## Cointegrating energy demand equations

Hunt and Manning (1989) estimate an aggregate energy demand in the UK on data for 1969-86 using cointegration techniques (see Engel and Granger 1991). The cointegration literature recognizes that the time-series properties of a set of observations are affected by their stationarity. In particular, if the variables in (9.1) are not stationary, the t statistics and the R2 are likely to be invalid (Engel and Granger 1987).

When the time-series variables used to estimate (9.1) are tested for stationarity, using the Dickey-Fuller and augmented Dickey-Fuller tests (Pesaran and Pesaran 1991:48), it appears that all the variables with the exception of temperature must be differenced once to produce stationarity, i.e. they are integrated of order 1, a result also found by Hunt and Manning (1989) for aggregate energy use by all sectors. These results suggest the two-stage procedure (Hall 1986; Engel and Granger 1987, 1991) of (i) estimating a long-term relationship from a set of cointegrating variables ((9.2) below) and testing that the residuals, EC, from the regression are stationary (Pesaran and Pesaran 1991:96) and then (ii) estimating a dynamic equation, including these residuals lagged one period ((9.3) below).

In E = a, + a2*\nY + a,*lnRPE + T + «5*time d In £ = b, + &2*d Ln £(-1) + b?*d In T + &4*dlny

where ln denotes natural logarithm, d ln denotes differences in logarithms, (-1) denotes a lag of one year, aj, a2,a3, a4, a5, b1, b2,b3, b4, b5, b6, b7, b8 are parameters, E is total delivered energy in million therms, Y is a measure of economic activity, RPE is the price of energy relative to that of all goods and services, T is deviation from trend temperature, time is a time trend, EC is the error correction term in (9.3) from the residuals in (9.2) and e2 is an error term.

This more general specification allows for much more possibility of short-term effects than (9.1), including a short-term income elasticity distinct from that in the long term. Table 9.5 shows the long-term equations with the price elasticities imposed at base specification values. In three sectors (chemicals, other industry and rail transport) the activity elasticity was also imposed to prevent negative estimated values. Wrong-signed parameters for temperature were dropped. The parameters and t ratios (in absolute values) for the short-term equations are shown in Tables 9.6 and 9.7; the full specification in (9.3) was estimated first and insignificant parameters were dropped; the tables show the parameters remaining after this procedure was completed. Table 9.8 shows the R1 statistic from the difference equation, the Durbin-Watson statistic (DW) and the standard error. There are some econometric problems with these equations, but the estimated parameters are more or less satisfactory.

Intercept |
Economic activity |
Long-term price effect Air temperature |
Time trend (%p.a.) | ||

Iron and steel |
4.93 |
0.49 |
-0.35a 0.0 |
-3.7 | |

Mineral products |
5.69 |
0.34 |
-0.40a -0.05 |
-1.7 | |

Chemicals |
4.25 |
0.62a |
-0.65a 0.0 |
-1.0 | |

Other industry |
3.79 |
0.64a |
-0.65a -0.14 |
-0.9 | |

Rail transport |
3.71 |
0.42a |
-0.20a 0.0 |
0.0 | |

Road transport |
8.65 |
0.24 |
-0.30a 0.0 |
2.1 | |

Water transport |
5.07 |
0.17 |
-0.10a 0.0 |
0.0 | |

Air transport |
5.74 |
0.31 |
-0.20a 0.0 |
3.8 | |

Domestic final use |
6.64 |
0.35 |
-0.30a -0.08 |
0.0 | |

Other final use |
6.30 |
0.31 |
-0.30a -0.06 |
0.0 | |

Note: aImposed parameters. | |||||

Table 9.6 Parameters for the dynamic cointegrating energy equations—base long-term price elasticities | |||||

Variable |
Intercept |
d In Y d In RPE |
d In y(-1) d In RPE (-1) d In £(-1) |
d In T |
EC(-1) |

Iron and steel |
-0.04 |
1.07 |
0.20 |
-0.16 | |

Mineral products |
-0.02 |
0.66 |
-0.06 |
-0.37 | |

Chemicals |
-0.01 |
0.49 |
-0.19 | ||

Other industry |
-0.02 |
0.79 |
-0.04 |
-0.01 | |

Rail transport |
-0.01 |
-0.07 |
-0.42 | ||

Road transport |
0.02 |
-0.18 |
0.24 |
-0.70 | |

Water transport |
0.03 |
-0.49 0.50 |
-0.65 | ||

Air transport |
0.03 |
-0.17 |
0.21 |
-0.03 |
-0.63 |

Domestic final use |
0.01 |
-0.25 |
-0.07 |
-0.48 | |

Other final use |
0.01 |
-0.26 |
-0.04 |
-0.12 | |

Note: See equation (9.1) for definitions of variables shown at the head of each column. | |||||

Table 9.71 ratios for the dynamic cointegrating energy equations—base long-term price elasticities | |||||

Variable |
Intercept |
d In Y d In RPE |
d In y(-1) d In RPE (-1) d In e(-1) |
) d In T |
EC(-1) |

Iron and steel |
3.48 |
10.5 |
1.95 |
1.02 | |

Mineral products |
2.71 |
3.71 |
2.87 |
1.48 |

Variable |
Intercept |
d In Y d In RPE |
d In y(-1) |
d In RPE (-1) |
d In e(- |
-1) d In T |
EC(-1) |

Chemicals |
0.60 |
2.57 |
2.79 | ||||

Other industry |
3.11 |
3.27 |
2.45 |
0.13 | |||

Rail transport |
1.36 |
0.99 |
2.89 | ||||

Road transport |
4.97 |
5.01 |
2.09 |
3.49 | |||

Water transport |
1.44 |
1.63 |
2.55 |
3.52 | |||

Air transport |
3.61 |
7.16 |
1.92 |
1.98 |
2.23 | ||

Domestic final use |
1.91 |
2.34 |
6.20 |
2.42 | |||

Other final use |
1.48 |
3.75 |
3.23 |
0.80 | |||

Table 9.8 Test statistics for the dynamic cointegrating energy equations—base long-term price elasticities | |||||||

DW |
SE(%) | ||||||

Iron and steel |
0.90 |
2.13 |
4.7 | ||||

Mineral products |
0.67 |
1.92 |
3.6 | ||||

Chemicals |
0.55 |
1.73 |
4.3 | ||||

Other industry |
0.56 |
1.60 |
3.0 | ||||

Rail transport |
0.36 |
1.64 |
4.8 | ||||

Road transport |
0.74 |
1.38 |
1.5 | ||||

Water transport |
0.39 |
2.39 |
6.7 | ||||

Air transport |
0.77 |
1.34 |
2.4 | ||||

Domestic final use |
0.74 |
2.22 |
1.9 | ||||

Other final use |
0.52 |
1.73 |
2.3 |

The results for short- and long-term price elasticities are summarized in Table 9.9 and those for activity elasticities in Table 9.10. The summary includes estimates from a set of equations with lower imposed elasticities following an examination of the freely estimated long-term cointegrating equations which suggested that the imposed price elasticities may be too high. A striking feature of the summary of activity elasticities is the set of insignificant short-term elasticities which are restricted to zero for transport and final use.

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