As explained, the electricity demand model is estimated using the approaches detailed in the previous section and as explained in the data section, for the empirical analysis, the variables in natural logarithms used are
. In line with the methodology above, the ADF and PP tests are undertaken to determine order of integration of the level and first difference of the variables. Initially, the full specifications, with both a constant and a trend are considered, then, depending on the significance of the deterministic regressors, the final UR test equations include only an intercept, an intercept and trend, or none of them; Table 3
reports the results.
Both the ADF and PP test statistics clearly fail to reject the null hypothesis of unit root for the
variables but rejects the null hypothesis for the first differences of them. Both ADF and PP test equations for the first difference of
include neither the trend nor intercept. The insignificance of both deterministic regressors is consistent with Figure 2
, which suggests that the growth of both variables are highly likely to have a mean-zero process—in fact, for the period 1996 to 2013 the mean values of
are 0.0009 and 0.007, respectively. As discussed in the methodological section, ADF with structural breaks tests are also run for
. Figure 2
experienced a sudden break in 2007, whereas
experienced a gradual structural break from 2007 up to 2010. Therefore, as a break type, an additive outlier is selected for
and an innovative outlier for
, but both for 2007. Additionally a lag length of three is specified for
given the innovative outlier and a lag order of two for
. Finally, a break in both intercept and trend is allowed. This gives calculated ADF statistics of −2.68 and −3.66 for
, respectively compared to the critical values from [53
] of −3.87, −4.19, and −4.71 at the 10%, 5%, and 1% significance levels, respectively. Evidently, for
, the null hypothesis of UR cannot be rejected in favor of the alternative hypothesis of trend stationary with break. Thus, the results from the ADF with breakpoint support those from the standard ADF and PP tests. Furthermore, the null hypotheses of a unit root for
are both rejected. Therefore, it can be concluded from the UR tests that
are integrated of order one, i.e., they are I(1) variables, whereas
are level stationary, i.e., they are I(0) variables. This implies that
do not contain any long-run information in explaining
; however, this does not rule out the possibility that they may be useful in explaining the short-run dynamics of
. It is worth noting that similar results were also found by [36
] in their electricity and energy demand modeling.
Since the variable of interest,
, as well as
are found to be I(1) processes, it is meaningful to test whether a long-run cointegrating relationship exists between them. According to the cointegration concept, if there are n
variables, then there can be, at most, n
− 1 cointegrating relationships ([50
] inter alia) that implies, in this case, a maximum of two. However, as explained above, only the Johansen approach is able to discover more than one cointegrating relationship (see [55
] among others); hence, given that three variables (
) are considered here, the Johansen test for cointegration is considered first. To do this, a VAR with endogenous variables,
is constructed. Note that according to the Johansen cointegration approach, only the variables with the same order of integration can be cointegrated. It implies that
can be cointegrated but they cannot be cointegrated with
as the integration order of the former variables is I(1) and that for the latter variables is I(0). Therefore,
are excluded from this part of the cointegration analysis, which is in line with previous electricity demand analysis (such as [48
]). In addition to the endogenous variables, an exogenous dummy variable for 2007 is included in the VAR to capture the sharp decline in
and the very large increase in
that year—the year that the government raised the nominal electricity price by three times. This dummy variable proves to be highly significant in both the
equations and helps to reduce the huge outliers in the residuals of these equations. Note that time trend was also included in the VAR as an exogenous variable; however, it was statistically insignificant in all three equations and hence excluded. Therefore, the VAR contains only an intercept and the dummy variable as deterministic regressors with initially a maximum of two lags set for the endogenous variables. However, both the lag selection criteria and the lag exclusion tests suggested that two lags was the optimum order so were maintained, which is intuitively appropriate given the small number of observations in the sample. The VAR with two lags successfully passes all the residual diagnostics as indicated in Panels A–C in Table 4
. The Johansen cointegration test results from the transformed version of the VAR, which means that the resulting VECM with one-lag are presented in Table 4
Despite the economic drivers usually represented by the cointegration equation type (c), where there is an intercept but not trend, a check for the existence of cointegration in all possible combinations of the deterministic regressors is undertaken, i.e., in five test types. As [92
] show, a pulse (blip) dummy does not distort the distribution of the critical values of the cointegration tests. However, they do make the sample values of the tests smaller and therefore reduce the chance of rejecting the null hypothesis of no cointegration. Even, in the presence of the dummy variables, the test statistics in almost all types indicate one cointegrated relationship among the variables as reported in Panel D of Table 4
