CARBON LOCK‐IN: THE ROLE OF EXPECTATIONS

• DOI: http://doi.org/10.1111/iere.12255
• Published date: 01 November 2017
• Date: 01 November 2017
• Author: Gerard Meijden,Sjak Smulders

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 4, November 2017

CARBON LOCK-IN: THE ROLE OF EXPECTATIONS∗

BYGERARD VAN DER MEIJDEN AND SJAK SMULDERS1

Vrije Universiteit Amsterdam, The Netherlands, and Tinbergen Institute,The Netherlands;

Tilburg University, The Netherlands, and CESifo, Germany

We argue that expectations about future energy use affect the transition from fossil to renewables because

of an interaction between innovation and resource scarcity. This article presents a model of directed technical

change to study this interaction. We find that fossil-saving technical change erodes the incentives to implement

renewables. Conversely, the anticipation of a transition to renewables diminishes the incentives to invest in

fossil technology. As a result, two equilibria may arise, one with a transition to renewables and with low fossil

efficiency and one without renewables and with high fossil efficiency. Expectations determine which equilibrium

arises.

1. INTRODUCTION

For many decades, a major engine of growth in the world economy has been the reliable

supply of fossil energy resources. Policymakers have been forced, however, to rethink the

dominant role of fossil fuels in energy supply when facing the challenge of combating climate

change and the global concern about the sustainability of current living standards. Part of

the solution to both the climate change and the sustainability problem may be a phasing out

of nonrenewable natural resources such as fossil fuels and the implementation of backstop

technologies that provide renewable substitutes. A more incremental solution would arise from

improving resource efficiency and slowing depletion of fossil resources. The question arises

how market parties respond to the challenges and which incentives arise over time to invest in

resource saving and energy transition. We argue that the energy future of a growing economy

is crucially shaped by a two-way interaction between innovation decisions and energy supply

decisions. Prospects about future energy generation technologies may affect not only the time

path of fossil fuel supply, but also the pace and direction of technical progress. Conversely,

the speed and direction of technical progress are crucial for the transition from fossil fuels to

backstop technologies. This two-way interaction or complementarity between innovation and

resource supply may create multiple equilibria and self-fulfilling prophecies.

Since our question concerns the dynamics of energy use and technology in a growing economy,

we naturally frame our analysis in a growth model with natural resources and endogenous

technical change. Our starting point is the Dasgupta–Heal–Solow–Stiglitz (DHSS) model2in

which a scarce nonrenewable resource (fossil) is an essential input in production. We allow fossil

energy to be replaced by renewable energy that can be generated at a constant cost, the so-called

backstop technology (cf. Nordhaus, 1973). As is well known, in the DHSS model, growth cannot

∗Manuscript received December 2014; revised June 2016.

1The authors would like to thank Christian Bogmans, Reyer Gerlagh, David Hemous, Jenny Ligthart, Rick van

der Ploeg, Francesco Ricci, Luc Rouge, Mark Schopf, Cees Withagen, Aart de Zeeuw, Gijsbert Zwart, participants of

conferences and seminars in Amsterdam, Berlin, Fontainebleau, Hamburg, London, and Toulouse, and two anonymous

referees for their valuable comments. The authors gratefully acknowledge financial support from FP7-IDEAS-ERC

Grant No. 269788 (GP) and FP7-SSH Grant No. 613420 (GLAMURS). Please address correspondence to: Gerard

van der Meijden, Department of Spatial Economics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV,

Amsterdam, The Netherlands. Phone: +31-20-598-2840. E-mail: g.c.vander.meijden@vu.nl.

2See Dasgupta and Heal (1974), Solow (1974a, 1974b), Stiglitz (1974a, 1974b), Benchekroun and Withagen (2011),

and Van der Ploeg and Withagen (2014).

1371

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1372 VAN DER MEIJDEN AND SMULDERS

be sustained unless resource-augmenting technical change offsets the negative growth impact

of declining availability of the nonrenewable resources. At the same time, labor-augmenting

technical change fuels growth and boosts the demand for energy. Energy demand thus results

from the balance between two types of innovation, resource-augmenting and labor-augmenting

technical change. We incorporate both types in our analysis and allow profit incentives to guide

innovators in how much and in which direction to innovate. Thus, we merge the DHSS model

with a model of directed technical change.3

Our main finding is that the replacement of fossil resources might require a coordination of

expectations, because a coordination failure may arise due to the existence of a strategic com-

plementarity in investment in resource conservation and investment in resource-augmenting

technologies. High investment in resource conservation stimulates investment in resource-

augmenting technologies and vice versa, so that if atomistic investors make investment deci-

sions on resource conservation or innovation, their return depends positively on the investment

decisions of other investors on the complementary investment, innovation, or conservation,

respectively (cf. Cooper and John, 1988). Intuitively, the reasoning is as follows: If the costs of

generating energy with the backstop technology are sufficiently low, it is a viable alternative

to fossil fuels in the long run. However, resource conservation together with investment in

resource-saving technical change can make fossil effectively cheaper to use than the backstop.

Whether fossil is phased out or not in equilibrium then depends on the expectations of fossil

suppliers and innovators. A self-fulfilling prophecy arises since, when it is expected that the

backstop will be implemented, the market for the resource and for resource-saving inventions

will be small, implying that conservation and innovation incentives will be eroded; this makes

the backstop relatively more attractive and thus justifies the expectation that the backstop

will be implemented. Conversely, when no future backstop deployment is expected, resource

conservation and resource-saving technical change become more profitable, thus making the

resource indeed relatively more attractive in the long run. Only when the backstop cost is below

a certain threshold will it always be deployed in the long run.

