32 Keywords: Oil price Dynamics Developing economy

a b s t r a c t This paper analyzes the impact of an increase in the price of oil on a small developing economy. We consider the extent to which the impacts of oil price shocks depend upon the economy's internal production structure and its access to the world financial market, and find that the long-run impact depends much more on the former than the latter. Two critical quantities summarizing the long-run effects are (i) the relative share of oil to labor in output and (ii) the elasticity of substitution in production. We supplement the formal analysis with numerical simulations, thereby enabling us to characterize the short-run dynamics. Overall, the simulations can replicate much of the empirical evidence used to characterize the effects of the recent oil price increases on the economy. They also highlight the sensitivity of the effect of the oil price to the elasticity of substitution. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Over the four year-period prior to the summer of 2008, the inflation-adjusted price of crude oil approximately quadrupled, peaking at nearly $US150/barrel. At that time some analysts were predicting that the oil price could soon reach $200/barrel, although the subsequent turmoil in world financial markets and the accompanying drop in the price of oil have led to a scaling down of these predictions. But despite their recent dramatic reversal, oil prices are still substantially higher than they were a few years ago. With the rapid development of the BRIC (Brazil, Russia, India, and China) economies and their growing claim on world resources, most economists expect higher oil prices to be a permanent reality and that they will continue to rise over the long term. The dramatic price increase in oil prices during the past several years and the fear that they will continue to rise are causes for concern. There is convincing historical evidence regarding the negative relationship between oil price increases and economic downturns. Hamilton (1983) found that seven of the eight post World War II recessions in the US have been preceded by substantial increases in oil prices. More recently, Dhawan and Jeske (2006) have observed that since 1973, every recession has been preceded by a rise in energy prices, and that almost every energy price rise has been followed by a recession, citing several studies as supporting this position.1 Thus, ⁎ Corresponding author. E-mail address: [email protected] (S.F. Schubert). 1 These include Hamilton (1983, 2003) among others. 0304-3878/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jdeveco.2009.12.003

given the key role that energy plays in modern economies, it is important to understand the channels through which oil price shocks influence economic performance and personal welfare. The discussion of the potential effects of oil price shocks is not new. The occurrence of the “oil crisis” in the 1970s first stimulated interest in this question, generating extensive research into how oil price shocks affect the economy. This literature was almost entirely short run in nature, paying particular attention to the problem of “stagflation” and the appropriate policy responses to deal with it; see, e. g., Corden (1975), Findlay and Rodriguez (1977). By emphasizing the short run, most of the early literature ignored the longer-run role of capital accumulation and its implications for economic growth. Since then, with the ongoing instability in the Middle East, the energy sector has continued to receive the attention of economists and policy makers. Much of the focus is on identifying the channels through which the oil price shocks influence the performance of the economy, including its growth rate, though mostly from the standpoint of advanced nations; see Barsky and Kilian (2004) for a recent review. The present paper analyzes the effect of oil price increases on the longer-run growth and output performance of a small oil-importing developing economy. This is important, since less developed economies have typically been more oil-dependent than are the more developed economies, and as a result more adversely affected by oil price increases, particularly in the long run. Contrary to common perception, recent research suggests that the effects of the recent oil price shocks on real economic activity have been much milder than were those of the 1970s and 1980s, despite the fact that the earlier oil shocks were of approximately comparable

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

relative magnitudes.2 Most of this evidence is for developed economies and in some cases output growth has barely been affected at all.3 The most common explanation for the reduced vulnerability of developed economies to oil price shocks is that energy intensity in production in these countries has declined by roughly 50%; see e.g. Dhawan and Jeske (2006), Nakov and Pescatori (forthcoming) and the World Economic Outlook (2008). Other explanations include better monetary policy (Nordhaus, 2007; Blanchard and Galí, forthcoming) and a decline in real wage rigidity (Blanchard and Galí, forthcoming).4 In contrast, OECD (2004) finds that in non-OECD countries oil intensities have generally increased slightly up to the mid 1990s, before falling marginally. The World Economic Outlook (2008) reports that whereas energy consumption per unit of GDP has fallen by about 40% in advanced countries since the 1970s, emerging and especially developing countries are generally considerably more energy intensive. This evidence suggests that it is quite natural to expect an oil price shock to have more severe economic effects in a developing country than in a modern industrialized economy.5 By focusing on the long-run secular impact of oil price shocks on a developing economy, our analysis contrasts in several key respects with a growing literature analyzing the effects of oil shocks employing dynamic stochastic general equilibrium (DSGE) models. Building upon the seminal work of Kydland and Prescott (1982), Kim and Loungani (1992) introduce energy use and the energy price as a second exogenous shock into the Kydland–Prescott framework. Backus and Crucini (2000) incorporate a third oil-selling country into the Backus et al. (1994) two-country DSGE model to analyze an oil supply shock. Bodenstein et al. (2007) modify the Backus–Crucini model in various dimensions, adopting a two-country setting, where both countries produce oil, but where one is a net oil importer and the other a net oil exporter. This literature focuses entirely on industrialized countries and does not consider developing economies. Nor does it address the longrun growth issues with which this paper is concerned. Rather, Backus and Crucini (2000) are concerned with explaining the variations in the terms of trade in a subset of OECD countries, and demonstrating how these can be largely attributed to oil supply shocks. Bodenstein et al. (2007) analyze the effects of an oil price shock on a large industrialized country like the US, Japan, or the Euro area on the trade balance and real exchange rate, contrasting the responses under incomplete financial markets, with those under complete financial markets, as assumed by Backus and Crucini. In contrast, the small developing country we consider faces restricted access to the world financial market, specified in the form of borrowing costs that increase with its level of debt. As a result, we find that a sustained oil price increase is likely to have sharply different consequences for such an economy than for a developed economy. By focusing more on the macroeconomic effects of oil price shocks on larger, developed economies, the impact of oil shocks on the external sector has been underemphasized relative to its effect on internal productive activity. This is particularly important in the case 2 This comparison is documented in detail by Blanchard and Galí (forthcoming); see also Nordhaus (2007). 3 See e.g. Nordhaus (2007), Blanchard and Galí (forthcoming), OECD (2004). Using data for OECD countries over the period 1972–2001 Jiménez-Rodríguez and Sánchez (2005) find that a 100% increase in the price of oil leads to an accumulated output loss ranging from 1% for Canada, to 2% for the Euro area, 3% for France, 4% for Italy, and 5% for USA and Germany. 4 Kilian and Lewis (2009) and Herrera and Pesavento (2009) decompose output fluctuations in industrial economies in terms of oil price shocks, monetary policy, and other factors, suggesting that the effect of oil price shocks on output may be linked to the monetary policy implemented in the specific country. This suggests that differential effects of oil price shocks in developing countries might also be attributed to the implementation of different forms of monetary policy. 5 There is also the question of the less efficient use of energy in developing countries, briefly discussed in Section 4.2.3.

