Capital Adjustment and the Optimal Fuel Choice.

• Author: Hyland, Marie

1. INTRODUCTION

   This paper aims to bring a new perspective on the issue of interfuel substitution by revisiting the important and largely overlooked relationship between the dynamics of capital stocks and the optimal fuel choice. The ability of firms to switch between fuel sources has important implications for economic growth, particularly in the context of economic adjustment to oil price shocks and climate policies (as highlighted by Hall (1986), Acemoglu et al. (2012), Stern (2012), and Papageorgiou et al. (2017), among others). While there is a large body of economic literature that looks at the issue of fuel substitution, few of these studies explicitly model the choice of fuels and corresponding fuel-using capital stocks. Earlier empirical studies of interfuel substitution, such as Fuss (1977) and Pindyck (1979), employ a two-stage approach that, in the first stage, estimates the degree of substitutability between different fuels and, in the second stage, estimates the relationship between the energy aggregate and other factors of production. More recent studies (for example, Jones, 1995; Bjorner and Jensen, 2002; Urga and Walters, 2003; Serletis and Shahmoradi, 2008; Serletis et al., 2010) follow the same approach and mainly focus on methodological innovations of the first stage, introducing dynamic functional forms for estimating demand for different fuels. The validity of such approaches hinges on the assumption that energy and other factors are weakly separable in the production process. This assumption rules out the possibility that firms determine jointly their fuel mix and capital stock, and it does not allow for the possibility that there may be capital adjustment costs associated with a change in the energy inputs used. (1)

   A similar approach has been used to address inter-fuel substitution in large scale energy and environmental computational models, in particular, computable general equilibrium (CGE) models and integrated assessment models. For example, in the energy-environment extension of a well known GTAP CGE model, the GTAP-E model (Burniaux and Truong, 2002), the production function is modeled using a technology tree, based on a nested CES production function. This structure assumes that primary and intermediate factors of production are weakly separable. In the first nest of the production function, the energy aggregate is calculated based on substitution between different fuel types. In the second nest, this energy aggregate is combined with capital inputs to form a capital-energy composite. In the following nest, capital and energy are combined with labor and material inputs to produce output. This approach has been largely adopted in a variety of other climate-economy integrated assessment models (see, e.g., Paltsev et al., 2005; Burniaux and Chateau, 2008).

   We argue that this approach, adopted in both econometric and economic modeling studies of energy and environment, has several important limitations. The first limitation relates to the choice of the nesting structure used by these models. The assumption that the choice of fuels used in the aggregate energy mix is separable from decisions related to the optimal choice of capital ignores the short-run complementarity between energy and capital inputs for a given production technology. In reality, capital stocks tend to be highly idiosyncratic, and very few types of energy-using technologies can utilize multiple fuels (Steinbuks, 2012). (2) This is especially relevant for electricity-using capital stocks, which are particularly difficult (if not impossible) to convert to accepting other fuels. That is, the relationship between capital technologies and corresponding fuels is fixed, at least in the short term. This implies that firms do not pick a particular fuel, but rather a particular technology bundle that combines capital with a specific type of energy input. (3)

   The second potential limitation of the approach is that the capital adjustment process is not properly accounted for. The economic and econometric models of interfuel substitution are either static, where capital adjustment is ignored, or recursive dynamic, where capital adjustment costs are implicitly estimated using lagged values of output or prices as a proxy for capital. This implicit estimation largely ignores asymmetries in capital adjustment due to irreversibilities of capital, and is prone to measurement error as non-capital inputs to production tend to adjust faster. Failing to account for the capital adjustment process and its associated costs contradicts the economic literature that finds these costs non-trivial; see, for example, Caballero (1999), Caballero and Engel (1999), and Caballero and Engel (2003). Furthermore, the more specific role of adjustment costs in the transition to low-carbon and energy-efficient technologies has been highlighted by Jacoby and Sue Wing (1999), Wing (2008), and Steinbuks and Neuhoff (2014).

