A single-equation study of U.S. petroleum consumption: the role of model specification.

• Author: Jones, Clifton T.

1. Introduction

   The price responsiveness of U.S. petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of U.S. energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas & electricity) for various consumer sectors (residential, industrial, commercial).(1) Following these early multi-equation studies there have been several single-equation studies of aggregate U.S. petroleum consumption |4; 3; 9; 5; 6~. These single-equation studies have found that U.S. demand for petroleum products can be quite price inelastic in the short run (estimates range from -0.04 to -0.08) but exhibits long lags of anywhere from 6 to 10 years that yield long run price elasticities ranging from -0.25 to -0.56. Income or GNP elasticities are usually found to be much higher (0.69 to 1.13) with the complete response often assumed to occur in the current period.

   Single-equation studies are often justified as efficient shortcuts, or reduced forms for identifying the central behavioral aspects of a particular market. The main issue addressed in this paper is the extent to which the existing empirical results from single-equation studies of aggregate U.S. petroleum consumption have been influenced by the researchers' choice of dynamic model specification. This question is relevant because the econometric methodology usually followed in such studies is to start with a relatively simple specification, such as a partial adjustment model or some kind of a distributed lag structure on price alone. This initial specification choice is rarely justified, except possibly to cite its previous success in similar work. Given that models which produce insignificant or perverse coefficient estimates are not usually publishable, the reported specification is almost certain to provide "reasonable," statistically significant estimates with the correct signs.

   The primary diagnostic test of the chosen specification is the Durbin-Watson test statistic, or perhaps Durbin's "h" statistic in the presence of lagged dependent variables. When this test gives evidence of serial correlation in the residuals, the usual response is to "correct" for this by estimating a first or second-order autoregressive model (AR(1) or AR(2)). Should this easily-implemented correction not solve the problem, there is a tendency to chalk it up to some kind of unknown specification error or deficiency in the data, leaving any further investigation as a suggestion for future research.

   Hendry |12, 223~ argues that this type of specification search (from simple to general) characterizes much of applied work, and is "a reasonably certain path to concluding with a mis-specified relationship" if it is not accompanied by rigorous diagnostic testing.(2) Additionally, he believes that a simple-to-general modeling approach often involves "excessive presimplification with inadequate testing" |12, 222~ or what Leamer has called a "prejudiced search for an acceptable model" |13, 126~.

   Mis-specification of the dynamic adjustment process for U.S. petroleum consumption could lead to biased elasticity estimates with corresponding inaccurate forecasts. A mis-specified model might appear to suffer structural shifts or "changes in regimes" when in reality the true underlying structural economic relationship has remained unchanged while one or more of the exogenous variables have somehow changed their behavior |12, 219~. Similarly, a mis-specified model may provide biased evidence of parameter symmetry, leading to further inaccuracies in forecasting. Structural change and/or parameter symmetry have been the focus of many single-equation studies of U.S. petroleum consumption |3; 9; 5; 6~.

   Given the importance of oil to the U.S. economy and the high degree of uncertainty associated with the future path of world oil prices, it seems appropriate to stop and closely investigate the issue of possible model mis-specification in the U.S. demand for petroleum products. Following Hendry's suggestions |12~, we first pursue a general-to-simple dynamic specification search, sequentially testing various restrictions on a deliberately overparameterized general model. The aim is to obtain a data-based simplification of a general model that provides a parsimonious representation of the underlying data generation process. Among other topics |7; 15~, Hendry's modeling approach has been used to analyze aggregate OECD energy demand |1~, yielding price elasticity estimates comparable to existing studies but a long run income elasticity twice as large as the consensus estimate of unity.

   Next, rather than to just report "one more set" of elasticity estimates, we use the same data set to estimate the parameters of several typical alternative single-equation models, including the widely-used partial adjustment model, a simple static model, and the popular polynomial distributed lag (PDL) on price. These alternative estimates over the same sample period provide some indication of how our results differ from those of other researchers who might have chosen a different specification by following a simple-to-general approach.

   Besides revealing the impact of model specification on our elasticities, all but one of these alternative models (the PDL) can be seen as nested or restricted versions of a more general dynamic specification, and therefore can be tested for their acceptability using standard statistical tests. In each case, we find that the restrictions implied by the alternative models are not supported by the data, suggesting that their selection and use to analyze U.S. petroleum consumption is inappropriate. Furthermore, a comparison of forecast errors (ex post and historical) shows substantial variation in forecasting performance across the various models. Hendry's general-to-simple modeling approach is seen to provide a data-acceptable restricted model that outperforms the alternatives and is free of the prior subjective prejudices of the researcher for a particular specification.

2. Data

   The data set used for the following estimations contained annual observations over the period 1947-89. U.S. petroleum consumption (in thousand barrels per day) was measured by "petroleum products supplied" as reported in Table 50 of Annual Energy Review 1989 by the Energy Information Administration of the U.S. Department of Energy (DOE/EIA). The price of oil (in current dollars per barrel) was measured by refiner acquisition cost (composite) as calculated by DOE/EIA for 1968-89, published in Table 68 of Annual Energy Review 1989. Oil prices prior to 1968 were generously supplied by Dermot Gately, calculated as the domestic average wellhead price plus a 10 percent markup for transportation costs. All prices were converted to 1982 dollars using the implicit GNP deflator (1982 = 100) published in Survey of Current Business by the U.S. Department of Commerce. U.S. GNP (in billions of 1982 dollars) was also obtained from the Survey of Current Business.

3. General-to-Simple Modeling Approach

   An application of Hendry's general-to-simple modeling approach to the study of U.S. petroleum consumption would involve first estimating an unrestricted autoregressive distributed lag model (denoted ADL (|m.sub.0~, |m.sub.1~, |m.sub.2~)) of the form:

   |q.sub.t~ = |Alpha~ + |summation of~ ||Delta~.sub.j~|q.sub.t-j-1~ where j=0 to |m.sub.0~ + |summation of~ ||Beta~.sub.j~|p.sub.t-j~ where j=0 to |m.sub.1~ + |summation of~ ||Gamma~.sub.j~|y.sub.t-j~ where j=0 to |m.sub.2~ + |u.sub.t~ t = 1,2,...,T (1)

   where the three lag lengths (|m.sub.0~, |m.sub.1~, |m.sub.2~) are initially set at the same maximum value (in this case, 4). All variables...