Since, the theoretical framework behind the estimation is demand side modeling of per capita electricity, Types (a), (b) and (e) should not be considered. Type (a) assumes that there is no intercept in the cointegrating relationship so there is no autonomous level of per capita electricity demand. Type (b) however, assumes that there is an intercept in the cointegrating relationship but no intercept in the VAR, thus implying that over the sample period the average growth in per capita electricity demand is zero, which is not the case here. Type (e) assumes that the per capita electricity demand contains a quadratic trend in the general VAR (one in the cointegrating relationship and another in the short-run part), which was not confirmed by the UR test results. Hence, only type (c) or (d) are applicable here. For type (d), where both an intercept and a linear trend are included in the cointegrated equation, the coefficient on income switches its sign from positive to negative, which is hard to explain and goes against economic intuition. Moreover, the normality condition of the VECM residuals is violated and income is not weakly exogenous to the cointegration parameters. It appears, therefore, that the trend is not part of the data generating process for per capita electricity demand in Azerbaijan. Unlike type (d), the theoretically expected signs for the coefficients of income and price are found and additionally, the residuals are normally distributed in type (c), where an intercept but no trend is included in the equation. Thus, it seems reasonable to choose type (c), thus there is no explicit role for the deterministic trend in the cointegration space.
The unadjusted and adjusted (for small sample bias) values of the Trace and Max-eigenvalues statistics are given in Panel E of Table 4
. This shows that all tests reject the null hypothesis of no cointegration and fail to reject the null hypotheses of more than one long-run relationship among the variables; this suggests that there is only one cointegrating relationship among
Before making any inference about the cointegration space, the statistical significance, stationarity, and weak exogeneity of the level variables in that space of the VECM are tested as summarized in Table 5
. Panel A shows that the sample values of the χ2
distribution are greater than the critical values at the 1% significance level, meaning that
are statistically significant. In addition, the multivariate test results for stationarity shown in Panel B indicate that none of the variables are stationary and therefore confirm the univariate UR tests results, given in Table 3
The results reported in Panel C of Table 5
are weakly exogenous to the cointegration relationship at the 5% significance level, whereas
is not weakly exogenous. Using the 10% significance level,
also becomes not weakly exogenous. However, the joint test on the loading (speed of adjustment) coefficients in the p
and the gdp
equations produce sample values of 3.62 for the χ2
distribution with a probability of 0.16, thus leading to the conclusion that both
are weakly exogenous to the cointegration relationship. This all implies that it is acceptable to proceed from the VECM to the single equation ECM analysis (as discussed in [61
] inter alia).
It is worth highlighting that the cointegration analysis using the Johansen approach was conducted first because it outperforms all its alternatives in correctly determining the number of cointegrated relationships in the case of more than two variables. The Johnsen test indicated that there is only one cointegrating relationship among the variables. Then, as a robustness check, the ARDLBT was also run for the same purpose. The results (which are not reported here, but are obtainable from the authors under request) also indicate that there is a cointegrating relationship among the variables, which suggest that the cointegration test results from the Johansen approach are robust.
Given that the Johansen test concluded that there was no more than one cointegrated relationship between the variables, the ARDLBT, FMOLS, DOLS and CCR methods are also be employed alongside the VECM in estimating the long- and short-run coefficients. Note that a maximum lag order of two is set when running the ARDLBT estimation, similar to that for the VAR. The optimum lag order for the dependent variable and the regressors being selected by the Schwarz criterion, which is the more relevant information criterion in the case of small samples. For the DOLS estimation, a maximum of one lag and one lead was set as for the VECM, with the optimal order selected by the Schwarz criterion for the same reason.
Since there is no dynamic part in the FMOLS and CCR estimations, two pulse dummies are included for 2007, in order to capture the sharp decline in electricity consumption for that year. A time trend was also included in the ARDLBT, FMOLS, DOLS, and CCR to capture technological and other changes, which is not accounted for explicitly, however, like the Johansen estimation, it proved to be insignificant in all estimators and hence was excluded. Table 6
presents the results from these five different procedures and shows that they all produce statistically significant coefficients that are very close; moreover, the residuals from the ARDLBT, DOLS, FMOLS and CCR estimations successfully pass the residuals diagnostics tests—another indication of the robustness of the estimation results (these results are not reported here, but are available from the authors on request). Furthermore, the estimated long-run coefficients are very similar across all the procedures, suggesting that the long-run price and income elasticities of electricity demand are between −1.0 to −0.8 and 0.1 to 0.2, respectively. In fact, the VECM, the ARDLBT, the DOLS and the CCR all produce estimated price and income elasticities of about −1.0 to −0.9 and 0.2, respectively—the FMOLS estimates being the slight outliers at −0.8 and 0.1, respectively.