   Our paper proposes a novel approach to analyze interfuel substitution that explicitly incorporates heterogeneous energy-using capital stocks in the estimation of optimal fuel choice. We model the capital and energy use decisions jointly, implying that firms choose capital and energy inputs concurrently. The fundamental choice that firms make is among different competing fuel-using technologies; this contrasts with the traditional approach in which firms first choose which fuels to use and then choose the other factor inputs. (4)

   The model we formulate draws on two previous studies; one that is concerned with energy and capital utilization (Atkeson and Kehoe, 1999), and another that deals with the adjustment dynamics of heterogeneous capital goods (Goolsbee and Gross, 2000). Following Atkeson and Kehoe (1999), we assume that energy inputs and capital stocks are complements in the short run as, for a given level of capital stocks, a fixed quantity of energy inputs is needed. In the long run capital and energy will be substitutable as firms can respond to rising energy prices by investing in new, presumably less energy-intensive, capital stocks. We incorporate this "putty-clay" structure of Atkeson and Kehoe (1999) in the modeling framework of Goolsbee and Gross (2000) to estimate the form of adjustment costs for heterogeneous capital stocks.

   Specifically, we develop a structural model to estimate the frictionless stock of capital for different types of fuel-using technologies. In this context, the "types" of energy-using capital refer to the specific fuels used to run the capital stocks, whereas the frictionless stock of capital is the optimal amount of each type of capital that firms would employ in the absence of any adjustment costs. We then outline how to non-parametrically estimate the relationship between frictionless and actual capital stocks to reveal information on the nature of the adjustment costs faced by firms.

   The main contribution of our paper is methodological. That is, we develop and outline an appropriate model of fuel substitution, which can be applied to the firm-level data. To illustrate how the model is estimated we use a rich firm-level panel data for the Republic of Ireland, which is, to our knowledge, the best available dataset that has been previously employed to analyze fuel choice problems. Because of the imperfect nature of our data, most importantly due to the absence of clearly delineated fuel-using capital stocks, our estimates should be interpreted with a degree of caution. This caveat notwithstanding, our empirical results suggest that the costs of adjusting capital stocks in response to changing fuel prices are large for all types of capital. These costs are an order of magnitude higher than in studies where capital adjustment costs are implicitly estimated. Furthermore, these results suggest that investment in fuel-using capital stocks may be irreversible; this is indicative of prohibitively large adjustment costs associated with divestment of assets.

   These findings have important implications for both econometric and economic modeling studies of interfuel substitution. Failure to incorporate proper heterogeneous fuel-using capital adjustment dynamics in econometric studies will likely result in the downward biased long run elasticities of optimal fuel choice. Similarly, considering more appropriate nesting structure of capital energy interaction and revising the magnitude of fuel-using capital adjustment costs would yield an improvement in robustness of dynamic forward looking energy-environmental CGE models.

   Our paper proceeds as follows: in section 2 we explain our theoretical model and outline our estimation strategy. In section 3 we present the data used in our analysis. Section 4 outlines the results of the empirical illustration our model. Finally, in section 5 we briefly draw some concluding remarks.

   (2.) METHODS

   2.1 Theoretical model

   The conceptual framework for estimating fuel choice is based on the putty-clay model of energy use described by Atkeson and Kehoe (1999), extended to account for heterogeneous fuels. In our model there is a number of energy-using capital technologies (V) which are combined with energy fuels (E) in fixed proportions to yield a given amount of capital services (Z). Thus, in the short run, each type of capital is tied to a particular energy source, making energy and capital complementary inputs for a given technology choice. In the long run, the technologies will be substitutable as firms can adjust their capital stocks by investing in machinery and equipment that utilizes other fuels.

   Following Atkeson and Kehoe (1999) we assume that, in the short run, a unit of capital of fuel using technology V provides capital services in combination with a fixed quantity, 1 / V, of fuel E. Combining K units of capital of technology V with E units of fuel yields capital services (Z) as determined by:

   Z = min(K / V, E) f (V) (1)

   The intuition behind this is that if E &gt...