Our results imply that it might be hard to steer the economy away from the current dependence

on fossil fuels because it is “locked into fossil” (cf. Unruh, 2000): Mutual welfare gains from

an economy-wide change in investment decisions may not be realized, because no individual

investor has an incentive to deviate from the initial market equilibrium (cf. Cooper and John,

1988).

Lock-in and multiple equilibria are studied in the literature in several settings.4Cooper

and John (1988) show that a necessary condition for obtaining multiple equilibria in a static

setting is the existence of strategic complementarities, which are said to arise “when the optimal

strategy of an agent depends positively upon the strategies of the other agents” (Cooper and

John, 1988, p. 441). Murphy et al. (1989) use a model with strategic complementarities between

industrializing sectors to show that self-fulfilling expectations may exist: The willingness of

firms to invest depends on their expectation that other firms invest, because the future market

size that a single firm faces depends on the investment by the other firms. In the growth

literature, the strategic complementarities are between different capital stocks. In Chamley

(1993) and Benhabib and Farmer (1994), a strategic complementarity between the stocks of

physical and human capital may create a multiplicity of equilibria (or, in their terminology:

“indeterminacy”) in Uzawa-Lucas or Romer type of endogenous growth models (cf. Uzawa,

1965; Romer, 1986; Lucas, 1988). Benhabib and Perli (1994) show that the traditional distinction

between physical capital and human capital is not necessary: Even with only human capital,

self-fulfilling prophecies can arise as long as the return to investment in an individual’s private

human capital stock depends on the human capital investments of others through an aggregate

3The literature on induced innovations was introduced by Hicks (1932) and more recently formalized in the directed

technical change models of Acemoglu (1998, 2002, 2003) and Kiley (1999). We choose for investment in knowledge

instead of in physical capital to orient our analysis toward the long run, when technical change instead of capital

accumulation is the determinant of output growth.

4Arthur (1989) and David (1985) introduce the notion of lock-in into economics.

CARBON LOCK-IN:THE ROLE OF EXPECTATIONS 1373

capital stock externality. Benhabib and Perli (1994) make a distinction between local and global

indeterminacy as a reason for the existence of multiple equilibria. Local indeterminacy occurs

if there exist multiple transitional paths toward a certain balanced growth path, whereas global

indeterminacy arises from the existence of multiple balanced growth paths that each can be

approached by identically endowed economies with identical initial conditions. Recently, Cozzi

(2005, 2007) has explored the role of multiple equilibria in a Schumpeterian quality ladders

model. He shows that the number of sectors in which research and development (R&D) takes

place may depend on self-fulfilling expectations. Our study complements the literature on

multiple equilibria by showing that the existence of global indeterminacy may have important

consequences for the transition from fossil fuels to renewable energy sources in a model with

directed technical change.

Although strategic complementarity is a necessary condition for self-fulfilling prophecies, the

seminal paper by Krugman (1991) shows that initial conditions, represented by the initial value

of a stock variable, matter as well. The role of “history” can dominate that of “expectations”

for selecting one of the multiple equilibria. In his model, the historically determined costs

advantage of one of the two production sectors must be small enough to make investment into

the other sector an equilibrium. Krugman’s model features a single state variable and a single

non-predetermined variable and can be reduced to an insightful phase diagram with multiple

adjustment paths to the two steady states.5Our model is more complex due to multiple state

and non-predetermined variables and due to regime changes, but our analysis of the role of

history versus expectations relies heavily on Krugman’s.

In the context of energy use, there are only a few other studies in which multiple equilibria are

discussed. Acemoglu et al. (2012) construct a model with a fossil and a renewables’ steady state

to study lock-in that arises from initial conditions or “history,” viz. innovation in pollution-

intensive sectors in the past. Our analysis is complementary to theirs in that we emphasize

lock-in that arises from expectations instead of history. Moreover, we adopt a different view

of technical change in which society has to choose between incremental change that cannot

make scarce resource inputs redundant (because of poor substitution) and radical change in

the form of the transition to the backstop. Also, in the context of energy use, Schmidt and

Marschinski (2009) construct a static, partial equilibrium model to show that, due to a strategic

complementarity between investment in technology and production capacity, two equilibria

can coexist: one with a low and one with a high supply of renewable energy. They use their

model to study the possibility of a “technological breakthrough” in the renewable energy sector.

Cheikbossian and Ricci (2013) consider a game between a resource owner and an R&D firm and

show that depending on expectations one out of two equilibria is selected, one with high R&D

and slow depletion and one with low R&D and high depletion. Their two-period framework

cannot explicitly address the link to economic growth and ignores the possibility of a radical

technology change in the form of a backstop, which is the focus of our study.

Directed technical change has been studied in the context of energy scarcity in several stud-

ies, with Smulders and de Nooij (2003) as an early example. A key question in this literature

concerns the role of resource-augmenting technical change relative to other types of technical

change. With resource inputs growing at a lower rate than other inputs, resource-augmenting

technical change dominates along a balanced growth path, provided that substitution possibili-

ties are poor, as shown in, e.g., Andr´

e and Smulders (2014). With good substitution, however,

resources are not essential for growth and growth can be sustained without technical change

in the resource sector, as in Acemoglu et al. (2012). In the model of Di Maria and Valente

(2008), in which a nonrenewable resource and physical capital are both essential for produc-

tion, there may be capital-augmenting technical progress in the short run, but technical change

5Technically, Krugman (1991) shows that, in his model, the existence of a role for expectations in selecting the

equilibrium requires complex roots around the internal steady state. However, this result depends on the linearity of

his system. Matsuyama (1991) shows that, in a more general model, expectations may select the equilibrium also in the

case of real roots.