19

of small, trade-dependent, developing economies, where the two sectors are likely to be highly interdependent. But several recent exceptions should be noted. First, Rebucci and Spataforta (2006) find that oil price shocks tend to reduce asset prices — including equities and exchange rates — and have a noticeable effect on a country's net foreign asset (NFA) position. Second, although Bodenstein et al. (2007) find that a sustained increase in the relative price of oil improves the long-run nominal trade balance, the adjustment is nonmonotonic. The comprehensive study by Kilian et al. (2009) detects asymmetric effects of oil price shocks on a country's net foreign asset position. For the US, the NFA position does not change significantly. It actually improves with some delay, whereas for other advanced oilimporting countries the NFA position is reduced in most cases. For middle-income oil-importing countries they find that the current account deteriorates significantly in response to oil supply disruptions. In the expanded working paper version of their published study, they also find that the effects on external balances is more pronounced in emerging Asia than it is in Latin America, and as a potential explanation for this difference they conjecture that it is because of Latin America's more limited access to world capital markets. Another explanation, supported by our numerical simulations, is the lower energy intensity of Latin American countries compared to emerging Asian economies; see e.g. Alaimo and Lopez (2008). Clearly the role of oil in a developing trading economy raises many important questions that merit further investigation. In particular, the effects of oil price shocks on a country's external asset position have important consequences for its internal productive capacities, its consumption possibilities, and most importantly, its welfare. To what extent do these aspects depend upon the country's degree of oil dependence, its production structure, and the extent of its financial integration in the world economy? To address these questions, we develop a neoclassical growth model of a small oil-importing developing economy, in which production depends upon labor, capital, as well as imported oil. The macroeconomic equilibrium we derive is described by a dynamic system involving the interaction between: (i) the allocation of labor, (ii) the relative price of capital, (iii) the accumulation of capital, and (iv) the accumulation of foreign debt. While the complexity of the model requires its transitional dynamics to be analyzed using numerical simulations, we are able to provide a comprehensive analytical characterization of the longrun responses to a permanent oil shock. Not only are these of interest in their own right, but they also help us interpret the dynamic simulations. In particular, they suggest how the long-run effects of an oil price increase on a small developing economy are determined primarily by its internal production conditions. In the long run, its accessibility to the world financial is unimportant, though it does play a more significant role in the short run and during the transition. The accumulation of these short-run effects means that accessibility to the world financial market does have consequences for intertemporal welfare. One key productive characteristic is the relative share of oil usage costs in GDP. Oil shares in production differ across economies. For a sample of 22 countries ranging across various stages of development, Gupta (2008) has found that in 2004 the lowest value of oil imports in GDP is in Australia with 0.44% and the highest in the Philippines with 5.18%, whereas in Europe it is on average 2.78%. Plausible calibrations of the model, generally confirm these empirical findings. For plausible magnitudes of the elasticities of oil in production, we find that both the short-run and steady-state effects on output are quite small, thus confirming the findings of OECD (2004), Jiménez-Rodríguez and Sánchez (2005), Dhawan and Jeske (2006), Nordhaus (2007) and Blanchard and Galí (forthcoming). Since developing countries tend to have higher oil shares, [see OECD, 2004; World Economic Outlook,

20

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

2008], as well as in light of the observed changes in the oil share over time, (see Segal, 2007; Nakov and Pescatori, forthcoming; Dhawan and Jeske, 2006, and others), we also perform a sensitivity analysis with respect to the weight of oil in production and thus the oil share in GDP.6 These simulations confirm the empirical findings that lower oil shares moderate the adverse effects of oil price shocks. The other key production characteristic is the elasticity of substitution. Sensitivity analysis with respect to the elasticity of substitution in the productive inputs — labor, capital, and oil — reveals that the more substitutable are the three factors of production, the less adverse is the impact of an oil price shock on the economy. These effects are highly sensitive to small variations in the elasticity of substitution. Moreover, the accuracy of these output losses stemming from oil price shocks as measures of the intertemporal welfare losses is also dependent upon the elasticity of substitution. The model can also replicate some of the transitional dynamic behavior of the financial variables studied by Rebucci and Spataforta (2006). By causing an initial increase in the interest rate, an oil price shock renders investment in capital less attractive, causing the market price of capital to decline, as Rebucci and Spataforta (2006) found. The dynamic adjustment of key financial variables is nonmonotonic. Interestingly and perhaps surprisingly, our sensitivity analysis with respect to financial integration reveals that the more a country is integrated into the world financial market, the stronger are the effects of an oil price rise. The model thus provides a theoretical underpinning of the Kilian et al. (2009) findings that Latin America suffers less under an oil price shock than do the emerging Asian economies.

The agent also accumulates capital, Ki, with expenditure on a given change in the capital stock, Ii, involving installation (adjustment) costs specified by the quadratic cost function ΦðIi ; Ki Þ = Ii + h


 Ii2 h Ii = Ii 1 + ; 2 Ki 2Ki

ð1cÞ

where adjustment costs are proportional to the rate of investment per unit of installed capital, Ii/Ki. Letting δ denote the rate of depreciation, and n be the population growth rate, the agent's net rate of capital accumulation is thus K˙ i = Ii −ðn + δÞKi

ð1dÞ

The economy has access to a world capital market, allowing it to borrow internationally. Being a developing economy it faces restrictions in doing so, according to lenders' assessment of its creditworthiness. We assume that the world capital market assesses the economy's ability to service its debt costs, and views the country's debt–capital (equity) ratio as an indicator of its potential default risk. Accordingly, the interest rate a country is charged on the world capital market increases with this ratio. This is summarized by an upwardsloping supply schedule for debt, which we express by assuming that the borrowing rate, r, charged on national foreign debt, B, increases with the ratio, B/qK, where q denotes the market price of equity, [to be determined in equilibrium]
r≡r

B qK




 B  ′ =r +ω ; ω >0 qK

ð1eÞ

2. Analytical framework We employ a standard one-sector neoclassical model of an open economy that imports a foreign good, oil, used solely as an intermediate input in domestic production. The economy is small and produces a traded good, Y, that can be consumed, invested, or exported. The relative price of oil in terms of traded output, p, is determined exogenously in the world market. We assume that p remains constant over time and analyze the dynamic effects of a onetime unanticipated permanent increase in p. The economy is populated with a large number of identical agents, and each individual i is endowed with one unit of time, a fraction of which, li, can be allocated to leisure, and the reminder, Li ≡ 1 − li, to employment. The population, N, grows at the exogenously given constant rate Ṅ/N = n. Each individual produces traded output, Yi, using capital, Ki, labor, Li, and imported oil, Zi, according to the neoclassical production function Yi = FðKi ; Li ; Zi Þ

ð1aÞ

where each factor has positive, but diminishing, marginal product [Fi > 0, Fii < 0, i = K, L, Z]. In addition to constant returns to scale, we assume that the cross derivatives satisfy Fij > 0, i, j = K, L, Z, i ≠ j, implying that all three factors are “cooperative” in production. The representative agent consumes the traded good at the rate, Ci, and enjoys leisure, li, deriving utility over an infinite horizon represented by the isoelastic utility function

B˙ i = ½rðB = qKÞ−nBi + Ci + pZi + ΦðIi ; Ki Þ−FðKi ; Li ; Zi Þ:

γ−1 θγ li

ð1bÞ

6 According to Segal (2007), the share of energy expenditures in total output for the US was 4–5% in the late 1970s, 8% from 1979 to 1980, 1–2% for the 1990s and early 2000s, and 3.3% in 2005.

