Explaining regional differences in Japan’s residential energy demand:
Grouped regressor effect approach
Keita Honjo
Center for Environmental Science in Saitama, Japanhonjo.keita@pref.saitama.lg.jp

Introduction

Dummies for 47 prefectures(Hokkaido, Aomori, …, Okinawa)

Regional effectlog(Energy demand)• Residential energy demand varies with socioeconomic andclimate conditions. How should we formulate regional
differences in people’s energy consumption behavior?
• Method 1: Estimates energy demand models for all regions.
Each region is characterized by a unique regression
coefficient vector [1].
• Method 2: Conducts a panel-data analysis. Each region ischaracterized by a regional effect (an individual fixedeffect).
• Here, I propose the third method, grouped regressor
effect model (GREM). The GREM classifies regions
into several groups and estimates a regression
coefficient vector for each group.

Time effectType: electricity and fuelData source: ANRE

Dummies for 2007, 2008, …, 2019log(Population)

Offset term (coefficient = 1)
Data source: MIC Stat. Bureau

Grouped regressor effectRegressor

Data sourcelog(Average household size)

MIC Stat. Bureau

log(Income level) (income tax per taxpayer)

MIC Stat. Bureau

log(Energy CPIs) (electricity, town gas, and kerosene)

MIC Stat. Bureau

CDDs (base temperatures = 18℃, 23℃, and 28℃)

JMA

HDDs (base temperatures = 8℃, 13℃, and 18℃)

JMA

Step 1: Classifies regions into several groups.
• I classified Japan’s 47 prefectures into 10 groups:
Hokkaido, Tohoku, Kanto, Hokuriku, Chubu, Kansai,Chugoku, Shikoku, Kyushu, and Okinawa.
Step 2: Constructs the GREM (Figure 1).
• The GREM is a Gaussian linear regression model that
decomposes energy demand into four effects: regional,time, population, and grouped-regressor.
• The effect of each regressor differs among the groups.
Step 3: Estimates the GREM parameters.
• I estimated the model parameters using elastic net [2] andLOOCV. Unnecessary regressors were automaticallyremoved from the model.
• R 4.2.1 and glmnet 4.1-4 [3] were used for parameter
estimation.
[1] Honjo and Fujii. 2014. Reg. Sci. Pol. Pract., 6, 13-30.
[2] Zou and Hastie. 2005. J. R. Stat. Soc. B, 67, 301-320.
[3] Friedman et al. 2022. https://cran.r-project.org/web/packages/glmnet/index.html

Regressor 𝑋 𝑚 in prefecture 𝑗 in year 𝑡𝑅𝑖

Set of prefectures that belong to region 𝑖𝟏 𝑗 ∈ 𝑅𝑖

Indicator function that returns 1 if 𝑗 ∈ 𝑅𝑖 and 0otherwise

𝛽𝑖𝑚

Coefficient of regressor 𝑋 𝑚 for region 𝑖

Hyperparameter selection (LOOCV)Regressor selection and parameter estimation (elastic net)
Model performance assessment (In-sample MAPE and CV RMSE)

Figure 1: Structure of the GREM

Methods◆ Grouped regressor effect model (GREM)

𝑋𝑗𝑡𝑚Results• The estimated GREMs could explain historicalchanges in residential electricity and fueldemands in Japan’s 47 prefectures (Table 1).

• The regressor effects differed among the regions(Figure 2).
• Figure 3 shows the temperature response
functions of electricity and fuel demands per capita,
calculated from the regression coefficients of CDDsand HDDs.
• The estimation results suggest that the grouped
regressor effects are necessary to explain
Japan’s residential energy demand.

Group ID: Hokkaido = 1, Tohoku = 2, Kanto = 3,Hokuriku = 4, Chubu = 5, Kansai = 6, Chugoku = 7,Shikoku = 8, Kyushu = 9, and Okinawa = 10

Figure 2: Elasticities of the grouped regressors with respect toelectricity and fuel demands per capita• A future challenge is to find the best way ofclassifying Japan’s 47 prefectures into groups.
Table 1: Summary of the estimated models
EnergyMixing
Regularization In-sample
CV RMSEparameter (α) parameter (λ) MAPE (%)

Electricity 0.96

9.890e-06

4.194

0.062

Fuel

2.071e-05

5.979

0.090

1.00

Figure 3: Temperature response functions of electricity and fuel demands per capita