On the estimation of short- and long-run elasticities in U.S. petroleum consumption: comment.

• Author: Bentzen, Jan
• Position: Comment on article by C.T. Jones, Southern Economic Journal, p. 687, 1993

1. Introduction

   In a recent paper in this journal, Jones [13] has advocated for the use of the general-to-simple modelling strategy in estimating short- and long-run elasticities in energy consumption. In contrast to the simple-to-general modelling approach, which is most often used in energy demand studies, the general-to-simple strategy starts by estimating a deliberately overparameterized unrestricted autoregressive distributed lag model. Various parameter restrictions are then tested sequentially until a parsimonious representation of the underlying data-generating-process is obtained.(1)

   In an empirical application using this approach, with U.S. time-series data for petroleum consumption, the real price of oil, and real GNP, Jones ends up with an apparently well-specified restricted model containing only seven parameters, and with economically plausible estimates of short- and long-run price and income elasticities.

   In this note we argue that there is an important initial step missing in the analysis carried out by Jones, namely an investigation of the time-series properties in terms of integration and cointegration of the time series involved. The implicit assumption underlying the modelling approach followed by Jones is that the variables are stationary stochastic processes, which means that they have constant unconditional means and variances. However, recent research suggests that the variables involved in energy demand relationships are usually not stationary in levels, but have to be differenced in order to be stationary.(2) Such variables are said to be integrated of order one, I(1), which means that they have a unit root in their autoregressive representation, see Engle and Granger [3]. I(1) behavior of economic variables has profound implications for estimation and statistical inference. First, the use of traditional asymptotic inference (e.g., t-tests and F-tests of linear restrictions on the parameters) may become invalid in regressions containing the levels of the variables, like equation (1) in Jones [13]. Second, the calculation of long-run elasticities from such level-regressions presupposes that the variables are cointegrated in the sense of Engle and Granger [3], since cointegration among non-stationary variables is a necessary condition for the existence of a long run relationship between them.

   Below we investigate the time-series properties of the data used by Jones, and find that petroleum consumption, the real price of oil, and real GNP all appear to be I(1) processes that do not cointegrate. This implies either that there does not exist a stable long run relationship between the levels of petroleum consumption, oil prices and income, or that there is one or more important variables missing in explaining energy consumption in the long run. Furthermore, it implies that the proper specification of the energy demand schedule is a first-difference specification without an error-correction term. When we estimate such a model using Jones's data, we end up with a structurally stable model, which is more parsimonious compared to his final model (in the sense that fewer parameters are estimated). In accordance with the time-series properties of the data, our model does not contain any long-run relationships between the levels of the variables. It...