Finally, the single equation ECMs were estimated using the General to Specific modeling strategy outlined in the methodological section. The general specifications included an intercept term, contemporaneous and one lagged values of
, one-lagged values of the ECTs, and the
. The resulting final specifications found by the estimation strategy outlined above and test statistics are reported in Table 7
. This shows that the SoA coefficients across all the methods are negative and statistically significant; indicating that the short-run disequilibrium adjusts to the long-run equilibrium path and therefore, the cointegrating relation among the variables is stable. Additionally, the estimates are very close to each other, generally being about −0.9, although again the FMOLS estimates are an outlier, given the estimated SoA is about −1.0.
4.3. Discussion of the Estimation Results
The UR test results suggest that the natural logarithms of electricity consumption per capita, Non-oil GDP per capita and the real electricity price are non-stationary in levels, but stationary in first difference, i.e., they are all I(1) processes. This means that they are trending and thereby do not return to their mean and the mean is changing over time. This implies that future values of the variables form randomly and thus are difficult to predict and any shock to the variables would have a permanent effect. However, the UR tests for the natural logarithms of heating degree days and cooling degree days suggest that they are both stationary in levels, i.e., they are both I(0) processes.
The results from the Johnsen cointegration tests suggest that there is a common trend among the trending, I(1), variables and that the cointegration between the per capita electricity consumption, Non-oil GDP per capita and, real electricity prices implies that the relationship between their levels is not spurious—thus the coefficients from this relationship are suitable for analysis and forecasting. Moreover, it provides acceptable estimated (constant) elasticities (since the variables are in natural logarithms) for the variables of interest from the five different estimators employed: Johansen, ARDL, DOLS, CCR and FMOLS. Thus, the estimated long-run price elasticity of per capita electricity demand is found to be around −0.9, which is a relatively strong response although still suggesting that per capita electricity demand in Azerbaijan is inelastic—i.e., ceteris paribus, a 1% rise in the real electricity price leads to a 0.9% decrease in per capita electricity demand in the long run. The estimated income elasticity of electricity demand however is found to be more inelastic at around 0.2—i.e., ceteris paribus, a 1% increase in the per capita Non-oil GDP leads a 0.2% increase in per capita electricity demand in the long run. This is somewhat lower than the assumed income elasticities in the reports that produced forecasts of electricity demand for Azerbaijan discussed in the literature review.
The estimated final five ECM specifications demonstrate economically meaningful findings with the estimated SoA coefficients being very close across the different estimators, with the average being −0.94, suggesting fast adjustment of over 90% of any disequilibrium in per capita electricity demand “corrected” within a year. (Although the FMOLS estimates suggest a slight overcorrection since the estimated SoA coefficient is larger than −1 (in absolute terms), so that the adjustment process back to equilibrium path is sooner than one year.) These estimates therefore suggest that electricity system in Azerbaijan is ‘reform friendly’, in that if policy makers implement changes to the system, the effects of the shock (such as a large price increase) will be absorbed very quickly.
Turning to the ECM results, the estimated short-run per capita electricity price elasticity is found to be −0.4 for the Johansen, ARDLBT, DOLS and CCR, estimates but slightly lower (in absolute terms) for the FMOLS estimates at −0.3. Thus, as would be expected, the price elasticity is smaller (in absolute terms) than in the long run; however, this is not the case for the income elasticity. The estimated short-run income elasticities are 0.4 for ARDLBT and CCR, 0.5 for Johansen, 0.6 for DOLS, and for FMOLS, somewhat larger at 0.7—a similar relationship between the short-run and the long-run income elasticities found for UK total energy demand by [85
Finally, in terms of the weather variables, which were found to be I(0) and therefore only considered for the short-run ECM, both
were found to be not statistically significant and hence excluded from the final ECM specifications. For cooling degree-days this is not surprising given Azerbaijan’s climate and similarly for heating degree-days, given it is natural gas and diesel (particularly in rural areas)—not electricity—that are primarily used for heating purposes. These results are similar to [48
] who found heating and cooling degree-day variables to be insignificant in their electricity demand estimation.