ð1fÞ

Since we are concerned with a small developing country facing some limited access to the world financial market, it is natural to focus on a debtor economy, which corresponds to Bi > 0 (or B > 0). But in fact whether the country turns out to be a debtor or creditor is endogenous, depending upon whether (β + n) > (<)r⁎, and indeed the latter case corresponds to Bi < 0.7 The representative agent chooses consumption, leisure (labor), oil imports, investment, and the rates of capital and debt accumulation, to maximize utility (1b), subject to the capital accumulation Eq. (1d) and his budget constraint (1f). This yields the following conventional optimality conditions with respect to the individual's choices of Ci, li, Zi, and Ii Ci

∞

1 θ γ −βt Ui ≡ ∫ ½Ci li  e dt; −∞ < γ < 1; β > 0 γ 0

where r⁎ is the exogenously given riskless world interest rate [for example, the LIBOR], and ω(B/qK) is the country-specific borrowing premium that increases with the nation's debt–capital ratio. In making his individual decisions, the representative agent takes the interset rate as given. This is because the interest rate facing the debtor nation is an increasing function of the economy's aggregate debt, which the individual agent rationally assumes that he cannot influence. Given this access to the world goods and financial market, the domestic agent's instantaneous budget constraint is specified by

= λi

γ θγ−1

θCi li

= λi FL ðKi ; Li ; Zi Þ

ð2aÞ ð2bÞ

7 Because of space limitations we restrict our attention to the more prevalent case of a debtor country. The case of a creditor country is discussed in an expanded version of this paper, although some qualitative aspects are briefly reported in Section 4.2.4.

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

FZ ðKi ; Li ; Zi Þ = p 1+h

ð2cÞ

Ii =q Ki

ð2dÞ

where λi is the shadow value of wealth in the form of internationally traded bonds, and q is the value of capital in terms of the (unitary) price of foreign bonds. Eq. (2a) equates the marginal utility of consumption to the marginal utility of wealth, while Eq. (2b) equates the marginal utility of leisure to the shadow value of its opportunity cost, the real wage (the marginal product of labor). Eq. (2c) equates the marginal product of oil to its market price, p, whereas Eq. (2d) equates the marginal cost of an additional unit of (new) capital to the market price of capital. The demand for oil, given labor and capital, can be derived from Eq. (2c) and expressed as Zi = Zi ðKi ; Li ; pÞ

Zi;K > 0; Zi;L > 0; Zi;p < 0

ð3aÞ

An increase in the relative price of oil reduces its demand, while the mutual “cooperation” among factors in production implies that the usage of oil increases with both capital and labor. For convenience, we can write Eq. (3a) equivalently in terms of capital and leisure (omitting p for simplicity) Zi = φðKi ; li Þ

ð3a′Þ

21

conditions, Eqs. (2a)–(2d) and Eqs. (4a)–(4c), must hold continuously for all agents. Moreover, in steady-state equilibrium all aggregate quantities grow at the constant rate n, whereas the market price of capital, q, and the labor allocation, li, remain constant. Since all agents are identical, it is convenient to express the dynamics in per-capita (or average) magnitudes, which are constant in steady-state equilibrium, where henceforth we drop the subscript i. The dynamics can be expressed as an autonomous system in the four stationary variables, K, B, q, and l. This is accomplished as follows. First, combining Eqs. (1d) and (2d), we may express the per capita accumulation of physical capital in the form: q−1 K˙ −δ−n = h K

ð5aÞ

Next, substituting for I, C and Z into the agent's flow constraint (Eq. (1f)), we may express the per capita accumulation of debt as 
  B −nB + ψðK; lÞ + pφðK; lÞ + B˙ = r qK

! 2 q −1 K−FðK; 1−l; ψðK; lÞÞ 2h

ð5bÞ Third, we rewrite the arbitrage condition (4b) in the form
 2 q˙ B ðq−1Þ F ðK; 1−l; φðK; lÞÞ =r + δ− − K q qK q 2hq

ð5cÞ

Dividing Eq. (2b) by Eq. (2a) gives the standard optimality condition equating the marginal rate of substitution between leisure and consumption to the real wage. This condition can be expressed as

Finally, we derive the dynamic adjustment for leisure as follows. First, taking the time derivative of the equilibrium condition (2a) and combining with Eq. (4a), yields

θCi = FL ðKi ; Li ; Zi Þ li

ðγ−1Þ

ð3bÞ

which we can write in the form ð3b′Þ

Optimizing with respect to Bi and Ki leads to the usual no-arbitrage conditions, equating the rates of return on consumption and investment in capital to the costs of borrowing abroad,
 λ˙ i B −n =r qK λi

ð4aÞ


q˙ FK ðKi ; Li ; Zi Þ ðq−1Þ2 B + + −δ = r q q qK 2hq

−βt

lim λi Bi e

= lim qλi Ki e t→∞

−βt

=0

ψ ðK; lÞK C˙ = K ψðK; lÞ C

K˙ K

! +

ψl ðK; lÞl l˙ ψðK; lÞ l

! ð6bÞ

Solving Eqs. (6a) and (6b) and combining with Eq. (5a), we may express the dynamics of leisure in the form h   i h i B K ðK;lÞK q−1 −ðβ + nÞ −ð1−γÞ ψψðK;lÞ r qK −ðδ + nÞ l˙ h = l ð1−γÞ ψl ðK;lÞl −γθ

ð6cÞ

ψðK;lÞ

 ð4bÞ

The return to domestic capital comprises four elements. The first is the “dividend” yield, the second the capital gain, the third reflects the fact that an additional benefit of a higher capital stock is to reduce the installation costs (which depend upon Ii/Ki) associated with new investment, whereas the fourth represents a loss due to the depreciating capital stock. Finally, in order to ensure that the agent's intertemporal budget constraint is met, the following transversality conditions must hold: t→∞

ð6aÞ

Next, taking the time derivative of Eq. (3b′) we obtain

l Ci = i FL ðKi ; 1−li ; φðKi ; li ÞÞ≡ψðKi ; li Þ θ

β−


 C˙ B l˙ + θγ = β + n−r C qK l

ð4cÞ

Eqs. (5a)–(5c) and (6c) complete the description of the equilibrium dynamics. Clearly it describes a relatively high order nonlinear system, the formal analysis of which is completely intractable. In Section 4 below we analyze it numerically in the case where the aggregate production function is of the Constant Elasticity of Substitution (CES) form. However, it is possible to derive the longrun equilibrium properties for the general system. 3.1. Steady-state The steady-state of the economy, denoted by tildes, is reached when K̇ = Ḃ = q̇ = l ̇ = λ̇ = 0, and is determined by the following set of equations:

3. Macroeconomic equilibrium

˜ −1 q =n+δ h

We now combine the optimality conditions with the budget constraints and accumulation equations to derive the macroeconomic equilibrium. In equilibrium, all static and dynamic optimality

r˜ = r

B˜ q˜ K˜

ð7aÞ

! =β+n

ð7bÞ

22

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

l˜ + L˜ = 1

ð7cÞ

˜ L; ˜ ZÞ ˜ Y˜ = Fð K;

ð7dÞ

θC˜ ˜ L; ˜ ZÞ ˜ = FL ðK; l˜ ˜ L; ˜ ZÞ ˜ =p FZ ðK; ˜ ˜ ˜ FK ðK; L; ZÞ ðq˜ −1Þ2 + −δ = β + n ˜ q˜ 2hq ! 2 q˜ −1 ˜ ˜ ˜ ˜ ˜ L; ˜ ZÞ ˜ β B + C + pZ + K = FðK; 2h

ð7eÞ

θ 1+θ

ð7fÞ ð7gÞ

ð7hÞ

ð8Þ

3.2. Long-run effect of an increase in the price of oil Table 1 summarizes the long-run effects of an increase in the price of oil where output is generated by the non-nested CES production function used to analyze the transitional dynamics:9 Y = A½α1 L−ρ + α2 Z −ρ + α3 K −ρ −1 = ρ α1 + α2 + α3 = 1; and − 1 ≤ ρ < ∞

