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

• Author: Jones, Clifton T.
• Position: Response to article by J. Bentzen and T. Engsted in this issue, p. 783

1. Introduction

   In the preceding comment [3], Bentzen and Engsted present evidence that U.S. oil consumption ([q.sub.t]), U.S. real oil prices ([p.sub.t]) and U.S. real GNP ([y.sub.t]) - all measured in natural logarithms - are not cointegrated over the period 1947-1989. This conclusion is based upon results from the two-step cointegration testing procedure suggested by Engle and Granger [5] and the multivariate cointegration testing procedure of Johansen [6; 7]. If [q.sub.t], [p.sub.t] and [y.sub.t] are not cointegrated, then a long-run equilibrium relationship between the levels of these three model variables does not exist, rendering any estimates of long-run price and income elasticities "unreliable". In this reply I use an alternative approach to estimating the long-run relationship, or cointegrating vector, and find that [q.sub.t], [p.sub.t] and [y.sub.t] are, in fact, cointegrated, so that long-run petroleum demand elasticities can legitimately be calculated.

2. Evidence for Cointegration

   Like Bentzen and Engsted, my cointegration analysis is based on the data set of annual observations from 1947 to 1989 I provided in an appendix to my earlier article [8, 699]. I accept without comment the findings presented in their Table I that all three model variables are non-stationary over this period, a necessary pre-condition for the existence of a cointegrating relationship between them. However, unlike Bentzen and Engsted, I do not estimate the long-run relationship, or cointegrating vector, from a simple static regression as suggested by Engle and Granger. Instead, I follow the suggestions of Banerjee, Galbraith and Dolado [2] and Charemza and Deadman [4, 157-8] and estimate the long run relationship from an unrestricted autoregressive-distributed lag (ADL) model with five lags on each model variable. This ADL (5,5,5) model can be written as:

   [q.sub.t] = [Alpha] + [summation of] [[Delta].sub.j][q.sub.t-j] where j=1 to 5 + [summation of] [[Beta].sub.j][p.sub.t-j] where j=0 to 5 + [summation of] [[Gamma].sub.j][y.sub.t-j] where j=0 to 5 + [u.sub.t]. (1)

   The cointegrating vector which defines the long run equilibrium relationship has the form (-1, [[Alpha].sup.*], [[Beta].sup.*], [[Gamma].sup.*]) where [[Alpha].sup.*] = [Alpha]/(-1 + [Sigma][[Delta].sub.i]) and [[Beta].sup.*] and [[Gamma].sup.*] are the long run price and income elasticities, respectively, calculated as [[Beta].sup.*] = -[Sigma][[Beta].sub.i]/(-1 + [Sigma][[Delta].sub.i]) and...