# The Relationship between Residential Electricity Consumption and Income: A Piecewise Linear Model with Panel Data

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## Abstract

**:**

## 1. Introduction

## 2. Methodology and Data

#### 2.1. Methodology

_{2}emissions and per capita income. The principle of piecewise linear model is that if the data follow different linear trends over different ranges, then the regression function should be modeled in “pieces”. Its graph consists of two or more straight line segments with a certain number of breakpoints. The foremost step is to figure out where the meaningful breakpoints are, and then estimate the coefficients of each segment. At the point of the structural break, the slope changes, but the lines remain continuous. Therefore, the model has the advantage of allowing the curve to assume a much wider range of shapes rather than being only linear, quadratic or cubic [7]. The piecewise linear model implies that the income elasticity of residential electricity consumption can differ at various income levels. In reduced form, the model can be presented as follows:

#### 2.2. Data

## 3. Empirical Results and Robustness Check

#### 3.1. Empirical Results

#### 3.2. Robustness Check

#### 3.2.1. Estimate Methods

#### 3.2.2. Segment Specifications

## 4. Comparisons and Discussion

## 5. Conclusions and Policy Implications

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Residential electricity consumption per capita and GDP per capita. Note: It covers 538 observations of 30 provinces in mainland China during 1995–2012 (excluding Tibet due to lacking too many data). The per capita income was an approximate alternative to per capita GDP and adjusted to 1995 constant price.

**Figure 4.**Estimated income effect on residential electricity consumption. Note: The income range has been divided into 10 segments by percentile so each segment contains the same number of observations. The residential electricity consumption per capita on the vertical axis has been adjusted for the effect of income excluding the province-fixed effect.

**Figure 5.**Estimated income effects using different segmentation. Note: 8-, 10-, 12-segment models are divided by percentile, and the 10-segment (equally spaced) model divides the income range into 10 intervals of equal width. The residential electricity consumption per capita on the vertical axis has been adjusted for the effect of income excluding the province-fixed effect.

**Figure 6.**Estimated income effects of Models (2) and (3). Note: The residential electricity consumption per capita on the vertical axis has been adjusted for the effect of income, excluding the province-fixed effect. The red solid line captures the estimated income effects of Model (2) in the sample. The blue solid line and dotted line capture the estimated income effects of Model (3) in the sample and out of the sample, respectively.

**Table 1.**Electricity access in 2012: regional aggregates. Data source: IEA, World Energy Outlook 2014 [17].

Region | Electrification Rate (%) | Urban Electrification Rate (%) | Rural Electrification Rate (%) |
---|---|---|---|

Developing countries | 76.3 | 91.1 | 64.0 |

Africa | 42.5 | 68.0 | 25.6 |

Developing Asia | 83.0 | 95.2 | 74.4 |

China | 99.8 | 100.0 | 99.6 |

India | 75.4 | 93.9 | 66.9 |

Latin America | 95.0 | 98.5 | 81.9 |

Middle East | 91.7 | 98.3 | 78.0 |

Transition economies & OECD | 99.9 | 100.0 | 99.7 |

World | 81.7 | 94.1 | 68.0 |

Variable | Definition | Observations | Mean | Std. Dev. | Min | Max |
---|---|---|---|---|---|---|

ln(E) | Residential electricity consumption per capita (kWh) | 538 | 5.4 | 0.7 | 3.4 | 6.9 |

ln(Y) | GDP per capita (Yuan) | 538 | 9.5 | 0.6 | 7.5 | 11.1 |

Modified Wald Test | |
---|---|

H0: sigma(i)^2 = sigma^2 for all i | Chi 2 (30) = 7442.88 |

Prob > chi2 = 0.0000 | |

Wooldridge Test | |

H0: no first-order autocorrelation | F(1, 29) = 15.722 |

Prob > F = 0.0004 |

Income | OLS | IV | FGLS |
---|---|---|---|

0–3991 | 1.211 *** | 1.208 *** | 0.905 *** |

(8.43) | (5.17) | (9.50) | |

3991–5130 | 1.120 *** | 1.337 ** | 1.061 *** |

(4.98) | (2.73) | (9.72) | |

5130–6438 | 1.231 *** | 1.215 | 1.029 *** |

(4.81) | (1.71) | (9.58) | |

6438–8002 | 0.850 ** | 0.499 | 1.040 *** |

(3.12) | (0.60) | (10.02) | |

8002–9902 | 1.101 *** | 1.631 * | 0.990 *** |

(3.98) | (2.02) | (9.77) | |

9902–12,365 | 0.888 *** | 0.458 | 1.019 *** |

(3.33) | (0.66) | (10.39) | |

12,365–15,210 | 1.073 *** | 1.435 * | 1.052 *** |

(3.70) | (2.27) | (10.35) | |

15,210–19,331 | 0.895 *** | 0.673 | 1.130 *** |

(3.59) | (1.64) | (11.92) | |

19,331–28,541 | 0.783 *** | 0.877 *** | 0.707 *** |

(5.16) | (4.68) | (8.08) | |

>28,541 | 0.943 *** | 0.894 *** | 0.941 *** |

(7.49) | (6.75) | (12.43) | |

constant | −5.818 *** | −5.824 ** | −3.246 *** |

(−4.98) | (−3.07) | (−4.17) | |

N | 538 | 509 | 538 |

Variables | Model (2) | Model (3) |
---|---|---|

$\mathrm{ln}({\mathrm{Y}}_{it}$) | 0.996 *** | 2.396 *** |

(58.08) | (7.83) | |

${\left(\mathrm{ln}{Y}_{it}\right)}^{2}$ | - | −0.0757 *** |

- | (−4.58) | |

constant | −4.006 *** | −10.44 *** |

(−25.27) | (−7.39) | |

N | 538 | 538 |

Fixed Effects | YES | YES |

Random Effects | NO | NO |

${R}^{2}$ | 0.8694 | 0.8746 |

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**MDPI and ACS Style**

Liu, Y.; Gao, Y.; Hao, Y.; Liao, H.
The Relationship between Residential Electricity Consumption and Income: A Piecewise Linear Model with Panel Data. *Energies* **2016**, *9*, 831.
https://doi.org/10.3390/en9100831

**AMA Style**

Liu Y, Gao Y, Hao Y, Liao H.
The Relationship between Residential Electricity Consumption and Income: A Piecewise Linear Model with Panel Data. *Energies*. 2016; 9(10):831.
https://doi.org/10.3390/en9100831

**Chicago/Turabian Style**

Liu, Yanan, Yixuan Gao, Yu Hao, and Hua Liao.
2016. "The Relationship between Residential Electricity Consumption and Income: A Piecewise Linear Model with Panel Data" *Energies* 9, no. 10: 831.
https://doi.org/10.3390/en9100831