ð9Þ

The elasticity of substitution is denoted by σ ≡ 1/(1 +ρ), while α2 parameterizes the degree of oil dependence. Our choice of the specification (9) for our simulations is somewhat pragmatic. Early literature that introduced energy into aggregate production functions focused on the substitutability–complementarity of energy with the other productive factors. For this purpose various nested forms of the CES production function, as well as generalizations to the translog form, have been employed. Since (i) these generalizations increase the number of parameters significantly, and (ii) the diversity of the empirical evidence characterizing the substitutability–complementarity relationship, making the appropriate nesting structure unclear, we feel that Eq. (9) serves as a natural benchmark.10

8

This is derived in the Appendix, available on request. An expanded version of the paper reports the long-run responses for a general neoclassical production function. In fact, the CES production function provides most of the insights. 10 As examples of the alternative “nestedness” assumptions employed in the recent DSGE literature, we note that Backus and Crucini (2000) specify the production function to be of the form Y = ALα[ηK− ρ + (1 − η)Z− ρ]−(1 − α)/ρ, while Bodenstein et al. (2007) first combine capital and labor to produce a composite factor that then combines with oil. Kemfert (1998) and van der Werf (2008) test for the nestedness properties of production functions for energy and obtain results that are generally supportive of the non-nested specification (9). 9

d L˜ = L˜ dp = p d Y˜ = Y˜ dp = p

=

dZ˜ = Z˜ dp = p dC˜ =C˜ dp = p

Eqs. (7a), (7b), (7g), and (7h) are the stationary relationships corresponding to Eqs. (5a)–(5c), (6c); (7e), (7d), and (7f) restate Eqs. (3b), (1a), and (2c) respectively; while Eq. (7c) restates the agent's time allocation constraint. These eight equations determine the steady-state values of the eight variables, K̃, L̃, l ̃, Z̃, Ỹ, B̃, q̃, and C̃. Because of the recursive structure, (i) the long-run market price of installed capital, q̃, (ii) the common growth rate of all aggregate variables, (iii) the long-run borrowing rate, and (iv) the steady-state debt–equity ratio, B̃/q̃K̃, are all independent of the price of oil, p. From the steady-state equations we can show that if the economy is intertemporally viable in the sense of having net positive wealth, so that q̃K > B̃, the steady-state leisure must satisfy the restriction8 l˜ >

Table 1 Long-run effects of increase in oil price. ½θ−ð1 + θÞ˜l ss˜˜ZL ð1−σÞ d K˜ = K˜ dp = p

=

d B˜ = B˜ dp = p

½ð1 + θÞð1−l˜Þð1−σÞ−1 ss˜˜ZL < 0 dK˜ = K˜ −σ dp = p

Z = ½ð1 + θÞð1−l˜Þð1−σÞ−1 ˜s ˜sL −σ < 0

˜ dK˜ = K˜ s˜Z − θð1− l Þð1−σÞ dp = p s˜L l˜ h ð1−l˜Þ

− 1+

l˜

=

½θ−ð1 + θÞl˜ ð1−σÞ

i

s˜Z s˜L

<0

(i) The condition θ < (1 + θ)l ̃ is equivalent to q̃K̃ > B̃, i.e. the country has positive net wealth. (ii) s̃Z, s̃L denote the shares of oil and labor, respectively, in GDP.

With the long-run equilibrium marginal product of capital being independent of p [Eq. (7g)] and the equilibrium marginal product of oil increasing with p [Eq. (7f)], the diminishing marginal productivity of capital implies that the ratio of oil to labor, Z̃/L̃, declines. Given the cooperation between capital and oil in production, the ratio K̃/L̃ declines as well. The response of the labor–leisure allocation is subject to two offsetting effects. First, the reduction in both the relative usage of oil and capital reduces the real wage, inducing agents to take more leisure (supply less labor). But the need to devote more resources to oil requires a reduction in consumption, which reduces the marginal utility of leisure, encouraging agents to work more. Which effect dominates depends upon the elasticity of substitution. It is seen from Table 1 that the elasticity describing the long-run response of labor is in fact small. Parameter values employed in our simulations suggest that the deviation in the elasticity of substitution from unity, (1 − σ), is multiplied by a number of the order of 0.02.11 Hence, as one would expect, the net effect of the higher oil price is to reduce the overall capital stock, K̃, and oil usage, Z̃, and for long-run output, Ỹ, to decline as well.12 With the long-run ratio of bonds to capital independent of the oil price, an increase in p reduces the capital stock, bond holdings, and overall wealth, in the same proportions. Moreover, Row 2 of Table 1 implies that the increase in the oil price reduces long-run output by the same proportionate amount as well. The decline in oil usage specified in Row 3 implies that the capital–oil(energy) ratio increases by σ, while consumption declines relatively more (less) than does capital, according to whether σ < (>)1. In the case of the Cobb–Douglas production function (σ = 1) the long-run effects of an oil price increase are very simple. First the two effects noted above on employment are exactly offsetting, leaving employment unchanged. Capital, output, debt, and consumption all decline at the same proportionate rate given by the ratio of the elasticity of oil dependence to that of labor in the production function. The usage of oil is reduced proportionately more. Overall, the expressions in Table 1 suggest that the key factor determining the long-run impact of an oil price increase on a small developing economy are its internal production conditions, rather than its access to external financial markets. Indeed, for the Cobb– Douglas technology the relative shares of oil to labor, which are fixed, are the only relevant determinant. As the production function diverges from the Cobb–Douglas, the relative shares, which become endogenously determined, remain important as does the elasticity of substitution itself. The country's access to the international financial markets which is irrelevant for the Cobb–Douglas technology, assumes some secondary role insofar as it influences the long-run factor shares and the labor–leisure allocation.

11 Our simulations are based on θ = 1.75, l ≈ 0.7, and the ratio of the shares of oil to output in GDP, sZ/sL ≈ 0.10. 12 We see from the table that the percentage decline in oil usage exceeds that of capital.

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29 Table 2 The benchmark economy. Preference parameters Production parameters

World interest rate Borrowing premium Population growth rate Price of oil

γ = − 1.5, β = 0.04,θ = 1.75 α1 = 0.6, α2 = 0.02, α3 = 0.38 α1 = 0.6, α2 = 0.06, α3 = 0.34 σ = 0.75, 1, 1.25, A = 1, h = 12,δ = 0.05 r⁎ = 0.045, r⁎ = 0.065 η = 0.01, 0.1, 1a n = 0.015 p doubles from 1 to 2

a The functional specification of the upward-sloping supply curve of debt that we use is r(b) = r⁎ + eηb − 1. Thus, in the case of a perfect world capital market, when η = 0, we obtain r(b) = r⁎, the world interest rate.

