A life-cycle theory analysis of French household electricity demand

Abstract

This paper develops a pseudo-panel approach to examine household electricity demand behavior through the household life cycle and its response to income variations to help strengthen the energy policy-making process. Our empirical methodology is based on three rich independent microdata surveys (the National Housing Surveys), which are representative of the French housing sector. The resulted sample covers the 2006–2016 period. Using within estimations, this paper finds striking evidence that the income elasticity of French residential electricity demand is 0.22, averaged over our four cohorts of generations. In light of other works, our estimate stands in the lower range. The empirical results also show that residential electricity consumption follows an inverted U-shaped distribution as a function of the age of the household’s head. Most notably, it appears that households at the mid-point of their life cycle are relatively the largest consumers of electricity. This outcome has important implications for policy-making. Any public policy aimed at reducing household energy consumption should consider this differentiation in consumption according to the position of households over the life cycle, and therefore target as priority households at the highest level of consumption.

Appendix

1.1 A. Hausman test for cohort 1

The Hausman test permits to choose between fixed effects and random effects. The null hypothesis is that the two estimation methods are both suitable and deliver consistent estimators, which should therefore yield similar coefficients, whereas the alternative hypothesis is that fixed effects are suitable but not random effects. If this is the case, differences between the two sets of coefficients would be expected. A large and significant Hausman statistics means a large and significant difference (Hausman 1978).

Table 7

Table 7 Hausman test for eq. (4) estimated on cohort 1

Here, for cohort 1, the Hausman test statistics is found at 19.92 and is statistically significant (p value of zero). Therefore, the null hypothesis that the two methods are suitable is rejected in favor of the alternative hypothesis that fixed effects are suitable and random effects are not.

1.2 B. Mundlak test for cohort 1

The Mundlak test permits to check the validity of the assumptions on which random effects are based upon, being that there is no correlation between time-invariant effects and regressors. The null hypothesis states that the panel-level averages of time-varying covariates are jointly zero and the alternative hypothesis states that at least one of the panel-level averages is different from zero. The test follows a three-step procedure:

• Compute the panel-level average of time-varying covariates;

• Regress the dependent variable on the set of covariates and their panel-level averages with random effects;

• Compute the test-statistics and conclude.

If the null hypothesis is rejected, i.e., that panel-level averages are not jointly zero, then it indicates that there is a correlation between the time-invariant unobservable and other covariates. In this case, the violation of the hypothesis on which random effects are based upon implies the inconsistency of random-effects parameters. Therefore, the fixed effects should be favored (Mundlak 1978).

Here, for eq. (4) estimated on cohort 1, the test statistics of 28.83 is large and statistically significant (p value of zero), so the null hypothesis that panel-level averages of time-varying covariates are jointly zero is rejected, meaning that there is evidence that time-invariant unobservables are correlated to regressors. Therefore, the random effects assumption is not satisfied, making the estimators inconsistent. Consequently, fixed effects should be favored.

1.3 C.Normality of residuals

Figure 4 is the Kernel estimation of the density of the residuals from the estimation of eq. (4) performed on cohort 1, cross-sectional data, with Epanechnikov Kernel and an optimal bandwidth of 0.0348. A quick glance at it confirms the normality of residuals.

Fig. 4

Kernel density estimation of residuals from the regression estimation of eq. (4) on cohort 1, cross-sectional data

1.4 D. Breusch-Pagan heteroskedasticity test

The Breusch-Pagan heteroskedasticity test investigates the presence of heteroskedasticity in the model. Heteroskedasticity happens when the error term’s variance is not constant across individuals, which, if omitted, can yield non-robust standard errors. This test’s null hypothesis is that there is homoskedasticity and the alternative hypothesis is that there is not (Breusch and Pagan 1979). This test follows a three-step procedure:

• Run an OLS regression of the independent variable on the dependent variables and compute squared residuals;

• Run the auxiliary regression, that is to say, regress the squared residuals on the set of dependent variables;

• Compute the test-statistics and conclude.

Here, for the estimation of eq. (4) on the cross-sectional data of the three stacked surveys (i.e., parameter estimates derived from column 1 of Table 5), a p value of 0.2612 is obtained. Therefore, the null hypothesis is not rejected, which indicates that the residuals of eq. (4) are homoskedastic.

1.5 E. Number of observations by cohort

Table 8

Table 8 Complete number of observations in cohort 1

Table 9

Table 9 Complete number of observations in cohort 2

Table 10

Table 10 Complete number of observations in cohort 3