4. Numerical simulations To analyze the dynamics, we shall assume that output is produced by the CES production function defined in Eq. (9) above and consider the corresponding linear approximation to the equilibrium dynamic system, Eqs. (5a)–(5c) and (6c), involving the four variables, K̇, Ḃ, q̇, and l ̇.13 To be saddle-point stable, there must be two unstable roots to match the two “jump” variables q and l. For all plausible sets of parameter values our simulations yield this required pattern of eigenvalues. To obtain further insight into the transitional path following an increase in the oil price, we resort to numerical simulations. These are based on the parameter values listed in Table 2. Our choices of preference parameters, β and γ, corresponding to a rate of time preference of 4% and an intertemporal elasticity of substitution of 0.4, respectively, are standard. The elasticity of leisure, θ = 1.75, is conventional in the real business cycle literature, and plays a critical role in ensuring a labor allocation in the empirically plausible range (l ≈ 0.7). The elasticity of labor α1 = 0.6 in production is also noncontroversial, as is the rate of depreciation, δ = 0.05, and the population growth rate of 1.5%, while A scales the initial productivity. The world interest rate is set at 4.5%. The choice of installation costs is less clear. Setting h = 12 is within the range 10–15 generally assumed in the literature.14 Our focus on a small developing economy introduces three critical, and less documented, parameters. First, we consider the degree of oil dependence of the economy, with the corresponding productive elasticities α2 = 0.02, 0.06 characterizing a relatively low oil-dependent and a relatively high oil-dependent economy, respectively.15 While on average developing countries are more oil-dependent than are OECD countries [see OECD, 2004, and World Economic Outlook, 2008], there is substantial variation across such economies. The average share of oil in GDP in OECD countries is around 4% [see World Energy Outlook, 2008]. Some developing countries like India, China, Pakistan, Indonesia, Mozambique are substantially above the OECD average, while other countries (particularly many Latin American countries) are well below the OECD average [see Key World Energy Statistics, 2008]. Thus, our values α2 = 0.02, 0.06 seem to span a plausible range.16 Second, we characterize the degree of flexibility in production in terms of the elasticity of substitution, allowing it to vary between 0.75 and 1.25. This is consistent with the comprehensive cross-country study by Duffy and Papageorgiou (2000), who found that for the poorest developing countries the elasticity of substitution is less than 13 The formal details of the linearized dynamic system are provided in an Appendix, available on request. 14 For example, Ortigueira and Santos (1997) find h = 16 leads to a plausible speed of convergence of around 2% per annum. Auerbach and Kotlikoff (1987) assume h = 10, and recognize that this is at the low value of estimates. We have also assumed values of h lying outside this range with little change in results. 15 In order to maintain constant returns to scale, we adjust α3 correspondingly, namely α3 = 0.38, α3 = 0.34. 16 See also Gupta (2008).

23

unity (around 0.8), that for next poorest countries (initial capital per worker $US1000–$US3000) it is not significantly different from unity, and for middle-income countries (initial capital per worker $US3000– $US10,000) it is around 1.1.17 On this basis, and given its prominent role in macrodynamics in general and in modern growth theory in particular, it seems reasonable to take the Cobb–Douglas specification as a benchmark and to vary the elasticity between 0.75 and 1.25, thereby spanning plausible values.18 The third crucial parameter, η, summarizes the sensitivity of the borrowing premium to the country's debt position, and thus characterizes its degree of access to the world financial market. Empirical evidence on this is somewhat mixed though most studies, and particularly the more recent ones, obtain a significant positive and convex relationship.19 Since these empirical studies embed this effect in larger structural empirical relationships, it is hard to relate the impact of the debt–output ratio to the value of η.20 However, we can note that our benchmark value of η = 0.1 implies that each percentage point increase in debt raises the country borrowing premium by something over 1 basis point. This is of the same order of magnitude as implied by the empirical studies of Edwards (1984) and Chung and Turnovsky (2010) (2 basis points), and Zoli (2004) (4–7 basis points). But, because of the variation in the empirical evidence, we allow η to vary between η = 0.01, proxying unhindered access, and η = 1, providing a good approximation to exclusion from the international bond market.21 The value of η is the crucial determinant of the equilibrium debt–output ratio and further support for the benchmark value η = 0.1 is that it yields a plausible equilibrium debt–output ratio of around 40% (depending upon oil usage). 4.1. Initial equilibria Table 3 summarizes the initial equilibria corresponding to the benchmark parameter values and for alternative values of η and σ. Of these alternative values we identify the values η = 0.1, σ = 1 (set in bold) as the most plausible benchmark. The critical equilibrium ratios are all in their respective plausible ranges.22 In particular, the weight of oil in GDP is 0.02 or 0.06, depending upon the dependence as parameterized by α2, which generally spans the observed range. Overall, the equilibrium is a plausible characterization of a small developing economy having limited access to the world financial market. Toward the right hand side of each panel, we have computed the corresponding level of the welfare integral (1b), when the economy is in the corresponding steady-state. In general, normalizing the initial population to N0 = 1, welfare is

W=

1 ∞ γ θγ −βt ∫ CðtÞ lðtÞ e dt γ 0

ð10Þ

17 See Duffy and Papageorgiou (2000, Table 3). As they note, their point estimates are not very precise, although both 0.8 and 1.1 are significantly different from Cobb– Douglas. 18 A further advantage of the Cobb–Douglas specification as benchmark is that exponents reflect factor shares and this helps in calibration. Backus and Crucini (2000) set the elasticity of substitution between oil and capital to be 0.09. While they argue that this low value seems plausible for their study that focuses on business cycles, they also suggest that an elasticity closer to one is more appropriate for analyzing secular changes in oil usage, as is the case here. 19 See e.g. Edwards (1984), Min (1998), Zoli (2004), and Chung and Turnovsky (forthcoming), among others, who obtain significant positive effects for the effect of debt on the borrowing premium. Zoli emphasizes the nonlinear increasing (convex) feature of this relationship, an aspect that is incorporated in the exponential formulation we employ. 20 For example, Chung and Turnovsky (forthcoming) find that both the Debt/GDP ratio and its interaction with risk measures (output volatility and real exchange rate volatility) are significant determinants of the borrowing premium. 21 Extending η beyond 1 has virtually no effect on the equilibrium. 22 Note that while the capital–output ratio is somewhat over 2, valuing capital at its equilibrium price 1.78, implies an equilibrium capital (value)–output ratio of around 4.

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S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

Table 3 Initial equilibrium [parameter values: r⁎ = 0.045, A = 1, α1 = 0.6, γ = − 1.5, n = 0.015, h = 12, β = 0.04, θ = 1.75, δ = 0.05, p0 = 1]. Oil dependence α2 = 0.02

Oil dependence α2 = 0.06

Y0

l0

K0/Y0

Z0/Y0

B0/Y0

C0/Y0

W0

μ1, μ2

Y0

l0

K0/Y0

Z0/Y0

B0/Y0

C0/Y0

W0

μ1, μ2

σ = 0.75 η = 0.01

0.441

0.637

1.899

0.0532

3.364

0.641

− 363.19

0.357

0.637

1.747

0.1212

3.095

0.597

− 554.02

η = 0.1

0.394

0.676

1.899

0.0532

0.336

0.762

− 284.14

0.319

0.675

1.747

0.1212

0.309

0.709

− 434.62

η=1

0.389

0.679

1.899

0.0532

0.034

0.774

− 278.23

− 0.0780 − 0.0149 − 0.1529 − 0.0442 − 0.4952 − 0.0489

0.316

0.679

1.747

0.1212

0.031

0.720

− 425.68

− 0.0797 − 0.0148 − 0.1526 − 0.0439 − 0.4942 − 0.0486

σ=1 η = 0.01

0.548

0.637

2.352

0.0200

4.166

0.601

− 288.45

0.418

0.637

2.104

0.0600

3.727

0.601

− 433.21

η = 0.1

0.473

0.687

2.352

0.0200

0.417

0.751

− 211.40

0.366

0.682

2.104

0.0600

0.373

0.735

− 326.39

η=1

0.467

0.691

2.352

0.0200

0.042

0.766

− 206.10

− 0.0653 − 0.0119 − 0.1427 − 0.0334 − 0.4733 − 0.0363

0.362

0.686

2.104

0.0600

0.037

0.748

− 318.77

σ = 1.25 η = 0.01

0.730

0.637

2.913

0.0075

5.159

0.523

− 231.27

0.509

0.637

2.535

0.0297

4.490

0.562

− 356.23

η = 0.1

0.595

0.704

2.913

0.0075

0.516

0.709

− 153.08

0.430

0.693

2.535

0.0297

0.449

0.723

− 251.23

η=1

0.584

0.709

2.913

0.0075

0.052

0.727

− 148.36

− 0.0524 − 0.0088 − 0.1327 − 0.0239 − 0.4502 − 0.0256

0.424

0.698

2.535

0.0297

0.045

0.739

− 244.35

− 0.0676 − 0.0131 − 0.1459 − 0.0358 − 0.4824 − 0.0389

− 0.0566 − 0.0106 − 0.1378 − 0.0277 − 0.4641 − 0.0297

Bold denotes the most plausible scenario.

which in steady-state equilibrium simplifies to

W=

γ θγ 1 C˜ l˜ : γ β

ð10′Þ

Subsequent changes in welfare resulting from increases in the oil price are obtained by expressing the change in the welfare measure (Eq. (10)) in terms of the equivalent variations in the flow of income necessary to equate the initial levels of welfare to what they would be following the oil price increase, (both long run and short run). Finally, we report the eigenvalues, which together contain information relevant to the speed of convergence.23 The three panels of Table 3 yield some interesting features of the steady-state equilibrium. First, unsurprisingly, greater oil dependence, α2, implies a larger share of GDP attributable to oil usage. Oil usage is exactly proportional to oil dependence, α2, if the production function is Cobb–Douglas, more than proportional if σ < 1, and less than proportional if σ > 1. An increase in oil dependence lowers the capital– output ratio. The country's position in the international bond market declines in that a debtor country reduces its debt. The steady-state work–leisure allocation is barely sensitive to the dependence on oil so that the reduction in the use of capital leads to a decline in output. The greater usage of imported oil means that consumption in the more oildependent economy is lower, although whether it is relatively lower than output depends upon the elasticity of substitution in production. As η increases and the economy's access to the world financial market declines, the country reduces its debt. This allows it to enjoy more consumption and more leisure. On the production side, the equilibrium capital–output and oil–output ratios remain unchanged, implying that the output–employment ratio remains unchanged as well. The increase in leisure, and associated decrease in employment, implies a reduction in output. Thus, with more consumption and leisure as well as less debt to service, the country is better off by having its access to the world capital market restricted. 23 Since the stable adjustment path is two-dimensional, the speed of convergence varies over time and across variables. The asymptotic speed of convergence is given by the larger of the two stable eigenvalues.

Third, more flexibility in production (larger elasticity of substitution) implies more capital and output, more leisure, more consumption, less oil usage and more debt. Finally, the fact that the eigenvalues increase with the borrowing premium, (larger η), and production inflexibility (smaller σ), implies that less developed countries will adjust faster to structural changes, consistent with the empirical results of Ibrahim and Hurst (1990) for oil shocks. 4.2. Dynamic adjustment to an increase in the price of oil Figs. 1 and 2 illustrate the dynamic adjustments of key variables in response to a doubling of the oil price from p = 1 to 2. Fig. 1 illustrates the sensitivity of the responses to variations in the elasticity of substitution in production, σ, while Fig. 2 compares the responses as the country's accessibility to the international financial market, η, varies. Table 4 summarizes the short-run and long-run changes in output and welfare following the price increase, as both σ and η vary. The short-run change measures the impact effect that occurs when the higher oil price hits the economy. The long-run output change describes the steady-state response [as given in Table 1], while the long-run welfare change measures the accumulated change in well being, as measured by the intertemporal utility function, Eq. (10), as the economy traverses its transitional path.24 4.2.1. Sensitivity to elasticity of substitution σ Turning to Fig. 1, this is illustrated for η = 0.1 and α3 = 0.06, the case of the more heavily oil-dependent economy; the case α3 = 0.02 is qualitatively similar, but more moderate. Except for the interest rate, the adjustments are presented relative to their respective initial base levels, thus enabling us to see the sensitivity of the relative responses to the structural change.25 From these figures, one can identify several qualitative types of transitional adjustment paths. First, oil usage, output, consumption, and instantaneous welfare all complete the major part of their 24 In comparing the steady-state output responses to those reported in Table 1, one must bear in mind that the latter is only a linear approximation, valid for small changes in p, whereas our numerical simulations pertain to a doubling of p. 25 Thus all variables except r, the initial value of which is 0.055, are normalized to an initial value of one.

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

25

Fig. 1. Sensitivity of response to oil price increase to elasticity of substitution.

respective adjustments with an initial drop on impact, although they continue to decline during the subsequent transition. Second, capital, constrained to adjust continuously, declines gradually. In contrast, debt, which also is constrained to continuous adjustments, partially reverses its time path during the transition. Finally, the price of capital and the interest rate, which also undergo initial jumps on impact, both fully revert to their respective pre-shock levels.

Taking the Cobb–Douglas production function as a convenient benchmark, the immediate effect of doubling the oil price is to reduce its usage dramatically by 52%. The effect on labor is negligible (not illustrated), and with the capital stock fixed instantaneously, output immediately drops by 4.07%. Given the complementarity of oil in production, the decline in its usage reduces the productivity of capital, the immediate effect of which is to reduce its price, q, by around 3% on

26

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

Fig 2. Sensitivity of response to oil price increase to access to world financial market.

impact. The short-run decline in q(t), by reducing the value of capital, raises the borrowing premium, albeit by a very small amount. This leads to a decline in investment, and in the long run the capital stock falls by around 6.7%. Over time, the decline in the capital stock raises the productivity of capital and its value, so that the price of capital, q(t), ultimately reverts back to its pre-shock equilibrium level. For

reasons discussed previously, offsetting effects cause long-run employment to remain unchanged. The net effect is that following an initial decline of around 4%, output declines steadily over time, its proportional long-run reduction being equal to that of capital [6.7%]. Given the productive capacity of the economy, the higher oil costs mean a decline in consumption, the time path of which closely follows

S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

27

Table 4 Changes in output and welfare [parameter values: r⁎ = 0.045, A = 1, α1 = 0.6, γ = − 1.5, n = 0.015, h = 12, β = 0.04, θ = 1.75, δ = 0.05, p0 = 1, p = 2]. Oil dependence α2 = 0.02

Oil dependence α2 = 0.06

ΔY(0)%

ΔW(0)%

ΔỸ%

ΔW̃ %

ΔY(0)%

ΔW(0)%

ΔỸ%

ΔW̃%

σ = 0.75 η = 0.01 η = 0.1 η=1

− 2.319 − 2.900 − 3.100

− 5.014 − 4.121 − 3.976

− 4.644 − 4.807 − 4.822

− 5.725 − 5.130 − 5.033

− 5.575 − 6.989 − 7.479

− 12.077 − 9.920 − 9.568

− 11.101 − 11.477 − 11.510

− 13.582 − 12.190 − 11.969

σ=1 η = 0.01 η = 0.1 η=1

− 1.067 − 1.317 − 1.395

− 1.936 − 1.498 − 1.415

− 2.285 − 2.285 − 2.285

− 2.124 − 1.852 − 1.817

− 3.331 − 4.071 − 4.310

− 5.797 − 4.591 − 4.348

− 6.698 − 6.698 − 6.698

− 6.276 − 5.559 − 5.469

σ = 1.25 η = 0.01 η = 0.1 η=1

− 0.459 − 0.567 − 0.597

− 0.790 − 0.561 − 0.522

− 1.138 − 1.097 − 1.093

− 0.843 − 0.701 − 0.687

− 1.880 − 2.281 − 2.400

− 2.925 − 2.182 − 2.034

− 4.107 − 3.983 − 3.973

− 3.085 − 2.658 − 2.615

Bold denotes the most plausible scenario.

that of output. Moreover, with the small employment effects, the response of welfare mirrors that of consumption, as is seen by comparing Panels vii and viii. The short-run reduction in oil usage dominates the current account and in the short run debt begins to decline. This is accentuated by the declining demand for capital and consumption, but offset by the decline in output. Over the first several years of the transition the decline in debt exceeds that of capital (with its adjustment costs) and the interest rate begins to decline, albeit mildly. After some 15 years or so the decline in output dominates the decline in demand and debt starts to rise, and along with it the interest rate, both reversing the previous trends. Fig. 1 illustrates how, as σ decreases and the flexibility of the production technology is reduced, the ability of the economy to absorb a higher oil price, with less adverse effects on domestic activity, declines. Indeed, the extent to which this occurs is sensitive to relatively modest changes in σ. For example, if σ = 0.75 the shortrun decline in the price of capital is around 6.5%; leading to a long-run reduction in capital and output of over 11%, substantially larger than for the Cobb–Douglas case, with correspondingly larger declines in consumption and welfare. On the other hand, the losses are moderated if σ = 1.25. In all these cases, in the long run oil intensity, (Z/Y), falls, indicating that the empirically established decline in oil intensity is in fact a result of the endogenous response of firms to oil price increases.26 These aspects are reflected in the figures summarized in Table 4. As an example, consider the case of a heavily oil-dependent economy (α2 = 0.06) having moderate access to the world financial market (η = 0.1). Such an economy will suffer a long-run output loss of between approximately 11.5% (for σ = 0.75) and 4% (for σ = 1.25). In the short run, the doubling of the oil price will cause the economy to suffer an output loss of between 7.0% and 2.3%. For a slightly oildependent economy (α2 = 0.02) having moderate access to the world financial market (η = 0.1), these losses are essentially similar, although substantially smaller. They decline approximately proportionately for the Cobb–Douglas to around 2%, and even more than proportionately if σ = 1.25. These numbers are generally consistent with the empirical issues discussed. They confirm the observation that the recent shocks having been less costly than those of the 1970s is a reflection of the decline in

26 In general, the decline in oil intensity seems to be a generalized phenomenon, see, e. g., World Economic Outlook (2008), Nakov and Pescatori (forthcoming), or Dhawan and Jeske (2006). For Latin American countries it seems to be the case that oil intensities did not respond to oil price increases, but this is due to the fact that oil intensities there where already quite low and that energy prices in Latin America are heavily regulated, see Alaimo and Lopez (2008).

the importance of oil in production. They are also consistent with the notion that developing economies, which typically have less flexible production technologies, are more adversely affected by world-wide oil shocks. Indeed, output and welfare losses are very sensitive to further declines in σ. For example, for σ = 0.5, a plausible value for a developing economy (η = 0.1), a slightly oil-dependent (α2 = 0.02) country will suffer a long-run output loss of 10.5% and a corresponding decline in welfare of over 15%. Moreover, our results are in line with recent findings of Bodenstein et al. (2007), who found in their simulations that the higher the elasticity of substitution, the higher the decline in oil usage and the smaller the wealth effect. The response of oil usage is less straightforward to reconcile. While the long-run price elasticity of oil usage slightly in excess of unity [see Table 1, row 3] is plausible, and consistent with empirical evidence [see e.g. Pindyck and Rotemberg, 1983; Atkeson and Kehoe, 1999], the fact that most of the response occurs on impact appears less so. However, these results apply to developed economies and Ibrahim and Hurst (1990) have shown that the time profile of the response of developing countries to oil price shocks is rather different. They find that while the substitution is more limited, the adjustments occur rapidly, leaving little difference between the short-run and long-run responses. Moreover, one can easily reduce the initial response in oil usage and slow down its subsequent adjustment by introducing an adjustment cost function for oil usage, as do Bodenstein et al. (2007). This would augment the dimensionality of the transitional dynamics but would have no consequences for long-run growth and capital accumulation. 4.2.2. Sensitivity to accessibility to world financial market η Fig. 2 illustrates the sensitivity of the response to the accessibility to the world financial market. Since for the Cobb–Douglas production function the long-run responses are independent of the country's accessibility to the world financial market [see Table 1], we consider the case where σ = 0.75, which is also typical for poorer developing economies. We also maintain α2 = 0.06, and allow η to vary by a factor of 100 between 0.01 and 1. Setting σ = 0.75, we still find that the long-run sensitivity to η remains modest (but not zero), so that most of the impact of market accessibility on the economy's response to the oil price shock occurs during the early phases of the transition. If the economy has easy access to the world bond market [η = 0.01], it contracts a large amount of debt with large debt service costs [see Table 3]. While the increase in the oil price will reduce its demand, and therefore the need for additional debt, the substantial servicing of the existing debt will prevent debt from declining too fast, and this in turn will dampen the decline in the interest rate. In addition, the need to service the debt will impose pressure on trying to maintain the output. With the

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S.F. Schubert, S.J. Turnovsky / Journal of Development Economics 94 (2011) 18–29

capital stock fixed in the short run, the decline in oil usage will require an immediate increase in employment, and indeed, we find that employment increases on impact by 3%. The increase in employment increases the productivity of oil and reduces the incentive to cut its usage, which it does by 44% [see Fig. 2(v)]. With debt and the borrowing rate declining slowly, the price of capital, q, rises slowly [after its initial decline], so that capital declines relatively quickly. As access to the world financial market declines, these effects are moderated. The need to increase employment to finance the short-run service declines, and with it the productivity of oil, the use of which declines more rapidly in the short run. In addition, the restricted access to the world capital market leads to the reversal of debt and interest, illustrated in Fig. 2(ii) and (iv), and discussed previously. One further point of interest is that the initial 3% increase in employment that arises when η = 0.01 has significant (negative) welfare effects. From Table 4 we see that as accessibility to the world financial market declines from η = 0.01 to η = 1 the decline in welfare due to a higher oil price (and the corresponding employment effects) declines from 13.6% to 12.0%. In effect, limited access to the world capital market partially insulates a debtor economy from the adverse effects of a higher world oil price. This helps explain why Latin American countries, having more limited access to international financial markets and being less oil-dependent than emerging Asian economies, suffered less from an oil price increase, as Kilian et al. (2009) found. 4.2.3. Losses due to inefficient usage A second reason, in addition to greater oil dependency, why the adverse effect of higher oil prices on a net oil-importing developing country are more severe than for OECD countries is because of their less efficient usage; see International Energy Agency (2004). We briefly address this issue by modifying the augmented CES production function to Y = A½α1 ð1−lÞ

−ρ

−ρ

+ α2 ðεZÞ

+ α3 K

−ρ −1 = ρ



ð9′Þ

where ε; 0 ≤ ε ≤ 1 parameterizes the degree of oil efficiency usage and ε = 1 denotes the benchmark case of completely efficient usage. We have conducted extensive numerical simulations with respect to oil dependence and its efficient usage. Space limitations permit only a brief summary of these results. First, we may note that for the benchmark Cobb–Douglas function (ρ = 0, σ = 1), variations in the degree of oil efficiency have no effect on either output or welfare changes following an oil price increase.27 For σ < 1, (σ > 1) lowering the degree of oil efficiency has qualitatively the same effects on the output- and welfare changes and on the time paths for economic key variables as increasing (decreasing) the degree of oil dependency. As a specific example, consider a debtor country characterized by the parameters σ = 0.75, η = 0.1, α2 = 0.02 (relatively low elasticity of substitution, intermediate access to the world financial market and low oil dependence). With efficient usage a doubling of the oil price leads to short-run losses in output and welfare of 2.90% and 4.12%, respectively, with the corresponding long-run losses being 4.81% and 5.13% [see Table 4]. If ε = 0.5 (50% loss in efficiency) the short-run losses in output and welfare are increased to 3.47% and 4.94%, while the corresponding long-run losses are 5.79% and 6.15%. These are roughly equivalent to increasing the oil dependence parameter to α2 = 0.035, with full oil efficiency, ε = 1. Thus our simulations support the empirical observation that inefficiency in oil usage is a significant issue for developing economies.

27 This can be seen by observing that for the Cobb–Douglas case, Eq. (9) becomes Y= Aεα2(1 − l)α1Zα2Kα3 so that the efficiency parameter is equivalent to the general productivity parameter, A, rather than specific to oil usage.

4.2.4. Creditor country Although our focus has been restricted to the case of a debtor oilimporting country, it is useful to briefly compare the responses of a creditor country to an oil price increase.28 First, the long-run responses are approximately the same for both debtor and creditor economies, reflecting the fact that the long-run responses are essentially independent of the economy's access to the world financial market, and hence its net asset position.29 Differences during the transition are more significant. For example, the creditor economy will suffer a slightly larger short-run output reduction. This is because, having more resources, it enjoys higher equilibrium leisure, and lower employment. While the impact effect of the higher oil price on both economies is roughly equal, it leads to a larger proportional reduction in employment in the creditor economy, causing a larger reduction in its initial output. But this in turn means a larger increase in leisure, so that despite its greater reduction in initial output, welfare in the creditor economy is less adversely affected. Compounding this effect is the response in the interest rate during the transition. The fact that it remains (marginally) below its equilibrium during the transition imposes additional small welfare loss on the creditor economy, so that the accumulated intertemporal welfare losses of the creditor nation ends up being almost the same as that of the debtor. The other difference to note is that the effects of a higher oil price on both the short-run and intertemporal welfare of a creditor country are less sensitive to its access to the world financial market than they are for a debtor nation. This is because, for a creditor economy, as η increases, the smaller reduction in consumption which occurs is offset by a larger increase in leisure, leaving a small net effect on welfare; for a debtor economy these two effects are mutually reinforcing.

5. Conclusions In this paper we have analyzed the impact of an increase in the price of an imported intermediate input (oil) on the economic performance of a small developing economy. The key feature of the economy is that it has limited access to the world financial market, specified in terms of borrowing costs that increase with its debt/ equity ratio, as an index of its debt serviving ability. Being based on a neoclassical growth model, our analysis incorporates the feature that the oil price has no long-run growth effects, although it does have permanent level effects. Attention has been focused on the extent to which the impacts of oil price shocks are sensitive to structural characteristics such as the economy's internal production structure and its access to the world financial market. In this regard we show that the long-run impact is much more dependent upon the former than on the latter. The two critical quantities summarizing the long-run effects are (i) the share of oil to labor in output and (ii) the elasticity of substitution in production. In the case of the Cobb–Douglas production function, international financial market accessibility is irrelevant in determining the long-run effects, although it is important in the short run. It is also important in determining how rapidly the economy adjusts to structural changes, including an oil price increase. Our analysis has supplemented the formal theoretical analysis with numerical simulations, thereby enabling us to characterize the short-run dynamics. Some elements of the adjustments to an oil price shock are completed relatively quickly, while other parts of the adjustments occurs gradually. Overall, our numerical simulations are able to replicate much of the empirical evidence used to characterize 28 The corresponding numerical simulations for the creditor country are available in an expanded version of this paper. 29 Line 2 of Table 1 brings out an important asymmetry between a debtor and a creditor. While an increase in the oil price will cause a debtor country's long-run net foreign asset position to improve, it will cause a creditor country's net long-run foreign asset position to deteriorate.

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the effects of the recent oil price increases on the economy. The numerical simulations we undertake highlights just how sensitive the effect of the oil price is to changes in the elasticity of substitution. For example, decreasing the elasticity of substitution from 1 to 0.75 increases the adverse effects by over 100%. This suggests that developing economies can benefit substantially from increasing the flexibility of their production technologies if they wish to avoid the costs associated with higher oil prices. Finally, we conclude with two caveats. First, one issue that has received attention and we have not addressed concerns possible asymmetric responses to oil price shocks; see Mork (1989), Hamilton (1996). Reasons for the asymmetry include policy responses and adjustment costs associated with changes in oil usage [see Atkeson and Kehoe, 1999, and Wei, 2003]. While this nonlinearity is important if one deals with short-run oil price fluctuations where both price increases and decreases occur with regularity, it is less relevant for our analysis where our concern has been with studying a secular, long-run change (increase) in the oil price, which is not reversed. Moreover, the evidence of asymmetric effects of oil price shocks for developing countries is less compelling than it is for OECD countries; see Dargay and Gately (1995), who conduct such a comparison. And in fact, even for OECD countries the evidence in favor of asymmetries has recently been questioned [Kilian and Vigfusson, 2009]. In any event, our framework can accommodate asymmetric adjustments to positive and negative changes in oil prices by, for example, specifying the adjustment cost parameter, h, in investment that is much larger for economic expansions (positive investment) than it is for contractions. Second, our analysis has treated the oil price as being exogenous. For the small developing country we are envisioning this is plausible. But in reality, oil prices are determined by OPEC as part of strategic negotiations with the developed Western economies. An interesting extension would be to model this process and to study its impact on the developing economies of the world. Acknowledgements Much of the research for this paper was completed while Schubert was visiting the University of Washington, funded by a grant from the Free University of Bozen-Bolzano. Turnovsky's research was supported in part from the Castor endowment at the University of Washington. The constructive comments of two anonymous referees and the editor, Gordon Hanson, are gratefully acknowledged. References Alaimo, V., Lopez, H., 2008. Oil intensities and oil prices: Evidence for Latin America. Policy Research Working Paper 4640, The World Bank, Washington DC. Atkeson, A., Kehoe, P.J., 1999. Models of energy use: putty-putty versus putty-clay. American Economic Review 89, 1028–1043. Auerbach, A., Kotlikoff, L., 1987. Dynamic Fiscal Policy. Cambridge Univ. Press, New York. Backus, D.K., Crucini, M.J., 2000. Oil prices and the terms of trade. Journal of International Economics 50, 185–213. Backus, D.K., Kehoe, P.J., Kydland, F.E., 1994. Dynamics of the trade balance and the terms of trade: the J-curve? American Economic Review 84, 84–103. Barsky, R.B., Kilian, L., 2004. Oil and the macroeconomy since 1970s. Journal of Economic Perspectives 18, 115–134. Blanchard, O.J., Galí, J., forthcoming. The macroeconomic effects of oil price shocks: Why are the 2000s so different from the 1970s? In: Galí, J., M. Gertler, M. (eds.), International Dimensions of Monetary Policy, University of Chicago Press (Chicago, IL). Bodenstein, M., Erceg, C.J., Guerrieri, L., 2007. Oil shocks and external adjustment. International Finance Discussion Papers Number 897.

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